diff --git "a/batch_s000014.csv" "b/batch_s000014.csv" new file mode 100644--- /dev/null +++ "b/batch_s000014.csv" @@ -0,0 +1,10321 @@ +source,target + These differences are caused bv the enhanced (turbulent diffusion of dust particle motions through5 enhanced 5eas drag., These differences are caused by the enhanced turbulent diffusion of dust particle motions through enhanced gas drag. +el Indeed. Fiewe lice shows that the turbulent seattering ci dominates over the steady migration ey in most areas of the simulation box.," Indeed, Figure \ref{fig:t01-dust}c c shows that the turbulent scattering $v_{\rm t}$ dominates over the steady migration $v_{\rm f}$ in most areas of the simulation box." + Figure 11bb shows the estimated. radial velocity of particles vy., Figure \ref{fig:t01-dust}b b shows the estimated radial velocity of particles $v_{\rm d}$. +" The radial velocity of the simulated particles. ¢,. are also shown by dots."," The radial velocity of the simulated particles, $v_{x}$, are also shown by dots." + Although dust particles ave swept out of the unstable region. in most parts of the unstable region. max[e4]>0 and min|e4]<0 are satisfied. so the dust particles are broadly distributed in (he stable region with lower concentration.," Although dust particles are swept out of the unstable region, in most parts of the unstable region, $v_{\rm d}] > 0$ and $v_{\rm d}] < 0$ are satisfied, so the dust particles are broadly distributed in the stable region with lower concentration." + Nevertheless. identity of the clump with the highest dust concentration is sill maintained (Figure 12aa).," Nevertheless, identity of the clump with the highest dust concentration is still maintained (Figure \ref{fig:t01-clump}a a)." + Indeed the velocity dispersion around center of the traced clump shown is not increased significantly (Figure 12bb)., Indeed the velocity dispersion around center of the traced clump shown is not increased significantly (Figure \ref{fig:t01-clump}b b). + We also run a high global pressure gradient model (2=—0.10)., We also run a high global pressure gradient model $\beta=-0.10$ ). + Though the inwud migration of dust particles becomes faster on average. the maximunm density is unclianged because (he remnant turbulence that scatters the dust particles in the dust concentrated region is the dominant [actor for this τε)=0.1 case.," Though the inward migration of dust particles becomes faster on average, the maximum density is unchanged because the remnant turbulence that scatters the dust particles in the dust concentrated region is the dominant factor for this $\tau_f\Omega=0.1$ case." + Recent works (e.g..Johansen&Youdin2007) proposed that turbulence itself concentrates dust particles in turbulent eddies.," Recent works \citep[e.g.,][]{joh07a} proposed that turbulence itself concentrates dust particles in turbulent eddies." + In their models. lifetime of the eddies has to be longer than the timescale to form dense enough particle clumps lor formation of planetesimals.," In their models, lifetime of the eddies has to be longer than the timescale to form dense enough particle clumps for formation of planetesimals." + On the other hand. our model proposes another path to accumulate dust particles Chat turbulence plavs a role in transformation of the nearly Ixeplerian gas [low into (he quasi-steady flow wilh a local rigid rotation region.," On the other hand, our model proposes another path to accumulate dust particles that turbulence plays a role in transformation of the nearly Keplerian gas flow into the quasi-steady flow with a local rigid rotation region." + Because the dust particles accumulate near the outer edge of super-Ixeplerian parts produced by the rigid rotation aud the flow pattern is quasi-steady. ihe timeseale problem does not exist in our model.," Because the dust particles accumulate near the outer edge of super-Keplerian parts produced by the rigid rotation and the flow pattern is quasi-steady, the timescale problem does not exist in our model." + Actually. in the case of model-s40. and model-t01 with f«c0.096. the same chunp with the highest density is maintained until the end of simulations (/€9 80).," Actually, in the case of model-s40 and model-t01 with $R_{\rm m,ave} \simeq 0.096$, the same clump with the highest density is maintained until the end of simulations $t \Omega \simeq 80$ )." + llowever. in our model. as A44: increases 0o unity. stronger residual turbulence may destroy the chunps. although the clumps are repeatedly created. which may inhibit planetesimal formation.," However, in our model, as $R_{\rm m,ave}$ increases to unity, stronger residual turbulence may destroy the clumps, although the clumps are repeatedly created, which may inhibit planetesimal formation." +" Ilere. we examine the cases with larger A224, (but still H4,< 1) to find the critical value of Ryaye for persistent clumping."," Here, we examine the cases with larger $R_{\rm m,ave}$ (but still $R_{\rm m,ave}<1$ ) to find the critical value of $R_{\rm m,ave}$ for persistent clumping." +" In moclel-s055. the width of the stable region L, is one eighth of modelst0."," In model-s055, the width of the stable region $L_{\rm s}$ is one eighth of model-s40." + Accordingly. Haas=0.64 compared (to 0.096 of model-s40.," Accordingly, $R_{\rm m,ave}=0.64$ compared to 0.096 of model-s40." + Figure 13aa shows that the AUR turbulence, Figure \ref{fig:s055-3D}a a shows that the MRI turbulence +be intrinsically faint (e.g. Kolb 1993: Howelletal. 1997)): Pretoriusctal.(2007a) and Pretorius&Ixnigge(2008b) find that. although an as vet undetected fant CV population cannot dominate the overall population to. the extent predicted. observed. CV. samples are nevertheless strongly biased against [aint svstemis.,"be intrinsically faint (e.g. \citealt{Kolb93}; ; \citealt{howell2}) ); \cite{PretoriusKniggeKolb07} and \cite{halpha2} find that, although an as yet undetected faint CV population cannot dominate the overall population to the extent predicted, observed CV samples are nevertheless strongly biased against faint systems." + The faintest secular average Lx expected ofCVs can be estimated from the gravitational radiation-driven AZ., The faintest secular average $L_X$ expected of CVs can be estimated from the gravitational radiation-driven $\dot{M}$. + We find that the Patterson&Rav-mone(1985a). relation between Lx and Al predicts that the majority ofCVs in the theoretical population of Ixolb(1993) should have time-averaged X-ray luminosities ofa lew times 10o0eres+ and higher.," We find that the \cite{PattersonRaymond85a} relation between $L_X$ and $\dot{M}$ predicts that the majority of CVs in the theoretical population of \cite{Kolb93} should have time-averaged X-ray luminosities of a few times $10^{29}\,\mathrm{erg\,s^{-1}}$ and higher." +". In intrinsically⋠⋠⋠ faintD. ""CVs. however. the rate of transfer of material onto the white ονα surface (which determines Lx). is not the the same as the secular AL. since these svstems are dwarf novae."," In intrinsically faint CVs, however, the rate of transfer of material onto the white dwarf surface (which determines $L_X$ ), is not the the same as the secular $\dot{M}$, since these systems are dwarf novae." + HU is possible that. in the faintest CVs. hardly any material reaches the white dwarf surface during quiescence. so that they may. spend most of their time at very faint Ly (perhaps with X-ray emission from the donor star being brighter than from the accretion Low).," It is possible that, in the faintest CVs, hardly any material reaches the white dwarf surface during quiescence, so that they may spend most of their time at very faint $L_X$ (perhaps with X-ray emission from the donor star being brighter than from the accretion flow)." + The faintest. short-period CVs in our sample have luminosities of a few times 10eres+.," The faintest short-period CVs in our sample have luminosities of a few times $10^{30}\,\mathrm{erg\,s^{-1}}$." + Several intrinsically faint. short-periocd systems are now known to have Ly<10erests (κου Byeklingetal2010... as well as Peter Wheatles. publie )).," Several intrinsically faint, short-period systems are now known to have $L_X<10^{29}\,\mathrm{erg\,s^{-1}s}$ (see \citealt{Byckling10}, as well as Peter Wheatley, public )." + Lt is not known how intrinsically common such systems are. but they may. well dominate the population.," It is not known how intrinsically common such systems are, but they may well dominate the population." + The standard. theory of CV evolution predicts that 2704 of CVs are period. bouncers citealtIxolb03))., The standard theory of CV evolution predicts that $\simeq$ of CVs are period bouncers \\citealt{Kolb93}) ). + Using the observed mass-radius relationship of CV donors. Ixniggo.ctal.(2011) predict an even arecr fraction. of period bouncers.," Using the observed mass-radius relationship of CV donors, \cite{KBP11} predict an even larger fraction of period bouncers." + Observations are also now indicating a large population of intrinsically faint CVs (probably both normal short-period CVs and. period. x»incers)., Observations are also now indicating a large population of intrinsically faint CVs (probably both normal short-period CVs and period bouncers). + First. Gansickeetal.(2009). find a large number of intrinsically faint CVs at the shortest. orbital periods.," First, \cite{Gansicke09} find a large number of intrinsically faint CVs at the shortest orbital periods." + Furthermore. several period bouncers ancl good candidate »eriod. bouncers are now known citealtLittlefairDhillonMarsh06:::— Littlefairοal.2008: Patterson2011)). and Patterson(2011). argue that these systems may be common enough to make up most of the intrinsic population.," Furthermore, several period bouncers and good candidate period bouncers are now known \\citealt{LittlefairDhillonMarsh06}; \citealt{LittlefairDhillonMarsh08}; \citealt{Patterson11}) ), and \cite{Patterson11} argue that these systems may be common enough to make up most of the intrinsic population." + Two (related) properties of the sample used here show hat it probably. does not. fairly represent. the underlying population: it contains no faint short-period. CVs. and it obabls contains no period bouncers (see Section 2)).," Two (related) properties of the sample used here show that it probably does not fairly represent the underlying population: it contains no faint short-period CVs, and it probably contains no period bouncers (see Section \ref{sec:sample}) )." + The ack of period bouncers alone likely means that it has missed ab least half the intrinsic population., The lack of period bouncers alone likely means that it has missed at least half the intrinsic population. + Furthermore. it is disconcerting that the faintest member of our sample. and herefore the svstem that dominates our p measurement. is a lone-period CV. EXDra.," Furthermore, it is disconcerting that the faintest member of our sample, and therefore the system that dominates our $\rho$ measurement, is a long-period CV, EX." +. Population svnthesis models owediet that at most a few percent of all CVs are above he period σαρ (Ixolb1993 finds less than 1l'A.. while Ixniggeetal.2011. predict. 320).," Population synthesis models predict that at most a few percent of all CVs are above the period gap \citealt{Kolb93} finds less than , while \citealt{KBP11} predict )." + Although we find. that ong-period systems account for. slightly. more than of our total space density. the data do not rule out these heoretical predictions.," Although we find that long-period systems account for slightly more than of our total space density, the data do not rule out these theoretical predictions." +" For example. using the Ixnigeeοἱal.(2011). fraction of long-period systems. ancl assuming hat we have not significantly under-estimated. the space density of long-period CVs. the space density of short-period. CVs dis 02«10""pe(97/3)e&67pe. 7."," For example, using the \cite{KBP11} fraction of long-period systems, and assuming that we have not significantly under-estimated the space density of long-period CVs, the space density of short-period CVs is $\simeq 2 \times 10^{-6}\,\mathrm{pc^{-3}}(97/3) \simeq 6 \times 10^{-5}\,\mathrm{pc^{-3}}$ ." + Using the upper limit on p from Section 5.1..« we find that a short- CY population of this size could. escape detection in the two surveys. provided that the systems have ἅlOeres+ (for the simple case of a hypothetical Lx population of faint. undetected CVs).," Using the upper limit on $\rho$ from Section \ref{sec:limits}, we find that a short-period CV population of this size could escape detection in the two surveys, provided that the systems have $L_X \la 8 \times 10^{28}\,\mathrm{erg\,s^{-1}}$ (for the simple case of a hypothetical $L_X$ population of faint, undetected CVs)." + Clearly. i£ CVs are arbitrarily faint in N-ravs. the data allow for an arbitrarily large population to escape detection.," Clearly, if CVs are arbitrarily faint in X-rays, the data allow for an arbitrarily large population to escape detection." + Llowever. we can also choose to place a restriction in ternis of what we might consider reasonable X-ray Iuminosities or active CVs.," However, we can also choose to place a restriction in terms of what we might consider reasonable X-ray luminosities for active CVs." +" For example. if we integrate the it power law Luminosity function over the range 28.7< (this is a luminosity range where CVs are known to exist. but where we detect. none) we ind po=1.2;10.""pe for svstems at those luminosities. a factor of almost 3 larger than our.po estimate from the detected. CVs."," For example, if we integrate the best-fit power law luminosity function over the range $28.7<\mathrm{log}(L_X/\mathrm{erg\,s^{-1}})<29.7$ (this is a luminosity range where CVs are known to exist, but where we detect none), we find $\rho_0=1.2 \times 10^{-5}\,\mathrm{pc^{-3}}$ for systems at those luminosities, a factor of almost 3 larger than our$\rho_0$ estimate from the detected CVs." + Thisagain indicates that it is reasonable to hink that our po estimate is low by a factor of more than 2, Thisagain indicates that it is reasonable to think that our $\rho_0$ estimate is low by a factor of more than 2. + We find that a power law X-ray luminosityfunction, We find that a power law X-ray luminosityfunction +turbulence in the Local Clouds of the VLISM resembles the turbulence in the solar wind and solar corona.,turbulence in the Local Clouds of the VLISM resembles the turbulence in the solar wind and solar corona. + The Verv Local Interstellar Medium (VLISM) is loosely defined: as the interstellar medium within about 15 parsecs of the Sun., The Very Local Interstellar Medium (VLISM) is loosely defined as the interstellar medium within about 15 parsecs of the Sun. + One of the interesting aspects of the VLISM is that it contains about 15 clouds with diameters of a few parsecs (RecllieldandLinsky2005)., One of the interesting aspects of the VLISM is that it contains about 15 clouds with diameters of a few parsecs \citep{Redfield08a}. +. It appears Chat the Sun is near the interface and region of interaction of (wo of these clouds. the Local Interstellar Cloud. or LIC. and the G cloud (BedtieldandLinskv2008)..," It appears that the Sun is near the interface and region of interaction of two of these clouds, the Local Interstellar Cloud, or LIC, and the G cloud \citep{Redfield08a}." + Reviews ol (he properties of these clouds may be found in Frisch.(2000).. Redlield(2009).. and (2011).," Reviews of the properties of these clouds may be found in \cite{Frisch00}, , \cite{Redfield09}, and \cite{Frisch11}." +. Most of the information we have about these clouds comes from UV and visible wavelength spectroscopy., Most of the information we have about these clouds comes from UV and visible wavelength spectroscopy. + Absorption lines attributable to these clouds are measured. along lines of sight to nearby stars wilh precisely known distances., Absorption lines attributable to these clouds are measured along lines of sight to nearby stars with precisely known distances. + Properties of these clouds are deduced [rom the Doppler shift. strength. ancl width of the spectral lines.," Properties of these clouds are deduced from the Doppler shift, strength, and width of the spectral lines." + These clouds are plasmas because absorption lines of ious as well as neutral atoms are observed: (he ionization fraction is about 50 (ReclfieldandFaleon3005].., These clouds are plasmas because absorption lines of ions as well as neutral atoms are observed; the ionization fraction is about 50 \citep{Redfield08b}. + Although the information available on these clouds is not as extensive as for the solar wind or solar corona. it is sufficient to. place the Local Clouds among the best-diagnosed astrophysical plasmas.," Although the information available on these clouds is not as extensive as for the solar wind or solar corona, it is sufficient to place the Local Clouds among the best-diagnosed astrophysical plasmas." + There are several reasons for this state of affairs., There are several reasons for this state of affairs. + First. because (he absorption lines are nieasured in (he spectra of nearby stars wilh precisely known distances. the spatial extent of the clouds is well determined.," First, because the absorption lines are measured in the spectra of nearby stars with precisely known distances, the spatial extent of the clouds is well determined." + Second. the neutral component of the clouds [lows into the inner solar svstem. where it can be measured in situ 2009).," Second, the neutral component of the clouds flows into the inner solar system, where it can be measured in situ \citep[e.g.][]{Moebius09}." +. Finally. the heliosphere is embedded in one of these clouds. the LIC cloud. and the solar wind interacts with it.," Finally, the heliosphere is embedded in one of these clouds, the LIC cloud, and the solar wind interacts with it." + The shape and other characteristics of the solar wind interaction provide constraints on the LIC cloud properties (Lallementetal2005;Opher2009).," The shape and other characteristics of the solar wind interaction provide constraints on the LIC cloud properties \citep{Lallement05,Opher09}." +. The mean plasma properties of the turbulent clouds are given in Table 1 2003)..," The mean plasma properties of the turbulent clouds are given in Table 1 \citep[adapted from][]{Redfield08a,Redfield08b}." + Information on turbulence in the Local Clouds is discussed in Redfield (2004)., Information on turbulence in the Local Clouds is discussed in \cite{Redfield04}. +. Such information is retrievable because the absorption line width 6 can be measured for transitions of several atoms or ions., Such information is retrievable because the absorption line width $b$ can be measured for transitions of several atoms or ions. + ReclfieldandLinsky(2004) fit the line width data for each line ofsight and Doppler component to the formula, \cite{Redfield04} fit the line width data for each line ofsight and Doppler component to the formula +number too small to give meaningful results to study their radial distributions.,number too small to give meaningful results to study their radial distributions. + It dis very likely that the majority of cluster RGB variables ave brighter than our magnitude limit., It is very likely that the majority of cluster RGB variables are brighter than our magnitude limit. + A shorter exposure search lor variability amone 47 Tuc RGB stars has recently been started by Ixiss et al (2003. private communication. also with WEI on the MSSSO 40-inch). ancl our LPV sample will overlap somewhat with their results.," A shorter exposure search for variability among 47 Tuc RGB stars has recently been started by Kiss et al (2003, private communication, also with WFI on the MSSSO 40-inch), and our LPV sample will overlap somewhat with their results." + This should allow a more accurate study into the eluster LPV radial distribution., This should allow a more accurate study into the cluster LPV radial distribution. + A small number of other variables were also discovered in our dataset. including two Cepheids. four ὁ Scuti stars. and an anomalous short-period red variable. which is a likely SAIC star.," A small number of other variables were also discovered in our dataset, including two Cepheids, four $\delta$ Scuti stars, and an anomalous short-period red variable, which is a likely SMC star." + The two Cepheids (V24 and. V37) are identified from their position in the schematie cluster CMD (Fig.11))., The two Cepheids (V24 and V37) are identified from their position in the schematic cluster CMD \ref{linecmd}) ). + They are significantly brighter and redder than the RR Lyrae stars. but ave of short period (O.387d ancl 2.572d respectively) lor Cepheids. and as such could be classified as anomalous.," They are significantly brighter and redder than the RR Lyrae stars, but are of short period (0.387d and 2.572d respectively) for Cepheids, and as such could be classified as anomalous." + V24 has been tentatively identified as a Tvpell Cepheid based on the secondary variation seen on (he lightcurve at phase 70.5., V24 has been tentatively identified as a TypeII Cepheid based on the secondary variation seen on the lightcurve at phase $\sim$ 0.5. + We detected four 0 Seni stars in our search (V35. V54. V67 and V30).," We detected four $\delta$ Scuti stars in our search (V35, V54, V67 and V80)." + All are certainly members of the SAIC. as thev have Ve21.," All are certainly members of the SMC, as they have $\sim$ 21." + This is at the limit of our detectabilitv. but they were found due to their large amplitude of variation.," This is at the limit of our detectability, but they were found due to their large amplitude of variation." + V35.V54 and V6T all have very short periods 0$, such a trend disappears, as the corrections partially account for the relative strengthening of the features produced by $\alpha-$ elements relative to iron." + Phe polvnomial fittinge usinge the algorithmo> describe in Section 2 was then repeated. using the original grid. of synthetic spectra and the rederived atmospheric parameters.," The polynomial fitting using the algorithm described in Section \ref{procedure} + was then repeated using the original grid of synthetic spectra and the rederived atmospheric parameters." +" and its determinant 4 is — J-—1| - IO where z=re"",","g = +, and its determinant $J$ is J = 1 - - + ) where $z = r e^{i\theta}$." + The critical condition is given bv coe LqAd, The critical condition is given by = r^2 -. +) From the simple graph of the RIIS. it can be seen that there is a solution space in the neighborhood of r=1.," From the simple graph of the RHS, it can be seen that there is a solution space in the neighborhood of $r=1$." + Set r=1+0 and find 9 using eq.(A)) to obtain r= 1 +2, Set $r = 1 + \delta$ and find $\delta$ using \ref{eqBiJ}) ) to obtain r = 1 +. +2(À5) €cos286—lH is a peanut-shape curve squeezed along the imaginary axis even though the small coefficient e/2(7 makes it difficult to discern from a circle. 0=0. 7/2. π.," It is a peanut-shape curve squeezed along the imaginary axis even though the small coefficient $\epsilon/2\ell^2$ makes it difficult to discern from a circle. $\theta =0$, $\pi/2$, $\pi$," + and 32/2 are the precusps., and $3\pi/2$ are the precusps. + H can be confirmed by ealeulating OJ as it was done for an arbitrary d in the main text., It can be confirmed by calculating $\partial_- J$ as it was done for an arbitrary $d$ in the main text. + The cusps are (wo on (he real axis and (wo on (he imaginaray axis., The cusps are two on the real axis and two on the imaginaray axis. + In order to estimate the size of (he caustic. measure (he cusp-lo-cusp distances on the real axis and on the imaginary axis.," In order to estimate the size of the caustic, measure the cusp-to-cusp distances on the real axis and on the imaginary axis." +" ia : vw, =+(AG) = TW = cHT) The quaroid is equilateral and its orientation is opposite to the critical curve.", = _0 - = = - = -i The quaroid is equilateral and its orientation is opposite to the critical curve. + The diagonal length of the quadroicd will be comapred to that of the large separation DSTP lens caustics., The diagonal length of the quadroid will be comapred to that of the large separation DSTP lens caustics. + — — i, = = = + — — ic, = = = +As cosmic microwave background (CMB) travel through the diffuse hot gas comprising the bulk of photonsbaryons in clusters. a fraction of them are upscattered the in à galaxyprocess called the thermal Sunyaev-Zel'dovich by(tSZ) gaseffect (?)..,"As cosmic microwave background (CMB) photons travel through the diffuse hot gas comprising the bulk of baryons in galaxy clusters, a fraction of them are upscattered by the gas in a process called the thermal Sunyaev-Zel'dovich (tSZ) effect \citep{1970Ap&SS...7....3S}." + This scattering produces a unique spectral signature in the CMB. with a decrement in thermodynamic temperature below v~220 GHz. and an excess above.," This scattering produces a unique spectral signature in the CMB, with a decrement in thermodynamic temperature below $\nu +\sim 220$ GHz, and an excess above." + The tSZ effect is typically seen on are-minute scales. and is referred to às à secondary anisotropy. às it originates between us and the surface of last scattering. unlike the primary CMB anisotropies.," The tSZ effect is typically seen on arc-minute scales, and is referred to as a secondary anisotropy, as it originates between us and the surface of last scattering, unlike the primary CMB anisotropies." + In the non-relativistic limit. the tSZ is directly proportional to the integrated electron pressure along the line-of-sight.," In the non-relativistic limit, the tSZ is directly proportional to the integrated electron pressure along the line-of-sight." + It typically traces out the spatial distribution of clusters and groups. since the hot intracluster medium (ICM) dominates the line-of-sight pressure integral.," It typically traces out the spatial distribution of clusters and groups, since the hot intracluster medium (ICM) dominates the line-of-sight pressure integral." + Thus. the tSZ provides an excellent tool to examine the bulk of cluster baryons.," Thus, the tSZ provides an excellent tool to examine the bulk of cluster baryons." + Found at the intersections of filaments in the cosmic web (2).. clusters form at sites of constructive interference of long waves in the primordial density fluctuations.the coherent peak-patches (22)..," Found at the intersections of filaments in the cosmic web \citep{1996Natur.380..603B}, clusters form at sites of constructive interference of long waves in the primordial density fluctuations,the coherent peak-patches \citep{1986ApJ...304...15B,1996ApJS..103....1B}." + Clusters are sign posts for the growth of structure in the Universe. and are a potentially powerful tool for probing underlying cosmological parameters. such as w. the dark energy to-density ratio.," Clusters are sign posts for the growth of structure in the Universe, and are a potentially powerful tool for probing underlying cosmological parameters, such as $w$, the dark energy pressure-to-density ratio." + The of the tSZ effect is extremely sensitive to angularcosmologicalpower spectrumparameters like oy. the root mean square (RMS) amplitude of the (Iinearized) density fluctuations on 8/r! Mpe scales.," The angular power spectrum of the tSZ effect is extremely sensitive to cosmological parameters like $\sigma_8$, the root mean square (RMS) amplitude of the (linearized) density fluctuations on $h^{-1}$ Mpc scales." + In fact. the amplitude of the tSZ power spectrum scales at least as steeply as the seventh power of oy (222?) and improving the constraints on ay will aid in breaking the degeneracies found between oy and w when using only primary CMB constraints.," In fact, the amplitude of the tSZ power spectrum scales at least as steeply as the seventh power of $\sigma_8$ \citep{2002ASPC..257...15B,2002MNRAS.336.1256K,2005ApJ...626...12B,2011ApJ...727...94T} + and improving the constraints on $\sigma_8$ will aid in breaking the degeneracies found between $\sigma_8$ and $w$ when using only primary CMB constraints." + An advantage of using the tSZ angular power spectrum over counting clusters is that no explicit measurement of cluster masses is required., An advantage of using the tSZ angular power spectrum over counting clusters is that no explicit measurement of cluster masses is required. + Also. lower mass. and therefore fainter. clusters that may not be significantly detected as 1individual objects in CMB maps contribute to this statistical signal.," Also, lower mass, and therefore fainter, clusters that may not be significantly detected as individual objects in CMB maps contribute to this statistical signal." + However. disadvantages of using the tSZ angular power spectrum include potential contamination from point sources ard that no redshift information from the clusters is used.," However, disadvantages of using the tSZ angular power spectrum include potential contamination from point sources and that no redshift information from the clusters is used." + Previous observations by the Berkeley-Illinois-Maryland Association (BIMA.?).. the Atacama Path-finding Experiment (APEX-SZ.?).. the Quest at DASI (QUaD.?).. Arc-minute Cosmology Bolometer Array Receiver (ACBAR.?).. and the Cosmic Background Imager (CBI.?) all measured excess power above that expected from primary anisotropies. which have been attributed to some combination of the tSZ effect and point source contamination.," Previous observations by the Berkeley-Illinois-Maryland Association \citep[BIMA,][]{2006ApJ...647...13D}, the Atacama Path-finding Experiment \citep[APEX-SZ,][]{2009ApJ...701.1958R}, the Quest at DASI \citep[QUaD,][]{2009ApJ...700L.187F}, Arc-minute Cosmology Bolometer Array Receiver \citep[ACBAR,][]{2009ApJ...694.1200R}, and the Cosmic Background Imager \citep[CBI,][]{2009arXiv0901.4540S} all measured excess power above that expected from primary anisotropies, which have been attributed to some combination of the tSZ effect and point source contamination." + The measurements from these experiments provided upper limits to the tSZ power spectrum amplitude., The measurements from these experiments provided upper limits to the tSZ power spectrum amplitude. + More recently. the Atacama Cosmology Telescope (ACT.??) and the South Pole Telescope (SPT.???) have detected the SZ effect in the CMB powerspectrum!.," More recently, the Atacama Cosmology Telescope \citep[ACT,][]{2010ApJ...722.1148F,2010arXiv1009.0866D} and the South Pole Telescope \citep[SPT,][]{2010ApJ...719.1045L,2010arXiv1012.4788S,2011arXiv1105.3182K} have detected the SZ effect in the CMB power." +". The results from ACT and SPT emphasize that the ""sweet spot"" for measuring the tSZ signal is between (~20004000.", The results from ACT and SPT emphasize that the “sweet spot” for measuring the tSZ signal is between $\ell \sim 2000 - 4000$. + Silk (?) suppresses the of primary anisotropies— so that dampingtheir contributions to the power spectrum are much smaller than the tSZ contribution at even higher (.," Silk damping \citep{1968ApJ...151..459S} + suppresses the power of primary anisotropies so that their contributions to the power spectrum are much smaller than the tSZ contribution at even higher $\ell$ ." + At these scales there are important additional contributions to the power, At these scales there are important additional contributions to the power +respectively with the inverse-variance weighting where/ corresponds to one smoothing scale and Nici represents the number of scales used in the combination.,respectively with the inverse-variance weighting where$i$ corresponds to one smoothing scale and $N_{\rm fwhm}$ represents the number of scales used in the combination. + The combined x7 is then computed This combination makes an integrated estimation of wwhich includes the non-Gaussian signal at several cilferent scales with a mild weighting., The combined $\chi^2$ is then computed This combination makes an integrated estimation of which includes the non-Gaussian signal at several different scales with a mild weighting. + We first compare the observed. results with our Gaussian model predictions., We first compare the observed results with our Gaussian model predictions. + In this case. we perform. 10240 Gaussian simulations of the VVW-band. properties.," In this case, we perform 10240 Gaussian simulations of the VW-band properties." + Dilferent. base-masks. as well as the mecdian-ilter. are applied. independently to both the real and the simulated: skies to study the foreground. effect. on the skeleton results.," Different base-masks, as well as the median-filter, are applied independently to both the real and the simulated skies to study the foreground effect on the skeleton results." + Phe corresponding X7 values are then computed to enable the frequentist test., The corresponding $\chi^2$ values are then computed to enable the frequentist test. + For each smoothing scale. the skeleton length departure from the Gaussian expectation. ALG.Üpwgar)=ZG.PpwHa)CC(pBrew D. is computed. from samples obtained with the WOT5B masked. maps.," For each smoothing scale, the skeleton length departure from the Gaussian expectation, $\Delta \mathcal{L}(\nu,\theta_{\rm FWHM}) = +\mathcal{L}(\nu,\theta_{\rm FWHM})-\langle \mathcal{L}^{\rm +G}(\nu,\theta_{\rm FWHM}) \rangle$ , is computed from samples obtained with the KQ75B masked maps." + The results are shown in the lef two columns (for both the dillerential ancl cumulative distributions) of Figure 5. for Gps;=0764. 0785. 1228. 1770. 2798 and 3740.," The results are shown in the left two columns (for both the differential and cumulative distributions) of Figure \ref{fig_dske_KQ75} for $\theta_{\rm FWHM} += 0\fdg64$, $0\fdg85$, $1\fdg28$ , $1\fdg70$, $2\fdg98$ and $3\fdg40$." + The στον bands demonstrate the le and 20 confidence regions of the Gaussian. prediction., The grey bands demonstrate the $1\sigma$ and $2\sigma$ confidence regions of the Gaussian prediction. + The observed ones are rebinned to 25 bins and depicted by filled circles with the lo-error bar of each bin., The observed ones are rebinned to 25 bins and depicted by filled circles with the $1\sigma$ -error bar of each bin. + The rebinning is necessary since the clilferential skeleton elistribution is relatively. noisy., The rebinning is necessary since the differential skeleton distribution is relatively noisy. +" In the case of the cumulative distributions. AL,(7) for WALTPS5. some features consistent with a positive value are observed. albeit within the de Caussian confidence. level."," In the case of the cumulative distributions, $\Delta +\mathcal{L}_{a}(\nu)$ for 5, some features consistent with a positive value are observed, albeit within the $1\sigma$ Gaussian confidence level." + Phe behaviour of the dilferential distribution. ALsz). supports this inference. —despite the existence of a higher level of Luctuations.," The behaviour of the differential distribution, $\Delta \mathcal{L}_{d}(\nu)$, supports this inference despite the existence of a higher level of fluctuations." + Llowever. there aredifferences between the new results ancl the corresponding WAZLAPIL ones (Eriksenetal.2004).," However, there aredifferences between the new results and the corresponding 1 ones \citep{Eriksen_etal_2004}." +. For cach smoothing scale. the latter show a LIe-Ievel peak around 7=0 while the neighbouring troughs show less Ductuations especially in the vol region.," For each smoothing scale, the latter show a $1\sigma$ -level peak around $\nu=0$ while the neighbouring troughs show less fluctuations especially in the $\nu>1$ region." + In contrast. asshown in Figure 5. (the left two columns). the former's peak is less apparent but the troughs are much more distinct particularly. for. Opwgsr=—1728 and. 1770.," In contrast, asshown in Figure \ref{fig_dske_KQ75} (the left two columns), the former's peak is less apparent but the troughs are much more distinct particularly for $\theta_{\rm FWHM}=1\fdg28$ and $1\fdg70$ ." + The comparison between WALL?IL and our new results is shown inFigure 7? [or psg;= 0764. 0785 and 1:2 ," The comparison between 1 and our new results is shown inFigure \ref{fig_syseff} for $\theta_{\rm +FWHM}=0\fdg64$ , $0\fdg85$ and $1\fdg28$ ." +There are several possibilities associated: with such a discrepancy., There are several possibilities associated with such a discrepancy. +Nem berms of equation (8)) are uncorrelated for different pulsars. but the second. term of (his equation provides a common change of periods ancl period derivatives for all objects.,"$\eta_{em}$ terms of equation \ref{eq_gwshift}) ) are uncorrelated for different pulsars, but the second term of this equation provides a common change of periods and period derivatives for all objects." + The difference between the expected and the measured values of the period derivatives in individual objects. sueh as those listed in Table 1. can be directly used to constrain the enerev densitv in gravitational waves in this frequency regime (Bertolli&Weisberg1989:ThorsettDewey 1996).. giving Qeayh?<0.04 1996).," The difference between the expected and the measured values of the period derivatives in individual objects, such as those listed in Table 1, can be directly used to constrain the energy density in gravitational waves in this frequency regime \citep{bert83, tayl89, thor96}, giving $\Omega_{GW} h^2 \la 0.04$ \citep{thor96}." +. The accuracy of the AP/P measurement for PSR 1010-10 (which dominated this constraint) has improved by about a factor of three since the publication by Thorsett (1996).. so the current upper limit on Qc?xGXP/P)? is approximately an order of magnitude better.," The accuracy of the $\Delta \dot{P}/P$ measurement for PSR B1913+16 (which dominated this constraint) has improved by about a factor of three since the publication by \citet{thor96}, so the current upper limit on $\Omega_{GW}h^2 \propto (\Delta \dot{P}/P)^2$ is approximately an order of magnitude better." + In contrast to the case of the peculiar solar acceleration. the ellect of eravitational waves in this frequency range on liming measurements does not depend on the position on the sky. so it cannot be extracted statistically [rom the imine data as we did in Seclion 2 [or the solar acceleration.," In contrast to the case of the peculiar solar acceleration, the effect of gravitational waves in this frequency range on timing measurements does not depend on the position on the sky, so it cannot be extracted statistically from the timing data as we did in Section \ref{sec_stat} for the solar acceleration." + Finally. for very. low frequency gravitational waves (f.10."," The energy generated by the reactions is therefore at most $3 \times 10^{51}$ ergs $/$ $M$ $^{56}$ $/\msun$ ), and even smaller in a typical case because most of the materials burned into $^{56}$ Ni are heavier than $^{16}$ O. Because $M$ $^{56}$ Ni) is of the order of $0.1\msun$, This energy is about $10 - 20$ for the models with $E_{51} \sim 1$ and much smaller for the models with $E_{51} +\gsim 10$." + With the lvdrodvnuamical calculation. woe trace hermodvnamical histories of individual Lagrangian elements.," With the hydrodynamical calculation, we trace thermodynamical histories of individual Lagrangian elements." + 3000) particles are used for stellar imautle., 3000 particles are used for stellar mantle. + At the base of the jet. new particles flow iuto the unuerical domain. aud are also traced.," At the base of the jet, new particles flow into the numerical domain, and are also traced." + These histories are used to caleulate uucleosvuthesis as post-processing., These histories are used to calculate nucleosynthesis as post-processing. + The reaction network includes 222 isotopes up to “Ce (lis. Thiclemamu 1996. 1999).," The reaction network includes 222 isotopes up to $^{71}$ Ge (Hix, Thielemann 1996, 1999)." + The initial compositions of the particles in the processing are taken as follows: Because of the lavee unecrtainty in the initia composition of the jet material. we restrict ourselves iu his paper to parameter space where the mass of the isotopes newly svuthesized in the shocked stellar wautles overwhelins the mass contained iu the jets.," The initial compositions of the particles in the post-processing are taken as follows: Because of the large uncertainty in the initial composition of the jet material, we restrict ourselves in this paper to parameter space where the mass of the isotopes newly synthesized in the shocked stellar mantles overwhelms the mass contained in the jets." + We postpone he whole survey. such as very massive jets. to future works.," We postpone the whole survey, such as very massive jets, to future works." + This should require to follow the accretion process o determined the initial composition and will involve he physics neglected imthe prescut study. c.g. angular nomenti transport. nuclear cucrey eeueration. and cooling by photocdisintegration aud ucutring enüssions. as well as lighly resolved ποΊσα simulation around the ceutral remuaut.," This should require to follow the accretion process to determined the initial composition and will involve the physics neglected inthe present study, e.g., angular momentum transport, nuclear energy generation, and cooling by photodisintegration and neutrino emissions, as well as highly resolved numerical simulation around the central remnant." + We perform lvdrocdvuamic calculations for tle models in Table 1., We perform hydrodynamic calculations for the models in Table 1. + The models are named with the nuubers, The models are named with the numbers +spectral type and its neighbours 1s about 0.2 mag. so this value was assumed in all subsequent caleulations.,"spectral type and its neighbours is about 0.2 mag, so this value was assumed in all subsequent calculations." + This error of 0.2 mag corresponds to an error of iin distance (see reftable:comparison.. 7th column).," This error of 0.2 mag corresponds to an error of in distance (see \\ref{table:comparison}, 7th column)." + The corresponding error in the parallax was used for the correction of the relative parallaxes., The corresponding error in the parallax was used for the correction of the relative parallaxes. + Given the relation between parallax and distance. the error in the former is not symmetric 1f that of the former ts.," Given the relation between parallax and distance, the error in the former is not symmetric if that of the former is." + The asymmetric nature of the parallax error is represented in column 8 of reftable:comparison.., The asymmetric nature of the parallax error is represented in column 8 of \\ref{table:comparison}. + The errors given in reftable:comparison do not represent the overall error., The errors given in \\ref{table:comparison} do not represent the overall error. + A main source of error will most likely be the photometry. which is not of the highest precision.," A main source of error will most likely be the photometry, which is not of the highest precision." + Moreover. our spectra do not allow us to determine the exact evolutionary status of the objects. which influences the accuracy of the absolute magnitude.," Moreover, our spectra do not allow us to determine the exact evolutionary status of the objects, which influences the accuracy of the absolute magnitude." + For the same reason. the influence of metallicity cannot be taken into account. and all stars are assumed to be of solar abundance.," For the same reason, the influence of metallicity cannot be taken into account, and all stars are assumed to be of solar abundance." + Adding these uncertainties with some margin leads to an overall error in distance of20-30%.. with the stars Ref7-9 having the larger errors. since we only have one spectrum (red of Ref7. blue for the other two) for these objects.," Adding these uncertainties with some margin leads to an overall error in distance of, with the stars Ref7-9 having the larger errors, since we only have one spectrum (red of Ref7, blue for the other two) for these objects." + Since the parallax is the reciprocal of the distance. the stars with a large distance are the more reliable ones. especially the two giants (Ref3 and 5).," Since the parallax is the reciprocal of the distance, the stars with a large distance are the more reliable ones, especially the two giants (Ref3 and 8)." + Our astrometric measurements used Ir in position mode to observeREJ0317-853..9802.. and the associated reference field stars.," Our astrometric measurements used 1r in position mode to observe, and the associated reference field stars." + At each of the three epochs. two," At each of the three epochs, two" +magnitude relation varving with metallicity.,magnitude relation varying with metallicity. + Hence them salple is dominated by what we usually call the thick disc population., Hence their sample is dominated by what we usually call the thick disc population. + They deduce an IME slope of a=0.10 or a=0.17 with or without the metallicity eradieut taken into account., They deduce an IMF slope of $\alpha=-0.10$ or $\alpha=-0.47$ with or without the metallicity gradient taken into account. +" 1ic saniple considered. m this paper Ts significantly ifferent. frou the UST sample. as it is dominated by stars at distances. above the plane of. -150 to 150 pe withH a mean distance of 350 pe for stars at r=1.6 and 210 pe for stars having ri""=2.0."," The sample considered in this paper is significantly different from the HST sample, as it is dominated by stars at distances above the plane of 150 to 450 pc with a mean distance of 350 pc for stars at $r'-i'=1.6$ and 210 pc for stars having $r'-i'=2.0$." + This has two consequences: 1) the sample is less biased by unresolved binaries aud 2) it is dominated by the normal thin dise population aud more comparable with the local sample which is used. to eternune the LE in the solar neighbourhood (Reid et al. 2001))., This has two consequences: 1) the sample is less biased by unresolved binaries and 2) it is dominated by the normal thin disc population and more comparable with the local sample which is used to determine the LF in the solar neighbourhood (Reid et al. \cite{Reid2004}) ). + Revlé Robin (2001)) have performed the first etevinination of the thick disc IMF from a αμdirectional analysis of star counts., Reylé Robin \cite{Reyle2001}) ) have performed the first determination of the thick disc IMF from a multi-directional analysis of star counts. +" They obtained au IMF.— dINidinxii""7 in the wass range 0.23$ then the P-L relation is nonlinear." +" The results are summarized in Table Ἐν, ", The results are summarized in Table \ref{tab1}. . +From this table it can be seen that the nonlinear P-L is clearly evideut from the, From this table it can be seen that the nonlinear P-L is clearly evident from the +"These two equations show how the measured /,, and V, arecontaminated by {εςQ,.U, and V, depending on the values of the D-terms.","These two equations show how the measured $I_m$ and $V_m$ arecontaminated by $I_s, Q_s, U_s$ and $V_s$ depending on the values of the D-terms." +" To measure the linear polarization components. Q,,and U,,. the measurements VyViTIuV. and (VnV;−Iu are made using a multiplying polarimeter."," To measure the linear polarization components, $Q_m$and $U_m$, the measurements $\widetilde V_R \widetilde V_L^*+\widetilde V_L\widetilde V_R^*$ and $i\left(\widetilde V_R\widetilde V_L^*-\widetilde V_L\widetilde V_R^*\right) $ are made using a multiplying polarimeter." + The outputs of the Vi)multipliers in the polarimeter are related to the incoming electric fields by The Eqs., The outputs of the multipliers in the polarimeter are related to the incoming electric fields by The Eqs. + can be expressed in terms of Stokes parameters or in terms of linearly polarized flux density., can be expressed in terms of Stokes parameters or in terms of linearly polarized flux density. +" By assuming that Ss""m6o=gu and yo=ye (standard procedure at Effelsberg). it Iss possible to apply to both the Q and U channels the same calibration factor. according to the following where Q, and U, Po.are the Teal signals coming through the ο and U channels and measured at the end of the backend."," By assuming that $g_Q=g_U$ and $\gamma_Q=\gamma_U$ (standard procedure at Effelsberg), it is possible to apply to both the Q and U channels the same calibration factor, according to the following where $Q_c$ and $U_c$ are the Tcal signals coming through the $Q$ and $U$ channels and measured at the end of the backend." + The Teal is applied analogously to Eqs., The Tcal is applied analogously to Eqs. +(A2).. The ratio between the {ως value and the corresponding measured voltage gives the conversion factor K/V to be applied to the on-source Q and U measurements Discarding the terms of order > 3 the following is obtained The channels Q and U could also be calibrated separately., The ratio between the $I_{lpc}$ value and the corresponding measured voltage gives the conversion factor $K/V$ to be applied to the on-source $Q$ and $U$ measurements Discarding the terms of order $\geq$ 3 the following is obtained The channels Q and U could also be calibrated separately. + In this case in Eqs., In this case in Eqs. + two different denominators. one for each channel. would be present.," two different denominators, one for each channel, would be present." + With Eqs., With Eqs. + and we have all 16 elements of the Mülller matrix in terms of D-terms. required to relate measured and true Stokes parameters.," and we have all 16 elements of the Mülller matrix in terms of D-terms, required to relate measured and true Stokes parameters." + From Eqs. (," From Eqs. ," +A3).. and recalling the definition (5).. the coefficients. of the instrumental Mülller matrix T can be summarized as," and recalling the definition , the coefficients of the instrumental Mülller matrix $\mathbf{T}$ can be summarized as" +underneath (Chandrasekhar1961).,underneath \citep{CHAN1961}. +. In the case where 4A—1 the formation of rising bubbles and Falling spikes is common (Daly1967)., In the case where $A \rightarrow 1$ the formation of rising bubbles and falling spikes is common \citep{DALY1967}. +. Stone&Gardiner(2007) investigated (he impact of shear in the magnetic field across the contact discontinuityv. finding that. this suppressed the small wavenumbers creating wider filamentary structures.," \cite{Stone2007} investigated the impact of shear in the magnetic field across the contact discontinuity, finding that this suppressed the small wavenumbers creating wider filamentary structures." + Recent observations by Bergerαἱal.(2010). of dark upllows that. propagate from underdense bubbles through quiescent prominences appear to be the observational signature of the havleigh-Tavlor instability in quiescent. prominences., Recent observations by \cite{BERG2010} of dark upflows that propagate from underdense bubbles through quiescent prominences appear to be the observational signature of the Rayleigh-Taylor instability in quiescent prominences. + Quiescent prominences are large structures of relatively cool (10000 1995))). dense (~I10!*em. ? plasma. that exist in quiet regions of the solar corona. predominantly al high heliographic latitudes.," Quiescent prominences are large structures of relatively cool \citep[10000 K][]{TH1995}) ), dense \citep[$\sim 10^{11}$ $^{-3}$ plasma, that exist in quiet regions of the solar corona, predominantly at high heliographic latitudes." + Using a characteristic gas pressure of 0.6dynem7 (liravama1986) and magnetic field of 3—30 G (Lerov1989).. gives a plasma ο~ 0.01-1.," Using a characteristic gas pressure of $0.6~dyn~cm^{-2}$ \citep{HIR1986} and magnetic field of $3 \sim 30$ G \citep{LER1989}, gives a plasma $\beta \sim 0.01$ $1$." + Linear magnetohvdrostatic modelling of a quiet region filament has shown plasma ο<1 and strong departures [rom [orce-[ree magnetic field 2008)., Linear magnetohydrostatic modelling of a quiet region filament has shown plasma $\beta \leq 1$ and strong departures from force-free magnetic field \citep{DUD2008}. +. Globally . quiescent prominences are incredibly stable structures (hat often exist in the corona for weeks.," Globally , quiescent prominences are incredibly stable structures that often exist in the corona for weeks." + In contrast to this global stability. locally quiescent prominences are hiehlv dynamic phenomena.," In contrast to this global stability, locally quiescent prominences are highly dynamic phenomena." + Observations of quiescent prominences have shown downllows (Engvold1981).. vortices of approximately 10? kin xLO? km in size and a bubble of size 2800 km forming a kevhole shape with a brieht center with velocities of kkmi +.," Observations of quiescent prominences have shown downflows \citep{ENG1981}, vortices of approximately $10^5$ km $\times 10^5$ km in size \citep{LZ1984} and a bubble of size $2800$ km forming a keyhole shape with a bright center \citep{DT2008} with velocities of km $^{-1}$." + There are many reviews that give a full description of the current. understanding of the structure and dynamics of quiescent. prominences example.Tancdbere-Tanssen1995:Labrosseetal.2010:Mackay. 2010).," There are many reviews that give a full description of the current understanding of the structure and dynamics of quiescent prominences \citep[see, for example,][]{TH1995,LAB2010,MAC2010}." +. Observations by the Solar Optical Telescope (Ixosugiatal.2007) on the IHinocde satellite CIsunetaetal.2007) have shown that on a small scale quiescent prominences are highly dvnamic and unstable phenomena., Observations by the Solar Optical Telescope \citep{KOS2007} on the Hinode satellite \citep{TSU2007} have shown that on a small scale quiescent prominences are highly dynamic and unstable phenomena. + Bergeretal.(2008) ancl Dergeratal.(2010). reported dark plumes that propagated from. large bubbles (approximately 10 MMmr in size) that form at the base of some quiescent prominences., \cite{BERG2008} and \cite{BERG2010} reported dark plumes that propagated from large bubbles (approximately $10$ Mm in size) that form at the base of some quiescent prominences. + Plumes form at the bubble prominence boundary and (hen flow through a height of approximately MMm belore dispersing into the background. prominence material (see Figure 1))., Plumes form at the bubble prominence boundary and then flow through a height of approximately Mm before dispersing into the background prominence material (see Figure \ref{obs_bubble}) ). + Observations imply that the plumes and the cavities have a column density about 20% of the prominence density 2008)., Observations imply that the plumes and the cavities have a column density about $20$ of the prominence density \citep{HEINZEL2008}. +. The dark upllows maintained an almost constant velocity of approximately 20kkmss ! throughout their rise phase., The dark upflows maintained an almost constant velocity of approximately $20$ $^{-1}$ throughout their rise phase. + Often these plumes would separate [rom the large scale bubble forming smaller bubbles inside (he prominence material., Often these plumes would separate from the large scale bubble forming smaller bubbles inside the prominence material. + Dergeretal. presents observations of large scale prominence bubbles using the Atmospheric Imaging Assembly (ALA) on the Solar Dynamics Observatory (5DO) that show the temperature of the material inside the bubble to be >250.000 Ix.," \cite{BERG2011} presents observations of large scale prominence bubbles using the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO) that show the temperature of the material inside the bubble to be $>250,000$ $K$ ." +Exposed water ice on main-belt asteroids is Caermocdvnamically unstable. on timescales that are very short compared to the age of the Solar svstem.,"Exposed water ice on main-belt asteroids is thermodynamically unstable, on timescales that are very short compared to the age of the Solar system." + Ice is therelore not expected on, Ice is therefore not expected on +Comparing equation (127)) with equation (113)). one can see (hat the ellective bending constant is given bv This is the same result that we have obtainedin section 3..,"Comparing equation \ref{app3-z5}) ) with equation \ref{app3-z0}) ), one can see that the effective bending constant is given by This is the same result that we have obtainedin section \ref{results}. ." +are indistinguishable from the nearby dust. emission in the (PALL S yam)160 pm ratio maps.,are indistinguishable from the nearby dust emission in the (PAH 8$\mu$ m)/160 $\mu$ m ratio maps. + Nonetheless. keep in mind that enhancements/ in the (PALL S j/m)/160 jim ratios are still visible in the large scale structures such as the spiral arms in NGC 3031 and NGC 69046.," Nonetheless, keep in mind that enhancements in the (PAH 8 $\mu$ m)/160 $\mu$ m ratios are still visible in the large scale structures such as the spiral arms in NGC 3031 and NGC 6946." + Figure 5. shows how the (PALES sam)/160 jim surface brightness ratio varies with 160 jun surface brightness among the sample galaxies. and the slopes ancl intrinsic scatter for the best fit lines as well as Spearman's correlation coelTicients for the data are given in Table 5..," Figure \ref{f_pahvs160} shows how the (PAH 8 $\mu$ m)/160 $\mu$ m surface brightness ratio varies with 160 $\mu$ m surface brightness among the sample galaxies, and the slopes and intrinsic scatter for the best fit lines as well as Spearman's correlation coefficients for the data are given in Table \ref{t_pahvs160}." + Again. the best fitting lines are determined using uncertainties in both the x- and v-directions to weight the data.," Again, the best fitting lines are determined using uncertainties in both the x- and y-directions to weight the data." + For all galaxies in the sample. the (PALL S j/m)/160 pm ratio generally increases as the 160 jm surface brightness increases. although the slopes of the relations are relatively shallow for some galaxies. such as NGC 3031. NGC 3351. and NGC 4725.," For all galaxies in the sample, the (PAH 8 $\mu$ m)/160 $\mu$ m ratio generally increases as the 160 $\mu$ m surface brightness increases, although the slopes of the relations are relatively shallow for some galaxies, such as NGC 3031, NGC 3351, and NGC 4725." + UW the slopes of the best fit lines in Figure 5 were equivalent to 0. this would. indicate that a one-to-one correspondence exists between the PALL S and. 160 pena bands.," If the slopes of the best fit lines in Figure \ref{f_pahvs160} were equivalent to 0, this would indicate that a one-to-one correspondence exists between the PAH 8 and 160 $\mu$ m bands." + Llowever. since the slopes are instead all positive. this indicates that the colours change from low to high surface brightness regions.," However, since the slopes are instead all positive, this indicates that the colours change from low to high surface brightness regions." + The scatter in the data around the best [it lines eenerallv appears to be at the level in many cases., The scatter in the data around the best fit lines generally appears to be at the level in many cases. + According to the intrinsic scatter measurement used. here. the seatter in many of the plots can be explained. mostly bv uncertainties in the measurements.," According to the intrinsic scatter measurement used here, the scatter in many of the plots can be explained mostly by uncertainties in the measurements." + For most. galaxies. the intrinsic scatter measurements in Table ο are either similar to or notably lower than the values in Table 3..," For most galaxies, the intrinsic scatter measurements in Table \ref{t_pahvs160} + are either similar to or notably lower than the values in Table \ref{t_pahvs24}." + Decause the data used for Tables 3. and 5 were measured in images that were degraded to the resolution of the 160 jum images. resolution ellects should. not be a factor in this comparison.," Because the data used for Tables \ref{t_pahvs24} and \ref{t_pahvs160} were measured in images that were degraded to the resolution of the 160 $\mu$ m images, resolution effects should not be a factor in this comparison." + lence. this comparison between the intrinsic scatter measurements demonstrates quantitatively that the relation between PALL S ancl 160 jm emission may exhibit less scatter than the relation between PALL 8 and 24 jun emission.," Hence, this comparison between the intrinsic scatter measurements demonstrates quantitatively that the relation between PAH 8 and 160 $\mu$ m emission may exhibit less scatter than the relation between PAH 8 and 24 $\mu$ m emission." + Also note that very low and very high surface brightness 45 aresce regions in NGC 5194 and NGC 5055 fall below the best fit line., Also note that very low and very high surface brightness 45 arcsec regions in NGC 5194 and NGC 5055 fall below the best fit line. + A related phenomenon is visible in NGC 1725. where the 45 aresee regions within the inner ring Fall below the best fit line in Figure 5..," A related phenomenon is visible in NGC 4725, where the 45 arcsec regions within the inner ring fall below the best fit line in Figure \ref{f_pahvs160}." + The disparity in the slopes between the high and low surface brightness data for some galaxies demonstrates that the (PALL S μαι)/160 p/m ratio either stops rising or decreases in the high surface brightness centres of the galaxies. as can also be seen in the maps of the (PALL 8 jam)/160 pam ratio in Figure 1. and in the plots of the (PALES sam)/160 pim ratio versus radius in Figure 6..," The disparity in the slopes between the high and low surface brightness data for some galaxies demonstrates that the (PAH 8 $\mu$ m)/160 $\mu$ m ratio either stops rising or decreases in the high surface brightness centres of the galaxies, as can also be seen in the maps of the (PAH 8 $\mu$ m)/160 $\mu$ m ratio in Figure \ref{f_map} and in the plots of the (PAH 8 $\mu$ m)/160 $\mu$ m ratio versus radius in Figure \ref{f_pah160vsdist}." + Figure 1. illustrates how the (PALL 8. sam)/160 iim ratio may peak outside the nuclei of nearby galaxies., Figure \ref{f_map} illustrates how the (PAH 8 $\mu$ m)/160 $\mu$ m ratio may peak outside the nuclei of nearby galaxies. + From the ratio maps alone. it is apparentthat the (PALL S μπι)/160 jm ratio does not. necessarily monotonically decrease from the nuclei to the edges of the optical disces as was suggested by Bendoetal.(2006).," From the ratio maps alone, it is apparentthat the (PAH 8 $\mu$ m)/160 $\mu$ m ratio does not necessarily monotonically decrease from the nuclei to the edges of the optical discs as was suggested by \citet{betal06}." +. Both Figure 6.. which plots the (PALL δ jm)/160. pmi ratio versus deprojected ealactocentric radius for 45 aresec regions in these galaxies. and “Table 6.. which gives the slopes and intrinsic scatter measurements for the best fit lines in Figure G6 as well," Both Figure \ref{f_pah160vsdist}, , which plots the (PAH 8 $\mu$ m)/160 $\mu$ m ratio versus deprojected galactocentric radius for 45 arcsec regions in these galaxies, and Table \ref{t_pah160vsdist}, , which gives the slopes and intrinsic scatter measurements for the best fit lines in Figure \ref{f_pah160vsdist} as well" +was accordingly taken to be £0.09.,was accordingly taken to be $\pm$ 0.09. + We used the above results for density. temperatures. and ICE determinations to derive new values for the O/T] anc N/O ratios lor our sample objects.," We used the above results for density, temperatures, and ICF determinations to derive new values for the O/H and N/O ratios for our sample objects." + The corresponding uncertainties were obtained using standard error propagation. where (he quantities considered in our estimation of the abundance errors is given in Table 4..," The corresponding uncertainties were obtained using standard error propagation, where the quantities considered in our estimation of the abundance errors is given in Table \ref{error}." + The «quantües listed in column (1) were assumed to be functions of the variables given in column (2)., The quantities listed in column (1) were assumed to be functions of the variables given in column (2). + Note that because depends on ancl visa versa. and since in addition. had to be assumed for a significant number of objects (see below). does not appear in Table 4..," Note that because depends on and visa versa, and since in addition, had to be assumed for a significant number of objects (see below), does not appear in Table \ref{error}." + For each object in our sample. Table 5. gives (he object name in column (1). in column (2).2)..TO)... and in columns (3). (4). and (5). respectively. and 7/IL .and in columns (6). (7). and (8). respectively.," For each object in our sample, Table \ref{ionabun} gives the object name in column (1), in column (2), and in columns (3), (4), and (5), respectively, and $^+$ $^+$, $^{+2}$ $^+$, and $^{+}$ $^+$ in columns (6), (7), and (8), respectively." +" Our final abundance results are given in Table 6.. which lists object name in column (1). references for the observed emission-line strengths in column (2). our derived values lor sa and log(N/O) x¢ in columns (3) and (4). and literature values and relerences in columns (5). (6). aud (7). respectively,"," Our final abundance results are given in Table \ref{bigtable}, which lists object name in column (1), references for the observed emission-line strengths in column (2), our derived values for $\pm~\sigma$ and log(N/O) $\pm~\sigma$ in columns (3) and (4), and literature values and references in columns (5), (6), and (7), respectively." + Figures 9 and 10 leature comparisons of our Ο/Η and N/O values (vertical axes) against published values., Figures \ref{oldnew_o2h} and \ref{oldnew_n2o} feature comparisons of our O/H and N/O values (vertical axes) against published values. + The diagonals show points of one-to-one correspondence., The diagonals show points of one-to-one correspondence. + Our O/II values are systematically lower will respect to past calculations due primarily to our new temperature scheme for calculating ., Our O/H values are systematically lower with respect to past calculations due primarily to our new temperature scheme for calculating $^+$ $^+$. + ILowever. in general. the error bars show agreement between our results and literature values.," However, in general, the error bars show agreement between our results and literature values." + Our N/O values are also offset (higher bv ~ 0.05 to 0.1 dex) due the use of new temperature parameltrizations and an ICE. lor obtaining N/O. In Figure ll.. we plot our uncertainties in log(N/O) against corresponding literature values.," Our N/O values are also offset (higher by $\sim$ 0.05 to 0.1 dex) due the use of new temperature parametrizations and an ICF for obtaining N/O. In Figure \ref{oldnew_sigma_n2o}, we plot our uncertainties in log(N/O) against corresponding literature values." + Some of the published uncertainties were estimated using Monte Carlo simulations lo propagate the errors in (he relevant line strengths. (Campbelletal.&Skillman 1996).. ancl thus points occupy. both sides of the diagonal due to the random nature of (he latter technique.," Some of the published uncertainties were estimated using Monte Carlo simulations to propagate the errors in the relevant line strengths \citep{campbell86, kobulnicky96}, and thus points occupy both sides of the diagonal due to the random nature of the latter technique." + We point out that log(N/O) values with small uncertainties eenerallv correspond to objects with small uncertainties in relevant emission-line strengths., We point out that log(N/O) values with small uncertainties generally correspond to objects with small uncertainties in relevant emission-line strengths. + The tendency for our error estimates (o svstematically exceed published ones is primarily due to the contribution of ICF uncertainty for each of our objects., The tendency for our error estimates to systematically exceed published ones is primarily due to the contribution of ICF uncertainty for each of our objects. + However. we strongly argue (hat inclusion of this additional factor produces more realistic uncertainties (han Chose," However, we strongly argue that inclusion of this additional factor produces more realistic uncertainties than those" +observations aud the search for an optical counterpart to the X-ray source.,observations and the search for an optical counterpart to the X-ray source. + Our results and their implications are ciseussed im LI., Our results and their implications are discussed in 4. + The X-ray observations were obtained with the ROSAT AN-Rav Telescope CTPrimnuper et 11991) iu combination with the Ihebh-Resolution Jaeger (IRI. David ct 11995).," The X-ray observations were obtained with the ROSAT X-Ray Telescope (Trümmper et 1991) in combination with the High-Resolution Imager (HRI, David et 1995)." + The los of the observations is eiven iu Table 1: the last entry in that table is the oue obtained near the BeppoSAX observations. the other entries refer to earlier observations in the ROSAT data archive.," The log of the observations is given in Table \ref{tablog}; the last entry in that table is the one obtained near the BeppoSAX observations, the other entries refer to earlier observations in the ROSAT data archive." + The standard data reduction was done with the Extended Scicutific Aalysis Svstena (Zinuucrinann et 11996)., The standard data reduction was done with the Extended Scientific Analysis System (Zimmermann et 1996). + To take inO account f re-calibration of the pixel size (lasinger et 11998). we uultiplv the ον pixel coordinates of eac1i photon wihi respect to the URI ceuter with 0.9972," To take into account the re-calibration of the pixel size (Hasinger et 1998), we multiply the $x,y$ pixel coordinates of each photon with respect to the HRI center with 0.9972." + Then a senich Or sources Is ας by comparing counts in a box wihi he counts in a rineC» surroundiugC» it. aud by moving tlus detection box across the inage.," Then a search for sources is made by comparing counts in a box with the counts in a ring surrounding it, and by moving this detection box across the image." + The sources thus detected are excised from the image aud backerounuc nap is nade for the remaining photons., The sources thus detected are excised from the image and a background map is made for the remaining photons. + A search for sources is uade by comparing the nuuber of photons iu a moving )ox With resect to the munor expected on the basis of he backerorud map., A search for sources is made by comparing the number of photons in a moving box with respect to the number expected on the basis of the background map. + Finally. at cach position in which a source was found. a maniuuu-likelihood technique is used to coixwe the observed photon distribution with he poiut spread fiction o: the IIRI (Cruddace et 119855).," Finally, at each position in which a source was found, a maximum-likelihood technique is used to compare the observed photon distribution with the point spread function of the HRI (Cruddace et 1988)." + The resulting countraes for significant detections near the centre of cach image are eiven in Table 1, The resulting countrates for significant detections near the centre of each image are given in Table \ref{tablog}. + No source is detected in the 1998 Sep & observation., No source is detected in the 1998 Sep 8 observation. +" For a poiut source at the center of the image. oof the photous arrive within a circle with a 5"" yadinIn. in stable TRI poiitings (David et 11995)."," For a point source at the center of the image, of the photons arrive within a circle with a $''$ radius, in stable HRI pointings (David et 1995)." + At the time of «observatioi the ROSAT satellite poiutiug was experiencing cdiffüct]ties. effectively. exteudiug the radius of the point sprcad function. by a few ircseconds.," At the time of observation the ROSAT satellite pointing was experiencing difficulties, effectively extending the radius of the point spread function by a few arcseconds." +" We therefore search a circle with a 10"" radius around the center of 6610 (according to Picard JJohustou 1995: see roftabpos)). oulv five photons are detected."," We therefore search a circle with a $''$ radius around the center of 6440 (according to Picard Johnston 1995; see \\ref{tabpos}) ), only five photons are detected." +" The iain of five photoIs ¢etected remains if we move the center of the circle to anv location withiu 30"" of the nominal cluster. centre. lus allowing for possible inaccurate reconstructioiof the satellite poiutiug."," The maximum of five photons detected remains if we move the center of the circle to any location within $''$ of the nominal cluster centre, thus allowing for possible inaccurate reconstruction of the satellite pointing." + For an expeced number of 10 piotons. the Poisson xobabilitv. of dcAtecting 5 or fewer plotous is ," For an expected number of 10 photons, the Poisson probability of detecting 5 or fewer photons is ." +We hus take LO plMons as the 2-0 upper linüt. which for he exposure of ss IVES an upper lait for the count ratee of O.005ctssτ," We thus take 10 photons as the $\sigma$ upper limit, which for the exposure of s gives an upper limit for the count rate of $\cts$." +", To convert this couutrate ito a huuimositvowoe use one of the fits made to the BeppoSAX data win f Zaud et ((1999). aa suum O |n black body with temperature AL=0.51 κο aud brenissrahluus» spectrum with temperature 16.6 kkeV. sorbed by a ¢ola Nyy6.9«10?tan7."," To convert this countrate into a luminosity we use one of the fits made to the BeppoSAX data by in 't Zand et (1999), a sum of a black body with temperature $kT=0.84$ keV and a bremsstrahlung spectrum with temperature $46.6$ keV, absorbed by a column $N_H=6.9\times10^{21}\cmsq$." +" Iu he OSAT baudpas of O.5-2.5kkeV the ΠΠντΓηug xd blackbody components contribute SN) and 17 respectively, to tie total dux."," In the ROSAT bandpass of keV the bremsstrahlung and blackbody components contribute 83 and 17 , respectively, to the total flux." + For this s)ectiui. the up201’ lait of ctss Liu the URI corresponds to an Narav nünositv of 6«LOeres1 between 0.5 and 2.5 keV. Or 1.5«lo?lores between 2 aud 10 keV. Note tha 1o OSAT ranec froni kkeV is effectively linuted to above O.5kkeV because of the hieh reddening.," For this spectrum, the upper limit of $\cts$ in the HRI corresponds to an X-ray luminosity of $6\times 10^{33}\ergs$ between 0.5 and 2.5 keV, or $1.5\times 10^{34}\ergs$ between 2 and 10 keV. Note that the ROSAT range from keV is effectively limited to above keV because of the high reddening." + Since SAN measures the flux down to 2 keV. the estimates of the ROSAT flux are quite accurate.," Since SAX measures the flux down to 2 keV, the estimates of the ROSAT flux are quite accurate." + This nuplies that the flux of the transient iu NGC66LL0 droppedby a factor 250 or more between the BeppoSAX observation ou Aug26 aud the ROSAT URI observation ou Sep 8., This implies that the flux of the transient in 6440 dropped by a factor 250 or more between the BeppoSAX observation on Aug 26 and the ROSAT HRI observation on Sep 8. +" The ROSAT data archive contains several litherto nupublished observatious of ""66LI0 made with the ROSAT IIRI after the 1991 observation reported ly Joinston et ((1995).", The ROSAT data archive contains several hitherto unpublished observations of 6440 made with the ROSAT HRI after the 1991 observation reported by Johnston et (1995). + A list of all ROSAT observations is given in 1t ftablog.., A list of all ROSAT observations is given in \\ref{tablog}. + We rave analyzed cach observation separatelv with the stanard procedure. and detect the source iu NOC66LL0 iu he 1993 observation audin the Sep 1991 observation. iin the observations with the longer CN)osure times.," We have analyzed each observation separately with the standard procedure, and detect the source in 6440 in the 1993 observation and in the Sep 1994 observation, in the observations with the longer exposure times." + Iu the shorter observations. we only obtain upper liits.," In the shorter observations, we only obtain upper limits." +" From the olserved. uber —of: counts iu a cncle with 5"" radius near the cluster we derive an upper linit to the couutrate of 8 counts for the ceutral source for both the 1992 and the March 1991 o)bservatikDI", From the observed number of 3 counts in a circle with $''$ radius near the cluster center we derive an upper limit to the countrate of 8 counts for the central source for both the 1992 and the March 1994 observation. +R Thethree detections are compatible witha coustan countrate. at a level below the derived," Thethree detections are compatible witha constant countrate, at a level below the derived" + , +states low-hard and ligh-soft simular to NX-1 and has been observed up to 500 keV during the flare modo.,states low-hard and high-soft similar to X-1 and has been observed up to 500 keV during the flare mode. + The quasi-periodic oscillatious with periods between 50 1500 s are the kev characteristics of the source (vau der Whs Jausou 1985)., The quasi-periodic oscillations with periods between 50 $--$ 1500 s are the key characteristics of the source (van der Klis Janson 1985). + A detailed analysis of the. X-rav spectrin sugeests that the total no of ταν photons seenis to be conserved at all times irrespective of the state aud the observed spectrum is cousistent with a thermal source embedded ii a hot plasma aud enveloped iu a cold hydrogen shell (Mauchauda 2002)., A detailed analysis of the X-ray spectrum suggests that the total no of X-ray photons seems to be conserved at all times irrespective of the state and the observed spectrum is consistent with a thermal source embedded in a hot plasma and enveloped in a cold hydrogen shell (Manchanda 2002). + The X-ray light curve of the source in the 2-12 keV baud from the RNTE/ÀASM data shows frequent spectral changes between the high-soft to low-hard states thereby sueecsting large. changes in the accretion rate on to the compact object., The X-ray light curve of the source in the 2-12 keV band from the RXTE/ASM data shows frequent spectral changes between the high-soft to low-hard states thereby suggesting large changes in the accretion rate on to the compact object. + At radio wavelengths. XX-3 is the most huuinous A-rav binary du both its quiescent and flaring states (Waltman et al.," At radio wavelengths, X-3 is the most luminous X-ray binary in both its quiescent and flaring states (Waltman et al." + 1995)., 1995). +" IIuge radio outbursts have becu reported in NN-39 durus which the fux density can increase up to levels of ~20JJv: radio cussion is suppressed (""queuched""} to levels below nuuJx for some clays fore large radio flares (Waltinan ct al.", Huge radio outbursts have been reported in X-3 during which the flux density can increase up to levels of $\sim$ Jy; radio emission is suppressed (“quenched”) to levels below mJy for some days before large radio flares (Waltman et al. + 1991)., 1994). + Jet-ike structures with repeated relativistic ejection have )een observed at various radio frequencies (6.8. Schalinski et al., Jet-like structures with repeated relativistic ejection have been observed at various radio frequencies (e.g. Schalinski et al. + 1998)., 1998). + Ou an are-secoud scale. two-sidec jets have con seen from the source in the N-S orientation. whereas a highh-relativistic (9 2 0.81) one-sidedjet with the same orientation has been reported on qulli-arcsec scales with he VLBA ct al.," On an arc-second scale, two-sided jets have been seen from the source in the N-S orientation, whereas a highly-relativistic $\beta$ $\ge$ 0.81) one-sided jet with the same orientation has been reported on milli-arcsec scales with the VLBA et al." + 2001: Mioduszewski et al., 2001; Mioduszewski et al. + 2001)., 2001). + Iu the Table 2 above we lave σπαΊος the radio flux deusities of the source as measured during various observations with CAIRT aud from the Ryle Telescope data., In the Table 2 above we have summarized the radio flux densities of the source as measured during various observations with GMRT and from the Ryle Telescope data. + Fig., Fig. + 6 shows a fiuxflux plot for (νοκ for the GAIRT and 15-GIIz data. and Fig.," 6 shows a flux–flux plot for X-3 for the GMRT and 15-GHz data, and Fig." + 7 shows the 15-CIIz and RNTE ASM data for the whole period., 7 shows the 15-GHz and RXTE ASM data for the whole period. + The timing of the GAIRT observations is again marked with vertical lines in Fig., The timing of the GMRT observations is again marked with vertical lines in Fig. + 7., 7. + The last 1 GAIRT observations. all at GCIIz. were made during the high-soft state.," The last 4 GMRT observations, all at GHz, were made during the high-soft state." +" The mean fiux density at that frequency was ΗΝ, compared with Tuunaty for the 6 xevious data points: the 15-GIIz uean value was also üeher. 150nunJy compared withwi TluunJv for the correspouding 6 data points."," The mean flux density at that frequency was mJy, compared with mJy for the 6 previous data points; the 15-GHz mean value was also higher, mJy compared with mJy for the corresponding 6 data points." + We note hat the radio/N-rav correlation is in the opposite ποσο o that for NN-1., We note that the radio/X-ray correlation is in the opposite sense to that for X-1. +" MeColloush et al (1999) repor both anuti-correlatious (in the quiescent state) aud correlations (n the flaring state) between the hard ταν flux kkeV. as measured x DATSE) aud the cn-wave radio flux «eusitv of δν,"," McCollough et al (1999) report both anti-correlations (in the quiescent state) and correlations (in the flaring state) between the hard X-ray flux keV, as measured by BATSE) and the cm-wave radio flux density of X3." + We investigated the possibility that RISS mught be nuportaut iu the case of XNN3., We investigated the possibility that RISS might be important in the case of X3. + The propagation conciJos are more severe than for the case of NX-1: the path leusth is much lounger. and it has been kuownun for some tine (e.g. Wilkmson ct al. 1991) that the scatter-broadening for this source ds extreme.," The propagation conditions are more severe than for the case of X-1: the path length is much longer, and it has been known for some time (e.g. Wilkinson et al, 1994) that the scatter-broadening for this source is extreme." + The NE2001 model is cousisteut: it sugeests angular broadening of 20.59. aaresec at 0.61. GGITz.," The NE2001 model is consistent: it suggests angular broadening of 20.59, arcsec at 0.61, GHz." + The correspouding timescales would be many vears. and the narrow scintillation bandwidth ΠΠ) would suppress anv observed scintillation.," The corresponding timescales would be many years, and the narrow scintillation bandwidth Hz) would suppress any observed scintillation." + We conclude that RISS is uot relevant to this study of NX-3., We conclude that RISS is not relevant to this study of X-3. + To look for correlation between the radio emiüssiou fron the source with its X-ray cussion characteristics. we have plotted the RNTE/ASAI X-ray light curve for NN-3 in Fie.," To look for correlation between the radio emission from the source with its X-ray emission characteristics, we have plotted the RXTE/ASM X-ray light curve for X-3 in Fig." + 7 along with the radio data., 7 along with the radio data. + The timing of the CAIRT observations is shown by the vertical lines., The timing of the GMRT observations is shown by the vertical lines. + It can be seen that no large flares were observed dunue this interval., It can be seen that no large flares were observed during this interval. + The radio Cluission is iu the “quiescent” state. typically 50 to muuJy at 15 GIIz.," The radio emission is in the `quiescent' state, typically 50 to mJy at 15 GHz." + For the last mouth or so of this time- the N-rav spectrum softens: the RATE ASAI ratio IIR2 falls consistently below 2. aud the radio euiussion starts to become more erratic.," For the last month or so of this time-range, the X-ray spectrum softens: the RXTE ASM ratio HR2 falls consistently below 2, and the radio emission starts to become more erratic." + This behaviour faced away after another nouth or so. aud the source returued to the quiescent state.," This behaviour faded away after another month or so, and the source returned to the quiescent state." + As seen from the data in Table 2 and Fig., As seen from the data in Table 2 and Fig. + 6. NN-3 Is a persistcut radio source at all wavelengths.," 6, X-3 is a persistent radio source at all wavelengths." + NX-3 ds amore luninous at higher frequencies., X-3 is more luminous at higher frequencies. + The data in Table 2 clearly indicates a low frequenev turi-over in the ποος spectrmm below Πε., The data in Table 2 clearly indicates a low frequency turn-over in the source spectrum below GHz. + Às discussed earlier. such schaviour can arise due to svuchrotrou self absorption of the compact radio emüttiug plasima in an optically tick imediuu.," As discussed earlier, such behaviour can arise due to synchrotron self absorption of the compact radio emitting plasma in an optically thick medium." + The observed variability. of the flux ceusi vods consistent with tje asstuuption of a discrete cjection/plasimoid in adiabatic expansion., The observed variability of the flux density is consistent with the assumption of a discrete ejection/plasmoid in adiabatic expansion. + The, The +During most of the previous decade Lye emission was considered an inefficient. survey method for high-redshift galaxies due to a number of unsuccessful surveys (e.g. Prichet 1994 and references therein).,During most of the previous decade $\alpha$ emission was considered an inefficient survey method for high-redshift galaxies due to a number of unsuccessful surveys (e.g. Prichet 1994 and references therein). + It is now clear that the first surveys for Lyn emitters were unsuccessful mainly because they reached significantly too shallow detection limits., It is now clear that the first surveys for $\alpha$ emitters were unsuccessful mainly because they reached significantly too shallow detection limits. + The theoretical expectation was that todays large ellipticals formed in a fast. monolithic collapse (e.g. Patridge Peebles 1967).," The theoretical expectation was that todays large ellipticals formed in a fast, monolithic collapse (e.g. Patridge Peebles 1967)." + In the hierarchical picture of galaxy formation the high-redshift galaxies are smaller and hence fainter than expected when the first surveys were planned., In the hierarchical picture of galaxy formation the high-redshift galaxies are smaller and hence fainter than expected when the first surveys were planned. + The main advantage of LBG surveys is that they probe a very large volume and hence provide a large number of galaxies per field., The main advantage of LBG surveys is that they probe a very large volume and hence provide a large number of galaxies per field. + However. there is a number of studies that are most efficiently done with LEGOs as probes: LEGOs can be used to probe the faint end of the luminosity function (Fynbo et al.," However, there is a number of studies that are most efficiently done with LEGOs as probes: LEGOs can be used to probe the faint end of the luminosity function (Fynbo et al." + 2001): LEGOs can be detected and spectroscopically confirmed at both lower (Fynbo et al., 2001); LEGOs can be detected and spectroscopically confirmed at both lower (Fynbo et al. +" 1999, 2002) and higher redshifts (Dey et al."," 1999, 2002) and higher redshifts (Dey et al." + 1998; Ellis et al., 1998; Ellis et al. + 2001: Venemans et al., 2001; Venemans et al. + 2002: Hu et al., 2002; Hu et al. + 2002: Taniguchi et al., 2002; Taniguchi et al. + 2003) than is currently possible with techniques based on the continuum: the large space density reachable with surveys for LEGOs allows a detailed study of the underlying large scale structure and to probe the environments of other high-redshift objects such as radio galaxies (Kurk et al., 2003) than is currently possible with techniques based on the continuum; the large space density reachable with surveys for LEGOs allows a detailed study of the underlying large scale structure and to probe the environments of other high-redshift objects such as radio galaxies (Kurk et al. + 2000; Venemans et al., 2000; Venemans et al. + 2002). Gamma Ray Burst host galaxies (Fynbo et al.," 2002), Gamma Ray Burst host galaxies (Fynbo et al." + 2002) or QSO absorbers (e.g. Meller Warren 1993. Francis et al.," 2002) or QSO absorbers (e.g. ller Warren 1993, Francis et al." + 1995; and this paper)., 1995; and this paper). + The optimal way to proceed with Lya surveys seems to be the use of large area cameras on 8-m class telescopes., The optimal way to proceed with $\alpha$ surveys seems to be the use of large area cameras on 8-m class telescopes. + First results regarding the luminosity function and clustering properties of LEGOs using the Suprime Camera (Miyazaki et, First results regarding the luminosity function and clustering properties of LEGOs using the Suprime Camera (Miyazaki et +were (hen flatfielded by clividing by the internal «ΟΠΗ lamp frame.,were then flatfielded by dividing by the internal continuum lamp frame. + Object and telluric calibration spectra in each echelle order were extracted from a spatial profile that was fixed al z2.5 pixels (2:075) about the prolile peak., Object and telluric calibration spectra in each echelle order were extracted from a spatial profile that was fixed at $\pm$ 2.5 pixels $\pm 0\farcs5$ ) about the profile peak. + The object and telluric spectra extracted ad each nod position were wavelength calibrated. using selected tellurie absorption lines (Lor orders 33. 34. and 35) with wavelengths taken from the LITRAN database (Rothman et 11998). and emission lines of Areon. Krypton. Xenon. and Neon from exposures in the internal lamp spectra (for orders 36. 37. and 38).," The object and telluric spectra extracted at each nod position were wavelength calibrated using selected telluric absorption lines (for orders 33, 34, and 35) with wavelengths taken from the HITRAN database (Rothman et 1998), and emission lines of Argon, Krypton, Xenon, and Neon from exposures in the internal lamp spectra (for orders 36, 37, and 38)." + Telluric features in each of the four nod positions were removed fom our object spectra by dividing by the spectrum of the telluric standard star obtained at a similar nod position., Telluric features in each of the four nod positions were removed from our object spectra by dividing by the spectrum of the telluric standard star obtained at a similar nod position. + Order 35 contned emission Irom Dr? in our telluric standard., Order 35 contained emission from $\gamma$ in our telluric standard. + To avoid introducing spurious structure in the object spectra. we divided bv the telluric standard to correct [ον telluric absorption only in regions far from the Bro line.," To avoid introducing spurious structure in the object spectra, we divided by the telluric standard to correct for telluric absorption only in regions far from the $\gamma$ line." + Residual telluric features are therefore present in the spectral region within 415 kms+ ofthe Dr 5 line center (2.1638 — jm)., Residual telluric features are therefore present in the spectral region within $\sim$ 415 $\kms$ of the Br $\gamma$ line center (2.1638 – $\micron$ ). + Waveleneth calibrated spectra al different nod positions in each order were summed and then multiplied by a blackbody of KIX to restore the true continuum shape after division bv the D2V telluric standard., Wavelength calibrated spectra at different nod positions in each order were summed and then multiplied by a blackbody of K to restore the true continuum shape after division by the B2V telluric standard. + The fIux level in the V1331 spectrum was estimated bv the conversion from observed counts in the observations of the standard toits 2ALASS A- magnitude Gay = 4.48: JJv). and assuming; an equal slit loss between the stancard and object observations.," The flux level in the V1331 spectrum was estimated by the conversion from observed counts in the observations of the standard to its 2MASS $K$ -band magnitude $m_K$ = 4.48; Jy), and assuming an equal slit loss between the standard and object observations." + The MWCHS0AIWCAS0 observationsobservation werere reduced using a similar prprocedure., The MWC480 observations were reduced using a similar procedure. +lure. Since (1these bservatiolobservations made use of (he improved NIRSPEC array. there were significantly fewer bad. pixels.," Since these observations made use of the improved NIRSPEC array, there were significantly fewer bad pixels." + Thus. bad pixels were individually identified and their values fixed bv interpolation using the IRAF task “fixpix”.," Thus, bad pixels were individually identified and their values fixed by interpolation using the IRAF task “fixpix""." +" The observations of AIWC! 480 were taken with a wider slit (3-pixel. 07432) and in windy conditions with poor seeing. compared to V1331 (νο,"," The observations of MWC 480 were taken with a wider slit (3-pixel, $\farcs$ 432) and in windy conditions with poor seeing, compared to V1331 Cyg." + As a result. spectral images of MWC 480 and the tellurie standard star (IR 1412) that were observed at similar beam positions were sumed together without offsets. and their spectra were extracted from a relatively wide (£5 pixels) spectral profile.," As a result, spectral images of MWC 480 and the telluric standard star (HR 1412) that were observed at similar beam positions were summed together without offsets, and their spectra were extracted from a relatively wide $\pm$ 5 pixels) spectral profile." +" Good signal-to-noise in the exposures of (he arc lamps (i.e. Ar. νε, Xe. and Ne) permitted wavelength calibration of all orders except order 33. where telluric absorption lines were used."," Good signal-to-noise in the exposures of the arc lamps (i.e. Ar, Kr, Xe, and Ne) permitted wavelength calibration of all orders except order 33, where telluric absorption lines were used." + Telluric features in the IWC 480 spectra were removed by dividing by the spectrum of the standard star (II. 1412) obtained at a similar nod position., Telluric features in the MWC 480 spectra were removed by dividing by the spectrum of the standard star (HR 1412) obtained at a similar nod position. + Several weak stellar absorplion lines were present in (he standard star spectrum., Several weak stellar absorption lines were present in the standard star spectrum. + These were modeled and, These were modeled and +medium of Miller Cox (1993). which took into account the absorption of UV radiation by clouds with density larger than the surrounding medium in a statistical wav.,"medium of Miller Cox (1993), which took into account the absorption of UV radiation by clouds with density larger than the surrounding medium in a statistical way." + In Fig., In Fig. + 7 the vertical distribution of the mean LIL (solid lines) and. LILLE (dottec Lines) number densities is shown. for runs A and D with the above μι. in the case of a Gaussian (top panel) and. fractal (bottom panel). density fielcl at clifferent times after the source turn on.," \ref{fig07} the vertical distribution of the mean HI (solid lines) and HII (dotted lines) number densities is shown, for runs A and B with the above $N_{HI}$, in the case of a Gaussian (top panel) and fractal (bottom panel) density field at different times after the source turn on." + For both, For both +"Llere δν,; denotes the resulting. value of ⋅∕v7... when wesubstitute. 5,, ∕⋅for 5, ∕⋠in equation. (AL)).","Here $\nu'_{cr,m}$ denotes the resulting value of $\nu'_{cr,e}$ when wesubstitute $\gamma'_m$ for $\gamma'_e$ in equation \ref{nume}) )." + Ht surfaces⋅ when we switch. integration. variables. from⋅ .∕ to ∕vy...," It surfaces when we switch integration variables from $\gamma'_e$ to $\nu'_{cr,e}$." + The auxiliary function Q is defined as In practice. the computer code uses lookup tables for £67). PGr) and ρω).," The auxiliary function $Q$ is defined as In the limit of small and large $x$, $Q(x)$ behaves as follows: In practice, the computer code uses lookup tables for $F(x)$ , $\mathcal{P}(x)$ and $Q(x)$ ." + The three functions have been plotted in figure CX1)) (Q for both p=2.2 and p= 2.8). allowing for comparison between the spectra from a single electron. an angle-averaged electron and an ensemble electron.," The three functions have been plotted in figure \ref{FPQplot}) ) $Q$ for both $p = 2.2$ and $p = 2.8$ ), allowing for comparison between the spectra from a single electron, an angle-averaged electron and an ensemble electron." + Η the only. processes that are of importance are svnchrotron emission and acliahatic cooling. the evolution of the Lorentz [actor of a single electron is described by where er denotes the Thomson cross section.," If the only processes that are of importance are synchrotron emission and adiabatic cooling, the evolution of the Lorentz factor of a single electron is described by where $\sigma_T$ denotes the Thomson cross section." + In Ciranot&Sari(2002). this cdillerential equation is applied to the DM solution by expressing it in terms of the self-similar variable and solving it analytically., In \cite{Granot2002} this differential equation is applied to the BM solution by expressing it in terms of the self-similar variable and solving it analytically. + In our case we can use eq. CX12)), In our case we can use eq. \ref{gamma_m_equation}) ) +" to establish +5,; directly behind the shock front and initially put 55. the upper cut-off Lorentz [actor due to cooling. at a sullicienthy large value (instead. of infinity)."," to establish $\gamma'_m$ directly behind the shock front and initially put $\gamma'_M$, the upper cut-off Lorentz factor due to cooling, at a sufficiently large value (instead of infinity)." + SullicientIx large for example can be taken such that with c some tolerance lor the error in the energy., Sufficiently large for example can be taken such that with $\epsilon$ some tolerance for the error in the energy. +" The real 55, will quickly catch up with the approximated +4). as can be seen from equation (D1))."," The real $\gamma'_M$ will quickly catch up with the approximated $\gamma'_M$ , as can be seen from equation \ref{evolution_equation}) )." + The analytical solutionfor the particle distribution in the DM caseis given by, The analytical solutionfor the particle distribution in the BM caseis given by +al distance . (hen it contains a total number of particles and has emission measure where n is the mean mass per particle.,at distance $x$ then it contains a total number of particles and has emission measure where $m$ is the mean mass per particle. +" Using equation (17)) these vield where .V,=2x1Dpe""E and where EM,=2xRP(Eyl, "," Using equation \ref{rhod}) ) these yield where $N_o=2\pi R^3\frac {\rho_o}{m}$, and where $EM_o=2\pi R^3 (\frac {\rho_o}{m})^2$." +Following the Brown&McLean(1977). formulation. (he scattering polarization is T7(l- 3D)sin?;. where 7 is optical depth. P is the shape factor of the disk and 7 is the inclination angle.," Following the \citet{brown77} formulation, the scattering polarization is $P=\tau (1-3\Gamma)\sin^2 i$ , where $\tau$ is optical depth, $\Gamma$ is the shape factor of the disk and $i$ is the inclination angle." + Assuming the disk to be a slab with constant thickness //=Hh and including the finite source depolarization [actor D=/1—R?/r?γι1/4? 1939).. then we have the optical depth 7. Sepp. ⋅↴ − − − ⊔∐↲≼∐⊳∖⇁↳↽⋅≀↧↴∐≼⇂∕∣↥⊳∖⊽⊔∐↲≺∢∪⋝∖⊽↕∐≼↲∪↓≯⊔∐↲≀↧↴∐≸≟↥≼↲⊳∖⇁∣↽≻≼↲↥∖∖⊽≼↲≼↲∐⊔∐↲↕∐≺∢↕≼⇂≼↲∐↥∐↖⊂↽↔↴↥∐∩≻⊔∐↲≼∐⋝∖⊽↳↽≀↧↴∐≺⇂⊔∐↲ ↕⋅∪↥≀↧↴∐∪∐≀↧↴↥≀↧↴⇀↸↕⊳∖⇁⋅↼≚⊳∖⊽↥∐⇀∖↕⊺∐⋅∖∖↽≼↲∐≼↲↖⊂↽↔↴↥≼↲≺∢," Assuming the disk to be a slab with constant thickness $H=Rh$ and including the finite source depolarization factor $D=\sqrt +{1-R^2/r^2}=\sqrt{1-1/x^2}$ \citep{cassi87,brown89}, then we have the optical depth $\tau$, where $\tau_o=\frac {3\sigma_T R}{16}\frac{\rho_o}{ m}$, $\sigma_T$ is Thomson cross section, $n=\rho_D/m$ is the electron density of the disk, and $\mu$ is the cosine of the angles between the incident light to the disk and the rotational axis." +↥⊔∐↲≀↧↴∣↽≻⊳∖⇁∪↕⋅↕↽≻∐∪∐≀↧↴∐≼⇂⊳∖⊽∏↕↽≻↕↽≻∪⋝∖⊽≼↲≀↧↴↓≯∏∐⋡∖↽↕∪∐↕∠≼↲≼⇂≼∐⊳∖⇁↕≶⋅," As in MTD, we neglect the absorption and suppose a fully ionized disk." +↴∏∐↲, The +channels using this method.,channels using this method. + As can be seen each of the channels have been reconstructed. very. well (the dust templates have been added together to allow a with the input maps of Figure 1)., As can be seen each of the channels have been reconstructed very well (the dust templates have been added together to allow a comparison with the input maps of Figure 1). + Indeed. the error on the CMD comparisonreconstruction is still ομ]ν which is the same as in the case ofa single dust channel perwith pixelknown emissivity (ΕΤΟΣ).," Indeed, the error on the CMB reconstruction per pixel is still $6\mu$ K which is the same as in the case of a single dust channel with known emissivity (HJLB98)." + Vhis should be contrasted with the 1θμ]ν error obtained by performing the analysis with only one dust template (as in JL205) assuming a spectral index of 2.0., This should be contrasted with the $10\mu$ K error obtained by performing the analysis with only one dust template (as in HJLB98) assuming a spectral index of 2.0. + The free-free. svnchrotron ancl thermal SZ have been reconstructed to à lower amplitude than the input map (this is because most of the information on these foregrounds occur at the lower frequencies of the Planck Survevor which have lower resolutions: sec ILJLB98).," The free-free, synchrotron and thermal SZ have been reconstructed to a lower amplitude than the input map (this is because most of the information on these foregrounds occur at the lower frequencies of the Planck Surveyor which have lower resolutions; see HJLB98)." + The kinetic SZ is not reconstructed. to a very high. and only features associated with strong thermal SZ elfects are significance.reconstructed (see LEJEDON)., The kinetic SZ is not reconstructed to a very high significance and only features associated with strong thermal SZ effects are reconstructed (see HJLB98). +This estimate for the size of the flaring region has becu obtained under a few assuuptious which deserve some cohunents.,This estimate for the size of the flaring region has been obtained under a few assumptions which deserve some comments. + First. we have cousidered a flare occuring iu a single loo»," First, we have considered a flare occurring in a single loop." + This may uot hold true for such an intense aud oue-lasti1 fiare. Which may perhaps be described more oxoperlv as à ποπρο flare. cousistiie of progressively reconnecting higher and higher loops.," This may not hold true for such an intense and long-lasting flare, which may perhaps be described more properly as a two-ribbon flare, consisting of progressively reconnecting higher and higher loops." + Nevertheless. it often occurs in solar ποτοι flares hat the rise phase uostlv involves a dominant loop structure. aud then nevaditalv extends to others citealpaa2 )013).," Nevertheless, it often occurs in solar two-ribbon flares that the rise phase mostly involves a dominant loop structure, and then gradually extends to others \\citealp{aa2001}) )." + We nay associate the estimated length ο such donmunuanut structure., We may associate the estimated length to such dominant structure. + Anoher müuplicit nou-trivial assmnuption is that of a heatiis pulse coustautlv high during the rise phase., Another implicit non-trivial assumption is that of a heating pulse constantly high during the rise phase. + Tudeed. a gradually increasing heating function may drive he observed eradual rise of the Lelt curve. invalidating he estimations made above.," Indeed, a gradually increasing heating function may drive the observed gradual rise of the light curve, invalidating the estimations made above." + However. in such a case we should observe also a gradual increase of the temperature. while the i]idicatiojs are for a sudden jmp of the cluperature to the flare value. which is more typical of a heating pulse.," However, in such a case we should observe also a gradual increase of the temperature, while the indications are for a sudden jump of the temperature to the flare value, which is more typical of a heating pulse." + We uav be therefore quie confident that ιο total loop leugth i2.10H Cni.," We may be therefore quite confident that the total loop length is $\simeq 2 +\times 10^{11}$ cm." + Tf we asstme a loop aspect R/L~0.1. where Π> is re radius of the loop cross-section. assuied circular aud constant along the oop. we obtain a total loop volume Proxτή Clu? a WANT enission nieasure of 2.6&pl > tion dupies A niaxiumui average loop plasina density of ~2«10 ban3 and a maxiuun pressure of the order of 10 dvne D 7.," If we assume a loop aspect $R/L \sim 0.1$, where $R$ is the radius of the loop cross-section, assumed circular and constant along the loop, we obtain a total loop volume $V \sim 6 \times 10^{31}$ $^3$; a maximum emission measure of $\sim 2.6 \times 10^{54}$ $^{-3}$ then implies a maximum average loop plasma density of $\sim 2 \times +10^{11}$ $^{-3}$ and a maximum pressure of the order of $10^4$ dyne $^{-2}$ ." + This value is compatible with the equilibrium pressure obtained frou loop scaine laws (Rosneretal. 1978)) aud cousisteut wit1i the hypothesis of the loop at Παπά X-rav huninosity beime close to equilibriu coxditious., This value is compatible with the equilibrium pressure obtained from loop scaling laws \citealp{rtv78}) ) and consistent with the hypothesis of the loop at maximum X-ray luminosity being close to equilibrium conditions. + Iun order to confine a plasma at such a pressure. a inaenetic field of more tman e500 Cass is required.," In order to confine a plasma at such a pressure, a magnetic field of more than $\sim 500$ Gauss is required." + The origin of such a field i) stars that are thought to be tilly or uearly-fully radiative is ptzzlug., The origin of such a field in stars that are thought to be fully or nearly-fully radiative is puzzling. + Iu low-imass stars the presence of a significant convection zone supports the dynamo mechauisin that can generate the confining magnetic fields at the origin o| the rav flare events. but according to classical m0¢lols. pre- star with masses dn excess of 2 M: are expected to follow fully radiative tracks once tf1e qlasistatic contraction has euded.," In low-mass stars the presence of a significant convection zone supports the dynamo mechanism that can generate the confining magnetic fields at the origin of the X-ray flare events, but according to classical models, pre-main-sequence star with masses in excess of 2 $M_{\sun}$ are expected to follow fully radiative tracks once the quasi-static contraction has ended." + Palla&Stahler(1990) have nude the sugeestionCoco that the surface activity aid winds observed in Tarbie Ac/Be Way be related fo f1ο presence of an outer colnvecjon zone., \cite{ps90} have made the suggestion that the surface activity and winds observed in Harbig Ae/Be may be related to the presence of an outer convection zone. + Iu their interpretation. this αςoxvection zone results from the subsurface shell burning of residual deuteruu which was accreted «ming the protostar pliase.," In their interpretation, this convection zone results from the subsurface shell burning of residual deuterium which was accreted during the protostar phase." + Nevertheless Palla&Staller(1993) reconsider their hypothesis. a1Lexplain that accordiie to their models the retrea of the proto-star outer couvection zone docs last a substantial fraction of the preauairsequeuce lifetime of au intermeciaο lnass star.," Nevertheless \cite{ps93} + reconsider their hypothesis, and explain that according to their models the retreat of the proto-star outer convection zone does last a substantial fraction of the pre-main-sequence lifetime of an intermediate mass star." + Diving his retreat. however. the effective fc‘perature remains rclatively low. so that the star wouk not be observed witran A or D specral type.," During this retreat, however, the effective temperature remains relatively low, so that the star would not be observed with an A or B spectral type." + Thev coiclude that the preseice in Herbie Ae‘Be stars of surface| activitv aud strong winds is not linke to an otter convection zone. since tlieir model shows tlat such couvectiojiondbwayvs vanishes with t1e Visine effective (‘perature.," They conclude that the presence in Herbig Ae/Be stars of surface activity and strong winds is not linked to an outer convection zone, since their model shows that such convection always vanishes with the rising effective temperature." + Receutly Siessctal(2000) lavo presened calculatiois of pre-niadi-sequence evolulonarv tracks for ow- and iutermediate-nuass stars., Recently \cite{sdf00} have presented calculations of pre-main-sequence evolutionary tracks for low- and intermediate-mass stars. + These models precict he existeice of a thin convective cuvelo»( in voung AB stars., These models predict the existence of a thin convective envelope in young AB stars. + In their review. Favata&Micela(203) sugeest that his thin couvective envelope. of roughly 2.LO? times he stellar radius. could be at the origin of a low-coronal activity (at the level of the observed πάπια for solar vpe stars) in Altair (ATV) aud lus explain the source N-rav luminosity of Lx=3<10?Tored.," In their review, \cite{fm03} suggest that this thin convective envelope, of roughly $2 \times 10^{-3}$ times the stellar radius, could be at the origin of a low-coronal activity (at the level of the observed minimum for solar type stars) in Altair (A7V) and thus explain the source X-ray luminosity of $L_{\rm X} = 3 \times +10^{27}$." + According to the same imodels a star with mass LO AL:. the κιune ietallicitv of the Sun aud an age of 10 uillion years. would have a spectral type AG. à Iuninositv of 12 L;. not too far from the one of V892 Tau. iud a convective envelope of a fraction oa 0018 its raclius.," According to the same models a star with mass 1.9 $M_{\sun}$, the same metallicity of the Sun and an age of 10 million years, would have a spectral type A6, a luminosity of 12 $L_{\sun}$, not too far from the one of V892 Tau, and a convective envelope of a fraction of 0.0018 its radius." + Since 1e niodel prelicts a stellar radis of 1.2«LotLoan. the size of the convective region wotld be 2.2«10ys cn (~ Rs.)," Since the model predicts a stellar radius of $1.2 \times +10^{11}$ cm, the size of the convective region would be $2.2\times +10^8$ cm $\sim$ $R_{\sun}$ )." + Tt is not clear whether such a thin convective welope. that may be sufficieu to generate the low «€wonal activity mnuvokec to explaiu the 3 to 1 order of -magnitude faiter X-ray cussion of a man secποιος A ar. cadi sustain the dxiuo action necessary f» explain je strong X-rav activity of V892 Tan.," It is not clear whether such a thin convective envelope, that may be sufficient to generate the low coronal activity invoked to explain the 3 to 4 order of magnitude fainter X-ray emission of a main sequence A star, can sustain the dynamo action necessary to explain the strong X-ray activity of V892 Tau." + Dudeed. YOU OUr flare model we derive a flare oop leugth of ὃν101. oun.," Indeed, from our flare model we derive a flare loop length of $\simeq 2\times 10^{11}$ cm." + This is comparabe to the stellar radius aud corresponds oa size of ~500 times the hin convective euveope., This is comparable to the stellar radius and corresponds to a size of $\sim 500$ times the thin convective envelope. + An alteruative imechauisni fo sustain the cdynanaio activity in these xecdowinautly radiative stars las been xoposed by Tout&Pringe(1995)., An alternative mechanism to sustain the dynamo activity in these predominantly radiative stars has been proposed by \cite{tp95}. +. They argue that dviuainio activity can be ststained in AB stars for a substantial fraction oftieir preanain-sequence life time by apping the initial stelar differcutial rotation or shear CLOTSV., They argue that dynamo activity can be sustained in AB stars for a substantial fraction of their pre-main-sequence life time by tapping the initial stellar differential rotation – or shear energy. + We have analysed the lieht curves and spectral data of the system V892 Tau and V892 Tau NE ina 115 ks exposure and 2 cousecutive cexposures of 7 land L5 ks (nominal)., We have analysed the light curves and spectral data of the system V892 Tau and V892 Tau NE in a 18 ks exposure and 2 consecutive exposures of 74 and 45 ks (nominal). + In the data. the Herbig Ac star V892 Tau iswell resolved from the low niass later type apparent coniauion V892 Tau NE.," In the data, the Herbig Ae star V892 Tau iswell resolved from the low mass later type apparent companion V892 Tau NE." + During the, During the +et al. (,et al. ( +2001) with LIE detections.,2001) with HI detections. + An exponential law fails to fit the ealaxy simultaneously at both small anc laree radii. at a high level of significance: the reduced 47 (v7 = 10 degrees of freedom) for the r+1 and exponential fits ⋠⋅⋠in Figure 3 are 0.85 and 131 respectively.," An exponential law fails to fit the galaxy simultaneously at both small and large radii, at a high level of significance: the reduced $\chi^2$ $\nu$ = 10 degrees of freedom) for the $r^{1/4}$ and exponential fits in Figure 3 are 0.85 and 131 respectively." + Phe central surface-brightness derived from the r3 fit at radii larger than one aresecond (corresponding to the seeing radius) is fog = 15.2 mag 7., The central surface-brightness derived from the $r^{1/4}$ fit at radii larger than one arcsecond (corresponding to the seeing radius) is $\mu_{0R}$ = 15.2 mag $^{-2}$. + This extrapolated value is very much higher than themeasured central surface brightnesses of about. fro = 19.5 mag 2, This extrapolated value is very much higher than the central surface brightnesses of about $\mu_{0R}$ = 19.5 mag $^{-2}$. +" We can infer the star formation rate in Ark 1460. from measurements of the OLL line equivalent width (46.X: ""ustilnik et al.", We can infer the star formation rate in Mrk 1460 from measurements of the OII line equivalent width (46; Pustilnik et al. + 1999) and also the 1.4 C€llz continuum lux (Section 2.3. Verheijen et al.," 1999) and also the 1.4 GHz continuum flux (Section 2.3, Verheijen et al." + 2001)., 2001). + Both sets of measurements directly. probe high-mass stars and. their remnants and derivations of the star formation rate [rom hese measurements therefore require very substantial corrections for low-mass stars. which dominate the total mass.," Both sets of measurements directly probe high-mass stars and their remnants and derivations of the star formation rate from these measurements therefore require very substantial corrections for low-mass stars, which dominate the total mass." + Assuming a Salpeter (1955) stellar. initial mass unction. and the OIL line calibration of Gallego (1998). he current. star formation rate in Markarian 1460 is 00M.vr ," Assuming a Salpeter (1955) stellar initial mass function and the OII line calibration of Gallego (1998), the current star formation rate in Markarian 1460 is $0.09 \,{\rm M}_{\odot} {\rm yr}^{-1}$." +"Assuming the same stellar initial mass ""unction and the calibration of Cram et al. (", Assuming the same stellar initial mass function and the calibration of Cram et al. ( +1998). the 36 upper limit on the star formation rate derived from the 1.4 Gllz measurements described in Section 2.3 is 0.1Mor4 ,"1998), the $\sigma$ upper limit on the star formation rate derived from the 1.4 GHz measurements described in Section 2.3 is $0.11 \,{\rm M}_{\odot} {\rm yr}^{-1}$." +Deriving abundances from. emission-line properties is complicated and a detailed: analysis requires many more measurements than are available for this galaxy (Stasinska Leitherer. 1996)., Deriving abundances from emission-line properties is complicated and a detailed analysis requires many more measurements than are available for this galaxy (Stasinska Leitherer 1996). + However. the following simple analysis IS sUgeestec-," However, the following simple analysis is suggested." + From the Dux ratios H]J/IE3 and LU/LE7 (Dustilnik et al., From the flux ratios $\beta$ and $\beta$ (Pustilnik et al. + 1999). the abundance ratios /11 and Hare 3.7 5 7 and 46 s 7. leading to a value of the ionized gas oxvgen abundance of O/LE = 8.3 « 7.," 1999), the abundance ratios $^{+}$ /H and $^{++}$ /H are 3.7 $\times$ $^{-5}$ and 4.6 $\times$ $^{-5}$, leading to a value of the ionized gas oxygen abundance of O/H = 8.3 $\times$ $^{-5}$." + In this calculation we follow “Tully et al. (, In this calculation we follow Tully et al. ( +1981) and adopt a normal Whitford (1958) reddening curve.,1981) and adopt a normal Whitford (1958) reddening curve. + LE the. heavy element abundance is proportional to the oxvgen abundance. the total metallicity of the ionized eas in Alrk 1460 is then about 0.1 solar CXneders Grevesse 1989).," If the heavy element abundance is proportional to the oxygen abundance, the total metallicity of the ionized gas in Mrk 1460 is then about 0.1 solar (Anders Grevesse 1989)." + The colours of this galaxy are: ο[22083. BR1—0:31. and 4/— A'—191.," The colours of this galaxy are: $B-R=0.83$, $R-I=0.31$, and $I-K^{\prime}$ =1.91." +" The fA! colour is derived using aperture magnitudes within the A"" 2-0 isophote: this ensures that we are measuring the same part of the galaxy in both filters aud does not require us to make corrections for light lost. below the sky at large radius in the A image.", The $I-K^{\prime}$ colour is derived using aperture magnitudes within the $K^{\prime}$ $\sigma$ isophote; this ensures that we are measuring the same part of the galaxy in both filters and does not require us to make corrections for light lost below the sky at large radius in the $K^{\prime}$ image. + These optical colours suggest an age of approximately 1.8 Gyr if the galaxy has been forming stars either in an instantaneous burst at this time in the past or continuously with an exponential star-formation history profile with e-folcing time 1 Gwr. given the models of Bruzual Charlot (1993). assuming a Salpeter (1955) stellar. initial mass function from 0.1 AL. to 100 AL. ). negligible internal extinction and a metallicity of 0.4 solar.," These optical colours suggest an age of approximately 1.3 Gyr if the galaxy has been forming stars either in an instantaneous burst at this time in the past or continuously with an exponential star-formation history profile with $e$ -folding time 1 Gyr, given the models of Bruzual Charlot (1993), assuming a Salpeter (1955) stellar initial mass function from 0.1 $_{\odot}$ to 100 $_{\odot}$ ), negligible internal extinction and a metallicity of 0.4 solar." + Phe £0A colour above is. however. too red by about 0.7 magnitudes to be produced by the stars [from this burst alone.," The $I-K^{\prime}$ colour above is, however, too red by about 0.7 magnitudes to be produced by the stars from this burst alone." + This might sugeest the presence ofa population of older stars which only contribute in a small way to the optical D'uxes., This might suggest the presence of a population of older stars which only contribute in a small way to the optical fluxes. + Probably the, Probably the +explosions are more easier to be obtained for higher neutrino luminosity.,explosions are more easier to be obtained for higher neutrino luminosity. +" As is well known, the combination of (e,,) and L,, is an important quantity to diagnose the success or failure of explosions, because the neutrino heating rate in the so-calledgain region, Q7, is proportional to (&)Ly, (e.g., equation (23)in Janka (2001)))."," As is well known, the combination of $\bracket{\epsilon_{\nu_x}}$ and $L_{\nu_x}$ is an important quantity to diagnose the success or failure of explosions, because the neutrino heating rate in the so-calledgain region, $Q_\nu^+$, is proportional to $\bracket{\epsilon_{\nu_x}^2} L_{\nu_x}$ (e.g., equation (23) in \citet{jank01}) )." +" Figure 6 shows Eg, as a function of (e,L,,.", Figure \ref{fig:Ediag} shows $E_\mathrm{diag}^\infty$ as a function of $\bracket{\epsilon_{\nu_x}}^2L_{\nu_x}$. +" Note in the plot that we set the horizontal axis not as (εν)Ly, but as (c,,)?Ly, so that we can deduce the lodipgowin3xdepent dence more clearly andeasily®.", Note in the plot that we set the horizontal axis not as $\bracket{\epsilon_{\nu_x}^2}L_{\nu_x}$ but as $\bracket{\epsilon_{\nu_x}}^2L_{\nu_x}$ so that we can deduce the following dependence more clearly and. +". In this figure, let us fitst focus on red pluses, green crosses,by and blue squares whose difference is characterized s (2D results (filled circles) will be mentioned in the "," In this figure, let us first focus on red pluses, green crosses, and blue squares whose difference is characterized by $t_s$ (2D results (filled circles) will be mentioned in the later section)." +"L,-5x10b (1)p, "," Red $t_s=$ 100 ms), green $t_s=$ 150 ms), and blue $t_s=$ 200 ms) points have a clear correlation with $\bracket{\epsilon_{\nu_x}}^2L_{\nu_x}$." +"Orange and light-blue regions represent ón-explodng regions for red and blue points, f.."," Orange and light-blue regions represent the non-exploding regions for red and blue points, respectively." + indicating that the critical values of .," Both of them show that the minimum $E_\mathrm{diag}^\infty$ decreases with $t_s$, indicating that the critical values of $\bracket{\epsilon_\nu}^2L_\nu$ for explosion sharply depends on $t_s$." + This is S tain a er , This is because the mass outside the shock wave gets smaller with time so that the minimum energy to blow up star gets smaller too. +Ej.," By the same reason, $E_\mathrm{diag}$ becomes larger as $t_s$ becomes smaller given the same $\bracket{\epsilon_{\nu_x}}^2L_{\nu_x}$." + the earlier spectral swapping is MEO," To obtain a larger $E_\mathrm{diag}^\infty$, the earlier spectral swapping is more preferential." +"""Figureshows 7 the neutrino heating rate and the density distribution of NH13R30E13T1008S for 10 ms and 250 ms after t, (=100 ms after the bounce).", Figure \ref{fig:edot} shows the neutrino heating rate and the density distribution of NH13R30E13T100S for 10 ms and 250 ms after $t_s$ (=100 ms after the bounce). +" As the shock wave propagates outward, the density in the gain region sharply drops (e.g., 100-200km, dashed blue line), leading to the suppression of the heating rate (dashed red line)."," As the shock wave propagates outward, the density in the gain region sharply drops (e.g., 100-200km, dashed blue line), leading to the suppression of the heating rate (dashed red line)." + This is the reason of the saturation in Egjag as shown in Figure 4.., This is the reason of the saturation in $E_\mathrm{diag}$ as shown in Figure \ref{fig:time_ev}. + The remnant mass is an important indicator to diagnose the consequences of the explosion in producing either a neutron star or a black hole., The remnant mass is an important indicator to diagnose the consequences of the explosion in producing either a neutron star or a black hole. +" The last two lines in Table 1 show the integrated masses in the regions of p>1010 g cm? at t—t, and t= oo.", The last two lines in Table \ref{tab:models} show the integrated masses in the regions of $\rho\ge 10^{10}$ g $^{-3}$ at $t=t_s$ and $t=\infty$ . + The latter one is estimated by the fitting as where c and d are the fitting parameters., The latter one is estimated by the fitting as where $c$ and $d$ are the fitting parameters. +" For the exploding models, Mpg becomes generally smaller than Mis!* because of the mass ejection."," For the exploding models, $M_{10}^\infty$ becomes generally smaller than $M_{10}^{t=t_s}$ because of the mass ejection." + Exceptions, Exceptions +features with orbital phase (Section 3.4).,features with orbital phase (Section 3.4). + Each hemisphere is assumed to have uniform absorption. and we relate Lsfe to the mass ratio q using (I5eeleton. 1983).," Each hemisphere is assumed to have uniform absorption, and we relate $R_2/a$ to the mass ratio $q$ using (Eggleton, 1983)." + Consider the conservative mass transfer equation. where hj ds the radius of the Roche Lobe. J is the orbital angular momentum. and. -Mo is the instantanecga mass transfer rate (Frank. Wine Raine 1992).," Consider the conservative mass transfer equation, where $_L$ is the radius of the Roche Lobe, $J$ is the orbital angular momentum, and $\dot{M_2}$ is the instantaneous mass transfer rate (Frank, King Raine 1992)." + When αςΛοΑΙ)«5/6 then Rp70. so the toche lobe expands. reducing the mass transfer. ancl the system is stable.," When $q(=M_2/M_1)<5/6$ then $\dot{R_L}>0$, so the Roche lobe expands, reducing the mass transfer, and the system is stable." + In order to sustain long lived mass transfer he secondary star must expand. in size relative to. the toche lobe. otherwise the lobes detach from the star and mass transfer stops.," In order to sustain long lived mass transfer the secondary star must expand in size relative to the Roche lobe, otherwise the lobes detach from the star and mass transfer stops." + Evolution of the secondary. star is one xossibilitv. but for the secondary to evolve within the age of he Galaxy. it must be spectral tvpe GO or earlier (Patterson 1984).," Evolution of the secondary star is one possibility, but for the secondary to evolve within the age of the Galaxy, it must be spectral type G0 or earlier (Patterson 1984)." + Most €V secondaries have spectral types later than GO. so a more likely solution for stable mass transfer. is angular momentum loss due to either gravitational radiation and/or magnetic braking.," Most CV secondaries have spectral types later than G0, so a more likely solution for stable mass transfer is angular momentum loss due to either gravitational radiation and/or magnetic braking." + Phe loss of angular momentunir shrinks the binary system therefore enablingsustained mass transfer to occur., The loss of angular momentum shrinks the binary system therefore enablingsustained mass transfer to occur. +" When q>»5/6 then ""m<0. and the Roche lobe shrinks."," When $q>5/6$ then $\dot{R_L}<0$, and the Roche lobe shrinks." + Mass transfer will therefore increase. and the svsteni will become unstable unless the secondary star can contract rapidly enough to keep its radius smaller than the radius of the Roche lobe.," Mass transfer will therefore increase, and the system will become unstable unless the secondary star can contract rapidly enough to keep its radius smaller than the radius of the Roche lobe." + I£ the secondary star obevs the main sequence mass-racdius relation f»-xAle. and the radius of the star responds to changes in its mass on a thermal time scale. Equation 6. becomes. vielding a critical upper mass ratio (goa).," If the secondary star obeys the main sequence mass-radius relation $R_2\propto M_2$, and the radius of the star responds to changes in its mass on a thermal time scale, Equation \ref{e7} becomes, yielding a critical upper mass ratio $q_{crit}$ )." + When q> the secondary star will not shrink rapidly enough to keep pace with the Roche lobe., When $q>4/3$ the secondary star will not shrink rapidly enough to keep pace with the Roche lobe. + Phere will be à spontaneous overllow ancl mass transfer becomes unstable., There will be a spontaneous overflow and mass transfer becomes unstable. + The secondary star in a CV is a late type low mass star with a deep convective envelope. ancl therefore. loses mass on a clynamical time scale governed by the stars aciabatic response.," The secondary star in a CV is a late type low mass star with a deep convective envelope, and therefore loses mass on a dynamical time scale governed by the star's adiabatic response." +" Considering a complete polvtrope with a polvtropic index of n=3/2 (Iljellming Webbink 1987). the mass-radius relation for the secondary star becomes RoxAL,L7 and hence Equation 6 becomes. producing a lower mass ratio limit ($44,5:,)."," Considering a complete polytrope with a polytropic index of $n=3/2$ (Hjellming Webbink 1987), the mass-radius relation for the secondary star becomes $R_2\propto +M_2^{-1/3}$, and hence Equation \ref{e7} becomes, producing a lower mass ratio limit $q_{ad,fc}$ )." + When qc2/8 the star can not remain within its Roche lobe in hvdrostatic equilibrium. ancl mass transfer. occurs. on dyvnamical time scales.," When $q > 2/3$ the star can not remain within its Roche lobe in hydrostatic equilibrium, and mass transfer occurs on dynamical time scales." + When gq«2/3. the star becomes stable on a dynamical time scale and mass transfer occurs due to the slow expansion of the star via nuclear evolution or angular momentum loss causing the Roche lobe to contract.," When $q < 2/3$, the star becomes stable on a dynamical time scale and mass transfer occurs due to the slow expansion of the star via nuclear evolution or angular momentum loss causing the Roche lobe to contract." + The secondary star in RW Tri. may not. be. fully convective so the true adiabatic mass ratio will be higher., The secondary star in RW Tri may not be fully convective so the true adiabatic mass ratio will be higher. +" In the case where the secondary star has a convective envelope. but a vacliative core. the mass-racius relation becomes Aly”.Les leading. to a mass ratio. of. qi,=1 for. the adiabatic. response (ILellming Webbink 1987)."," In the case where the secondary star has a convective envelope, but a radiative core, the mass-radius relation becomes $R_2\propto M_2^{1/3}$ , leading to a mass ratio of $q_{ad,rc}=1$ for the adiabatic response (Hjellming Webbink 1987)." + We first calculate the mass ratio of RW ‘Tri using the various estimates of the component star radial velocity zumplitudes., We first calculate the mass ratio of RW Tri using the various estimates of the component star radial velocity amplitudes. + The most reliable. estimate for the secondary star velocity is [rom the W-baned data because there is not enough detail in the I-band data to be sure that they are not allected by elluric lines and background emission etc., The most reliable estimate for the secondary star velocity is from the K-band data because there is not enough detail in the I-band data to be sure that they are not affected by telluric lines and background emission etc. + When combined with the ραπ secondary. star velocity. (221+429km). he various estimates of the primary star velocity amplitude discussed in Section 4.1 lead to a range of mass ratios of ks3 as expressed in Table 4 (column +).," When combined with the K-band secondary star velocity $221\pm29$ km/s), the various estimates of the primary star velocity amplitude discussed in Section 4.1 lead to a range of mass ratios of $0.8-1.3$ as expressed in Table \ref{t3} (column 4)." +" The AN, velocity values that are most likely to reflect the motion of the white ciwarf are the UV absorption ines of Mason (2002). and the Le LL emission lines of Still (1995). because they both originate in regions close to the white chwarl."," The $K_1$ velocity values that are most likely to reflect the motion of the white dwarf are the UV absorption lines of Mason (2002), and the He II emission lines of Still (1995), because they both originate in regions close to the white dwarf." + Fhese velocities therefore give us acmost likely’ mass ratio in the range 1.001.3., These velocities therefore give us a `most likely' mass ratio in the range $1.0-1.3$. +" To consider the ellects of the ""Ix-correction on our most. likely mass ratio range. we use Equation 3.2 and 5.. and f—0.25 with q-—1.01.3. which corresponds to a range in A of ~19% to ~24."," To consider the effects of the “K-correction” on our most likely mass ratio range, we use Equation \ref{extra2} and \ref{eadded}, and $f\sim0.25$ with $q=1.0-1.3$, which corresponds to a range in $\Delta K$ of $\sim 19\%$ to $\sim24\%$." + Thus after applying the most likely value for the secondary star heating the value of A» in RAVTri is ~ liskni/s. implying a revised mass ratio. d. in the range 1317 (Yable 4.. column 5).," Thus after applying the most likely value for the secondary star heating the value of $K_2$ in RWTri is $\sim178$ km/s, implying a revised mass ratio, $q$, in the range $1.2-1.7$ (Table \ref{t3}, column 5)." + Alternatively we can caleulate the mass ratio of RW ‘Tri using the rotational broadening of the secondary star. independent of Ay.," Alternatively we can calculate the mass ratio of RW Tri using the rotational broadening of the secondary star, independent of $K_1$ ." + Assuming that the secondary star rotates in phase with the binary orbit we use. where fo/a@ is found using Equation 5..," Assuming that the secondary star rotates in phase with the binary orbit we use, where $R_2/a$ is found using Equation \ref{eadded}. ." + The results are shown in Figure 9 where the solid line represents the A» , The results are shown in Figure \ref{f7b} where the solid line represents the $K_2$ +Py/P—1 and « for P2 and Pl are shown in Fig.,$P_K/P - 1$ and $a$ for P2 and P1 are shown in Fig. + 1 with their 16 error bars.," \ref{fig:period} with their $1\,\sigma$ error bars." + The orbital periods are clearly shorter than the Ixepleriau values (by 2.160 and 3.26 lor P2 aud PI. respectively).," The orbital periods are clearly shorter than the Keplerian values (by $2.1\,\sigma$ and $3.2\,\sigma$ for P2 and P1, respectively)." + Ou the other hand. Pg/P—1 for P2 is in excellent agreement within 0.[Lo) with the analytic result. aud that for PI is in reasouable agreement (within 1.60) with the analytic result.," On the other hand, $P_K/P - 1$ for P2 is in excellent agreement (within $0.4\,\sigma$ ) with the analytic result, and that for P1 is in reasonable agreement (within $1.6\,\sigma$ ) with the analytic result." + The remainine discrepancy for Pl may be simply statistical. but it could also be due to the assumption in the fitting that the orbit is au unperturbed Ixepleriau orbit (see below for more details ou the expected uou-Ixepleriau behaviors).," The remaining discrepancy for P1 may be simply statistical, but it could also be due to the assumption in the fitting that the orbit is an unperturbed Keplerian orbit (see below for more details on the expected non-Keplerian behaviors)." +" With α fom Table Ἰ as Ry lor P2 aud Pl and aefin,=0.1165. we evaluate τν ny (Eq. [7]."," With $a$ from Table \ref{table1} as $R_0$ for P2 and P1 and $m_c/m_p = +0.1165$, we evaluate $P_K = P_{pc} (a/a_{pc})^{3/2}$ , $n_0/n_K$ (Eq. \ref{n0}] ])," + &o/n CEq. [22].," $\kappa_0/n_K$ (Eq. \ref{kappa0}] ])," + and ήν (Eq. [32] , and $\nu_0/n_K$ (Eq. \ref{nu0}] ]) +for the analytic theory. and they are listed in Table 2..," for the analytic theory, and they are listed in Table \ref{table2}." + The precession of the periapse is prograde with period aud 5280 days for P2 aud PL. respectively.," The precession of the periapse is prograde with period $2\pi/|\dot{\varpi}| = 2\pi/|n_0 - \kappa_0| = 1740$ and $5280\,$ days for P2 and P1, respectively." + The nodal precession bas a similar period 27/|Q=DcZH/ngL770 aud 5330 days for P2 aud PL. respectively) but it is retrograde.," The nodal precession has a similar period $2\pi/|\dot{\Omega}| = +2\pi/|n_0 - \nu_0| = 1770$ and $5330\,$ days for P2 and P1, respectively) but it is retrograde." + The periapse aud nodal precessious at uearly equal rates in opposite directions aud tle mean motion are similar to the behaviors of orbits arouud au oblate planet. (see. e.g.. Section 6.11 of MurrayaudDermott 1999)).," The periapse and nodal precessions at nearly equal rates in opposite directions and the faster-than-Keplerian mean motion are similar to the behaviors of orbits around an oblate planet (see, e.g., Section 6.11 of \citealt{mur99}) )." + This cau be uuderstood [rom the fact that the (pe/fR)-> 4tT‘us in the axisyiumetric components of the potential. yg aud Poy in Eqs. (7))," This can be understood from the fact that the $(a_{pc}/R)^2$ terms in the axisymmetric components of the potential, $\Phi_{00}$ and $\Phi_{20}$ in Eqs. \ref{Phi00}) )" + aud (11)). are identical to the Jo terms of an oblate planet with Jo=mimef[26g>Tan).," and \ref{Phi20}) ), are identical to the $J_2$ terms of an oblate planet with $J_2 = +m_p m_c/[2 (m_p + m_c)^2]$." + For the remaiuder of this paper we use Jacobi coordinates where the position of Charon is relative to Pluto. the position of the inuer satellite P2 is relative to the center of mass of aud the position of the outer satellite PI is relative to the center of mass of ," For the remainder of this paper we use Jacobi coordinates where the position of Charon is relative to Pluto, the position of the inner satellite P2 is relative to the center of mass of Pluto-Charon, and the position of the outer satellite P1 is relative to the center of mass of Pluto-Charon-P2." +Jacobi coordinates are the uatural generalization of the coordinates used in Section 2 (where the position of PI is relative to the center of mass of Pluto-Charou) when P2 aud PI are not test particles. and they reduce to the coordiuates used tu Section 2 iu the test-particle limit.," Jacobi coordinates are the natural generalization of the coordinates used in Section 2 (where the position of P1 is relative to the center of mass of Pluto-Charon) when P2 and P1 are not test particles, and they reduce to the coordinates used in Section 2 in the test-particle limit." +" Prom- P, aud dpe inn Table 41.. we adopt Gm,Y,+in.)=(22íi/HPy)>αρ.5—9.71791-—-—4x10ni?3sL7? (or; mpbay=41.1565-pn-x40221077 kg for. C:=6.672>pax10Hay*ke3ts9 7)."," From $P_{pc}$ and $a_{pc}$ in Table \ref{table1}, we adopt $G (m_p + m_c) = (2\pi/P_{pc})^2 a_{pc}^3 = +9.71791 \times 10^{11}\,{\rm m}^3\,{\rm s}^{-2}$ (or $m_p + m_c = 1.4565 \times 10^{22}\,$ kg for $G = 6.672 \times 10^{-11}\,{\rm m}^3\,{\rm kg}^{-1}\,{\rm s}^{-2}$ )." + ForE the mass ratio⋅ Πο/bp. we use the best-fit value 0.1165 from BOYYS.," For the mass ratio $m_c/m_p$, we use the best-fit value $0.1165$ from BGYYS." + We generate the initial position aud velocity of Cliarou relative to Pluto by using the orbital parameters in Table 1. at epoch JD 21252600.5 as the osculatiug Ixepleriaur orbital parameters., We generate the initial position and velocity of Charon relative to Pluto by using the orbital parameters in Table \ref{table1} at epoch JD 2452600.5 as the osculating Keplerian orbital parameters. + The orbits of P2 and PI are sulficiently non-Ixepleriau even iu tlie test-particle limit that. if we," The orbits of P2 and P1 are sufficiently non-Keplerian even in the test-particle limit that, if we" +significant role in the dynamics of the supernova and perhaps in the revival of the shockwave (e.g.Colgate&White1966:BetheWil-son1985).,"significant role in the dynamics of the supernova and perhaps in the revival of the shockwave \citep[e.g.][]{colgate66,bethewilson85}." +". Specitically. the “neutrino mechanism”. as formulated by Burrows&Goshy(1993)., states that the steady-state accretion through the shock turns into an explosion when Ly...care exceeds a critical value. 5,7""..."," Specifically, the “neutrino mechanism”, as formulated by \citet{bg93}, states that the steady-state accretion through the shock turns into an explosion when $\lcore$ exceeds a critical value, $\lcrit$." + In Pejeha&Thompson(2012) thereafter PaperD) we showed using steady-state calculations that L7! is equivalent to reaching max(οςfor.)e0.19 in the accretion flow. where es is the sound speed and 0... is the local escape velocity.," In \citet{pejcha12} (hereafter \citetalias{pejcha12}) ) we showed using steady-state calculations that $\lcrit$ is equivalent to reaching $\max\,(c_S^2/\vesc^2) \simeq 0.19$ in the accretion flow, where $c_S$ is the sound speed and $\vesc$ is the local escape velocity." +" This ""antesonic"" condition is a manifestation of the inabilitya T the flow to satisfy both the shock jump conditions and the Euler equations for the accretion flow simultaneously (Yamasaki&Ya-mada2005:Fernández 2012)."," This “antesonic” condition is a manifestation of the inability of the flow to satisfy both the shock jump conditions and the Euler equations for the accretion flow simultaneously \citep{yamasaki05,fernandez12}." +". We also determined the dependence of LY""... on the key parameters of the problem. including the energies of the neutrinos over a wide range of parameter values."," We also determined the dependence of $\lcrit$ on the key parameters of the problem, including the energies of the neutrinos over a wide range of parameter values." + Specifically. and most importantly for this paper. we found that Lius. ds proportional to the inverse square of the (. ands. energies. us expected from the heating rate.," Specifically, and most importantly for this paper, we found that $\lcrit$ is proportional to the inverse square of the $\nue$ and $\nuebar$ energies, as expected from the heating rate." + There are a number of time-dependent multi-dimensional effects that might modify the transition from accretion to explosion., There are a number of time-dependent multi-dimensional effects that might modify the transition from accretion to explosion. + For example. accretion luminosity from cooling of the accretion flow is an important contribution to LMore (PaperD. and accretion simultaneously powering an asymmetric explosion is possible only in 2D and 3D (e.g.Burrowsetal.2006:Marek&Janka2009:Suwa2010).," For example, accretion luminosity from cooling of the accretion flow is an important contribution to $\lcrit$ \citepalias{pejcha12} and accretion simultaneously powering an asymmetric explosion is possible only in 2D and 3D \citep[e.g.][]{burrows06,marek09,suwa10}." +. Furthermore. close to the critical condition for explosion the shock surface often exhibits oscillations that feed back on the neutrino emission (e.g.Murphy&Burrows2008:MarekJanka2009:Nordhausetal.2010:Hanke2011). potentially modifying LMop," Furthermore, close to the critical condition for explosion the shock surface often exhibits oscillations that feed back on the neutrino emission \citep[e.g.][]{murphy08,marek09,nordhaus10,hanke11} potentially modifying $\lcrit$." + At least in ID.these oscillations seem to occur only very close to the steady-state value of LUap (Fernandez20123.," At least in 1D,these oscillations seem to occur only very close to the steady-state value of $\lcrit$ \citep{fernandez12}." + The steady-state calculation is thus useful way to estimate Li)Hus and to examine effects of modified physics on the critical condition for supernova explosion., The steady-state calculation is thus useful way to estimate $\lcrit$ and to examine effects of modified physics on the critical condition for supernova explosion. + Within the parameterization of the neutrino mechanism of Burrows&Goshy(1993). the failure of supernova simulations implies. by detinition. that the neutrino luminosities in the models never reach Li.iie," Within the parameterization of the neutrino mechanism of \citet{bg93}, the failure of supernova simulations implies, by definition, that the neutrino luminosities in the models never reach $\lcrit$." + For successful explosions. either (i) L7;Mae needs to be decreased or (i) Licore Increased.," For successful explosions, either (i) $\lcrit$ needs to be decreased or (ii) $\lcore$ increased." +" As an example of the former. multi-dimensional effects like convection and SAST decrease L/775,,,. CYamasaki&Yamada2005. by making the heating more efficient (e.g.Herantetal.2004:Burasetal. 2006).."," As an example of the former, multi-dimensional effects like convection and SASI decrease $\lcrit$ \citep{yamasaki05,yamasaki06,murphy08,nordhaus10,hanke11,takiwaki12} by making the heating more efficient \citep[e.g.][]{herant94,bhf95,janka96,fryer04,buras06a}." + As an example of the latter. Ly.core can be enhanced by convection inside the PNS (e.g.Wilson&Mayle 1996).," As an example of the latter, $\lcore$ can be enhanced by convection inside the PNS \citep[e.g.][]{wilson88,bruenn96,keil96}." +. Another option is that cooling becomes less efficient in 2 and 3 spatial dimensions causing a decrease of LY!Maye (PaperD., Another option is that cooling becomes less efficient in $2$ and $3$ spatial dimensions causing a decrease of $\lcrit$ \citepalias{pejcha12}. + Most of the heating below the shock occurs due to absorption of v. and £. on neutrons and protons. while the 74 escape without much interaction.," Most of the heating below the shock occurs due to absorption of $\nue$ and $\nuebar$ on neutrons and protons, while the $\nux$ escape without much interaction." +" However. due to the high density of neutrinos in his region. self-interaction between neutrinos becomes important and ean lead to a range of phenomena called “collective neutrino oscillations"" (e.g.Pantaleone1992:Duanetal.2006.2010)."," However, due to the high density of neutrinos in this region, self-interaction between neutrinos becomes important and can lead to a range of phenomena called “collective neutrino oscillations” \citep[e.g.][]{pantaleone92,duan06,duan10}." +. In j»urticular. there is a possibility of an instability (Dasgupta2009) that exchanges part of the 74 spectra with the vu. and f. spectra.," In particular, there is a possibility of an instability \citep{dasgupta09} that exchanges part of the $\nux$ spectra with the $\nue$ and $\nuebar$ spectra." + If the luminosities and energies of ἐκ... and vy are right. his can produce significantly more heating below the shock than calculations neglecting neutrino oscillations. Le. effective Licore is increased byCvO.," If the luminosities and energies of $\nue$, $\nuebar$, and $\nux$ are right, this can produce significantly more heating below the shock than calculations neglecting neutrino oscillations, i.e., effective $\lcore$ is increased by." +". Specifically. a strong effect on heating can be expected if luminosities are similar and vy have significantly ligher energies than £. and v,.."," Specifically, a strong effect on heating can be expected if luminosities are similar and $\nux$ have significantly higher energies than $\nue$ and $\nuebar$." + The exact values of these quantities and their mutua ratios are model-dependent (e.g.Thompsonal.2010).. Chakraboryetal.(01lab). Dasguptaetal.(2012). Suwaetal.(2011.," The exact values of these quantities and their mutual ratios are model-dependent \citep[e.g.][]{thompson03,marek09,fischer10,fischer12,hudepohl10}. \citet{chakraborty11a,chakraborty11b}, \citet{dasgupta12}, \citet{suwa11}," + and Sarikasetal.(011). have investigated the role of iin the core-colapse simulations of several progenitor models., and \citet{sarikas11} have investigated the role of in the core-collapse simulations of several progenitor models. + They found that there are a number of multi-angle effects. especially the effect of matter suppression. that can reduce or entirely eliminaeCvO.," They found that there are a number of multi-angle effects, especially the effect of matter suppression, that can reduce or entirely eliminate." +". We address the issue of increased neutrino jeating due to aand matter suppression without reference to detailed supernova models and we evaluate them at Li""Peor. Which separates accretion rom explosion."," We address the issue of increased neutrino heating due to and matter suppression without reference to detailed supernova models and we evaluate them at $\lcrit$, which separates accretion from explosion." + We treat the oscillation physics in a schematic way and the supernova physies using a steady state model developed in PaperI.., We treat the oscillation physics in a schematic way and the supernova physics using a steady state model developed in \citetalias{pejcha12}. + Although this approach is less detailed than some recent wipers. e.g.. (e.g.Chakrabortyetal.201La.b:Dasgupta2012:Sarikasetal.2011). it allows for a parametric study to determine he potential role of iin shock reheating. and its dependence on the progenitor mass. radius. and accretion rate for a very broad range of parameters and without being tied to any particular progenitor model or simulation setup.," Although this approach is less detailed than some recent papers, e.g., \citep[e.g.][]{chakraborty11a,chakraborty11b,dasgupta12,sarikas11}, it allows for a parametric study to determine the potential role of in shock reheating, and its dependence on the progenitor mass, radius, and accretion rate for a very broad range of parameters and without being tied to any particular progenitor model or simulation setup." + The remainder of our paper is organized as follows., The remainder of our paper is organized as follows. + In Section 2.. we describe our steady state model for the accretion flow based on PaperL. and a scheme for collective neutrino oscillations based on Dasguptaetal.(2012).," In Section \ref{sec:method}, we describe our steady state model for the accretion flow based on \citetalias{pejcha12}, and a scheme for collective neutrino oscillations based on \citet{dasgupta12}." +. We present our results in Section 3.., We present our results in Section \ref{sec:results}. +" We quantify the changes to 777, and the shock radii. and compare the magnitude of the effect of tto other known pieces of physies."," We quantify the changes to $\lcrit$ and the shock radii, and compare the magnitude of the effect of to other known pieces of physics." + We also estimate the importance of multi-angle effects showing that they suppress iin the region of parameter space where they might otherwise be strong., We also estimate the importance of multi-angle effects showing that they suppress in the region of parameter space where they might otherwise be strong. + In Section 4.. we conclude with a discussion and review of our results.," In Section \ref{sec:disc}, we conclude with a discussion and review of our results." + In this Section we tirst describe the hydrodynamic equations that we shall solve. their boundary conditions. and the input neutrino physics (Section 2.1)).," In this Section we first describe the hydrodynamic equations that we shall solve, their boundary conditions, and the input neutrino physics (Section \ref{sec:hydro}) )." + We describe our scheme of coupling the eeffects to the hydrodynamical equations in Section 2.2..., We describe our scheme of coupling the effects to the hydrodynamical equations in Section \ref{sec:cno}. +" Our combination of steady-state approach and simple treatment of aallows us to calculate £77""... quantify the maximum possible effect of oon £577, as a function of boundary conditions. and set limits on the parameter space. which can then be probed with more realistic methods."," Our combination of steady-state approach and simple treatment of allows us to calculate $\lcrit$ quantify the maximum possible effect of on $\lcrit$ as a function of boundary conditions, and set limits on the parameter space, which can then be probed with more realistic methods." +" We use the code developed in PaperI. to calculate the structure of the steady-state accretion flow between the neutrinosphere at radius r7, and the standoff accretion shock at rs assuming spherical symmetry by solving the time-independent Euler equations", We use the code developed in \citetalias{pejcha12} to calculate the structure of the steady-state accretion flow between the neutrinosphere at radius $\rnu$ and the standoff accretion shock at $\rs$ assuming spherical symmetry by solving the time-independent Euler equations +curves is found by ruunimg mauv simulations for various initial densities and metallicities. wutil they satisfv the fraginentation criterion (C— E44) at Ζ and density ng.,"curves is found by running many simulations for various initial densities and metallicities, until they satisfy the fragmentation criterion ${\cal L} = \Gamma_{\rm ad}$ ) at $Z_{\rm crit}$ and density $n_f$." + The double-valucducss 3i imnauy of the parabolic curves is explained by Figure [. which shows the cooling rates and equilibria for gas with »;= lcm?5m and three mictallicitics.," The double-valuedness in many of the parabolic curves is explained by Figure \ref{fig:coolingequilib}, which shows the cooling rates and equilibria for gas with $n_i = 1$ $^{-3}$ and three metallicities." + Table 2 summuarizes the results of Figure 3. by choosing three particular values of temperature and deusity relevant for this studyw., Table \ref{tab:lowhighdcritm} summarizes the results of Figure \ref{fig:paracoolmcool} by choosing three particular values of temperature and density relevant for this study. + The first coluunu shows the temperature and density of the eas., The first column shows the temperature and density of the gas. + For the low-deusity case. we choose the set of three curves corresponding to an initial density of 0.1 7. while the high-density case starts at 105 3.," For the low-density case, we choose the set of three curves corresponding to an initial density of 0.1 $^{-3}$, while the high-density case starts at $10^4$ $^{-3}$." + We beein at 7;=200 Ix. aud after the eas cools down. we choose two more temperatures. 150 I& aud 100 I and their corresponding densities.," We begin at $T_i = 200$ K, and after the gas cools down, we choose two more temperatures, 150 K and 100 K and their corresponding densities." + The next four columns show the metallicity at those temperatures and deusities during fragmentation., The next four columns show the metallicity at those temperatures and densities during fragmentation. + In the fourth coluun. all metal lines are included in the cooling function.," In the fourth column, all metal lines are included in the cooling function." +"The last column shows the Jeaus mass. fp, at fragmentation. taken from ?.. where Thay is the temperature at fraeieutation aud ay is the hydrogen nuuber density.","The last column shows the Jeans mass, $M_J \propto T^{3/2}/\rho^{1/2}$ , at fragmentation, taken from \cite{CB03}, where $T_{\rm{frag}}$ is the temperature at fragmentation and $n_H$ is the hydrogen number density." + The ατα critical uectallicitics are calculated from Figure 3 and shown in Figure 5.., The minimum critical metallicities are calculated from Figure \ref{fig:paracoolmcool} and shown in Figure \ref{fig:minimetallicity}. + The bottom panel of Figure 5 shows two sets of curves. to illustrate the sleht differences in fragiieutation criteria when one equates Pag to cooling bv inetals-ouly (dashed dines) aud to total cooling (solid lines).," The bottom panel of Figure \ref{fig:minimetallicity} shows two sets of curves, to illustrate the slight differences in fragmentation criteria when one equates $\Gamma_{\rm ad}$ to cooling by metals-only (dashed lines) and to total cooling (solid lines)." + In both cases. oue cun see the transition frou non-LTE to LTE of particular ciissiou lues.," In both cases, one can see the transition from non-LTE to LTE of particular emission lines." + The iminimuuni value in each curve corresponds to the critical deusity of the line (see Table 1))., The minimum value in each curve corresponds to the critical density of the line (see Table \ref{tab:mabundances}) ). + Thecurves turn around when collisional de-excitation of the lues starts to dominate for each metal., Thecurves turn around when collisional de-excitation of the lines starts to dominate for each metal. + The volume cooling- rate then scales as à» rather than D»7., The volume cooling rate then scales as $n$ rather than $n^2$. + Thed cooling: eficiency is reduced. aud. higher abundanuces of metals are needed to reach fragmentation.," The cooling efficiency is reduced, and higher abundances of metals are needed to reach fragmentation." + Table 23. shows the values of the inuumnmui critical ietallicities for the fracmentation criterion. and for several values of gas density.," Table \ref{tab:minimumcritical} shows the values of the minimum critical metallicities for the fragmentation criterion, and for several values of gas density." + We choose a range iu deusities. from na=Ol cm C. just below the mean density of eas iu viralized halos at += 20. up to," We choose a range in densities, from $n = 0.1$ $^{-3}$ , just below the mean density of gas in virialized halos at $z = 20$ , up to" +"The ADAF accretion rates derived at 8.5 GHz. in both normalized (ir) and absolute (AL, form. have cousequences for the predicted levels of X-ray emission from these quiescent elliptica galaxies. aud these predicted levels must not violate the observed levels.","The ADAF accretion rates derived at 8.5 GHz, in both normalized $\dot{m}_{\rm A}$ ) and absolute $\dot{M}_{\rm A}$ ) form, have consequences for the predicted levels of X-ray emission from these quiescent elliptical galaxies, and these predicted levels must not violate the observed levels." + Only oue galaxy. 11291. is a weak X-ray emitter aud the other three remain undetected in the ROSAT All Sky Survey (Beuiugetal.1999).," Only one galaxy, 4291, is a weak X-ray emitter and the other three remain undetected in the ROSAT All Sky Survey \citep{beu99}." +. That survey was conducted with the Position Sensitive Proportional Counter at soft. X-rays (0.5-2 keV uid at an angular resolution of 0.5., That survey was conducted with the Position Sensitive Proportional Counter at soft X-rays (0.5-2 keV) and at an angular resolution of $\sim 0.5\arcmin$. + The table gives values for. or upper limits to. the observed soft. X-ray. luminosities. Lgvss. scaled to the Magorrianetal.(1995) distances.," The table gives values for, or upper limits to, the observed soft X-ray luminosities, $L_{\rm +RASS}$, scaled to the \citet{mag98} distances." + No deprojection analysis has yet been attempted for 11291. since no ROSAT data [rom the High Resolution Lnager are available.," No deprojection analysis has yet been attempted for 4291, since no ROSAT data from the High Resolution Imager are available." + Data at hard X-rays (2-10 keV) are also lackiug., Data at hard X-rays (2-10 keV) are also lacking. + Au elliptical galaxy harboring an ADAF will be a source of X-rays from the ADAF itself aud [rom the galaxys interstellar tmecium., An elliptical galaxy harboring an ADAF will be a source of X-rays from the ADAF itself and from the galaxy's interstellar medium. + Each photon source will be discussed in turn., Each photon source will be discussed in turn. + The normalized ADAF accretion rates derived at 8.5 GHz are so low that bremsstrahlung emission. not inverse Compton scattering. will dominate the ADAEs X-rays (Mahadevan 1998).," The normalized ADAF accretion rates derived at 8.5 GHz are so low that bremsstrahlung emission, not inverse Compton scattering, will dominate the ADAF's X-rays \citep{mah97,yi98}." +.. The latter authors provide an expression for the bremsstrahlung Iuminosity of a canonical ADAF that. at the T. adopted for Equation (1). reduces to at a fiducial soft. X-ray. frequency of v=2.12xLOM Hz: and reduces to at a fiducial hard.X-ray. frequency of vy=1.45x107 Hz.," The latter authors provide an expression for the bremsstrahlung luminosity of a canonical ADAF that, at the $T_e$ adopted for Equation (1), reduces to at a fiducial soft X-ray frequency of $\nu = 2.42\times10^{17}$ Hz; and reduces to at a fiducial hardX-ray frequency of $\nu = 1.45\times10^{18}$ Hz." + Applying the tabulated values for my aud mia to Equatious (2) aud (3) vields the tabulated preclictious for the soft aud harc X-ray luminosities of the ADAFs., Applying the tabulated values for $m_8$ and $\dot{m}_{\rm A}$ to Equations (2) and (3) yields the tabulated predictions for the soft and hard X-ray luminosities of the ADAFs. + The predicted Iuminosities at 1 keV are consistent with the published ROSAT limits for 11561. 11621. aud 11660. as well as for the ROSAT detection of [1291 but only if that detection is domiuated by the galaxys interstellar inecdiuum rather than by its ADAF (Beuiugetal.1999).," The predicted luminosities at 1 keV are consistent with the published ROSAT limits for 4564, 4621, and 4660, as well as for the ROSAT detection of 4291 but only if that detection is dominated by the galaxy's interstellar medium rather than by its ADAF \citep{beu99}." +. Note further that the ADAFs are expected to be six times more Iuininous at hard than at soft. X-rays. so these galaxies must must be cousidered prime targets for observations iu the 2-10 keV region with the Advanced Satellite for Cosmologyand. Astrophysics (Tanaka.Inoue.&Holt1991).," Note further that the ADAFs are expected to be six times more luminous at hard than at soft X-rays, so these galaxies must must be considered prime targets for observations in the 2-10 keV region with the Advanced Satellite for Cosmologyand Astrophysics \citep{tan94}." +. Solt X-rays can also arise from au elliptical’s general interstellar mecdituu (Fabian&CanizaresMahacevanL907:DiMatteoetal. 2000).," Soft X-rays can also arise from an elliptical's general interstellar medium \citep{fab88,mah97,dim00}." +. For the galaxies in this study. a Bondi analysis of that medium can produce an estimate for the Bondi accretion rate. Alp. which can then be compared with the absolute ADAF accretion rate. Aly. derived at 8.5 GHz.," For the galaxies in this study, a Bondi analysis of that medium can produce an estimate for the Bondi accretion rate, $\dot{M}_{\rm B}$, which can then be compared with the absolute ADAF accretion rate, $\dot{M}_{\rm A}$ , derived at 8.5 GHz." + The black hole masses from Magorrianetal.(1998).. in combination with 77=1 being typical for elliptical galaxies (DiMatteoetal.2000).. results in the Boncli radii listed in the table.," The black hole masses from \citet{mag98}, in combination with $T_7 = +1$ being typical for elliptical galaxies \citep{dim00}, results in the Bondi radii listed in the table." + Assuming further that the pressure. P=10°2 * K.at the Boudi radius satisfies 2;=1—10 (DiMatteoetal.2000).. then the table gives the correspouclit£& range in Boucdi accretion rates. Adp.," Assuming further that the pressure, $P = 10^6 P_6$ $^{-3}$ K, at the Bondi radius satisfies $P_6 = 1-10$ \citep{dim00}, then the table gives the corresponding range in Bondi accretion rates, $\dot{M}_{\rm B}$ ." + The Bondi rate estimates for P;=1 are generally consistent. with the limits on the absoluteADAF rates. Aa. imposed," The Bondi rate estimates for $P_6 += 1$ are generally consistent with the limits on the absoluteADAF rates, $\dot{M}_{\rm A}$ , imposed" +clusters reside. along with many metal-poor clusters).,"clusters reside, along with many metal-poor clusters)." + As described in Paper I. for the bulge clusters only skv spectra far [rom the bulge of M31. were used.," As described in Paper II, for the bulge clusters only sky spectra far from the bulge of M31 were used." + A separate offset exposure for such fields. taken concurrently and about 5” offset [rom the targets. was reduced in a similar wav (so (hat contemporaneous sky subtraction was performed for on- and off-target exposures). and then these off-target local background spectra were subtracted [rom the on-largel.," A separate offset exposure for such fields, taken concurrently and about $\arcsec$ offset from the targets, was reduced in a similar way (so that contemporaneous sky subtraction was performed for on- and off-target exposures), and then these off-target local background spectra were subtracted from the on-target." + Relative (lux calibration. aimed at removing the signatures of instrumental ancl abmospheric transmission. was achieved using observations of fIux stanclards.," Relative flux calibration, aimed at removing the signatures of instrumental and atmospheric transmission, was achieved using observations of flux standards." + The MW GC spectra were collected with the CTIO Blanco 4 m telescope. equipped with the Ritchey-Chréttien spectrograph. mounted at the telescopes Casseerain locus.," The MW GC spectra were collected with the CTIO Blanco 4 m telescope, equipped with the Ritchey-Chréttien spectrograph, mounted at the telescope's Cassegrain focus." + Given the extended nature of Galactic GCs. observations were executed by drift scanning the targets with a 5'.5-long slit. over the range of x one GC core radius. r.. taken from Ilarris(1996).," Given the extended nature of Galactic GCs, observations were executed by drift scanning the targets with a $\arcmin$ .5-long slit, over the range of $\pm$ one GC core radius, $r_c$, taken from \cite{ha96}." +. Additional exposures in areas surrounding the target GCs were obtained for background-subtraction purposes., Additional exposures in areas surrounding the target GCs were obtained for background-subtraction purposes. + One-dimensional spectra were extracted by coadcding the columns contained within a €~lr. spatial window centered on (he peak of each GC's light profile.," One-dimensional spectra were extracted by coadding the columns contained within a $\pm\,\sim\,1\,r_c$ spatial window centered on the peak of each GC's light profile." + Therefore. for most GCs. the 1-D spectra sample a core radius-sized square spatial region (butseeSchiavonetal.2005.lorexceptions).," Therefore, for most GCs, the 1-D spectra sample a core radius-sized square spatial region \citep[but see ][for exceptions]{s05}." + No significant. variations in Lick index measurements were found. between spectra (hat sample different spatial regions. for anv of the 9 GCs [or which such spectra were available.," No significant variations in Lick index measurements were found between spectra that sample different spatial regions, for any of the 9 GCs for which such spectra were available." + The spectra. were wavelength-calibrated in the usual fashion., The spectra were wavelength-calibrated in the usual fashion. + The resulüng 1D waveleneth-calibrated spectra cover the region between 3360 and 6430 A. with a spectral dispersion of L A ! and a resolution of ~ 3.1 A.," The resulting 1D wavelength-calibrated spectra cover the region between 3360 and 6430 ${\rm\AA}$, with a spectral dispersion of 1 ${\rm\AA}$ $^{-1}$ and a resolution of $\sim$ 3.1 ${\rm\AA}$." + Relative [αν calibration was achieved in the usual fashion. using observations of spectrophotometric standards.," Relative flux calibration was achieved in the usual fashion, using observations of spectrophotometric standards." + Even though the two sets of GC spectra were obtained with different instruments.," Even though the two sets of GC spectra were obtained with different instruments," +period.,period. + There is also no evidence for the secondary minima being shifted from phase 0.5. implying that eccentricity is negligible.," There is also no evidence for the secondary minima being shifted from phase 0.5, implying that eccentricity is negligible." + Our time-resolved spectroscopic dataset consists of 38 observations covering the wavelength rangeΑΑ.. of which six were taken during secondary eclipse when the wo stars have very similar velocities.," Our time-resolved spectroscopic dataset consists of 38 observations covering the wavelength range, of which six were taken during secondary eclipse when the two stars have very similar velocities." + We have measured radial velocities (RVs) from the remaining 32 spectra. concentrating on he wwavelength range which contains a multitude of spectral lines but avoids the very broad H feature.," We have measured radial velocities (RVs) from the remaining 32 spectra, concentrating on the wavelength range which contains a multitude of spectral lines but avoids the very broad $\gamma$ feature." + We have considered hree different methods of measuring the velocity amplitudes of he component stars of CCet. and this redundancy allows consistency checks and the assignment of robust measurement uncertainties.," We have considered three different methods of measuring the velocity amplitudes of the component stars of Cet, and this redundancy allows consistency checks and the assignment of robust measurement uncertainties." + A large number of standard stars were observed using the same observational setup as for our target star., A large number of standard stars were observed using the same observational setup as for our target star. + Inspection of these yielded five which have a similar appearance to the spectra of the components of CCet: 339945 (spectral type VV). 332115(AS8 TV). 337594 VVs). 9905 ITV» and 224740 TEV).," Inspection of these yielded five which have a similar appearance to the spectra of the components of Cet: 39945 (spectral type V), 32115 IV), 37594 Vs), 905 IV) and 24740 IV)." + These will be used as template spectra in the analyses below., These will be used as template spectra in the analyses below. + Numerical cross-correlation (Simkin1974:Tonry&Davis1979) is a standard approach for measuring RVs from the spectra of celestial objects.," Numerical cross-correlation \citep{Simkin74aa,TonryDavis79aa} is a standard approach for measuring RVs from the spectra of celestial objects." + We used our own implementation ofthis method(ONECOR: Southworth&Clausen 2007)) after binning all spectra onto a common logarithmic wavelength scale., We used our own implementation ofthis method; \citealt{MeClausen07aa}) ) after binning all spectra onto a common logarithmic wavelength scale. + The cross-correlation functions (CCFs) were interactively assigned weights based on two factors: signal to noise and the velocity separation of the components of CCet., The cross-correlation functions (CCFs) were interactively assigned weights based on two factors: signal to noise and the velocity separation of the components of Cet. + These weights were fixed for all subsequent analyses. and we have verified that their precise values do not have a significant effect on the resulting RVs.," These weights were fixed for all subsequent analyses, and we have verified that their precise values do not have a significant effect on the resulting RVs." + Each template spectrum was cross-correlated against the spectra of CCet. and the positions of the two peaks were measured using quadratic interpolation.," Each template spectrum was cross-correlated against the spectra of Cet, and the positions of the two peaks were measured using quadratic interpolation." + The resulting RVs were fitted with spectroscopic orbits using the code., The resulting RVs were fitted with spectroscopic orbits using the code. + Orbits were fitted for the two stars separately (see Southworthetal.2004a and Popper&Hill 1991»)., Orbits were fitted for the two stars separately (see \citealt{Me++04mn} and \citealt{PopperHill91aj}) ). + Fits including orbital eccentricity yielded values which were small and not significantly different from zero. as expected from the period study refsec:period)}. so our final results were calculated with eccentricity fixed at zero.," Fits including orbital eccentricity yielded values which were small and not significantly different from zero, as expected from the period study \\ref{sec:period}) ), so our final results were calculated with eccentricity fixed at zero." + The outcome of this analysis was velocity amplitude measurements for the two of CCet CAy and Aq) and for each of the five template spectra reftab:K IK)., The outcome of this analysis was velocity amplitude measurements for the two of Cet $K_{\rm A}$ and $K_{\rm B}$ ) and for each of the five template spectra \\ref{tab:k1k2}) ). + RVs found from cross-correlation analyses are known to show slight biases due to effects such as line blending (Petrie&An-drews1966) and individual spectral lines being Doppler-shifted into or out of the considered wavelength range (e.g.Torresetal.1997:Clausenetal. 2008)..," RVs found from cross-correlation analyses are known to show slight biases due to effects such as line blending \citep{PetrieAndrews66aa} and individual spectral lines being Doppler-shifted into or out of the considered wavelength range \citep[e.g.][]{Torres+97aj,Clausen+08aa}." + These biases can be measured and thus removed by constructing synthetic composite spectra with known RVs and measuring them in the same way as the observed spectra., These biases can be measured and thus removed by constructing synthetic composite spectra with known RVs and measuring them in the same way as the observed spectra. + We have performed this analysis using our five observed template spectra and the method discussed by Southworth&Clausen (2007)..., We have performed this analysis using our five observed template spectra and the method discussed by \citet{MeClausen07aa}. + We find that removing these biases from the measured RVs results in velocity amplitudes whose values are almost unchanged but whose uncertainties are noticeably lower: the results are given in reftab:Kk HK2.., We find that removing these biases from the measured RVs results in velocity amplitudes whose values are almost unchanged but whose uncertainties are noticeably lower; the results are given in \\ref{tab:k1k2}. +. The algorithm. introduced by Zucker&Mazeh(1994) calculates a two-dimensional CCF for a double-lined spectrum using two template spectra.," The algorithm, introduced by \citet{ZuckerMazeh94apj} calculates a two-dimensional CCF for a double-lined spectrum using two template spectra." + This approach is aimed at avoiding line blending when the two target stars have quite different spectral characteristics. although Southworth&Clausen(2007) found that it is no better than for spectroscopic binaries containing two similar stars.," This approach is aimed at avoiding line blending when the two target stars have quite different spectral characteristics, although \citet{MeClausen07aa} found that it is no better than for spectroscopic binaries containing two similar stars." + This is the case with CCet. but the relatively low rotational velocities of its components mean that line blending is not a significant problem.," This is the case with Cet, but the relatively low rotational velocities of its components mean that line blending is not a significant problem." + We used our own implementation of (Southworthal.20040) and the same method and template stars as for in deriving A and wp., We used our own implementation of \citep{Me++04mn} and the same method and template stars as for in deriving $K_{\rm A}$ and $K_{\rm B}$ . + This process included the measurement and removal of RV biases. using synthetic spectra constructed from the observed template spectra.," This process included the measurement and removal of RV biases, using synthetic spectra constructed from the observed template spectra." + In each case we, In each case we +and spatially-correlated signals from one another.,and spatially-correlated signals from one another. + The degeneracy caused by not being able to retrieve the component's signs or amplitudes can be circumvented in two ways: 1) The separated signals are used to construct a linear transformation to filter the astrophysical signal from the originally observed data and hence preserve all scaling information; 2) The separated astrophysical signal is not used directly but instead all systematic noise components are combined to form a ‘systematic noise model’ which can then be used to correct the original observed data., The degeneracy caused by not being able to retrieve the component's signs or amplitudes can be circumvented in two ways: ) The separated signals are used to construct a linear transformation to filter the astrophysical signal from the originally observed data and hence preserve all scaling information; ) The separated astrophysical signal is not used directly but instead all systematic noise components are combined to form a `systematic noise model' which can then be used to correct the original observed data. + We have explored the efficiency of the signal de-trending on two simulated and two HST/NICMOS data sets with different types of systematic noise due to different grisms., We have explored the efficiency of the signal de-trending on two simulated and two HST/NICMOS data sets with different types of systematic noise due to different grisms. + The simulations demonstrate the two methods of de-trending the data in an idealised case and explore the efficiency of the signal separation in the presence of varying Gaussian noise in the data., The simulations demonstrate the two methods of de-trending the data in an idealised case and explore the efficiency of the signal separation in the presence of varying Gaussian noise in the data. +" In the instantaneous mixing model employed here, Gaussian noise sources are only indirectly allowed and can interfere with the effectiveness of separating non-Gaussian vectors."," In the instantaneous mixing model employed here, Gaussian noise sources are only indirectly allowed and can interfere with the effectiveness of separating non-Gaussian vectors." + We tested this point by adding additional Gaussian noise components of variable amplitude to the simulations but did not observe any significant reductions in the signal separation efficiency., We tested this point by adding additional Gaussian noise components of variable amplitude to the simulations but did not observe any significant reductions in the signal separation efficiency. + We proceeded to analyse two HST/NICMOS data sets: the primary eclipses of HD189733b and XO1b., We proceeded to analyse two HST/NICMOS data sets: the primary eclipses of HD189733b and XO1b. + For both data sets we find the2 to yield better results., For both data sets we find the to yield better results. +" In the case of HD189733b, we can achieve a near perfect de-correlation of astrophysical signal and systematic noise and no further steps are necessary to the de-correlation process."," In the case of HD189733b, we can achieve a near perfect de-correlation of astrophysical signal and systematic noise and no further steps are necessary to the de-correlation process." + A more in depth discussion of this data set and HST/NICMOS systematics is beyond the scope of this publication., A more in depth discussion of this data set and HST/NICMOS systematics is beyond the scope of this publication. + In the case of XO1b the de-correlation is significant but incomplete., In the case of XO1b the de-correlation is significant but incomplete. + The difference in maximum de-correlation achievable can be attributed to the systematic noise sources being strong functions of wavelength in the case of HD189733b whilst almost with constant weighting (ay; in equation 2)) in the case of XO1b., The difference in maximum de-correlation achievable can be attributed to the systematic noise sources being strong functions of wavelength in the case of HD189733b whilst almost with constant weighting ${a}_{kl}$ in equation \ref{intro2}) ) in the case of XO1b. +" Whenever systematics have constant weighting per channel observed (2) and/or time, it becomes very difficult for PCA or ICA based approaches to de-correlate the signal from the systematics."," Whenever systematics have constant weighting per channel observed $x_{k}$ ) and/or time, it becomes very difficult for PCA or ICA based approaches to de-correlate the signal from the systematics." + Here auxiliary information of the instrument is, Here auxiliary information of the instrument is +The light curve for J060938—333508 (Fig. 27)),The light curve for $-$ 333508 (Fig. \ref{fig:J060938-333508}) ) + shows MOST and NVSS non-detections followed by a single MOST detection., shows MOST and NVSS non-detections followed by a single MOST detection. +" Unlike the vast majority of sources in the MOST archive, the MOST contours appear rotated with respect to the MOST beam possibly indicating a change in flux density over the 12 hr synthesis time."," Unlike the vast majority of sources in the MOST archive, the MOST contours appear rotated with respect to the MOST beam possibly indicating a change in flux density over the 12 hr synthesis time." +" The MOST contours are centred 9 arcsec from the centre of Fairall 1138, a galaxy with spectral type SBab D (?) and with redshift z=0.037 (?).."," The MOST contours are centred 9 arcsec from the centre of Fairall 1138, a galaxy with spectral type SBab D \citep{Dressler88} and with redshift $z=0.037$ \citep{1998AJ....115..418D}." +" Assuming the radio source and galaxy are associated, the inferred isotropic radio luminosity from the brightest epoch (2004 December 9) is Ly~6x10?ergs!Hz! at 843 MHz."," Assuming the radio source and galaxy are associated, the inferred isotropic radio luminosity from the brightest epoch (2004 December 9) is $L_{\nu} \simeq 6 \times 10^{29} \unit{erg~s^{-1}~Hz^{-1}}$ at 843 MHz." +" 'The offset from the centre of the optical galaxy, and the fact that spiral galaxies rarely contain an AGN argues against an AGN source for the radio variability."," The offset from the centre of the optical galaxy, and the fact that spiral galaxies rarely contain an AGN argues against an AGN source for the radio variability." +" The spectral luminosity is very high for à RSN and we are unable to discriminate between Type Ib/c or Type II RSNe by the light curve time-scales, as the time interval between the detection and non-detection epochs is too large."," The spectral luminosity is very high for a RSN and we are unable to discriminate between Type Ib/c or Type II RSNe by the light curve time-scales, as the time interval between the detection and non-detection epochs is too large." + The spectral luminosity of J060938—333508 is within the range of GRB afterglows., The spectral luminosity of $-$ 333508 is within the range of GRB afterglows. +" It is also within the error circle of GRB 940526B, which occurred after the MOST non-detection in 1993, and 10 years before the MOST detection."," It is also within the error circle of GRB 940526B, which occurred after the MOST non-detection in 1993, and 10 years before the MOST detection." +" If J060938—333508 is the radio afterglow of GRB 940526B, then the radio detection 10 years after the gamma ray event is unlike known GRB afterglows, which typically peak at 843 MHz a few weeks after the explosion and fade over about 3 years."," If $-$ 333508 is the radio afterglow of GRB 940526B, then the radio detection 10 years after the gamma ray event is unlike known GRB afterglows, which typically peak at 843 MHz a few weeks after the explosion and fade over about 3 years." + We consider an association of GRB 940526B and J060938—333508 unlikely., We consider an association of GRB 940526B and $-$ 333508 unlikely. + We consider an unusual stellar event in Fairall 1138 as the likely interpretations of this source., We consider an unusual stellar event in Fairall 1138 as the likely interpretations of this source. + The light curve for SUMSS J055712—381106 (Fig. 28)), The light curve for SUMSS $-$ 381106 (Fig. \ref{fig:J055712-381105}) ) +" shows an NVSS detection followed by a MOST detection approximately 10 years later and then a non-detection 6 days after that, consistent with either a flaring source or a highly variable source occasionally appearing above our sensitivity limit."," shows an NVSS detection followed by a MOST detection approximately 10 years later and then a non-detection 6 days after that, consistent with either a flaring source or a highly variable source occasionally appearing above our sensitivity limit." + The MOST contours appear slightly elongated and rotated with respect to the MOST beam possibly indicating achange in flux density over the 12 hr synthesis time., The MOST contours appear slightly elongated and rotated with respect to the MOST beam possibly indicating a change in flux density over the 12 hr synthesis time. + Flaring or scintillating AGN or flaring radio stars are possible counterparts with these properties., Flaring or scintillating AGN or flaring radio stars are possible counterparts with these properties. +" The SuperCOSMOS B image shows what appears to be a blend of three objects, a star-like object to the south, a faint star-like object immediately to its north, and an extended object to the north-east."," The SuperCOSMOS B image shows what appears to be a blend of three objects, a star-like object to the south, a faint star-like object immediately to its north, and an extended object to the north-east." + The MOST and NVSS radio sources cannot be conclusively associated with any of the three sources in the optical, The MOST and NVSS radio sources cannot be conclusively associated with any of the three sources in the optical +Yusifov. LAL. Alpar. M.A.. Gokk. F.. Guseinov. O.IL 1995. ΜΙΑ. Alpar. U.. Iizilogllu. J. van Paraclijs (eds.),"Yusifov, I.M., Alpar, M.A., Gökk, F., Guseinov, O.H. 1995, M.A. Alpar, Ü.. loğllu, J. van Paradijs (eds.)" + The Lives of the Neutron Stars. P.201. Dordrecht: Kluwer.," The Lives of the Neutron Stars, P.201, Dordrecht: Kluwer." +relative to the mean age remains constant.,relative to the mean age remains constant. + In the Appendix this effect is demonstrated analytically., In the Appendix this effect is demonstrated analytically. + Only in models with mild morphological evolution to z21 (indicated by the broken lines in refmodeldata.plot)) we find an increase of the scatter with redshift., Only in models with mild morphological evolution to $z=1$ (indicated by the broken lines in \\ref{modeldata.plot}) ) we find an increase of the scatter with redshift. + In these models the scatter is very low at z=0. and at z>0.5 reaches values similar to those in models with strong morphological evolution.," In these models the scatter is very low at $z=0$, and at $z>0.5$ reaches values similar to those in models with strong morphological evolution." + The progenitor bias of the models is shown in panel (c)., The progenitor bias of the models is shown in panel (c). + We define the progenitor bias at given redshift as the difference between the M/L ratio of early-type galaxies and the W/L ratio of all progenitors of present-day early-type galaxies., We define the progenitor bias at given redshift as the difference between the $M/L$ ratio of early-type galaxies and the $M/L$ ratio of all progenitors of present-day early-type galaxies. + This is the “error” m the observed M/L ratio that is caused by the late addition of early-type galaxies to the sample., This is the “error” in the observed $M/L$ ratio that is caused by the late addition of early-type galaxies to the sample. + As the figure shows. the bias increases with increasing tranformation time scale 7 and increasing. f...," As the figure shows, the bias increases with increasing tranformation time scale $\taustop$, and increasing $f_*$." + Both parameters also cause the scatter to (op.increase., Both parameters also cause the scatter to increase. + For models with strong morphological evolution the progenitor bias can be approximated by This approximation is accurate to <10 This result suggests that the progenitor bias can be estimated on the basis of the observed transformation rate. and the observed scatter.," For models with strong morphological evolution the progenitor bias can be approximated by This approximation is accurate to $\lesssim 10$ This result suggests that the progenitor bias can be estimated on the basis of the observed transformation rate, and the observed scatter." + The star formation history ας the individual galaxies. as parametrized by f... is not needed to estimate the effect.," The star formation history is the individual galaxies, as parametrized by $f_*$, is not needed to estimate the effect." + This 1s à very useful result. as it is difficult to constrain the value of f. directly from the observed colors and luminosities.," This is a very useful result, as it is difficult to constrain the value of $f_*$ directly from the observed colors and luminosities." + Panels (d). (e). and (f) show the effect of changing the time of onset of star formation fa44. While keeping the star formatio history constant at. f.=0.5 (Le. approximately constant star formation from £4 to 44).," Panels (d), (e), and (f) show the effect of changing the time of onset of star formation $\tstart$, while keeping the star formation history constant at $f_*=0.5$ (i.e., approximately constant star formation from $\tstart$ to $\tstop$ )." + The evolution of the mean M/L ratio for the vartous models is shown in panel (f)., The evolution of the mean $M/L$ ratio for the various models is shown in panel (f). + The evolutio is very sensitive to the time of onset of star formation: there is an almost linear relation between the time when star formatio commences and the rate of M/L evolution., The evolution is very sensitive to the time of onset of star formation: there is an almost linear relation between the time when star formation commences and the rate of $M/L$ evolution. + The reason for this behaviour is that the mean age of the stellar population in all galaxies is lower for higher values of 44., The reason for this behaviour is that the mean age of the stellar population in all galaxies is lower for higher values of $\tstart$. + As will be shown 1 the observed evolution of the mean M/L ratio places strong constraints on the time when star formation commenced in early-type galaxies., As will be shown in \\ref{mc.sec} the observed evolution of the mean $M/L$ ratio places strong constraints on the time when star formation commenced in early-type galaxies. + The scatter and the progenitor bias are shown in panels (e) and (f)., The scatter and the progenitor bias are shown in panels (e) and (f). + They both depend on the value of t44. such that the scatter is higher and the progenitor bias stronger for later onset of star formation.," They both depend on the value of $\tstart$, such that the scatter is higher and the progenitor bias stronger for later onset of star formation." + As a result of this dual dependence the relation between the progenitor bias and the observed scatter refprogz.eq)) Is not very sensitive to the value of t4. once again indicating that the observed rate of morphological evolution and the observed scatter suffice to estimate the progenitor bias.," As a result of this dual dependence the relation between the progenitor bias and the observed scatter \\ref{progz.eq}) ) is not very sensitive to the value of $\tstart$, once again indicating that the observed rate of morphological evolution and the observed scatter suffice to estimate the progenitor bias." + The models deseribed in the previous Section can be applied to observations of early-type galaxies in. clusters at I., The models described in the previous Section can be applied to observations of early-type galaxies in clusters at $00.3 the early-type fraction changes from mass galaxies has a minor effect on the fraction of early-type galaxies., If we limit the analysis to red galaxies with $(U-B)_z >0.3$ the early-type fraction changes from mass galaxies has a minor effect on the fraction of early-type galaxies. + Other effects may have the opposite effect., Other effects may have the opposite effect. + As an example. biases introduced by the selection of the clusters themselves probably cause us to underestimate the evolution of the early-type galaxy fraction (see. e.g.. Kauffmann 1995).," As an example, biases introduced by the selection of the clusters themselves probably cause us to estimate the evolution of the early-type galaxy fraction (see, e.g., Kauffmann 1995)." +" The evolution of the rest frame W/L, ratio with redshift is shown in refbestfit.plot((b) and is taken from van Dokkum et ((19982).", The evolution of the rest frame $M/L_B$ ratio with redshift is shown in \\ref{bestfit.plot}( (b) and is taken from van Dokkum et (1998a). + Data are from Jorrgensen et ((1996). van Dokkum Franx (1996). Kelson et ((1997). and van Dokkum et ((1998a).," Data are from rgensen et (1996), van Dokkum Franx (1996), Kelson et (1997), and van Dokkum et (1998a)." + The M/L ratio evolution is derived from the evolution of the zeropoint of the Fundamental Plane relation (see van Dokkum Franx 1996)., The $M/L$ ratio evolution is derived from the evolution of the zeropoint of the Fundamental Plane relation (see van Dokkum Franx 1996). + The evolution is well determined. because the Fundamental Plane has very small scatter.," The evolution is well determined, because the Fundamental Plane has very small scatter." + The seatter in InM/Lg) is shown in refbestfit.plot((c)., The scatter in $\ln (M/L_B)$ is shown in \\ref{bestfit.plot}( (c). + The data point at ς O is from Jérrgensen et ((1996)., The data point at $z\approx 0$ is from rgensen et (1996). + Data points at higher redshift are from Kelson et ((2000) (z2 0.33). Kelson et ((1997) (z2 0.58). and van Dokkum et ((1998a) (z= 0.83).," Data points at higher redshift are from Kelson et (2000) $z=0.33$ ), Kelson et (1997) $z=0.58$ ), and van Dokkum et (1998a) $z=0.83$ )." + The highest redshift points have considerable uncertainty. because theyare derived from small samples.," The highest redshift points have considerable uncertainty, because theyare derived from small samples." + The scatter in the UL—B color-magnitude relation is taken from van Dokkum et ((2000) and shown in refbestfit.plot((d)., The scatter in the $U-B$ color-magnitude relation is taken from van Dokkum et (2000) and shown in \\ref{bestfit.plot}( (d). + Data are from Stanford et ((1998). Bower. Lucey. Ellis (1992). Ellis et ((1997). van Dokkum et ((1998b). and vanDokkum et ((2000).," Data are from Stanford et (1998), Bower, Lucey, Ellis (1992), Ellis et (1997), van Dokkum et (1998b), and vanDokkum et (2000)." + The observations were brought to à common (rest frame) band by using o(U— and e(U—B)Z0.66(U ). as derived from the Worthey (1994) models.," The observations were brought to a common (rest frame) band by using $\sigma (U-B) = 1.4 \sigma (B-V)$ and $\sigma (U-B) = 0.6 \sigma (U-V)$ , as derived from the Worthey (1994) models." + The scatter is —Vroughly constant with redshift. at σι—B)~0.03 magnitudes.," The scatter is roughly constant with redshift, at $\sigma (U-B) \approx 0.03$ magnitudes." +We applied our orbit recovery technique to nine Milky,We applied our orbit recovery technique to nine Milky +for galaxies fünter than My=21.,for galaxies fainter than $M_K=-21$. + This treud is hardly seuificaut., This trend is hardly significant. + The fact that theεως and € estimates are very close means that tlrere are no artifacts due to clustering., The fact that the$1/V_{\rm max}$ and $C^-$ estimates are very close means that there are no artifacts due to clustering. + 0.15ca Tn Table 3H) we list the pax:uneters of the STY estimate or the [0.1] aud [1.2| samples.," 0.15cm In Table \ref{tab_lfk_sty} we list the parameters of the STY estimate for the $[0,1]$ and $[1,2]$ samples." + The most impressive results we can uote from Fie., The most impressive results we can note from Fig. + 11 are the very wide range of absolute maguitudes covered by the data aud the »ossibilitv of Comptine for the first time the NIR LES at redshifts iu the raneoe [1.2]. where many difficulties arise or the traditional spectrosccpy.," \ref{lf_k_hdfns} are the very wide range of absolute magnitudes covered by the data and the possibility of computing for the first time the NIR LFs at redshifts in the range $[1,2]$, where many difficulties arise for the traditional spectroscopy." + Moreover. this redshift range is of paraniotit importance in the study of galaxy onmuation aud evohion. as we will discuss iu Sect. 6..," Moreover, this redshift range is of paramount importance in the study of galaxy formation and evolution, as we will discuss in Sect. \ref{discuss}." + In Fig., In Fig. +" 15 We SILILewize the results given in Table .. showi18o 16 60 alu| AI,-(AB)ACAD) parameterst arc1 heir respective errors as a fππποτίοι of redshift. derived or the two adopte cosimologies."," \ref{zalpham} we summarize the results given in Table \ref{tab_lfk_sty}, showing the $\alpha$ and $M^*_K({\rm AB})$ parameters and their respective errors as a function of redshift, derived for the two adopted cosmologies." + We also compu LFs in tl1ο J-band., We also computed LFs in the $J$ -band. +" In this case. we selected eaaxies the J filter when considering the lowest redshift bi MN .cwlhDereas wο estimated. the J-baud i1 the highes redsdlüt range (2phor© [L.2]) using the A, bid seleced subsuuples."," In this case, we selected galaxies in the $J$ filter when considering the lowest redshift bin [0,1], whereas we estimated the $J$ -band in the highest redshift range $z_{\rm phot} \in [1,2]$ ) using the $K_s$ -band selected subsamples." + Iu his wav we select the object.. approxiuatelv i itie J-baud rest-frame aud we can check if the assuniptiolis made for t1ο A baud LE computation were safe., In this way we select the objects approximately in the $J$ -band rest-frame and we can check if the assumptions made for the $K_s$ band LF computation were safe. +" We seleced objects inthe IIDE-N with J<21.6 oe1i the redsüft range |0.1] arc Lwith A,x 21in :=[1.2]. COLYYCSDOLKΠιο to objects witi S/N&3."," We selected objects in the HDF-N with $J +\le 24.6$ in the redshift range $[0,1]$ and with $K_s \le 24$ in $z=[1,2]$, corresponding to objects with $S/N \ge 3$." +" At these limits the colours iu the IIDE-N anc LIIDF-S are very simular: at J—21.6. the mean ssi, id1 [0.1] is 0.57 in the HIDE-N and 0.50 i the IIDE-S: at Ay=21 the mean Ley)Iv in;=[1.2] is 1.65 in the IIDE-N aud it is 1.85 in the IIDE-S. The values of VYVinax? are 0.56.0.13 in he redshitt ranges thorC[O.1) anel |1.2]. respectively. for he ITIDE-N. and 0.51.0.17 int 1C sade redshift ranges for he IIDE-S. Iu Fig."," At these limits the colours in the HDF-N and HDF-S are very similar: at $J = 24.6$, the mean $I_{814}-J$ in $[0,1]$ is $0.57$ in the HDF-N and $0.50$ in the HDF-S; at $K_s = 24$ the mean $I_{814}-K$ in $z=[1,2]$ is $1.65$ in the HDF-N and it is $1.85$ in the HDF-S. The values of $\left$ are $0.56, 0.43$ in the redshift ranges $z_{\rm phot} \in [0,1]$ and $[1,2]$ , respectively, for the HDF-N, and $0.51, 0.47$ in the same redshift ranges for the HDF-S. In Fig." + 16 we ]dot the LFs obtained with the ado]ated parauetiric aud noL parametric imetrods in he redshitt ranges [U.1] aud |:2|. as well as the Cole et ((2001)) local LF estimate in the 2dFCRS. x1OWL as a reference.," \ref{lf_j_hdfns} we plot the LFs obtained with the adopted parametric and non parametric methods in the redshift ranges $[0,1]$ and $[1,2]$, as well as the Cole et \cite{cole1}) ) local LF estimated in the 2dFGRS, shown as a reference." +" Oi estimate and he Cole et ((2001)) 01ο, suitablv transforued in AB inaguitudes (AM,=—21.10. 0.03. o=(0.0108 computed with cosinclogy 09=1.04=0 and only f-correction to iatch the same conditiojs we used}. seen to be iu disagreement. mainviu he normalization."," Our estimate and the Cole et \cite{cole1}) ) one, suitably transformed in AB magnitudes $M^*_J=-21.40$, $\alpha=-0.93$ , $\phi^*=0.0108$ computed with cosmology $\Omega_0=1, \Omega_\Lambda=0$ and only $k$ -correction to match the same conditions we used), seem to be in disagreement, mainly in the normalization." + IToxees«y. the conrxuison between our LF estimate obtained iu tιο flat A-cdomiunated cosiioουν and the analogous one ccmuputed by Cole et al.," However, the comparison between our LF estimate obtained in the flat $\Lambda$ -dominated cosmology and the analogous one computed by Cole et al." + 2001 outiallv iitieates the difference., \cite{cole1} partially mitigates the difference. + Table 4| contains he values of the Scheciter xuadneters o ‘the J-haud LF obtained in the two redslift ranges for the IIDE-N aud IIDE-S. We have also compted he LF iu the Z7 aud £ baids for the IIDE-N aud IIDE-S catalogues., Table \ref{tab_lfj_sty} contains the values of the Schechter parameters of the $J$ -band LF obtained in the two redshift ranges for the HDF-N and HDF-S. We have also computed the LF in the $H$ and $I$ bands for the HDF-N and HDF-S catalogues. + Ii all cases. we found simular results for the wo fields.," In all cases, we found similar results for the two fields." + We estimated LEs in two cosmologies: the “old” Standard CDM wih Oy=I aud O4=0. aud a flat cosinological coustant donmünated motel. that nowadays is the inost accepted one. with 04=L3 and O4— 0.7.," We estimated LFs in two cosmologies: the “old” Standard CDM with $\Omega_0=1$ and $\Omega_\Lambda=0$, and a flat cosmological constant dominated model, that nowadays is the most accepted one, with $\Omega_0=0.3$ and $\Omega_\Lambda=0.7$ ." + The iuflueuce of cosmology in the photoletric redshift computatiou is uceelieible. as discussed ba* Dolzonella et (20003). thus we used the same photonetric redshifts to estimate the LFs in different cosinologles.," The influence of cosmology in the photometric redshift computation is negligible, as discussed by Bolzonella et \cite{hyperz}) ), thus we used the same photometric redshifts to estimate the LFs in different cosmologies." + When LFs are comp.ted at low redshifts. we expect little or no differences in the estimates. as in the caseofthe 24FGRS by Cole et ((2001)). where the difference," When LFs are computed at low redshifts, we expect little or no differences in the estimates, as in the caseofthe 2dFGRS by Cole et \cite{cole1}) ), where the difference" +The secondary. Roche-lobe-lilling stars in CVs are kev to our understanding of the origin. evolution and behaviour of this class of interacting binary.,"The secondary, Roche-lobe-filling stars in CVs are key to our understanding of the origin, evolution and behaviour of this class of interacting binary." + Fo best study the secondary stars in CVs. we would ideally like direct images of the stellar surface.," To best study the secondary stars in CVs, we would ideally like direct images of the stellar surface." + This is currently impossible. however. as typical CV. secondary stars have raclii of 400 000 km ancl distances of 200 xc. which means that to detect a feature covering 20 per cent of the star's surface requires a resolution of approximately l microarcsecond. LO 000 times greater than the dilfraction-imited resolution ofthe world's largest telescopes.," This is currently impossible, however, as typical CV secondary stars have radii of 400 000 km and distances of 200 pc, which means that to detect a feature covering 20 per cent of the star's surface requires a resolution of approximately 1 microarcsecond, 10 000 times greater than the diffraction-limited resolution of the world's largest telescopes." + ? and ?.iereafterreferredtoasPaperL described a way around this oblenm: using an indirect. imaging technique calledfomography which uses phasc-resolved spectra to reconstruct he line intensity distribution on the surface of the secondary star.," \citet{rutten94} and \citet[hereafter referred to as Paper +I]{watson01} described a way around this problem using an indirect imaging technique called which uses phase-resolved spectra to reconstruct the line intensity distribution on the surface of the secondary star." + Obtaining surface images of the secondary star in CVs ias far-reaching implications., Obtaining surface images of the secondary star in CVs has far-reaching implications. + For example. a knowledge of the irradiation pattern on the inner hemisphere of the secondary star in CVs is essential if one is to calculate stellar masses accurately enough to test binary star evolution models. (see. 2)).," For example, a knowledge of the irradiation pattern on the inner hemisphere of the secondary star in CVs is essential if one is to calculate stellar masses accurately enough to test binary star evolution models (see \citealt{smith98}) )." + Furthermore. the irradiation. pattern provides information on the geometry of the accreting structures around the white dwarf (see ?)).," Furthermore, the irradiation pattern provides information on the geometry of the accreting structures around the white dwarf (see \citealt{smith95}) )." + In this paper we present new Roche tomograms of the secondary star in the dwarf nova IP Pee. and the magnetic CVs AAL Her anc QQ Vul in the light of the Na E AASISA3.8195 absorption doublet.," In this paper we present new Roche tomograms of the secondary star in the dwarf nova IP Peg, and the magnetic CVs AM Her and QQ Vul in the light of the Na I $\lambda\lambda$ 8183,8195 absorption doublet." + In. addition. we also present a Roche tomogram of the magnetic CV LIU Aqr in the light of the Le LE A4686. emission. line component known to originate [rom the secondary star.," In addition, we also present a Roche tomogram of the magnetic CV HU Aqr in the light of the He II $\lambda$ 4686 emission line component known to originate from the secondary star." + These tomograms allow a study of the irradiation. pattern on the secondary stars as well as providing measurements of the binary parameters for all four CVs., These tomograms allow a study of the irradiation pattern on the secondary stars as well as providing measurements of the binary parameters for all four CVs. + The spectra of OX Vul and LIU Λα were taken on the 3.5-m telescope at Calar Alto and full details of the observations, The spectra of QQ Vul and HU Aqr were taken on the 3.5-m telescope at Calar Alto and full details of the observations +bbulge and its immediate implications.,bulge and its immediate implications. + We οποίο our statistical error estimates at the confidence level., We quote our statistical error estimates at the confidence level. + Our X-ray study was based on 31 ACIS archival observations of (taken by 2005., Our X-ray study was based on 31 ACIS archival observations of taken by 2005. + The majority (21 out of 31) of these observations were taken with the ACIS-I array ancl aimed toward the bbulge with the aim-points located within 1’ from the galactic center., The majority (21 out of 31) of these observations were taken with the ACIS-I array and aimed toward the bulge with the aim-points located within $^\prime$ from the galactic center. + To maximize the coverage and uniformity of the combined field. we utilized data only from the front-illnuminated CCDs (the ACIS-I array and the $2 chips) of the 21 observations.," To maximize the coverage and uniformity of the combined field, we utilized data only from the front-illuminated CCDs (the ACIS-I array and the S2 chips) of the 21 observations." + For same reason. we also included. I-chip data from four ACIS-8 observations.," For same reason, we also included I-chip data from four ACIS-S observations." + These data together cover a field of ro ουδ around the center ofM31., These data together cover a field of $r\sim$ $^\prime$ around the center of. +".. Furthermore. for local sky background. determination. we used six additional ACIS-I observations which were aimed toward an ""of(L-füekl ~20! southwest to the center."," Furthermore, for local sky background determination, we used six additional ACIS-I observations which were aimed toward an “off-field” $\sim$$20^\prime$ southwest to the center." + We reprocessed the data using CIAO (version 3.3). following the ACIS data analvsis guide.," We reprocessed the data using CIAO (version 3.3), following the ACIS data analysis guide." + We generated count ancl exposure maps [ον each observation in the 0.5-1. 1-2. 2-4 and 4-8 keV bands.," We generated count and exposure maps for each observation in the 0.5-1, 1-2, 2-4 and 4-8 keV bands." + Corresponding instrumental background maps were generated from the “stowed” data. after calibrating the 10-12 keV count rate with individual observations.," Corresponding instrumental background maps were generated from the “stowed” data, after calibrating the 10-12 keV count rate with individual observations." + The total effective exposure is 295 ks in the central region and gradually drops to < 20 ks at radii rZ10’., The total effective exposure is $\sim$ 95 ks in the central region and gradually drops to $\lesssim$ 20 ks at radii $r \gtrsim 10^\prime$. + Following a procedure detailed in Wang (2004). we performed source detection in the κο (0.5-2 keV). hard (2-8 keV) and broad (0.5-8 keV) bands.," Following a procedure detailed in Wang (2004), we performed source detection in the soft (0.5-2 keV), hard (2-8 keV) and broad (0.5-8 keV) bands." + With a local false detection probability Px10.5. a total of 305 sources are detected in the field.," With a local false detection probability $P \leq 10^{-6}$, a total of 305 sources are detected in the field." + To study the unresolved X-ray emission. we excluded each of (he sources from maps of individual observations with circular regions enclosing ~97% of the source counts.," To study the unresolved X-ray emission, we excluded each of the sources from maps of individual observations with circular regions enclosing $\sim$ of the source counts." + The residual of (his source removal contributes about. of the remaining unresolved X-ray emission in the field., The residual of this source removal contributes about of the remaining unresolved X-ray emission in the field. + The maps were (hen reprojected to generate combined images in the four bands., The source-removed maps were then reprojected to generate combined images in the four bands. + We [further statistically corrected for the variation of the detection incompleteness across the field. to a common detection limit of 8x10?!eress| (0.5-8 keV).," We further statistically corrected for the variation of the detection incompleteness across the field, to a common detection limit of $\times10^{34}{\rm~ergs~s^{-1}}$ (0.5-8 keV)." + Decause of the relatively flat luminosity function of the sources (mostly LAINBs: Li et al., Because of the relatively flat luminosity function of the sources (mostly LMXBs; Li et al. + 2007 in preparation: see also Voss CGilfanov 2007). the correction. (normalized. according to the 2ALASS K-band intensitv: Fig.," 2007 in preparation; see also Voss Gilfanov 2007), the correction (normalized according to the 2MASS K-band intensity; Fig." + Jaa: Jarrett et al., \ref{fig:unr}a a; Jarrett et al. + 2003) typically amounts to less than of the unresolved emission., 2003) typically amounts to less than of the unresolved emission. + For the same reason. the residual contribution [vont LAINBs at lower luminosities," For the same reason, the residual contribution from LMXBs at lower luminosities" +derived an EBL of 0.71-1.18. Wi? for the ALOG model in the UV band. while t and [S07 ones give 2.66 aud 3.26 (MUAm?/Sri;MORGANA respectively.,"derived an EBL of 0.71-1.18 $nW/m^2/Sr$ for the M06 model in the UV band, while the and K07 ones give 2.66 and 3.26 $nW/m^2/Sr$, respectively." + To sunmuarize the main results of the paper: A correct physical description of the MoACN feedback. dust properties aud star formation in the models is fundamental to cusure a reasonable agreement of the model predictions at the faint cud of the galaxy counts.," To summarize the main results of the paper: A correct physical description of the AGN feedback, dust properties and star formation activities in the models is fundamental to ensure a reasonable agreement of the model predictions at the faint end of the galaxy counts." + Adding colour information for ealaxies with UV enuüssiou as faiut as CU=2728 nuples very deep observations in the red bands which are feasible with several hours of integration at Sin class telescopes., Adding colour information for galaxies with UV emission as faint as $U=27-28$ implies very deep observations in the red bands which are feasible with several hours of integration at 8m class telescopes. + Very deep multicolour information ou areas of the order of the square deeree cau help in extracting plivsical information ou the star formation historv of the dwarf population at intermediate and high redshifts., Very deep multicolour information on areas of the order of the square degree can help in extracting physical information on the star formation history of the dwarf population at intermediate and high redshifts. +the QSO.,the QSO. + Our toy model assumes a simple cut-off radius inside of which no absorbers can exist. and beyond which power-law clustering dominates.," Our toy model assumes a simple cut–off radius inside of which no absorbers can exist, and beyond which power-law clustering dominates." + In a more realistic model. there might be variable cut-off radius (au) dependent on the density of the absorbing cloud.," In a more realistic model, there might be variable cut–off radius $R_{\rm cut}$ ) dependent on the density of the absorbing cloud." + Such models are beyond the scope of the present analysis., Such models are beyond the scope of the present analysis. + We note that a small offset remains between the line-of-sight distributions predicted by our model and the the observed one., We note that a small offset remains between the line-of-sight distributions predicted by our model and the the observed one. + The magnitude of the observed offset is around KKm/s or MMpc. and may be accounted for by the fact that galaxies in the vicinity of the QSO will have a net motion caused by infall into potential well of the QSO host halo.," The magnitude of the observed offset is around km/s or Mpc, and may be accounted for by the fact that galaxies in the vicinity of the QSO will have a net motion caused by infall into potential well of the QSO host halo." + This will alter the observed shape and peak position of the absorber distribution., This will alter the observed shape and peak position of the absorber distribution. + A full treatment of infall requires detailed cosmological simulations. and will be addressed in future work.," A full treatment of infall requires detailed cosmological simulations, and will be addressed in future work." + On the observational side. it is clear that a careful correction of the QSO redshifts for the effect of the blue-shifting of emission lines is warranted in order to constrain the detailed shape of the aabsorber distribution.," On the observational side, it is clear that a careful correction of the QSO redshifts for the effect of the blue-shifting of emission lines is warranted in order to constrain the detailed shape of the absorber distribution." + Follow-up observations in the near infra-red of the aand eemission lines in a relatively large sample of high-z QSOs would provide a very useful basis for measuring these effects., Follow-up observations in the near infra-red of the and emission lines in a relatively large sample of $z$ QSOs would provide a very useful basis for measuring these effects. + The increase in number of QSOs from SDSS DR3 to SDSS DR7 will also further enable us to constrain the precise shape of the velocity distribution. and the fraction of dense absorbers which survive the ionising radiation of the QSO.," The increase in number of QSOs from SDSS DR3 to SDSS DR7 will also further enable us to constrain the precise shape of the velocity distribution, and the fraction of dense absorbers which survive the ionising radiation of the QSO." + We have used a cross-correlation analysis of QSO-absorber pairs to measure the strength of narrow absorber clustering around QSOs., We have used a cross-correlation analysis of QSO-absorber pairs to measure the strength of narrow absorber clustering around QSOs. + A simple model to convert the 3-D distribution of QSO-absorber separations into a line-of-sight distribution in velocity space is presented., A simple model to convert the 3-D distribution of QSO-absorber separations into a line-of-sight distribution in velocity space is presented. + Our modelling allows us to reach the following conclusions for ssystems: For aabsorbers we find: In the future. the larger absorber samples provided by later releases of the SDSS survey data. improved methods for obtaining reliable QSO redshifts. and investigations of ionisation and line width trends with velocity. will contribute substantially to isolating the physical processes responsible for QSO outflows detected through narrow absorption lines.," Our modelling allows us to reach the following conclusions for systems: For absorbers we find: In the future, the larger absorber samples provided by later releases of the SDSS survey data, improved methods for obtaining reliable QSO redshifts, and investigations of ionisation and line width trends with velocity, will contribute substantially to isolating the physical processes responsible for QSO outflows detected through narrow absorption lines." + We would like to thank Craig Hogan. Stuart Sim. Philip Best. Jeremy Blaizot. Cheng Li. and Robert Brunner or useful discussions and comments.," We would like to thank Craig Hogan, Stuart Sim, Philip Best, Jeremy Blaizot, Cheng Li, and Robert Brunner for useful discussions and comments." + This paper made use of the IDL MPFIT package by Craig) Markwardt rttp://cow.physics.wisc.edu/ eraign/idl/. Funding for the SDSS and SDSS-II has been provided by he Alfred P. Sloan Foundation. the Participating Institutions. the ational Science Foundation. the U.S. Department of Energy. he National Aeronautics and Space Administration. the Japanese lonbukagakusho. the Max Planck Society. and the Higher Edueation Funding Council for England.," This paper made use of the IDL MPFIT package by Craig Markwardt http://cow.physics.wisc.edu/ craigm/idl/. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." + The SDSS Web Site is rtp://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions., The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. + The Participating Institutions are the American Museum of Natural History. Astrophysical Institute Potsdam. University of Basel. University of Cambridge. Case Western Reserve University. University of Chicago. Drexel University. Fermilab. the Institute for Advanced Study. the Japan Participation Group. Johns Hopkins University. he Joint Institute for Nuclear Astrophysics. the Kavli Institute or Particle Astrophysics and Cosmology. the Korean Scientist Group. the Chinese Academy of Sciences (LAMOST). Los Alamos ational Laboratory. the Max-Planck-Institute for Astronomy (ΜΡΙΑ). the Max-Planck-Institute for Astrophysics (MPA). New Texico State University. Ohio State University. University of Pittsburgh. University of Portsmouth. Princeton University. he United States Naval Observatory. and the University of Washington.," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington." +luminosity. of both AGN ancl quiescent nearby galaxies appears to be confined between two radio-power limits.,luminosity of both AGN and quiescent nearby galaxies appears to be confined between two radio-power limits. +" The lower radio-power limit defines the minimum raclio luminosity that can be emitted by a given black-hole mass. and is well described by a relation of the form LsegsκAM,» in good agreement with the correlation originally observed. for nearby quiescent galaxies by Franceschini. Verecllone Fabian (1998)."," The lower radio-power limit defines the minimum radio luminosity that can be emitted by a given black-hole mass, and is well described by a relation of the form $L_{5GHz} \propto M_{bh}^{2.5}$ , in good agreement with the correlation originally observed for nearby quiescent galaxies by Franceschini, Vercellone Fabian (1998)." + Phe upper radio-power limit ooposed by Dunlop AleLure (2003) appears to be well described by a relation of the same functional form. olfset rom the lower limit by some 5 decades in radio luminosity.," The upper radio-power limit proposed by Dunlop McLure (2003) appears to be well described by a relation of the same functional form, offset from the lower limit by some 5 decades in radio luminosity." + 1n contrast. the recent studies of Ho (2002) and Woo Urry (2002) find no convincing evidence for a correlation between Xack-hole mass and radio Luminosity. in ssumples comprising a range in nuclear activity [rom local quiescent galaxies up o and including powerful quasars.," In contrast, the recent studies of Ho (2002) and Woo Urry (2002) find no convincing evidence for a correlation between black-hole mass and radio luminosity, in samples comprising a range in nuclear activity from local quiescent galaxies up to and including powerful quasars." + In this section we investigate whether there is a correlation between black-hole mass and. racio luminosity within the ZP5 radio-galaxy sample., In this section we investigate whether there is a correlation between black-hole mass and radio luminosity within the ZP5 radio-galaxy sample. + In contrast to previous studies. the majority. of which have been based. on high requeney (5-Cillz) radio Iuminosity. the ZP5 radio-galaxy sample allows us to test lor à correlation between black-role mass and extended low-frequeney (151-MlIZ) racio uminositv.," In contrast to previous studies, the majority of which have been based on high frequency (5-GHz) radio luminosity, the ZP5 radio-galaxy sample allows us to test for a correlation between black-hole mass and extended low-frequency (151-MHz) radio luminosity." + Fhis distinction is potentially important. given hat Liziuuz is less alfected by beaming than τομ. (og., This distinction is potentially important given that $L_{151MHz}$ is less affected by beaming than $L_{5GHz}$ (eg. + Jarvis MeLure 2002) and has a close relationship to the inic-averaged kinetic energy of the jets (c.g. Rawlings Saunders 1991)., Jarvis McLure 2002) and has a close relationship to the time-averaged kinetic energy of the jets (e.g. Rawlings Saunders 1991). + The results. presented. thus far are consistent. with a picture in which extended. low-L[requeney radio Luminosity seales roughly with host-galaxv luminositv/mass., The results presented thus far are consistent with a picture in which extended low-frequency radio luminosity scales roughly with host-galaxy luminosity/mass. + dn combination with the latest. determination. of the A2 relation (Willott et al., In combination with the latest determination of the $K-z$ relation (Willott et al. + 2003) it appears that the most powerful 3C-class radio galaxies reside in galaxies with R band luminosities of ~4L°. while the lower-lumuinosity 6C and TC-class radio ὃνgalaxies typically inhabit hosts with uminosities of 23L* and z2L* respectively.," 2003) it appears that the most powerful 3C-class radio galaxies reside in galaxies with $R-$ band luminosities of $\simeq 4L^{\star}$, while the lower-luminosity 6C and 7C-class radio galaxies typically inhabit hosts with luminosities of $\simeq 3L^{\star}$ and $\simeq 2L^{\star}$ respectively." + At present it is unclear how the TOOT sub-sample its within this picture., At present it is unclear how the TOOT sub-sample fits within this picture. + It can be seen from the results oesented in “Table 4. that the POO galaxies co not appear to follow the rough scaling between extended. racio uminosity anc host-galaxy luminosity apparent in the BCRR. GCE and TORS sub-samples.," It can be seen from the results presented in Table \ref{tab4} that the TOOT galaxies do not appear to follow the rough scaling between extended radio luminosity and host-galaxy luminosity apparent in the 3CRR, 6CE and 7CRS sub-samples." + Lacteed. the mean uminositv of the “POO sub-sample (3.28+0.5447) is ereater than that of both the TORS and GCL sub-samples. and is consistent with the low-recshilt results of Owen Laing (1989) that fat coublejet/PRL sources reside in hosts which are on average 20.5 magnitudes brighter than those of classical doublesRIL sources of comparable racio luminosity.," Indeed, the mean luminosity of the TOOT sub-sample $3.28\pm0.54 L^{\star}$ ) is greater than that of both the 7CRS and 6CE sub-samples, and is consistent with the low-redshift results of Owen Laing (1989) that fat double/jet/FRI sources reside in hosts which are on average $\simeq +0.5$ magnitudes brighter than those of classical double/FRII sources of comparable radio luminosity." + However. as was mentioned in Section 2. the TOOT sub-sample was drawn from a preliminary version of the survey and it is unclear at the time of writing to what extent the current TOOT sub-sample is biased bv the exclusion of the optically faintest sources.," However, as was mentioned in Section 2, the TOOT sub-sample was drawn from a preliminary version of the survey and it is unclear at the time of writing to what extent the current TOOT sub-sample is biased by the exclusion of the optically faintest sources." + With this in mind. panel A of Fig 10. shows 151-MllIz radio luminosity versus estimated black-hole mass for the full ZP5 sample. where the black-hole mass estimates have been derived via the Mebure Dunlop (2002) ManAdmits. relation as described in Section S.," With this in mind, panel A of Fig \ref{fig10} shows 151-MHz radio luminosity versus estimated black-hole mass for the full ZP5 sample, where the black-hole mass estimates have been derived via the McLure Dunlop (2002) $M_{bh}-M_{bulge}$ relation as described in Section 8." +" Taken as a whole. there is only a weak (i7,=0.35.p0.027. 2.20) correlation between black-hole mass and radio luminosity within the ZP5 sample."," Taken as a whole, there is only a weak $r_{s}=0.35, p=0.027$, $2.2\sigma$ ) correlation between black-hole mass and radio luminosity within the ZP5 sample." +" Llowever. as suggested: previously. it can be seen from panel A of Fig 10. that the apparent weakness of the Lis,Mo, correlation displayed by the full ZP5 sample is due. at least in part. to the inclusion of the eleven POO'T objects."," However, as suggested previously, it can be seen from panel A of Fig \ref{fig10} that the apparent weakness of the $L_{151}-M_{bh}$ correlation displayed by the full ZP5 sample is due, at least in part, to the inclusion of the eleven TOOT objects." +" ‘To investigate the possible inlluence of radio structure and nuclear spectral type we have also plotted in Fig 10 the Lis)—Ads, relation for two sub-sets of the ZP5 sample.", To investigate the possible influence of radio structure and nuclear spectral type we have also plotted in Fig \ref{fig10} the $L_{151}-M_{bh}$ relation for two sub-sets of the ZP5 sample. +" In panel B of Fig LO we show the Lis,AM, relation for those objects which display high-excitation nuclear spectra (LIEG) only.", In panel B of Fig \ref{fig10} we show the $L_{151}-M_{bh}$ relation for those objects which display high-excitation nuclear spectra (HEG) only. + As is suggested by the figure. this sub-sample," As is suggested by the figure, this sub-sample" +additional optical images around five slightly more compact radio sources (also from the sample of 26 sources) to search for optical counterparts.,additional optical images around five slightly more compact radio sources (also from the sample of 26 sources) to search for optical counterparts. + These sources are not located in nearby galaxy clusters and their nature remains unclear., These sources are not located in nearby galaxy clusters and their nature remains unclear. + We end with à discussion and conclusions in Sects., We end with a discussion and conclusions in Sects. + 5 and 6.., \ref{sec:discussion} and \ref{sec:conclusion}. +" Throughout this paper. we assume à ACDM cosmology with Ho=71 km s! Mpc!. Q,,=0.3. and Q4=0.7."," Throughout this paper, we assume a $\Lambda$ CDM cosmology with $H_{0} = 71$ km $^{-1}$ $^{-1}$, $\Omega_{m} = 0.3$, and $\Omega_{\Lambda} = 0.7$." + All images are in the J2000 coordinate system., All images are in the J2000 coordinate system. + Radio continuum observations with the GMRT at 325 MHz were carried out on 14. 15. and 17 May. 2009.," Radio continuum observations with the GMRT at 325 MHz were carried out on 14, 15, and 17 May, 2009." + Both upper (USB) and lower (LSB) sidebands (IFs. which included RR and LL polarizations) were recorded with a total bandwidth of 32 MHz.," Both upper (USB) and lower (LSB) sidebands (IFs, which included RR and LL polarizations) were recorded with a total bandwidth of 32 MHz." + The observations were carried out in spectral line mode with 128 channels per IF to facilitate the removal of radio frequency interference (RFI) and reduce the effect of bandwidth smearing., The observations were carried out in spectral line mode with 128 channels per IF to facilitate the removal of radio frequency interference (RFI) and reduce the effect of bandwidth smearing. + The integration time per visibility was 8 sec., The integration time per visibility was 8 sec. + Each source was observed for about 4 hrs in total., Each source was observed for about 4 hrs in total. + The data were reduced with the NRAO Astronomical Image Processing System (AIPS) package., The data were reduced with the NRAO Astronomical Image Processing System (AIPS) package. + The data was visually inspected for the presence of ΕΚΕΙ. which was subsequently removed (re.. “flagged™).," The data was visually inspected for the presence of RFI, which was subsequently removed (i.e., “flagged”)." + We curied out an amplitude and phase calibration on the flux and bandpass calibrators 3C147 and 3C286 on a timescale of 8 sec., We carried out an amplitude and phase calibration on the flux and bandpass calibrators 3C147 and 3C286 on a timescale of 8 sec. + For this. we chose three neighboring frequency channels free of RFI.," For this, we chose three neighboring frequency channels free of RFI." + These gain solutions were applied before determining the bandpass response of the antennas., These gain solutions were applied before determining the bandpass response of the antennas. + This assures that any amplitude and/or phase variations during the scans on the calibrators are corrected before determining the bandpass solutions., This assures that any amplitude and/or phase variations during the scans on the calibrators are corrected before determining the bandpass solutions. + At higher frequencies (e.g.. 1.4 GHz). both amplitude and phases are assumed to be constant during bandpass calibration.," At higher frequencies (e.g., 1.4 GHz), both amplitude and phases are assumed to be constant during bandpass calibration." + However. for the GMRT observingσι at low frequencies. this assumption is not always valid and can affect the quality of the bandpass solutions as well as the determination of the flux seale.," However, for the GMRT observing at low frequencies, this assumption is not always valid and can affect the quality of the bandpass solutions as well as the determination of the flux scale." + After correcting for the bandpass response. both the amplitude and phase solutions for both primary and secondary calibrators were determined but in this case using the full channel range.," After correcting for the bandpass response, both the amplitude and phase solutions for both primary and secondary calibrators were determined but in this case using the full channel range." + The fluxes of the primary calibrators were set according to the ? extension to the ? scale., The fluxes of the primary calibrators were set according to the \cite{perleyandtaylor} extension to the \cite{1977A&A....61...99B} scale. + The flux densities for the secondary calibrators were bootstrapped from the primary calibrators., The flux densities for the secondary calibrators were bootstrapped from the primary calibrators. + The amplitude and phase solutions were interpolated and applied to the target sources., The amplitude and phase solutions were interpolated and applied to the target sources. +" Some targets were observed over multiple days (observing runs). the resulting different data sets were combined with the AIPS task '""DBCON':."," Some targets were observed over multiple days (observing runs), the resulting different data sets were combined with the AIPS task `DBCON'." + For each of the target sources. we created a model of the surrounding field using the NVSS survey with a spectral index scaling of —0.7.," For each of the target sources, we created a model of the surrounding field using the NVSS survey with a spectral index scaling of $-0.7$." + We carried out à phase-only self-calibration against this model to improve the astrometric accuracy., We carried out a phase-only self-calibration against this model to improve the astrometric accuracy. + This was followed by several rounds of phase self-calibration and two final rounds of amplitude and phase self-calibration., This was followed by several rounds of phase self-calibration and two final rounds of amplitude and phase self-calibration. + To produce the images. we used the polyhedron method (??) to minimize the effects of non-coplanar baselines.," To produce the images, we used the polyhedron method \citep{1989ASPC....6..259P, 1992A&A...261..353C} to minimize the effects of non-coplanar baselines." + The model was then subtracted from the data. a step that facilitated the removal of additional. RFI or baselines with. problems.," The model was then subtracted from the data, a step that facilitated the removal of additional RFI or baselines with problems." + Final images were made using robust weighting (robust20.5.?)..," Final images were made using robust weighting \citep[robust = 0.5,][]{briggs_phd}." + Images were cleaned using the automatic clean-box windowing algorithm in AIPS and cleaned down to 2 times the rms noise level (σημ) within the clean boxes., Images were cleaned using the automatic clean-box windowing algorithm in AIPS and cleaned down to $2$ times the rms noise level $2\sigma_{\mathrm{rms}}$ ) within the clean boxes. + The final images were corrected for the primary beamresponse-., The final images were corrected for the primary beam. +. The uncertainty in the calibration of the absolute flux-scale ts in the range 5—10%. see ?..," The uncertainty in the calibration of the absolute flux-scale is in the range $5-10\%$, see \cite{2004ApJ...612..974C}." + The resulting noise levels and beam sizes are shown in Table 1.., The resulting noise levels and beam sizes are shown in Table \ref{tab:gmrtobservations}. + Radio observations at 610 MHz were taken with the GMRT in February and November 2008 of the sources in Table l.., Radio observations at $610$ MHz were taken with the GMRT in February and November 2008 of the sources in Table \ref{tab:gmrtobservations}. + The reduction of these observations is similar to the GMRT 325 MHz data and is described in more detail in ?.., The reduction of these observations is similar to the GMRT 325 MHz data and is described in more detail in \cite{2009A&A...508...75V}. + We used these images to create the spectral index maps., We used these images to create the spectral index maps. + We carried out L-band observations of four sources with the VLA (see Table 2))., We carried out L-band observations of four sources with the VLA (see Table \ref{tab:vlaobservations}) ). + The observations were taken in standard continuum mode with two IFs. each having a bandwidth of 50 MHz recording all polarization products (RR. LL. RL. and LR).," The observations were taken in standard continuum mode with two IFs, each having a bandwidth of 50 MHz recording all polarization products (RR, LL, RL, and LR)." + Gain solutions were determined for the calibrator sources and transferred to the target sources., Gain solutions were determined for the calibrator sources and transferred to the target sources. + The fluxes for the primary calibrators were set according to the ? extension to the ? scale., The fluxes for the primary calibrators were set according to the \cite{perleyandtaylor} extension to the \cite{1977A&A....61...99B} scale. + The effective feed polarization parameters (the leakage terms or D-terms) were found by observing the phase calibrator over a wide range of parallactic angles and simultaneously solving for the unknown polarization properties of the source., The effective feed polarization parameters (the leakage terms or D-terms) were found by observing the phase calibrator over a wide range of parallactic angles and simultaneously solving for the unknown polarization properties of the source. + The polarization angles were set using the polarized sources 3C286 and 3C138., The polarization angles were set using the polarized sources 3C286 and 3C138. + For the R-L phase difference. we assumed values of —66.0 and 15.0 deg for 3C286 and 3C138. respectively.," For the R-L phase difference, we assumed values of $-66.0$ and $15.0$ deg for 3C286 and 3C138, respectively." + Stokes Q and U images were compiled for each source., Stokes Q and U images were compiled for each source. + From the Stokes Q and U images. the polarization angles (Y) were determined (V=4arctan (U/Q)).," From the Stokes Q and U images, the polarization angles $\Psi$ ) were determined $\Psi = \frac{1}{2} \arctan{(U/Q})$ )." + Total polarized intensity (P) images were also made (P=VQ+ U7)., Total polarized intensity $P$ ) images were also made $P = \sqrt{Q^2 + U^2}$ ). + The polarization fraction were found by dividing the total polarized intensity by the total intensity (Stokes D image Q7+ U7/D)., The polarization fraction were found by dividing the total polarized intensity by the total intensity (Stokes I) image $ \sqrt{Q^2 + U^2}$ /I). +EE pli ipeum,_2 = ( ) ds. + Note that X aud X» depend ou the density aud magnetic structure of the cloud. but not the eraiu properties.," Note that $\Sigma$ and $\Sigma_2$ depend on the density and magnetic structure of the cloud, but not the grain properties." + The polarization percentage is defined by p27 where Q. C. and Fare obtained by παπάς equations L.. 5.. and 3.1 over erain species j.," The polarization percentage is defined by , where $Q$ , $U$, and $I$ are obtained by summing equations \ref{eq:Q}, , \ref{eq:U}, and \ref{eq:I} over grain species $j$ ." + It is easy to show that equation 3.1 becomes where (a) is a weighted iieau of 6j defiued as follows: Equations 6.. 7.. aud 3.10 show that the polarization pattern is determined by the deusitv aud magnetic structure of the eas. plus a single paramucter £05 related to the grain cross-sections aud aliguinenut properties.," It is easy to show that equation \ref{eq:pdef} becomes where $\meanalpha$ is a weighted mean of $\alphaj$ defined as follows: Equations \ref{eq:q}, \ref{eq:u}, and \ref{eq:p} show that the polarization pattern is determined by the density and magnetic structure of the gas, plus a single parameter $\meanalpha$ related to the grain cross-sections and alignment properties." + We estimate (a; as follows., We estimate $\meanalpha$ as follows. + We assume that the optimal maguetic field geometry. ii which +=0 and oe—const. gives rise to the maxi polarizationpercentagepray that is normallyobserved.," We assume that the optimal magnetic field geometry, in which $\gamma=0$ and $\psi=const$, gives rise to the maximum polarizationpercentage$p_{max}$ that is normallyobserved." + TheaNpolarization percentage is obtained from equation 3.1.. with the help of equations 6 aud 7:," Themaximumpolarization percentage is obtained from equation \ref{eq:p}, , with the help of equations $\ref{eq:q}$ and \ref{eq:u}: :" +by 15-60 minutes.,by 15-60 minutes. + This is done to maximize the sensitivity to motion of solar svstem objects but also to benefit the detection of short period stellar variability., This is done to maximize the sensitivity to motion of solar system objects but also to benefit the detection of short period stellar variability. + The universal cadence excludes visits of 21.000 square degrees around the galactic center because of erowcding.," The universal cadence excludes visits of $\sim$ 1,000 square degrees around the galactic center because of crowding." + To simulate this universal cadence. we made use of the thal serves to evaluate the suitability of the scanning model and to (quantify the vield for individual scientific goals of the survey (7.83.1)..," To simulate this universal cadence, we made use of the that serves to evaluate the suitability of the scanning model and to quantify the yield for individual scientific goals of the survey \citepalias[\S3.1]{LSSTbook}." + The simulator provides an array of heliocentric Julian dates (ILJD) at which a given field will be observed., The simulator provides an array of heliocentric Julian dates (HJD) at which a given field will be observed. + We split the southern sky uniformly in declination: where .N is (he number of declination bands., We split the southern sky uniformly in declination: where $N$ is the number of declination bands. + The i-th band is then split into M; right ASCELISIONS: The factor 1.3 in the expression for M; makes the distribution in a denser to account for the pronounced universal cadence variability along a., The $i$ -th band is then split into $M_i$ right ascensions: The factor $1.3$ in the expression for $M_i$ makes the distribution in $\alpha$ denser to account for the pronounced universal cadence variability along $\alpha$. + Sky partitioning in this wav vielded 1558 [fields [or --30. covering all right ascensions and declinations between —90* and 10.," Sky partitioning in this way yielded 1558 fields for $N=30$, covering all right ascensions and declinations between $-90^\circ$ and $10^\circ$." + Fig., Fig. + 2. depicts the number of visits per field in the r band., \ref{EB_fig_skymap} depicts the number of visits per field in the $r$ band. + The numbers tvpically vary from almost GOO points per lighteurve close to (he celestial equator. down to," The numbers typically vary from almost 600 points per lightcurve close to the celestial equator, down to" +nuaee (Milios 2005).,image (Mihos 2005). + The nearby galaxy PGC 11098 (VCCILIS) also has a small stream emanatiug from it (Region 5)., The nearby galaxy PGC 41098 (VCC1148) also has a small stream emanating from it (Region 5). + There is a hint that this stream coutimucs to the northeast. ruining through the radial stream. aud connecting up with the N Phune (Region [). but this is just at our surface brightness limit we do uot consider it firmly enouch detected to photomoeter.," There is a hint that this stream continues to the northeast, running through the radial stream, and connecting up with the N Plume (Region 4), but this is just at our surface brightness limit we do not consider it firmly enough detected to photometer." + The Iuuinosity and λα surface brightuess of the detected features are given iu Table 1.., The luminosity and maximum surface brightness of the detected features are given in Table \ref{m87tab}. + To assess the autheuticitv of all these features. aud avoid confusiou with galactic cirrus. we have compared hem to far infrared IRIS observations over the same area (Miville-Descheuues Lagache 2005).," To assess the authenticity of all these features, and avoid confusion with galactic cirrus, we have compared them to far infrared IRIS observations over the same area (Miville-Deschênnes Lagache 2005)." + While the spatial resolution of the IRIS data is oulwLX... we fiud 10 correlation with regions of suspected galactic dust contamination. and are confident that these features are rue stellar features around MST.," While the spatial resolution of the IRIS data is only, we find no correlation with regions of suspected galactic dust contamination, and are confident that these features are true stellar features around M87." + Again. however. since we are explicitly avoiding the dust-coutaminated regeious o the southeast of AIST. our catalog of features is likely uuderestimating the total structure around ALS7.," Again, however, since we are explicitly avoiding the dust-contaminated regions to the southeast of M87, our catalog of features is likely underestimating the total structure around M87." + The long linear streams to the northwest of MBST. are sugecstive of simall satellites falling iu ou radial orbits. or onu inore tangential orbits viewed alone the orbital plane.," The long linear streams to the northwest of M87 are suggestive of small satellites falling in on radial orbits, or on more tangential orbits viewed along the orbital plane." + The larger NW Stream (Reeious 112) crosses the galaxy pair NGC 1158/61., The larger NW Stream (Regions 1+2) crosses the galaxy pair NGC 4458/61. + These two galaxies have a velocity difference of 1300 |au/s and are not likely eusaged iu any slow mutual interaction that would draw out loug tidal tails., These two galaxies have a velocity difference of 1300 km/s and are not likely engaged in any slow mutual interaction that would draw out long tidal tails. + It is possible. however. that the stripping of one of these galaxies as it orbits in the potential well of the cluster could have giveu rise to the NW Stream.," It is possible, however, that the stripping of one of these galaxies as it orbits in the potential well of the cluster could have given rise to the NW Stream." + The thinner WNW Stream (Region 3). projects across the dwarf galaxy VCC 1119. aud again could be duc to stripping of this galaxy as it orbits M87.," The thinner WNW Stream (Region 3), projects across the dwarf galaxy VCC 1149, and again could be due to stripping of this galaxy as it orbits M87." + The surface brightness profiles of M81 and M86 overlap at large radii Gwhere 25) and thus cannot be fit independeutlv., The surface brightness profiles of M84 and M86 overlap at large radii (where $\ga 25$ ) and thus cannot be fit independently. + We have µνenmiploved. an iterative process. bv alternately fitting and subtracting both galaxies.," We have employed an iterative process, by alternately fitting and subtracting both galaxies." + Our fit show that MSIE is better fit with a fixed center (a =12:25:03.8. 6= |12:53:13.2 T2000) and that AfSG best fit isophotes have a ceuter that drifts south cast sabout 150 aresecouds from the initial center of (a =12:26:11.8. 8 =|12:56:16.6 J2000).," Our fits show that M84 is better fit with a fixed center $\alpha=$ 12:25:03.8, $\delta=$ +12:53:13.2 J2000) and that M86's best fit isophotes have a center that drifts south east about $150$ arcseconds from the initial center of $\alpha=$ 12:26:11.8, $\delta=$ +12:56:46.6 J2000)." + The ceutroid diiff is small at high surface brishtuess. but is more significant for the faint outer isophotes.," The centroid drift is small at high surface brightness, but is more significant for the faint outer isophotes." +" At far= 25. the ceuter has drifted less than 107, auc the more significant drifting occurs fainter than j= 27."," At = 25, the center has drifted less than $10''$, and the more significant drifting occurs fainter than = 27." + We begin our iterative process by masking ALS6 and making au initial fit to AIS with limited radial extent.," We begin our iterative process by masking M86 and making an initial fit to M84, with limited radial extent." + We subtract this MSL fit L.from the nuage. mask the residuals near MISts center. unmask ALS6. and make au initial fit to M86.," We subtract this M84 fit from the image, mask the residuals near M84's center, unmask M86, and make an initial fit to M86." + We then subtract the M86 ft from the original iniage. again masking the iucr residual. aud make a new fit to M81. over a larger radial ranec.," We then subtract the M86 fit from the original image, again masking the inner residual, and make a new fit to M84, over a larger radial range." +" We continue this iterative process for 5 steps. uutil we have fit both galaxies out to Raj,= ffor MISG and Reyyy= Που M81."," We continue this iterative process for 5 steps, until we have fit both galaxies out to $\rsma =$ for M86 and $\rsma =$ for M84." + Because of the complexity of the fitting process. and the crowded nature of the field surromnding ALS1 aud AISG. our fits do not extend to the nominal limit of µη 29.," Because of the complexity of the fitting process, and the crowded nature of the field surrounding M84 and M86, our fits do not extend to the nominal limit of = 29." + As noted above. we find that as we reach jr 27. the ceutroid of the ft begius drifting siguificautly. at about he same point where the isoplotes beein cucoupassine other galaxies in the field.," As noted above, we find that as we reach = 27, the centroid of the fit begins drifting significantly, at about the same point where the isophotes begin encompassing other galaxies in the field." + We therefore take this brighter iudt of p— 27 as the liit of our fitting process when extracting the analytic profile fits. aud show this as our outermost isoplote in Figure L.," We therefore take this brighter limit of = 27 as the limit of our fitting process when extracting the analytic profile fits, and show this as our outermost isophote in Figure \ref{subtract_m84m86m89}." + The isophotal ELLIPSE fits for both M81 and M86 are shown in Figure 2.., The isophotal ELLIPSE fits for both M84 and M86 are shown in Figure \ref{allfits}. + We compare our surface brightness. ellipticity. aud xositiou angle profiles with those of Caon (1990). Poletier (1990). and I&09 in B8. R. and V. bauds. respectively.," We compare our surface brightness, ellipticity, and position angle profiles with those of Caon (1990), Peletier (1990), and K09 in $B$, $R$, and $V$ bands, respectively." + For M8SÍ. we again find good agrecment )etwoeen those studies aud ours. save for discrepancies in. the position⋅⋅ angle ucar Fi17d.," For M84, we again find good agreement between those studies and ours, save for discrepancies in the position angle near $\rsma^{1/4}\sim 4$." + Tn this. region.. rowever. the ellipticity is so close to zero that the exact value of the position angle has little weaning.," In this region, however, the ellipticity is so close to zero that the exact value of the position angle has little meaning." + The Sérrsic and 2dV fits for MBS1 (given in Table 2)) vield a total unumnositv of 7.2 and 6.5 «101E... respectively. aud iu he 2dV fit the outer component carrics of the total unmdnositv.," The Sérrsic and 2dV fits for M84 (given in Table \ref{sbfits}) ) yield a total luminosity of 7.2 and 6.5 $\times 10^{10} L_{\sun}$ respectively, and in the 2dV fit the outer component carries of the total luminosity." + For Ms6. the comparison between our profiles aud hose previously published is) eood throughout.," For M86, the comparison between our profiles and those previously published is good throughout." + Iu articular we uote that the hup in the surface xiehtuess profile of M86. near IRAN~d ds also seeu in the M86 profile of IK09., In particular we note that the hump in the surface brightness profile of M86 near $\rsma^{1/4}\sim 4$ is also seen in the M86 profile of K09. + This feature complicates the analytic fitting process (Table 2)). vielding u values sjenificautle worse thin for any other galaxy in our saluple.," This feature complicates the analytic fitting process (Table \ref{sbfits}) ), yielding $\chi^2$ values significantly worse than for any other galaxy in our sample." + Our Sévrsic fit differs dramatically from that of 09. but as IK09 shows. the rauge of radii chosen to fit he profile has a significant effect on the fit parameters.," Our Sérrsic fit differs dramatically from that of K09, but as K09 shows, the range of radii chosen to fit the profile has a significant effect on the fit parameters." +" 1909 do not fit past Ria—3,5, and so their fit excludes he hump."," K09 do not fit past $\rsma^{1/4} = 3.5$, and so their fit excludes the hump." + If sve Bit our fif to a similar range. our fit xuinueters more closely match those of I&09.," If we limit our fit to a similar range, our fit parameters more closely match those of K09." + The 2dV fit is similarly poor. consisting of a small high surface xiehtuess immer component. and an outer component which contains of the light.," The 2dV fit is similarly poor, consisting of a small high surface brightness inner component, and an outer component which contains of the light." + Civen the actual shape of the profile. we do not consider this 2dV fit to be physically mieaniusful.," Given the actual shape of the profile, we do not consider this 2dV fit to be physically meaningful." + The total huuinositv of MBSG is 9.3 and 9.2 «1019E. under the Séórrsie aud 2dV fits. respectively.," The total luminosity of M86 is 9.3 and 9.2 $\times 10^{10} L_{\sun}$ under the Sérrsic and 2dV fits, respectively." + We subtract the combined M86 aud MSIE models frou the original mage. vieldiug the residual iiage shown im Figure L.," We subtract the combined M86 and M84 models from the original image, yielding the residual image shown in Figure \ref{subtract_m84m86m89}." + We note that in this case the mask displaved ou the final residuals is a subset of the mask that is used in the fitting procedure., We note that in this case the mask displayed on the final residuals is a subset of the mask that is used in the fitting procedure. + The bright galaxies south aud cast of M86 have all been ageressively masked in the analysis. but are displaved im this niase for clarity.," The bright galaxies south and east of M86 have all been aggressively masked in the analysis, but are displayed in this image for clarity." + Iu the residual image. we mnunediatelv note the piuxclhiecl-like fins ceutered on M86. which are indicators of the boxy isophotes noted by Peletier (1990).," In the residual image, we immediately note the pinwheel-like fins centered on M86, which are indicators of the boxy isophotes noted by Peletier (1990)." + These features are usually represeuted as azimuthal Al Fourier colponcuts. bevoud a pure clliptical model.," These features are usually represented as azimuthal A4 Fourier components, beyond a pure elliptical model." + Since we do not inchide these hieher-order Fourier terms in our, Since we do not include these higher-order Fourier terms in our +(Socderblou et al.,(Soderblom et al. + 1991). have photometric metallicities lower than the spectroscopic values by a constant amount A.," 1991), have photometric metallicities lower than the spectroscopic values by a constant amount $\Delta$." + Infact. A is likely to depeud ou logRi. but for the sake of simplicity we shall adopt here an average value eiven by where \(logPu is the distribution of stellar chromospheric activity. that can be found from the combined data of Soderbloin (1985)) anc IHeurv et al. (1996)).," Infact, $\Delta$ is likely to depend on $\log R'_{\rm HK}$, but for the sake of simplicity we shall adopt here an average value given by where $\chi(\log R'_{\rm HK})$ is the distribution of stellar chromospheric activity, that can be found from the combined data of Soderblom \cite{soder})) and Henry et al. \cite{HSDB}) )," + auc A is estimated by usine Eq. (, and $\Delta$ is estimated by using Eq. ( +5) of Rocha- Maciel (1998)).,5) of Rocha-Pinto Maciel \cite{RPM98}) ). + Using Eq. (1)).," Using Eq. \ref{deltamean}) )," + we have A=0.119 dex., we have $\bar\Delta=0.149$ dex. + The normalized photometric mctallicity distibution of he active stars. D(OFe/TII]). frou: Rocha-Pinto Maciel (1998)). is shown in Table 3..," The normalized photometric metallicity distribution of the active stars, ${\cal D}({\rm [Fe/H]})$, from Rocha-Pinto Maciel \cite{RPM98}) ), is shown in Table \ref{xdist}." + Tustead of ideutifving he active stars in the data sample. the approach we inve taken here assumes that a fraction c of the total iiber of stars in the sample (Npor) are active stars.," Instead of identifying the active stars in the data sample, the approach we have taken here assumes that a fraction $c$ of the total number of stars in the sample $N_{\rm tot}$ ) are active stars." + Therefore. the umuber of active stars in each metallicity dn is eMSQPX[Fe/II]). aud to correct the metallicity distribution. these active stars should be allocated to more uetalrich bius bv an amount of A.," Therefore, the number of active stars in each metallicity bin is $cN_{\rm tot}{\cal D}({\rm [Fe/H]})$, and to correct the metallicity distribution, these active stars should be allocated to more metal-rich bins by an amount of $\bar\Delta$." + The fraction e is Likely to depend ou the spectral type considered. as the chromospheric activity is thought to be caused by the interaction between the stellar rotation aud the convection iu the stella envelope.," The fraction $c$ is likely to depend on the spectral type considered, as the chromospheric activity is thought to be caused by the interaction between the stellar rotation and the convection in the stellar envelope." + The decrease of the outer convective zone towards hotter stars iudicates that vouug hotter stars do not show mach activity (Elearoy et al. 19973)., The decrease of the outer convective zone towards hotter stars indicates that young hotter stars do not show much activity y et al. \cite{elgaroy}) ). + For a sample centered ou € clwarfs. we can take e=0.296 as à good value. according to Hourv et al. (1996)).," For a sample centered on G dwarfs, we can take $c=0.296$ as a good value, according to Henry et al. \cite{HSDB}) )." + Table 3| also preseuts the normalized. corrections r to the metallicity distribution., Table \ref{xdist} also presents the normalized corrections $r$ to the metallicity distribution. + The nuubers iu the table were found by the subtraction of D[Fo/TI] from a gaussian curve fitted to this distribution with a mean shifted by A., The numbers in the table were found by the subtraction of ${\cal D}{\rm [Fe/H]}$ from a gaussian curve fitted to this distribution with a mean shifted by $\bar\Delta$. + These corrections are to be multiplied first by οΆγ before they can be added to the metallicity distribution. aud the application of auv other correctious due to observational errors. cosmic scatter. stellar evolution or scale height.," These corrections are to be multiplied first by $cN_{\rm tot}$, before they can be added to the metallicity distribution, and the application of any other corrections due to observational errors, cosmic scatter, stellar evolution or scale height." + The absolute corrections to the Co dwart metallicity distribution of RPM aud the Is chwarf cistriliion derived in this work are shown in the last columus of Table Js where sey=ον) aud re=οντως). with τον)=218 aud New(G)=287.," The absolute corrections to the G dwarf metallicity distribution of RPM and the K dwarf distribution derived in this work are shown in the last columns of Table \ref{xdist}, where $r_K = r c N_{\rm tot}(K)$ and $r_G = r c N_{\rm tot}(G)$ with $N_{\rm tot}(K) = 218$ and $N_{\rm tot}(G) = 287$." + Note that we have assumed the same values for e aud A for C aud I& chwarts. as there is no information abot their depeudeuce on the stellar mass.," Note that we have assumed the same values for $c$ and $\bar\Delta$ for G and K dwarfs, as there is no information about their dependence on the stellar mass." + It should be stressed. that jese corrections are valid ouly for distributious biuned by 0.1 dex. with each biu centered at the metallicities presented iu the first coliuun of Table 3.. and for [Fe/TI| determined by Strónuugren photometry.," It should be stressed that these corrections are valid only for distributions binned by 0.1 dex, with each bin centered at the metallicities presented in the first column of Table \ref{xdist}, and for [Fe/H] determined by Strömmgren photometry." + In order to apply them to a distribution binned iu a differeut way. we provide the equations below: where à: is the bin size in dex. asstuned constant. aud is the gaussian fit to the normalized distribution iu Table 3..," In order to apply them to a distribution binned in a different way, we provide the equations below: where $\delta z$ is the bin size in dex, assumed constant, and is the gaussian fit to the normalized distribution in Table \ref{xdist}." + According to this fit. p=—OL13 and a=0.152.," According to this fit, $\mu=-0.143$ and $\sigma=0.152$." +" For distributions based on differeut plotometric systems. a new value for A should be computed. suce the extent of chromospheric activity effects on i6 photometric indices depends on the spectral rauge sampled bv the filters. as well as ou thei transmission ""uetious."," For distributions based on different photometric systems, a new value for $\bar\Delta$ should be computed, since the extent of chromospheric activity effects on the photometric indices depends on the spectral range sampled by the filters, as well as on their transmission functions." + This could be an explanation for the fact ji the metallicity distribution of Flvuu Morell is somewhat differeut from the others (ee Figure 1). as this distribution uses Ceneva photometry. and the indices of 1ο calibrations can be affected iu a differeut wav frou the eb dices. which are used by all other distributions iu Figure 3..," This could be an explanation for the fact that the metallicity distribution of Flynn Morell is somewhat different from the others (see Figure \ref{othercomp}) ), as this distribution uses Geneva photometry, and the indices of the calibrations can be affected in a different way from the indices, which are used by all other distributions in Figure \ref{othercomp}." + Morale et al. (1996)), Morale et al. \cite{morale}) ) + report that. in active I& cwarfs. Aimy is systematically greater than in active C dwiufs as a function of the stellar activity. which would iudicate a ereater A for those stars.," report that, in active K dwarfs, $\delta m_1$ is systematically greater than in active G dwarfs as a function of the stellar activity, which would indicate a greater $\bar\Delta$ for those stars." + This is not confirmed for the active stars in the sample studied by Rocha-Pinto Macicl (1998)). as can be seen from Fig. L.," This is not confirmed for the active stars in the sample studied by Rocha-Pinto Maciel \cite{RPM98}) ), as can be seen from Fig. \ref{m1active}." + This plot shows that the iy deficiency. reflected in a larger value for diy. is about the same for € and IS dwarfs. as a function of the activity.," This plot shows that the $m_1$ deficiency, reflected in a larger value for $\delta m_1$ , is about the same for G and K dwarfs, as a function of the activity." + Towever. the stars analyzed by Morale et al. (," However, the stars analyzed by Morale et al. (" +1996) are eonerally 10nchmore active than ours. as they were detected by the X-ray flus-limuited Exteuded Medium Seusitivitv Survey (Cüola et al. 19903).,"1996) are generally muchmore active than ours, as they were detected by the X-ray flux-limited Extended Medium Sensitivity Survey (Gioia et al. \cite{gioia}) )." +The treasury mosaic images were produced using the DRIZZLE procedure with context images (FruchterandHook2002).,The treasury mosaic images were produced using the DRIZZLE procedure with context images \citep{fru02}. +. The offsets lor the NICMOS images were determined bv registering the NICMOS FLLOW images onto the ACS FS50LP UDF image in the LIST archive which has a north up orientation and 0.03” pixel scale., The offsets for the NICMOS images were determined by registering the NICMOS F110W images onto the ACS F850LP UDF image in the HST archive which has a north up orientation and $0.03 \arcsec$ pixel scale. + The significant overlap between the two fillers greatly reduces any. errors due to color dependent morphology. however. see 2.1.3. [or an assessment of the accuracy of (he alignment.," The significant overlap between the two filters greatly reduces any errors due to color dependent morphology, however, see \ref{sss-psf} for an assessment of the accuracy of the alignment." + The NICMOS FIGOW images which always immeciately followed the FILOW images in an orbit were assumed to have the same offset as the FLLOW images preceding them., The NICMOS F160W images which always immediately followed the F110W images in an orbit were assumed to have the same offset as the F110W images preceding them. +" The ACS image was reduced. to 0.09"" pixels bv a simple 3x3 pixel addition of the image.", The ACS image was reduced to $0.09 \arcsec$ pixels by a simple 3x3 pixel addition of the image. +" Individual NICAIOS FLIOW images were then produced with a crizzle PINFRAC parameter of 0.6 and a SCALE parameter of 0.09/0.202863 to produce 0.09"" output pixels.", Individual NICMOS F110W images were then produced with a drizzle PIXFRAC parameter of 0.6 and a SCALE parameter of $0.09/0.202863$ to produce $0.09\arcsec$ output pixels. + The denominator in the scale factor is the pixel size of the distortion corrected NICAIOS pixel., The denominator in the scale factor is the pixel size of the distortion corrected NICMOS pixel. + The geometric distortion coefficients Bergeron(2004) are given in Table 4.., The geometric distortion coefficients \cite{berg04} are given in Table \ref{tb-dis}. + These coefficients are the constants for a cubic distortion correction of the form and an identical equation in b coefficients for the v position that governs the placement of the pixels., These coefficients are the constants for a cubic distortion correction of the form and an identical equation in b coefficients for the y position that governs the placement of the pixels. + Compared to other HIST. instruments the correction is relatively small., Compared to other HST instruments the correction is relatively small. + The main component is the difference in plate scale between the x and v directions due to a slight tilt in the camera 3 focal plane relative to the plane of the detector., The main component is the difference in plate scale between the x and y directions due to a slight tilt in the camera 3 focal plane relative to the plane of the detector. + The tilt is due to the curvature of the focal plane., The tilt is due to the curvature of the focal plane. +" Each 0.09"". NICMOS was rotated to a north up orientation using the ORIENTAT value in the image header.", Each $0.09 \arcsec$ NICMOS was rotated to a north up orientation using the ORIENTAT value in the image header. + A three step process provided the positions of each F110W image relative to the ACS FS50LP image., A three step process provided the positions of each F110W image relative to the ACS F850LP image. + The list step was to shift the NICMOS images to the positions indicated bv their World Coordinate System. (WCS) position in the headers., The first step was to shift the NICMOS images to the positions indicated by their World Coordinate System (WCS) position in the headers. + The second step was a non-interactive chi squared. minimization of the differences between (he bright objects in ihe NICMOS image and the nearest corresponding bright ACS object., The second step was a non-interactive chi squared minimization of the differences between the bright objects in the NICMOS image and the nearest corresponding bright ACS object. + The ACS positions were determined with SE in the ABSOLUTE mode with the threshold set at 0.03 ADUs per second., The ACS positions were determined with SE in the ABSOLUTE mode with the threshold set at 0.03 ADUs per second. + Positions in the NIMCOS images were also determined with SE in ABSOLUTE mode with the threshold set at 0.01 ADUs per second., Positions in the NIMCOS images were also determined with SE in ABSOLUTE mode with the threshold set at 0.01 ADUs per second. + Both of these thresholds are quite bright to insure a low source count per area., Both of these thresholds are quite bright to insure a low source count per area. + This made the likelihood. of wrong object malching low., This made the likelihood of wrong object matching low. + The shifts were limited to plus or minus 10 pixels in the X and Y directions in single pixel steps., The shifts were limited to plus or minus 10 pixels in the X and Y directions in single pixel steps. +" The average position shift in this step was on the order of 2 to 3 0.09"" pixels.", The average position shift in this step was on the order of 2 to 3 $0.09 \arcsec$ pixels. + The final shifts were determined by a similar chi squared minimization of interactively, The final shifts were determined by a similar chi squared minimization of interactively +redshift.,redshift. + The Spearman-lxendall tests vielded a laree probability (0.560 and 0.33) that there is no correlation., The Spearman-Kendall tests yielded a large probability (0.80 and 0.33) that there is no correlation. + ILowever. it is worth noting that we do vet know ofa z>1.4 absorber with a high (close to solar) metallicity.," However, it is worth noting that we do yet know of a $z>1.4$ absorber with a high (close to solar) metallicity." + There are a few solar or higher metallicity absorbers of the sample) at 2< 1.4., There are a few solar or higher metallicity absorbers of the sample) at $z<1.4$ . + Figure 19 shows logZ/Z. vs. z for multiple cloud absorbers., Figure \ref{fig:MCZ} shows $\log{Z/\Zsun}$ vs. $z$ for multiple cloud absorbers. + Once again. we suffer [rom a small sample size. but the metallicities of the hieh redshift svstems are consistent with those of the low redshift svstems.," Once again, we suffer from a small sample size, but the metallicities of the high redshift systems are consistent with those of the low redshift systems." + First. we consider (he possible implications of our results on the multiple-cloud absorbers.," First, we consider the possible implications of our results on the multiple-cloud absorbers." + This class can be broadly grouped into two categories., This class can be broadly grouped into two categories. +" First. there are those multiple cloud absorbers (hat ave “kinematically spread” aud are likely to be ""almost-strong aabsorbers for which the line-of-sight simply does not pass (through dense regions of gas."," First, there are those multiple cloud absorbers that are “kinematically spread” and are likely to be “almost-strong” absorbers for which the line-of-sight simply does not pass through dense regions of gas." + second. (here are those multiple cloud absorbers that are “kinematically compact” and are likely clhwarl galaxies or are associated with cdwarf galaxies (Zonaketal.2004:Ding2005:Masieroetal. 2005).," Second, there are those multiple cloud absorbers that are “kinematically compact” and are likely dwarf galaxies or are associated with dwarf galaxies \citep{Zonak04,Ding05,Mas05}." +. The z=1.450109 svstem toward Q0122-380 is an example of a kinematically compact absorber., The $z = 1.450109$ system toward Q0122-380 is an example of a kinematically compact absorber. + The metallicity of this svstem is constrained to be —1.0< «0.0., The metallicity of this system is constrained to be $-1.0 \le \log{Z/\Zsun} \le 0.0$ . + The z=1.555845 svstem towards HI22211-2818 and the 2=1.558380 system toward Q0453-423 are examples of kinematically spread absorbers., The $z = 1.555845$ system towards HE2217-2818 and the $z = 1.858380$ system toward Q0453-423 are examples of kinematically spread absorbers. + The metallicities of these two svslems are constrained (o be logZ/Z.>—1.l aud logZ/Z.>—2.0., The metallicities of these two systems are constrained to be $\log{Z/\Zsun} \ge -1.1$ and $\log{Z/\Zsun} \ge -2.0$. + Because the metallicities of our svstems are not well constrained. we cannot draw any definite conclusions about the environments in which each (wpe of svstem arises.," Because the metallicities of our systems are not well constrained, we cannot draw any definite conclusions about the environments in which each type of system arises." + The recdshilt path density of single cloud weak aabsorbers is observed to decrease between z~I and z~2 etal. 2006).," The redshift path density of single cloud weak absorbers is observed to decrease between $z \sim 1$ and $z \sim 2$ \citep{Church99b,Lynch06}." +. Some of this evolution is due to the changing EBR which ranges from —4.33< between 1.4<22.4. respectively.," Some of this evolution is due to the changing EBR which ranges from $-4.83 < \log{n_{\gamma}} < -4.71~ [\cc]$ between $1.4 < z < 2.4$, respectively." + The effect of the changing EBR is to lead to more low ionization goas al lower redshift., The effect of the changing EBR is to lead to more low ionization gas at lower redshift. + In addition. cosmological effects will lead to a decrease in the density ol weak aabsorbers al lower redshift.," In addition, cosmological effects will lead to a decrease in the density of weak absorbers at lower redshift." + When (hese (wo competing effects are taken together. they cannot fully account for the lower «Νας at z~ 2.," When these two competing effects are taken together, they cannot fully account for the lower $dN/dz$ at $z \sim 2$ ." + The range of physical conditions that were found in this study. (column density. Doppler parameter. density. and metallicity) Lor svstems al redshift 1.4<2«2.4 do not show a statistical variation [from svstems at recshilt Q.4«cz«LA.," The range of physical conditions that were found in this study (column density, Doppler parameter, density, and metallicity) for systems at redshift $1.4 < z < 2.4$ do not show a statistical variation from systems at redshift $0.4 < z < 1.4$." + The ranges are large. constraints are derived using different. transitions at different redshifts. ancl our samples are small. leacling to dilution of anv (rends.," The ranges are large, constraints are derived using different transitions at different redshifts, and our samples are small, leading to dilution of any trends." + However. at face-value our result is consistent with the idea that (he evolution in the weak aabsorber population Irom z~2 to z~ lids due (o an increase in the ellicieney of the mechanisms that create weak aabsorbers. and not due to a change in theactual mechanisms.," However, at face-value our result is consistent with the idea that the evolution in the weak absorber population from $z\sim 2$ to $z\sim 1$ is due to an increase in the efficiency of the mechanisms that create weak absorbers, and not due to a change in theactual mechanisms." + For example.if a collapse process gave rise to weak," For example,if a collapse process gave rise to weak" +the quoted uncertainties of the parameters are lo with 1 parameter of interest.,the quoted uncertainties of the parameters are $1\sigma$ with 1 parameter of interest. + We found that a single power-law model yields a photon index of Γκ=4.291100 which is found to be too steep to be physically reasonable., We found that a single power-law model yields a photon index of $\Gamma_{X}=4.29^{+1.72}_{-1.09}$ which is found to be too steep to be physically reasonable. + The large value does suggest the X-ray emission from iis rather soft which is consistent with the inference resulted from the aforementioned hardness analysis., The large value does suggest the X-ray emission from is rather soft which is consistent with the inference resulted from the aforementioned hardness analysis. +" We have also fitted the spectrum with thermal plasma models, namely MEwe-KAstra-Liedahl (MEKAL) and thermal bremsstrahlung."," We have also fitted the spectrum with thermal plasma models, namely MEwe-KAstra-Liedahl (MEKAL) and thermal bremsstrahlung." + MEKAL is the code that models the plasma in collisional ionization equilibrium which is widely utilized to describe the shock-heated plasma of early-type stars (e.g. Sana et al., MEKAL is the code that models the plasma in collisional ionization equilibrium which is widely utilized to describe the shock-heated plasma of early-type stars (e.g. Sana et al. + 2007; Stelzer et al., 2007; Stelzer et al. + 2005)., 2005). +" With the metal abundances fixed at solar values, the model yields a plasma temperature of kT=0.5110:50 keV. However, we note that there are systematic fitting residuals in ~1--2 keV. Repeating the analysis with metal abundances at 50% and 25% of the solar values, we found the systematic residuals still present."," With the metal abundances fixed at solar values, the model yields a plasma temperature of $kT=0.51^{+0.17}_{-0.20}$ keV. However, we note that there are systematic fitting residuals in $\sim1-2$ keV. Repeating the analysis with metal abundances at $50\%$ and $25\%$ of the solar values, we found the systematic residuals still present." +" Furthermore, the inferred column density is ng=1.63*082x1033 em~? which is found to be higher than the total Galactic neutral hydrogen absorption of 1.4x10?? em~? (Dickey Lockman 1990), unless the metal abundance is below 2596 of the solar values."," Furthermore, the inferred column density is $n_{H}=1.63^{+0.63}_{-0.33}\times10^{22}$ $cm^{-2}$ which is found to be higher than the total Galactic neutral hydrogen absorption of $1.4\times10^{22}$ $cm^{-2}$ (Dickey Lockman 1990), unless the metal abundance is below $25\%$ of the solar values." + It is possible that multiple temperature model might improve the fitting., It is possible that multiple temperature model might improve the fitting. +" Nevertheless, the limited photon statistic does not allow us to do so with the existing data."," Nevertheless, the limited photon statistic does not allow us to do so with the existing data." +" In view of its inadequacy in modeling the X-ray spectrum, we will no longer consider this model further in this paper."," In view of its inadequacy in modeling the X-ray spectrum, we will no longer consider this model further in this paper." +" For the thermal bremsstrahlung model, it provides a better description of the data in comparison with MEKAL."," For the thermal bremsstrahlung model, it provides a better description of the data in comparison with MEKAL." +" This model provides the description of the continuum of the coronal emission from a late-type star, which is presumably heated by the magnetic reconnection (cf."," This model provides the description of the continuum of the coronal emission from a late-type star, which is presumably heated by the magnetic reconnection (cf." + Dopita Sutherland 2003)., Dopita Sutherland 2003). +" It yields a plasma temperature of kT'— keV. The unabsorbed flux inferred by the best-fit model is 1.097938x107! erg cm? s! in 0.3—10 keV. If the X-ray emission is indeed from a late-type star, the upper-bound of its distance is estimated to be ~280 pc by comparing the best-fit flux to the saturated X-ray luminosity of ~10°° erg s! for the late-type stellar population (Pizzolato et al."," It yields a plasma temperature of $kT=0.81^{+0.54}_{-0.31}$ keV. The unabsorbed flux inferred by the best-fit model is $1.09^{+6.98}_{-1.09}\times10^{-13}$ erg $^{-2}$ $^{-1}$ in $0.3-10$ keV. If the X-ray emission is indeed from a late-type star, the upper-bound of its distance is estimated to be $\sim280$ pc by comparing the best-fit flux to the saturated X-ray luminosity of $\sim10^{30}$ erg $^{-1}$ for the late-type stellar population (Pizzolato et al." + 2003)., 2003). +" Adopting this estimate, we convert the limiting magnitude, mv>21, of the USNO catalog to an absolute magnitude of My>14 which suggests the star should not be more massive than a M-star."," Adopting this estimate, we convert the limiting magnitude, $m_{V}>21$, of the USNO catalog to an absolute magnitude of $M_{V}>14$ which suggests the star should not be more massive than a M-star." + A deeper optical observation will certainly provide a key role in confirming or refuting this scenario., A deeper optical observation will certainly provide a key role in confirming or refuting this scenario. +" For the blackbody model, assuming the source is a pulsar, it provides a description for the polar cap heating from the return current in the outergap (Cheng Zhang 1999)."," For the blackbody model, assuming the source is a pulsar, it provides a description for the polar cap heating from the return current in the outergap (Cheng Zhang 1999)." +" The blackbody model yields an effective temperature of kT=0.38+0.09 keV. Interestingly, this value is well consistent with the theoretical value of the polar cap temperature computed by the outergap model (i.e. equation 58 in Cheng Zhang 1999), which is kT =0.34 keV for the rotational period and the magnetic field ofJ2021+4026."," The blackbody model yields an effective temperature of $kT=0.38\pm0.09$ keV. Interestingly, this value is well consistent with the theoretical value of the polar cap temperature computed by the outergap model (i.e. equation 58 in Cheng Zhang 1999), which is $kT=$ 0.34 keV for the rotational period and the magnetic field of." +. The X-ray spectrum of wwith the best-fit absorbed blackbody model is displayed in Figure 6.., The X-ray spectrum of with the best-fit absorbed blackbody model is displayed in Figure \ref{x_spec}. +" The best-fit parameters of the blackbody model yield an unabsorbed flux of fx=0.367985x10:15 erg cm~? s! in 0.3—10 keV. Comparing the best-fit X-ray flux with the y—ray flux (see below), the flux ratio is found to be fx/fy2x10? which is consistent with the typical values of y—ray pulsars (e.g. Geminga)."," The best-fit parameters of the blackbody model yield an unabsorbed flux of $f_{X}=0.36^{+4.66}_{-0.32}\times10^{-13}$ erg $^{-2}$ $^{-1}$ in $0.3-10$ keV. Comparing the best-fit X-ray flux with the $\gamma-$ ray flux (see below), the flux ratio is found to be $f_{X}/f_{\gamma}\sim2\times10^{-5}$ which is consistent with the typical values of $\gamma-$ ray pulsars (e.g. Geminga)." +" On the other hand, with the limiting magnitude of my>21, the nominal X-ray-to-optical flux ratio is fx/fv>1."," On the other hand, with the limiting magnitude of $m_{V}>21$, the nominal X-ray-to-optical flux ratio is $f_{X}/f_{V}>1$." + This appears to be higher than that of a field star which typically has a ratio fx/fv<0.3 (Maccacaro et al., This appears to be higher than that of a field star which typically has a ratio $f_{X}/f_{\rm V}<0.3$ (Maccacaro et al. + 1988)., 1988). +" However, simply on the basis of the X-ray-to-optical flux ratio, the limit found for iis too low to rule out the possibility of an AGN which typically has a ratio of fx/fv«50 (Stocke et al."," However, simply on the basis of the X-ray-to-optical flux ratio, the limit found for is too low to rule out the possibility of an AGN which typically has a ratio of $f_{X}/f_{\rm V}<50$ (Stocke et al." + 1991)., 1991). +" 'Therefore, a deep optical observation would be important to tightly constrain its source nature."," Therefore, a deep optical observation would be important to tightly constrain its source nature." +" Although the blackbody model can yield a physically reasonable best-fit temperature and the flux for the interpretation of pulsar emission, one should notice that the spectral parameters and hence the fluxes are poorly constrained."," Although the blackbody model can yield a physically reasonable best-fit temperature and the flux for the interpretation of pulsar emission, one should notice that the spectral parameters and hence the fluxes are poorly constrained." +" Therefore, fx/f, and fx/fv cannot be tightly determined."," Therefore, $f_{X}/f_{\gamma}$ and $f_{X}/f_{\rm V}$ cannot be tightly determined." +" Hence, we have to admit that the source nature of ccannotMM be determined unambiguously."," Hence, we have to admit that the source nature of cannot be determined unambiguously." +" In the spectral analysis, we are not allowed to discriminate the pulsar interpetation from that of a star."," In the spectral analysis, we are not allowed to discriminate the pulsar interpetation from that of a star." +" As the flux variability cannot be well-constrained with the existing data, we also cannot completely exclude the possibility of the source as an AGN."," As the flux variability cannot be well-constrained with the existing data, we also cannot completely exclude the possibility of the source as an AGN." +" To further probe its X-ray emission nature, besides the aforementioned deep optical observation, a dedicated X-ray observation is very important in constraining the spectral properties, variability, as well as the flux ratios with respect to the y—ray and optical results."," To further probe its X-ray emission nature, besides the aforementioned deep optical observation, a dedicated X-ray observation is very important in constraining the spectral properties, variability, as well as the flux ratios with respect to the $\gamma-$ ray and optical results." +" Apart from yielding the physically reasonable temperature and the flux for the interpretation of pulsar emission, the blackbody model also provides relatively the least residuals among all the tested models though cannot be discriminated unambiguously with the small number of counts."," Apart from yielding the physically reasonable temperature and the flux for the interpretation of pulsar emission, the blackbody model also provides relatively the least residuals among all the tested models though cannot be discriminated unambiguously with the small number of counts." +" In view of these merits, we are going to use the results inferred from this model for further discussion in Section 3."," In view of these merits, we are going to use the results inferred from this model for further discussion in Section 3." + The robustness of the results quoted in this paper is checked by repeating the analysis by incorporating the background spectrum sampled from different source-free regions., The robustness of the results quoted in this paper is checked by repeating the analysis by incorporating the background spectrum sampled from different source-free regions. + It is found that within the 68% confidence intervals the spectral parameters inferred from independent fittings are all consistent with each other., It is found that within the $68\%$ confidence intervals the spectral parameters inferred from independent fittings are all consistent with each other. +" Although the detection of X-ray pulsations at the location of wwould provide us an unambiguous evidence that it is associated with a y—ray pulsar, the small photon statistics and the large frame time of the existing data do not allow any meaningful timing analysis."," Although the detection of X-ray pulsations at the location of would provide us an unambiguous evidence that it is associated with a $\gamma-$ ray pulsar, the small photon statistics and the large frame time of the existing data do not allow any meaningful timing analysis." + The identification of aas a possible X-ray counterpart of does provide us a position with arc-second accuracy., The identification of as a possible X-ray counterpart of does provide us a position with arc-second accuracy. + This is very helpful in facilitating further multiwavelength investigations., This is very helpful in facilitating further multiwavelength investigations. +" With this precise position, we have searched for any coherent radio pulse emission."," With this precise position, we have searched for any coherent radio pulse emission." +approximating to the first order. and solving. we obtain a linear system whose solutions are where we have used the definition of ᾧ (Eq. (23))),"approximating to the first order, and solving, we obtain a linear system whose solutions are where we have used the definition of $\Phi$ (Eq. \ref{eq:phi}) ))" + and neglected terms proportional to ago., and neglected terms proportional to $\alpha_0\delta$. + We note that & is of the order of8 or less. r.e.. it is negligible with respect to qo itself.," We note that $\varepsilon$ is of the order of $\theta$ or less, i.e., it is negligible with respect to $\varphi_0$ itself." + We can then assume that g)=go., We can then assume that $\varphi_1 \approx \varphi_0$. + Moreover. we know from Sect.," Moreover, we know from Sect." +" ?? also that g,=yo. thus we denote with y the nearly-common value of all these polar angles."," \ref{review} also that $\varphi_1 \approx \varphi_2$, thus we denote with $\varphi$ the nearly-common value of all these polar angles." + We then rewrite Eq. (B4)).," We then rewrite Eq. \ref{eq:xi0}) )," + using Eq. (BI)).," using Eq. \ref{eq:cone1}) )," + as Clearly. Zi>O only if €>0.," as Clearly, $Z_1>0$ only if $\xi >0$." + If the spacing of the two mirrors ts small enough. we may also approximate6°=6.," If the spacing of the two mirrors is small enough, we may also approximate$\delta^* \approx \delta$." + The first vignetting factor is thereby V|=|—4. 1.e.. recalling the definition of o4 (Eq. (3))).," The first vignetting factor is thereby $V_1 = 1-\frac{Z_1}{L_1}$, i.e., recalling the definition of $\alpha_1$ (Eq. \ref{eq:angle1}) ))," + if positive and less than 1., if positive and less than 1. + We have so obtained Eq. (30))., We have so obtained Eq. \ref{eq:V1_}) ). + As usual. if this expression returns a negative value at some y’. then Vi(z/)=0. or. if larger than one. Vi(z/)=1.," As usual, if this expression returns a negative value at some $\varphi'$, then $V_1(\varphi') = 0$, or, if larger than one, $V_1(\varphi') = 1$." +" TfL)=L, we find that V, takes the simple form of where in this case we also note that.if V were positive and smaller than one for all yg. the geometric area of the obstructed segment would become which — às expected — returns the area of the corona delimited by the largest radit of the two shells where we have used the relation Ry=Ro+aol."," If $L_1 = L_1^*$ we find that $V_1$ takes the simple form of where in this case we also note that, $V_1$ were positive and smaller than one for all $\varphi$, the geometric area of the obstructed segment would become which – as expected – returns the area of the corona delimited by the largest radii of the two shells where we have used the relation $R_{\mathrm M} \simeq R_0+\alpha_0L_1$." +" In this case. vignetting occurs after the first reflection from the primary segment of the inner shell. 1.e.. a point of the blocking shell's outer surface at z:=0. with coordinates Ko=(Ricosgo.Rosinqo.0). may intercept a ray reflected by the primary segment of the reflective shell at 7,=(rjcosqi.ri sinqgi.Zi). with ο«σιRy. we have Du>Ro. hence Zz"">0 (Eq.(BI)."," for $\theta =0$ is $\varphi_0 = \varphi_1$ and Since $R_0 > R_0^*$, we have $r_1^{(0)} > R_0$, hence $Z_1^{(0)} > 0$ (Eq.\ref{eq:cone1}) ))." + If @>0. we set 7j=mt£ qa=qup. and proceed as in Sect. ??..," If $\theta > 0$, we set $r_1 = r_1^{(0)}+\xi$ , $\varphi_0 = \varphi_1+\varepsilon$ , and proceed as in Sect. \ref{V1}. ." + The solution to a first orderapproximation is We are not interested in the exact expression of 5. which is of the order of &. so we can assume again that go=φι and neglect the y’s subseript.," The solution to a first orderapproximation is We are not interested in the exact expression of $\varepsilon$, which is of the order of $\theta$, so we can assume again that $\varphi_0 \approx \varphi_1$ and neglect the $\varphi$ 's subscript." + In contrast. from £ and Eq. (B14))," In contrast, from $\xi$ and Eq. \ref{eq:soluz0}) )" + we can derive an expression for rj. and using Eq. (BI))," we can derive an expression for $r_1$, and using Eq. \ref{eq:cone1}) )" + we obtain Z which is alwaysnon-negative., we obtain $Z_1$ which is always. + All points with z>Zi are then obstructed., All points with $z > Z_1$ are then obstructed. + The resulting vignetting coefficient is Lj. 1... using the definition of VY (Eq. (24))).," The resulting vignetting coefficient is $V_2 = Z_1/L_1$ , i.e., using the definition of $\Psi$ (Eq. \ref{eq:psi}) ))," + We have so obtained Eq. (31))., We have so obtained Eq. \ref{eq:V2_}) ). + In this case. the obscuration occurs after the second reflection. on the secondary segment of the blocking shell.," In this case, the obscuration occurs after the second reflection, on the secondary segment of the blocking shell." +" A generic point of the blocking shell at ς= -Li. dg. ny=L3). may intercept a ray after it was reflected at r,=U2cosyz.r2sings. Z:). with ο«Z»<0."," A generic point of the blocking shell at $z = -L_2^*$ , i.e., ${\underline r}_0 = (R_{\mathrm m}^*\cos\varphi_0, R_{\mathrm m}^*\sin\varphi_0, -L_2^*)$, may intercept a ray after it was reflected at $\underline{r}_2 = (r_2\cos\varphi_2, r_2\sin\varphi_2, Z_2)$ , with $-L_22$ galaxies only so that the accuracy of for these $z$ galaxies be better." + Accordingly. the accuracy Of for such low-: galaxies is not affected significantly by the optinuzation.," Accordingly, the accuracy of for such $z$ galaxies is not affected significantly by the optimization." + We compare OWL oof hieli-: galaxies in the TDF with those by Fernamudez-Soto et al. (, We compare our of $z$ galaxies in the HDF with those by Fern\'{a}nndez-Soto et al. ( +1999). which are based on the same sample and the same photometry as we use.,"1999), which are based on the same sample and the same photometry as we use." + Therefore. this is a direct comparison of the methods.," Therefore, this is a direct comparison of the methods." + Fernánudoez-Soto ct al., Fernánndez-Soto et al. + had two galaxies with catastrophic errors. while we have one.," had two galaxies with catastrophic errors, while we have one." +" The galaxy for which both of the authors eive à catastrophic error is located at 4,4=2.93.", The galaxy for which both of the authors give a catastrophic error is located at $z_{\rm spec}=2.93$. + This ealaxy is fitted by a young dusty spectrum of 0.5Cvr aud E(BVy--0.0. aud caunot be rejected by our tthreshold.," This galaxy is fitted by a young dusty spectrum of $0.5 {\rm Gyr}$ and $E(B-V)=0.5$, and cannot be rejected by our threshold." + The other galaxy which has a catastrophic error in Fernduudez-Soto’s study is rejected by the tthreshold iu our work. though it is also fitted by a dusty vouus disk SED.," The other galaxy which has a catastrophic error in Fernánndez-Soto's study is rejected by the threshold in our work, though it is also fitted by a dusty young disk SED." + Table 7. stummarizes the aaccuracy for galaxies of +>2. with catastrophic errors excluded.," Table \ref{table:soto} summarizes the accuracy for galaxies of $z>2$, with catastrophic errors excluded." + Our work gives a much improved accuracy for lieh-: galaxies., Our work gives a much improved accuracy for $z$ galaxies. + Wane. Turner. Balicall (1999) achieved σ.=0.08 and 0.30 for 2< and 2<| galaxies. respectively. which are comparable to our results.," Wang, Turner, Bahcall (1999) achieved $\sigma_z=0.08$ and $0.30$ for $z<2$ and $22-3$ by calculating the cosmic star formation rate and $E(B-V)$ values of galaxies iteratively. + Iu Figure 19((2)-(0). we see that galaxies af —2. especially for the sevenu-baud plotometiv ομωςtend to be generally estimated at lower redslüfts tha bby the three previous studies.," In Figure \ref{fig:comp}( (a)-(c), we see that galaxies at $z_{\rm spec}=2-4$, especially for the seven-band photometry, tend to be generally estimated at lower redshifts than by the three previous studies." +" We are ableza to remove this svstematic error by iucludius three values of opacity due to the interealactic Lyman absorption around the median opacity derived from Madau (1995): We imclude npe the exact value by Madeus 7,(=Orage). aud EL574)."," We are able to remove this systematic error by including three values of opacity due to the intergalactic Lyman absorption around the median opacity derived from Madau (1995): We include $\tau_{\it eff}$, the exact value by Madau, $\tau_{\it eff}^{-}(\equiv 0.5\tau_{\it eff})$, and $\tau_{\it eff}^{+}(\equiv 1.5\tau_{\it eff})$." + The systematic errors at 2=1 cluerge if we relove rs and τη aud use onlv 7.8 (Figure 21)).," The systematic errors at $z=2-4$ emerge if we remove $\tau_{\it +eff}^{+}$ and $\tau_{\it eff}^{-}$ and use only $\tau_{\it eff}$ (Figure \ref{fig:tau1}) )." + It is clear that includiug a variation of the opacity is essential., It is clear that including a variation of the opacity is essential. +" We also examine the template SEDs with 3z,g. lrg. 0.37,p. and 0.257,y. aud fud that the best combination is (7, 4.7 PP j "," We also examine the template SEDs with $\tau_{\it eff}$, $\tau_{\it +eff}$, $\tau_{\it eff}$, and $\tau_{\it eff}$, and find that the best combination is $\tau_{\it eff}$ $\tau_{\it eff}^+$ $\tau_{\it +eff}^-$ )." +We should point out that the ambieuitics of the stellar svuthesis mocel used for the template SEDs. especially those in the UV. fiux. may be coupled with the ambiguity of the internal absorption and the statistical fuctuation of the imterealactic Lyman absorption.," We should point out that the ambiguities of the stellar synthesis model used for the template SEDs, especially those in the UV flux, may be coupled with the ambiguity of the internal absorption and the statistical fluctuation of the intergalactic Lyman absorption." + If we look at Figure lr((c) best-fit 7 values seem fo chauge with redshift: τn is luore," If we look at Figure \ref{fig:param_specz}( (c), best-fit $\tau$ values seem to change with redshift: $\tau_{\it eff}^{+}$ is more" +contrary. information on Ravleigh stable Tavlor-C'óuette flows comes only [rom experiments.,"contrary, information on Rayleigh stable Taylor-Couette flows comes only from experiments." + Finally. (he shearing sheet approximation has been widely used as a local analvtic model of local accretion disks. and has been implemented in the numerical work of Balbus. Lawley and coworkers quoted in the introduction (Balbusetal.1996:Lawleyef1999).," Finally, the shearing sheet approximation has been widely used as a local analytic model of local accretion disks, and has been implemented in the numerical work of Balbus, Hawley and coworkers quoted in the introduction \citep{BHS96, HBW99}." +. For each of these flows. I characterize the geometry. the critical parameters which are important [or the question of the onset of turbulence. and I also give the governing dynamical equation (Navier-Stokes) in the form which is most suitable (to establish comparisons between (he various (vpes of flows.," For each of these flows, I characterize the geometry, the critical parameters which are important for the question of the onset of turbulence, and I also give the governing dynamical equation (Navier-Stokes) in the form which is most suitable to establish comparisons between the various types of flows." + The object of this section is (o (rv to give an answer to (he following question: il nunmerical simulations were perfect (ie.. not limited bv questions of resolution. numerical instabilities ete). would shear flows be turbulent in presence of the Coriolis lorce?," The object of this section is to try to give an answer to the following question: if numerical simulations were perfect (i.e., not limited by questions of resolution, numerical instabilities etc), would shear flows be turbulent in presence of the Coriolis force?" + This is done in section ??.. with the help of the material collected here.," This is done in section \ref{ssturb}, with the help of the material collected here." + In spite of their conceptual simplicity. plane Couette flows are difficult to produce in actual experiments. which explains why some of their basic turbulent properties have only recently been characterized.," In spite of their conceptual simplicity, plane Couette flows are difficult to produce in actual experiments, which explains why some of their basic turbulent properties have only recently been characterized." + The experimental setup is schematically represented on Fig. 4..," The experimental setup is schematically represented on Fig. \ref{fig1}," + along with a sketch of the turbulent mean flow profile (see TillmarkanclAlfredsson1992 for details)., along with a sketch of the turbulent mean flow profile (see \citealt{Till92} for details). + Ii practice the two walls are often made up of counteramoving (looped) infinite belts., In practice the two walls are often made up of counter-moving (looped) infinite belts. + Similarly. free shear lavers are produced by injecting fIuid with different velocities on each side of a separating plate.," Similarly, free shear layers are produced by injecting fluid with different velocities on each side of a separating plate." + The fluids come in contact at the end of the plate. and a turbulent laver develops ancl widens downstream (see Fig. 5)).," The fluids come in contact at the end of the plate, and a turbulent layer develops and widens downstream (see Fig. \ref{fig2}) )." + These flows are described bv (the Navier-Stokes equation in its simplest form. which reads with obvious notations.," These flows are described by the Navier-Stokes equation in its simplest form, which reads with obvious notations." + The viscous terms are displaved in (he incompressible form. as we are mostly concerned with subsonic turbulence.," The viscous terms are displayed in the incompressible form, as we are mostly concerned with subsonic turbulence." + It is customary to define (he Revnolds number of plane Couette flows based on the difference (i.e. £) and hall-width distance (i.e. ) between the (wo walls., It is customary to define the Reynolds number of plane Couette flows based on the half-velocity difference (i.e. $U$ ) and half-width distance (i.e. $h$ ) between the two walls. + ILowever. for the purpose of comparison with other setups. I shall define the Revnolds number as," However, for the purpose of comparison with other setups, I shall define the Reynolds number as" +but somewhat more slowly. ancl lags the other modes in time.,"but somewhat more slowly, and lags the other modes in time." + In the /=0 planet run. the planet develops an organized wake within about an ORP in which m»=3 is a dominant component (e5 global density perturbation).," In the $t = 0$ planet run, the planet develops an organized wake within about an ORP in which $m = 3$ is a dominant component $\sim 5$ global density perturbation)." + This nonlinear seecling causes m—3 to dominate (he GI burst. which also occurs ~ 2 ORDP earlier.," This nonlinear seeding causes $m = 3$ to dominate the GI burst, which also occurs $\sim$ 2 ORP earlier." + Because of our initial placement of the planet inside but close to the Q-minimum. the corotation radius (CR) of the a=3 mode is fairly. close to that of the planets orbit radius.," Because of our initial placement of the planet inside but close to the $Q$ -minimum, the corotation radius (CR) of the $m = 3$ mode is fairly close to that of the planet's orbit radius." + When the triggered 7»=3 mode becomes s(rouely nonlinear al about 3 ORI. planet migration is significantly afecte.," When the triggered $m = 3$ mode becomes strongly nonlinear at about 3 ORP, planet migration is significantly affected." + Figure 2 shows the evolution of the planet's radial position., Figure \ref{fig:a} shows the evolution of the planet's radial position. + From 0 to 2.5 ORI. the planet is torqued primarily by its own wake and migrates inward.," From 0 to 2.5 ORP, the planet is torqued primarily by its own wake and migrates inward." + Beginning at. about 3 ORD. the planet interacts with the now nonlinear m=3 GI mode.," Beginning at about 3 ORP, the planet interacts with the now nonlinear $m = 3$ GI mode." + At first. the planet gains angular momentum and moves outward. but. from 4 (o0 8 ORD. a time interval of about 720 vr. the plant experiences a negative torque and plunges from 23 to 17 AU.," At first, the planet gains angular momentum and moves outward, but, from 4 to 8 ORP, a time interval of about 720 yr, the plant experiences a negative torque and plunges from 23 to 17 AU." + After /=8 ORD. ihe main burst is over. and the disk transitions into ils asviptotic state. where modes of many m-values become comparably strong (see Fie. 1)).," After $t = 8$ ORP, the main burst is over, and the disk transitions into its asymptotic state, where modes of many $m$ -values become comparably strong (see Fig. \ref{fig:Am}) )." + The planets radial migration apparently stalls al about 16 to 17 AU., The planet's radial migration apparently stalls at about 16 to 17 AU. + From an analvsis of periodicities present in the gas disk between 8 and 12 ORD. the planet lies a few AU inside the inner Lindblad resonance of a strong m=2 mode with CR at 29 AU in this early part of the asymptotic phase.," From an analysis of periodicities present in the gas disk between 8 and 12 ORP, the planet lies a few AU inside the inner Lindblad resonance of a strong $m = 2$ mode with CR at 29 AU in this early part of the asymptotic phase." + The motion of the planet in this case is more difficult to interpret., The motion of the planet in this case is more difficult to interpret. + We see intervals of fairly rapid inward or outward migration over several orbits. as well as times when radial migration appears to stall.," We see intervals of fairly rapid inward or outward migration over several orbits, as well as times when radial migration appears to stall." + Between /=15 and 19 ORD. the pattern of outward migration lor 2 ORP followed by an inward plunge over the next 2 ORP resembles (he behavior in the /=0 planet run during (he burst. but. in this case. there is no distinet (transition between phases of GI activitv.," Between $t = 15$ and 19 ORP, the pattern of outward migration for 2 ORP followed by an inward plunge over the next 2 ORP resembles the behavior in the $t = 0$ planet run during the burst, but, in this case, there is no distinct transition between phases of GI activity." + Animations of the evolution of the midplane density (available at http://hdl.handle.net/2022/13304) show there is a complex interaction between the planet. its spiral wake. aud (he elobal spiral aris caused by the," Animations of the evolution of the midplane density (available at http://hdl.handle.net/2022/13304) show there is a complex interaction between the planet, its spiral wake, and the global spiral arms caused by the" +that one of the most efficient means of finding very high redshift Lye emitters is through spectroscopic surveys focused on gravitational lensing clusters.,that one of the most efficient means of finding very high redshift $\alpha$ emitters is through spectroscopic surveys focused on gravitational lensing clusters. + Lensing surveys could easily reach down to a luminosity limit of 10/ erg + in a few tens of hours., Lensing surveys could easily reach down to a luminosity limit of $10^{40.5}$ erg $^{-1}$ in a few tens of hours. + However. the surveyed volumes are very small. of the order of a hundred Μροῦ.," However, the surveyed volumes are very small, of the order of a hundred $^3$." + For a lensed survey. the area in the source plane is reduced by the same factor that the flux is amplified. so in principle one gains in the total number of objects detected relative to an unlensed survey if the luminosity function is steeper than V(>£L)xL+.," For a lensed survey, the area in the source plane is reduced by the same factor that the flux is amplified, so in principle one gains in the total number of objects detected relative to an unlensed survey if the luminosity function is steeper than $N(>L) \propto L^{-1}$." + In the GALFORM and ΤΜΟΦ models. the asymptotic faint-end slope is shallower than this. but at higher luminosities. the slope can be steeper.," In the GALFORM and TM05 models, the asymptotic faint-end slope is shallower than this, but at higher luminosities, the slope can be steeper." + For example. GALFORM predicts that at :=10. the average slope in the luminosity range 101—107? erg + is close to N(»L)xL? (see Fig.," For example, GALFORM predicts that at $z=10$, the average slope in the luminosity range $10^{41}$ $10^{42}$ erg $^{-1}$ is close to $N(>L) \propto L^{-2}$ (see Fig." + 8 in Le Delliou et al., 8 in Le Delliou et al. + 2006). so that a lensing amplification of 10 results in. 10 times more objects being detected. with intrinsic luminosities 10 times lower. compared to an unlensed survey with the same area and flux limit.," 2006), so that a lensing amplification of 10 results in 10 times more objects being detected, with intrinsic luminosities 10 times lower, compared to an unlensed survey with the same area and flux limit." + Therefore lensing and narrow-band surveys are complementary to each other as they probe different parts of the luminosity function., Therefore lensing and narrow-band surveys are complementary to each other as they probe different parts of the luminosity function. + With either type of survey. reaching a significant sample of redshift:~7 ὃ should be possible in the next few years with telescopes/instruments in use or soon available.," With either type of survey, reaching a significant sample of redshift $z +\sim 7 - 8$ should be possible in the next few years with telescopes/instruments in use or soon available." + An interesting type of object found recently in narrow-band surveys are the Lya blobs. large nebulae with diameters up to 150 kpe and Lya luminosities up to 101! erg | with or without counterpart galaxies (e.g. Steidel et al.," An interesting type of object found recently in narrow-band surveys are the $\alpha$ blobs, large nebulae with diameters up to 150 kpc and $\alpha$ luminosities up to $10^{44}$ erg $^{-1}$ with or without counterpart galaxies (e.g. Steidel et al." + 2000: Matsuda et al., 2000; Matsuda et al. + 2004: Nilsson et al., 2004; Nilsson et al. + 2006a)., 2006a). + Several mechanisms have been proposed to explain this phenomenon. including starburst galaxies and superwinds. AGN activity or cold accretion.," Several mechanisms have been proposed to explain this phenomenon, including starburst galaxies and superwinds, AGN activity or cold accretion." + It is interesting to consider if such objects would be detected in any of these surveys. assuming they exist at these redshifts.," It is interesting to consider if such objects would be detected in any of these surveys, assuming they exist at these redshifts." + A typical Lya blob will have a luminosity of ~10 eres ! and aradius of. say. 25 kpe.," A typical $\alpha$ blob will have a luminosity of $\sim 10^{43}$ erg $^{-1}$ and a radius of, say, 25 kpc." + This will result in a surface brightness of ~5«107? eres. tkpe 7.," This will result in a surface brightness of $\sim 5 +\times 10^{39}$ erg $^{-1}$ $^{-2}$." +" Thus. a narrow-band survey will have to reach a flux limit. as measured in a 2” radius aperture > 4a.,2 ερ, ∖∖ los∪↑∿↓∙⋅≩∖↓∩∟⊜∣⋪∶↔↾⋋↓∐⊓⋪⊜∐⋋∣∏⇈∶∶≺∖∙≺∖⋅∁⋯⋪∣⋪⊜⋋∣⊃∪⋯⋯⊱⊺↾∪ L—12.11.("," Thus, a narrow-band survey will have to reach a flux limit, as measured in a $2''$ radius aperture of $\sim 1.3 \times 10^{42}$ erg $^{-1}$ at redshift $z = +8.8$, corresponding to $\log{L} = 42.11$. (" +"An aperture radius of around 2"" is expected to be roughly optimal for signal-to-noise.)",An aperture radius of around $2''$ is expected to be roughly optimal for signal-to-noise.) + For lower or higher redshifts. this limit is higher or lower respectively.," For lower or higher redshifts, this limit is higher or lower respectively." + Thus. ELVIS will not be able to detect Ενα blobs unless they are brighter and/or more compact at higher redshift than a typical blob at lower redshift.," Thus, ELVIS will not be able to detect $\alpha$ blobs unless they are brighter and/or more compact at higher redshift than a typical blob at lower redshift." + DaZle and JWST could in principle detect this type of object. but only if they are very abundant in the very high redshift Universe. due to the small survey volumes of these instruments.," DaZle and JWST could in principle detect this type of object, but only if they are very abundant in the very high redshift Universe, due to the small survey volumes of these instruments." + It ts of course highly uncertain what properties such Ένα blobs would have at. 7—9. or their space density. but it appears unlikely that the future surveys presented here would detect any such objects.," It is of course highly uncertain what properties such $\alpha$ blobs would have at $z \sim 7 - 9$, or their space density, but it appears unlikely that the future surveys presented here would detect any such objects." + To find compact [δα emitters at redshifts 210 in significant numbers we will probably have to await instruments even further in the future., To find compact $\alpha$ emitters at redshifts $z \gtrsim 10$ in significant numbers we will probably have to await instruments even further in the future. + If a future 40-m ELT (Extremely Large Telescope) was equipped with a wide-field NIR imager and a narrow-band filter of similar width to ELVIS. it could reach a luminosity limit of £~10/77 erg ! at redshift 2=10.1 (where a suitably large atmospheric window exists) in approximately 20 hours.," If a future 40-m ELT (Extremely Large Telescope) was equipped with a wide-field NIR imager and a narrow-band filter of similar width to ELVIS, it could reach a luminosity limit of $L \sim 10^{41.2}$ erg $^{-1}$ at redshift $z = +10.1$ (where a suitably large atmospheric window exists) in approximately 20 hours." + Using the GALFORM model for : 10. the number density should be NC»L)z ες10 at this luminosity limit.," Using the GALFORM model for $z = 10$ , the number density should be $>$ $\approx 4 \times 10^{-3}$ $^{-3}$ at this luminosity limit." +" Thus. to get a sample of ten Ενα emitters would require imaging an area on the sky of approximately 16 square areminutes. assuming a narrow-band filter with redshift range 10.05L4 rad/aresec."," There is evidence that the actual MTF falls even faster, perhaps even reaching zero, for $k>1.4$ rad/arcsec." + Dividing the observed spectrum by expression (A)) is therefore a conservative correction at the very highest wave numbers., Dividing the observed spectrum by expression \ref{eq:MTF_empirical}) ) is therefore a conservative correction at the very highest wave numbers. + While (his cross comparison provides the ratio of the (wo ΛΕΤΕ. it cannot give any inlormation about either one alone.," While this cross comparison provides the ratio of the two MTFs, it cannot give any information about either one alone." + The most conservative correction to either specirun is to assume (he high-resolution mode is diffraction limited and in perlect focus., The most conservative correction to either spectrum is to assume the high-resolution mode is diffraction limited and in perfect focus. + In this case iis MEE would be (GhatakandThyagarajan1973) where Aj=2zd/Ax;5.63rad/arcsec/ for a primary mirror of diameter. d|uMIeVT E=," In this case its MTF would be \citep{Ghatak1978} + (k) = M_d(k) = ) - ], where $k_0=2\pi d/\lambda_{\rm Ni} = +5.63\,{\rm rad/arcsec}$ for a primary mirror of diameter, $d=12.5$ cm" +Starburst galaxies provide us with the opportunity to study star formation and its effect on the interstellar medium (ISM) in extreme environments.,Starburst galaxies provide us with the opportunity to study star formation and its effect on the interstellar medium (ISM) in extreme environments. + These galaxies combine large central gas concentrations and high ionizing radiation fields. resulting in bright molecular. neutral and tonized gas emission lines.," These galaxies combine large central gas concentrations and high ionizing radiation fields, resulting in bright molecular, neutral and ionized gas emission lines." + At a distance of 3.9 Mpe (Sakai&Madore1999).. is the most well-studied starburst galaxy in the local universe. and it is widely used as a starburst prototype in cosmological studies.," At a distance of 3.9 Mpc \citep{sakai99}, is the most well-studied starburst galaxy in the local universe, and it is widely used as a starburst prototype in cosmological studies." + Its infrared luminosity (5.6 10161... corresponds to a star-formation rate of 9.8 Μ.. γι]. which has almost certainly been enhanced by its interaction with and (Yunetal.1902].," Its infrared luminosity \citep[$5.6\times 10^{10}$ $_\odot$ corresponds to a star-formation rate of 9.8 $_\odot$ $^{-1}$, which has almost certainly been enhanced by its interaction with and \citep{yun93}." + With à reported molecular gas content of 1.3x10° M. (Walteretal.2002). its bright emission lines of CO and other molecules allow us to study its ISM in great detail 2003)..," With a reported molecular gas content of $1.3 \times 10^9$ $_\odot$ \citep{walter02}, its bright emission lines of CO and other molecules allow us to study its ISM in great detail \citep{shen95,walter02,ward03}. ." +the local rms of the continuume-subtracted spectra.,the local rms of the continuum-subtracted spectra. + These are considered to be broad-line AGNg, These are considered to be broad-line AGN. +alaxies? There are 32 narrow emission-line. ULIRGs.. for which more than two line ratios 111]A5007 aand at [east one of i1]A6584/Ho... SUJAAGTIT.6731/Lla.. and 6300 /110)) were measured. (hereafter Sample A).," There are 32 narrow emission-line ULIRGs for which more than two line ratios $\lambda5007$ and at least one of $\lambda6584$, $\lambda \lambda6717,6731$, and $\lambda6300$ ) were measured (hereafter Sample A)." + In Fie., In Fig. + 2. we show the diagnostic diagrams for these ULIRGs and divide them into star-forming. (starburst-AGN) composite. ancl narrow-line AGN galaxies based on their loci in the diagrams.," 2, we show the diagnostic diagrams for these ULIRGs and divide them into star-forming, (starburst-AGN) composite, and narrow-line AGN galaxies based on their loci in the diagrams." + Star-forming galaxies lie below the pure star formation line (Ixaulfmann et al., Star-forming galaxies lie below the pure star formation line (Kauffmann et al. + 2003) in the deiagramu]j/ and lic below the extreme starburst line (Ixewlevy et al., 2003) in the diagram and lie below the extreme starburst line (Kewley et al. + 2001) in other diagrams., 2001) in other diagrams. + Composite galaxies lic between the extreme starburst line and. the pure. star formation line in the deiagram., Composite galaxies lie between the extreme starburst line and the pure star formation line in the diagram. + Narrow-line ACGNs lie above the extreme starburst line in all three diagrams., Narrow-line AGNs lie above the extreme starburst line in all three diagrams. + Whenever possible. narrow-line AGNs are subdivided into Sevfert 2 and. low ionization narrow emission-line. region. (LINER) galaxies.," Whenever possible, narrow-line AGNs are subdivided into Seyfert 2 and low ionization narrow emission-line region (LINER) galaxies." + Sev[ert 2 galaxies lie above the Sevfert-LINIZB. classification lines (Ixewley et al., Seyfert 2 galaxies lie above the Seyfert-LINER classification lines (Kewley et al. + 2006) in the aan deiagrams. whereas LINERS lie below the lines.," 2006) in the and diagrams, whereas LINERs lie below the lines." + For ambiguous galaxies that are classified as one tvpe in two diagrams but another type in the remaining diagram. we adopt the types that are given in the first two diagrams.," For ambiguous galaxies that are classified as one type in two diagrams but another type in the remaining diagram, we adopt the types that are given in the first two diagrams." + There are 75 narrow emission-lino. ULIliCis without measurable ine mainly because falls outside the spectral coverage (hereafter Sample 1)., There are 75 narrow emission-line ULIRGs without measurable line mainly because falls outside the spectral coverage (hereafter Sample B). + These galaxies could not be. classified in the diagnostic iagrams so that we attempt to classify them in Dux ratio tween. aand ines versus ine width diagram as demonstrated in Fig., These galaxies could not be classified in the diagnostic diagrams so that we attempt to classify them in flux ratio between and lines versus line width diagram as demonstrated in Fig. + 3., 3. + Zakamska, Zakamska +maps (though this is entirely negligible). and apply a k-correction ofh(:)-Glog(1|z). following ?..,"maps (though this is entirely negligible), and apply a k-correction of $k(z)=-6\log(1+z)$, following \citet{Kochanek-KLF}." + For our most distant cluster. therefore. we are complete in luminosity for My«—23.5.," For our most distant cluster, therefore, we are complete in luminosity for $M_K<-23.5$." + First. we present the cumulative luminosity function from the combination of all eleven clusters with follow-up NIR data.," First, we present the cumulative luminosity function from the combination of all eleven clusters with follow-up NIR data." +" We include all galaxies with redshifts within 1500 km/s of the cluster redshift. and within a distance /2,4,, from thecentre."," We include all galaxies with redshifts within 1500 km/s of the cluster redshift, and within a distance $R_{\rm rms}$ from the." +".. We show the weighted number of galaxies brighter than a given AJ, absolute magnitude. per cluster in Figure 4.."," We show the weighted number of galaxies brighter than a given $M_k$ absolute magnitude, per cluster in Figure \ref{fig-totallf}." + Plotted for comparison are Schechter functions with Adj;=— 24.3(2) anda=0.5 (solid ora—1.0 (dashed)., Plotted for comparison are Schechter functions with $M_K^\ast=-24.3$ \citep{IRLF} and $\alpha=-0.5$ (solid) or $\alpha=-1.0$ (dashed). + These are not fit to the data. but are meant only to guide the eye.," These are not fit to the data, but are meant only to guide the eye." + The presence of central bright galaxies in most of our clusters leads to an excess relative to the Schechter function. at the bright end. as is seen in more massive clusters (e.g. ?)..," The presence of central bright galaxies in most of our clusters leads to an excess relative to the Schechter function, at the bright end, as is seen in more massive clusters \citep[e.g.][]{Popesso-II}." + Recall that. for Adj>—23.5 our sample is incomplete. and this limit is indicated by the dotted line.," Recall that, for $M_K>-23.5$ our sample is incomplete, and this limit is indicated by the dotted line." + We now proceed to calculate the total /& luminosity of each cluster. Li.," We now proceed to calculate the total $K$ luminosity of each cluster, $L_K$." + We simply sum the luminosity of all galaxies within 1500 km/s and Aya. of the cluster centre. brighter than the A. limit.," We simply sum the luminosity of all galaxies within 1500 km/s and $R_{\rm rms}$ of the cluster centre, brighter than the $K=14.5$ limit." + To correct for galaxies below this limit we model the luminosity function as a Schechter function with AJ;=—24.3 and a=1.0., To correct for galaxies below this limit we model the luminosity function as a Schechter function with $M_k^\ast=-24.3$ and $\alpha=-1.0$. + As our data reach at least 0.6 mag fainter than Ad; for all clusters. this correction is always less than20%..," As our data reach at least 0.6 mag fainter than $M_k^\ast$ for all clusters, this correction is always less than." + We also include the seven clusters without deeper NIR data in our analysis: these are shown as open symbols on the following Figures., We also include the seven clusters without deeper NIR data in our analysis; these are shown as open symbols on the following Figures. + For these clusters. the 2MASS limiting magnitude is much brighter. A.«18.7. and for three of them the corresponding correction for fainter galaxies is larger than a factor of two.," For these clusters, the 2MASS limiting magnitude is much brighter, $K<13.7$, and for three of them the corresponding correction for fainter galaxies is larger than a factor of two." + We do not attempt to measure or correct for intracluster light., We do not attempt to measure or correct for intracluster light. + This remains an important uncertainty in all such work. with some claims that a large fraction of the stars in galaxy groups are found in this component (2?)..," This remains an important uncertainty in all such work, with some claims that a large fraction of the stars in galaxy groups are found in this component \citep{GZZ1,McGee-ICL}." + For clusters in the mass range of our sample. however. we expect the intracluster light contribution to be less than about 20 per cent (e.g.2y..," For clusters in the mass range of our sample, however, we expect the intracluster light contribution to be less than about 20 per cent \citep[e.g.][]{Zibetti}." + The statistical. uncertainty on Ly is dominated by the statistical uncertainty on Ais. since that quantity determines the radius within which the luminosity is," The statistical uncertainty on $L_K$ is dominated by the statistical uncertainty on $R_{\rm rms}$, since that quantity determines the radius within which the luminosity is." +"integrated=.. In Figure 5 we show the cumulative luminosity as a function of rfi. only including clusters observed out to /77,,.. with AAT. CTIO or CFHT."," In Figure \ref{fig-dLkdr} we show the cumulative luminosity as a function of $r/R_{\rm rms}$, only including clusters observed out to $R_{\rm rms}$, with AAT, CTIO or CFHT." + The best-tit line to the data where {τμ<1 has a slope of 0.63., The best-fit line to the data where $R/R_{\rm rms}<1$ has a slope of $0.63$ . +" Thus. the statistical uncertainty on Ly: is only O.63ALRBus which. given the typical 10 per cent uncertainty on f/,.. corresponds to a 6 per cent uncertainty on Ly."," Thus, the statistical uncertainty on $L_K$ is only $\sim 0.63\Delta R/R_{\rm rms}$ which, given the typical 10 per cent uncertainty on $R_{\rm rms}$, corresponds to a $\sim 6$ per cent uncertainty on $L_K$." + In contrast. the typical uncertainty on Aou is 20—40 per cent. as it is proportional to 0 (see 22).," In contrast, the typical uncertainty on $M_{200}$ is 20–40 per cent, as it is proportional to $\sigma^3$ (see \ref{sec-obs}) )." + We use this relation for Ly:(2) to correct thetotal luminosity of those clusters for which NIR coverage only extends out tor< Aya., We use this relation for $L_K(R)$ to correct thetotal luminosity of those clusters for which NIR coverage only extends out to $r10MALv D)," When the opacity by the condensed ice is taken into consideration, we have found that the snow line location is shifted outwardly for the disk in the inward migration phase $\dot{M} \gtrsim 10^{-10}M_{\odot}\mathrm{yr^{-1}}$ )." + This is due to the additional blanket effect by the condensed ice particles in the upper laver of the disk., This is due to the additional blanket effect by the condensed ice particles in the upper layer of the disk. +" The shift ratio of the snow line (fai = Daewil/ sisi) Varies with the dust grain size: fa,=1.3 for the grain <10jan and [sy=1.6 for the grain 2100jmi."," The shift ratio of the snow line $f_{\rm SL} $ $=$ $ R_{\rm SL,ice+sil}/R_{\rm SL,sil}$ ) varies with the dust grain size: $f_{\rm SL}= 1.3$ for the grain $\lesssim 10\mathrm{\mu m}$ and $f_{\rm SL} = 1.6$ for the grain $\gtrsim 100\mathrm{\mu m}$." +" Our semi-analvtical estimation has shown that fai, increases with the water abundance in the disk gas around the snow line.", Our semi-analytical estimation has shown that $f_{\rm SL}$ increases with the water abundance in the disk gas around the snow line. + However. the snow line shift due {ο (he ice opacity is small compared to the total migration length during the disk evolution. ancl is limited in the early phase of the disk evolution.," However, the snow line shift due to the ice opacity is small compared to the total migration length during the disk evolution, and is limited in the early phase of the disk evolution." + The additional ice opacity does not change the snow line location of the disk in the outward migration phase., The additional ice opacity does not change the snow line location of the disk in the outward migration phase. + A vertically increasing temperature profile under the irradiation bv the central star prevents water molecules [rom condensing in the upper laver of the disk., A vertically increasing temperature profile under the irradiation by the central star prevents water molecules from condensing in the upper layer of the disk. + We have also found that the snow line comes inside the Earth's orbit as long as the dust-to-gas mass ratio is higher than about a tenth of the solar abundance. the viscosity parameter a is 0.001a<0.1. and the dust grain size is smaller than 1 mim.," We have also found that the snow line comes inside the Earth's orbit as long as the dust-to-gas mass ratio is higher than about a tenth of the solar abundance, the viscosity parameter $\alpha$ is $0.001\lesssim \alpha \lesssim 0.1$, and the dust grain size is smaller than 1 mm." + Then. if one thinks that terrestrial planets should be formed from water-devoid planetesimals. the dust grain growth should occur either before the snow line comes inside the Earth's orbit or alter the snow line passes outward the Earth's orbit.," Then, if one thinks that terrestrial planets should be formed from water-devoid planetesimals, the dust grain growth should occur either before the snow line comes inside the Earth's orbit or after the snow line passes outward the Earth's orbit." + In the latter case. the formation οἱ waler-devoil planuetesimals is impossible because of the deficit of solid mass (855.2).," In the latter case, the formation of water-devoid planetesimals is impossible because of the deficit of solid mass 5.2)." + In the former case. the dust grain growth should be completed within 1 yr because the snow line migrates inwardly with this timescale.," In the former case, the dust grain growth should be completed within 1 yr because the snow line migrates inwardly with this timescale." +with the A-band flux: this result is consistent with previous analysis of GIRS 19154105 2001c)..,with the $K$ -band flux; this result is consistent with previous analysis of GRS 1915+105 \citep{Greiner:2001uq}. + The correlation coelficieuts obtained are r=0.191 and 0.330. respectively. so the Ihiurdness correlation is stronger.," The correlation coefficients obtained are $r = 0.194$ and $0.330$, respectively, so the IR/hardness correlation is stronger." + Both correlation coelficieuts are found to be different from zero αἱ a p-level below LO° (Bevington&Robinson1992.p.200).. indicating that our result is statistically significant.," Both correlation coefficients are found to be different from zero at a $p$ -level below $10^{-6}$ \citep[p.200]{Bevington:1992uq}, indicating that our result is statistically significant." + The relation between A-baud flux aud X-ray. larduess ratio is depicted iu Figure 3.., The relation between $K$ -band flux and X-ray hardness ratio is depicted in Figure \ref{scatter}. + ]t is clear [rom figure 3. that there is no significant correlation at large A-baud flux., It is clear from figure \ref{scatter} that there is no significant correlation at large $K$ -band flux. + Since the correlation is established entirely by the points with low A flux. our linear fit to the full data set is not physically relevant.," Since the correlation is established entirely by the points with low $K$ flux, our linear fit to the full data set is not physically relevant." + This suggests that there are several sources of IR flux. not all of which are correlated with the X-ray. properties of the source.," This suggests that there are several sources of IR flux, not all of which are correlated with the X-ray properties of the source." + Thermal IR. flux. from the outer parts of the accretion disk is expected to correlate with the X-rays. since both depend ou the aceretion flow through the disk.," Thermal IR flux from the outer parts of the accretion disk is expected to correlate with the X-rays, since both depend on the accretion flow through the disk." + On the other haud. large uon-thermal IR. flares without au easily observed N-ray response have been reported in several other transients Jainetal. 2001)..," On the other hand, large non-thermal IR flares without an easily observed X-ray response have been reported in several other transients \citep{Buxton:2004zr,Jain:2001ly}." + We therefore suggest that the IR flux observed in GRS 1915+105 includes both a thermal component associated with the disk. aud occasionally larger. possibly uwou-thermal emission uncorrelated with the N-rays.," We therefore suggest that the IR flux observed in GRS 1915+105 includes both a thermal component associated with the disk, and occasionally larger, possibly non-thermal emission uncorrelated with the X-rays." + We also expect a contribution from the secoudary star. which will be cliscussect iu more detail in the uext section.," We also expect a contribution from the secondary star, which will be discussed in more detail in the next section." + Uufortunately. our ability to interpret the IR flux in greater cletail is linited by the fact that we have IR observatious in only one baud. aud so have no IR color information.," Unfortunately, our ability to interpret the IR flux in greater detail is limited by the fact that we have IR observations in only one band, and so have no IR color information." +" Conversion of our LR observations iuto frequency space. CLEANed aud cut at 12.5 mae. reveals a significant.e peak correspondingOm to a period of [5,4p—30.8+0.2 days."," Conversion of our IR observations into frequency space, CLEANed and cut at 12.5 mag, reveals a significant peak corresponding to a period of $P_{orb} = 30.8 \pm 0.2$ days." + The error is estimated by fitting a Gaussian to tlie frequency. spectrum atthe peak frequency. aud taking the standard deviation of the fit to be the associated error e., The error is estimated by fitting a Gaussian to the frequency spectrum atthe peak frequency and taking the standard deviation of the fit to be the associated error $\sigma$. + Monte Carlo statistical testing over 2000 trials vields a siguilicauce level of the period that is iudistinguisliable from 1., Monte Carlo statistical testing \citep{Nemec:1985fk} over $5000$ trials yields a significance level of the period that is indistinguishable from $1$. + Foldiug and biuniug the data according to phase at this period makes the periodic structure manifest in the time domain (see Figure L.), Folding and binning the data according to phase at this period makes the periodic structure manifest in the time domain (see Figure \ref{foldphase}. .) + Furthermore. our period agrees to «20 with previous spectroscopic observations of GRS 19154105. which determined an observed period of 33.5+1.5 days (Creiueretal.2001a)..," Furthermore, our period agrees to $< 2 \sigma$ with previous spectroscopic observations of GRS 1915+105, which determined an observed period of $33.5 \pm 1.5$ days \citep{Greiner:2001kx}." + For Pop=30.8 days. we find that our phase corresponds to a point of minium brightness at NLID 53915.7-0.2.," For $P_{orb} = 30.8$ days, we find that our phase corresponds to a point of minimum brightness at MJD $53945.7 \pm 0.2$." + Early in our ligit curve. minimum brightuess occurred at MJD 51666.5+0.2. in extremely good. agreement with the blue-to-red. radial velocity crossing observed by at MJD 251666 41.5.," Early in our light curve, minimum brightness occurred at MJD $51666.5 \pm 0.2$, in extremely good agreement with the blue-to-red radial velocity crossing observed by \cite{Greiner:2001kx} at MJD $51666 \pm 1.5$ ." + This agreement is consistent. with iuterpretatiou of the orbital inoculation as being due to the heated face of the secoucary star., This agreement is consistent with interpretation of the orbital modulation as being due to the heated face of the secondary star. +The distribution of orbital periods for binary stus in our sample is shown in Fie. &..,The distribution of orbital periods for binary stars in our sample is shown in Fig. \ref{periodsbin_pic}. + The periods of spectroscopic pairs are taken [rom Goldbereetal.(2002) and al. (2002)., The periods of spectroscopic pairs are taken from \citet{goldberg_2002} and \citet{latham_2002}. +. The periods of astrometric pairs were derived with the help of the generalized Kepler's third law on (he basis of an empirical relation of the projected angular separation between (he components ancl (he semi-major axis., The periods of astrometric pairs were derived with the help of the generalized Kepler's third law on the basis of an empirical relation of the projected angular separation between the components and the semi-major axis. + Knowing the svstem’s parallax π ancl the projectedangular separation between the components p. the expected value of the semi-major axis is calculated using the formula from Allenetal.(2000) where (d) is expressed in astronomical units. p and π in arcseconds.," Knowing the system's parallax $\pi$ and the projectedangular separation between the components $\rho$, the expected value of the semi-major axis is calculated using the formula from \citet{allen} + where $\left\langle a \right\rangle$ is expressed in astronomical units, $\rho$ and $\pi$ in arcseconds." + Taking each svstem individually. we derived the sum mass of the components [rom the temperatures ol the primary (CLLA) and secondary components. and from the magnitude difference. if the temperature of the secondary was unknown.," Taking each system individually, we derived the sum mass of the components from the temperatures of the primary (CLLA) and secondary components, and from the magnitude difference, if the temperature of the secondary was unknown." + To do (this. we used models from (1997)..," To do this, we used models from \citet{baraffe}." + Angular distances p between the components of astrometric pairs were obtained [rom speckle interferometric observations or adopted [from Allenetal.(2000) and ZapateroOsorio&Martin(2004).," Angular distances $\rho$ between the components of astrometric pairs were obtained from speckle interferometric observations or adopted from \citet{allen} + and \citet{zapatero}." +. If the svstems parallaxes were known [rom theHIPPARCOS catalog wilh an accuracy of better than 30%. we used them instead of the distances cited in (he CLLA catalog.," If the systems parallaxes were known from the catalog with an accuracy of better than $30\%$, we used them instead of the distances cited in the CLLA catalog." + As a result. we were able to determine the periods for 60 binary svstems oul of G4 in our sample.," As a result, we were able to determine the periods for 60 binary systems out of 64 in our sample." + The periods for the four remaining suspected binary svstenis. and and two blue stragglers. and (Carneyοἱal.2001).. are too long to be determined (Latham2008).," The periods for the four remaining suspected binary systems, — and and two blue stragglers, and \citep{carney_2001}, are too long to be determined \citep{latham_pc}." +. The period distribution for GO binaries aud 10 multiple svstems (18 subsystems of 9 (triple stars and 3J) subsystems of a quadruple star G839-14). is shown in Fig. 9..," The period distribution for 60 binaries and 10 multiple systems (18 subsystems of 9 triple stars and 3 subsystems of a quadruple star G89-14), is shown in Fig. \ref{periodsall_pic}. ." + The distributions corrected for Opik effect and unresolved components on Fig., The distributions corrected for $\mathrm{\ddot{O}}$ pik effect and unresolved components on Fig. + δ and 9 are marked bv a solid, \ref{periodsbin_pic} and \ref{periodsall_pic} are marked by a solid +X-ray observations of flows in clusters of hhave shown evidence of large masses of intrinsic X-ray absorbing material (White et al.,X-ray observations of s in clusters of have shown evidence of large masses of intrinsic X-ray absorbing material (White et al. + 1991: Allen ct al., 1991; Allen et al. + 1993: Allen Fabian 1997)., 1993; Allen Fabian 1997). + The X-ray spectra show excess photocleetric absorption over that detected in our Galaxy. and require an absorbing column of 101 ccovering the core of the cluster out to at least 100 κρο.," The X-ray spectra show excess photoelectric absorption over that detected in our Galaxy, and require an absorbing column of $\sim 10^{21}$ covering the core of the cluster out to at least $\sim 100$ kpc." + The absorbing material is probably in the form of cold clouds embedded in the ((White et al., The absorbing material is probably in the form of cold clouds embedded in the (White et al. + 1991: Ferlanc. Fabian Johnstone 1994).," 1991; Ferland, Fabian Johnstone 1994)." + The total amount of cole mass ranges [rom 107 to more than 1077.12M.., The total amount of cold mass ranges from $\sim 10^{11}$ to more than $10^{12}$. +. EThese masses are in. good agreement with those expected to accumulate from the Lows if the present deposition rates determined. from. deprojection of X-ray brightness profiles have been maintained during several Civr., These masses are in good agreement with those expected to accumulate from the s if the present deposition rates determined from deprojection of X-ray brightness profiles have been maintained during several Gyr. +. Only smaller masses of gas below X-rav-emitting temperatures have been derived [rom observations at wavelengths other than X-rays., Only smaller masses of gas below X-ray-emitting temperatures have been derived from observations at wavelengths other than X-rays. + Up to 107. oof ionized gas at ~10 IX is present in some clusters within the inner few kpc. in the form of optical line-emitting filaments (Lleckman et al.," Up to $^8$ of ionized gas at $\sim 10^4$ K is present in some clusters within the inner few kpc, in the form of optical line-emitting filaments (Heckman et al." +" 1989). although masses 5 müght be possible with a sufficieutlv large array of racio dishes., Detecting 21-cm emission at $z > 5$ might be possible with a sufficiently large array of radio dishes. + The Lya absorption from the neutral ICM prior to reionization might show up in high-: spectra of quasars at 2&5., The $\alpha$ absorption from the neutral IGM prior to reionization might show up in $z$ spectra of quasars at $z \approx 5$. + To probe even higher redshifts. one wight consider searches for redshifted metal finc-structure lines such as [C II| 155700 and [0 T| μαι. which would appear at (1.6πι)|2/10] aud (630μι.|:)/10].," To probe even higher redshifts, one might consider searches for redshifted metal fine-structure lines such as [C II] $\mu$ m and [O I] $\mu$ m, which would appear at $(1.6~{\rm mm})[(1+z)/10]$ and $(630~\mu{\rm m})[(1+z)/10]$." + The standard (CDM) model of galaxy formation predicts a “bottom-up hierarcliv of structure formation., The standard (CDM) model of galaxy formation predicts a “bottom-up” hierarchy of structure formation. + Tf clumps of 10°¢A. οτι massive stars at 23. μον could have significant effects on Lyman continua raciation. hot eas. and rcavy-clement trausport.," If clumps of $10^{5-7}~M_{\odot}$ form massive stars at $z > 3$, they could have significant effects on Lyman continuum radiation, hot gas, and heavy-element transport." + If the sub-chuups form in the halos of proto-galaxies. or fall iu gravitationallv. cloud-cloud collisions are likely to occur.," If the sub-clumps form in the halos of proto-galaxies, or fall in gravitationally, cloud-cloud collisions are likely to occur." + What are he implications of the resulting shock waves for hne profiles of Me II aud CIV absorbers?, What are the implications of the resulting shock waves for line profiles of Mg II and C IV absorbers? + Shocks will generate hot gas at Tzz(107K)|[V/100gns.2. sufficient to produce € IV by collisional ionization.," Shocks will generate hot gas at $T \approx (10^5~{\rm K})[V/100~{\rm km~s}^{-1}]^2$, sufficient to produce C IV by collisional ionization." + Are the observed line xofiles evidence for such effects?, Are the observed line profiles evidence for such effects? +" Finally, we heard severalspeakers speculate on the formation of large eas disks iu the context of damped ἵνα absorbers."," Finally, we heard severalspeakers speculate on the formation of large gas disks in the context of damped $\alpha$ absorbers." + Are these DLAs actually hick disks of 30 kpe size or 58 Ispe clumps as predicted by some nuuerical nodelers?, Are these DLAs actually thick disks of 30 kpc size or 5–8 kpc clumps as predicted by some numerical modelers? + If the DLAs are as small as 58 kpc. it mav be difficult to understand heir frequency. dAfds. aud there may be au augular momentum probler.," If the DLAs are as small as 5–8 kpc, it may be difficult to understand their frequency, $d{\cal N}/dz$, and there may be an angular momentum problem." + Following the implications of the CDM scenario. how are the small pieces of xoto-galaxies assembled?," Following the implications of the CDM scenario, how are the small pieces of proto-galaxies assembled?" + What are the roles of radiative cooling aud clap mergers?, What are the roles of radiative cooling and sub-clump mergers? + I conclude this review with lists of ideas and scicutific tools for workers in our field., I conclude this review with lists of ideas and scientific tools for workers in our field. + I have given separate discussions for observers and theorists., I have given separate discussions for observers and theorists. + 1 coutiuue to be amazed by the beauty of the WIRES spectra taken by theTelescope., I continue to be amazed by the beauty of the HIRES spectra taken by the. +" These new optical data havechanged the field of QSO absorption lues in so many areas,", These new optical data havechanged the field of QSO absorption lines in so many areas. + My first wish is that the new 10’ telescopes aud spectroerapls become sufficicutly productive to compete withNeck., My first wish is that the new $^m$ telescopes and spectrographs become sufficiently productive to compete with. + Eveu though many astronomers are actively using[νου for QSO studies. we cau foresce the time when several new telescopes come ou Lue: the Telescope. the VET. aud Gemdáni.," Even though many astronomers are actively using for QSO studies, we can foresee the time when several new telescopes come on line: the , the , and ." +5truciu BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures 12pt,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt} + = 12pt" +5truciu BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures 12pt-,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt} + = 12pt" +It is useful to consider the contribution of common-envelope survivors aud bbinaries separately.,It is useful to consider the contribution of common-envelope survivors and binaries separately. + To estimate the value of each term. we average over the results lor the simulations described above.," To estimate the value of each term, we average over the results for the simulations described above." + First. we note (hat simulation 1 is more appropriate for an old population in which the white dwarls would have long-ago formed [from (he primary stars in binaries wilh secondaries as massive as the (targets.," First, we note that simulation 1 is more appropriate for an old population in which the white dwarfs would have long-ago formed from the primary stars in binaries with secondaries as massive as the targets." + Sinnuation 2 applies to intermediate-age populations., Simulation 2 applies to intermediate-age populations. + We average (he resulls οἱ these (wo simulations., We average the results of these two simulations. + In each case we average over (he common envelope elliciency factors and also over the prescription lor the value ol 9. and Including stellar svstems wilh higher mutiplicity would increase (he numbers of systems with white chvarls in close orbits., In each case we average over the common envelope efficiency factors and also over the prescription for the value of $\delta.$ and Including stellar systems with higher mutiplicity would increase the numbers of systems with white dwarfs in close orbits. + The calculations described above suggest that.Aepler may identily transits in roughly a thousand mass-transler end states., The calculations described above suggest that may identify transits in roughly a thousand mass-transfer end states. + Each case provides a unique way to measure the white cwarf radius. luminosity and temperature. and even to explore its atmosphere.," Each case provides a unique way to measure the white dwarf radius, luminosity and temperature, and even to explore its atmosphere." + This is all in addition to the standard: “bag of tricks” that can be applied (to any. while dwarf in a binary., This is all in addition to the standard “bag of tricks” that can be applied to any white dwarf in a binary. + The ability to conduct. a large number of such studies in a uniform wav will determine the properties of the white dwarfs in terms of the mass lost historv of their progenitors., The ability to conduct a large number of such studies in a uniform way will determine the properties of the white dwarfs in terms of the mass lost history of their progenitors. + With regard to mass loss histories.Aepler studies will establish the relative Irequency of common envelope evolution and provide useful data points for determining the best way lo compute common envelope evolution in terms of the properties of the binary at the time (he dynamical instability was triggered.," With regard to mass loss histories, studies will establish the relative frequency of common envelope evolution and provide useful data points for determining the best way to compute common envelope evolution in terms of the properties of the binary at the time the dynamical instability was triggered." + The range of svstems producing stable mass transfer will also be better understood. including the all-important fraction. 2. of material (hat can be retained by: a main-sequence accretor.," The range of systems producing stable mass transfer will also be better understood, including the all-important fraction, $\beta,$ of material that can be retained by a main-sequence accretor." + Most of (heAepler stars ave field stars., Most of the stars are field stars. + Studvyiug, Studying +The plots are colour-coded to show the behaviour of the gas in the inner aresecond (red). the inner 5 areseconcls (orange). and outside the inner 5 areseconds (blue).,"The plots are colour-coded to show the behaviour of the gas in the inner arcsecond (red), the inner 5 arcseconds (orange), and outside the inner 5 arcseconds (blue)." + Whils the distribution just after the collision is fairly spread. ou for all the three regions. we note a clear dillerence at later times.," Whilst the distribution just after the collision is fairly spread out for all the three regions, we note a clear difference at later times." + In. particular. the innermost dise occupies à region positioned in between the two clouds! original positions.," In particular, the innermost disc occupies a region positioned in between the two clouds' original positions." + | is also the least spread: out structure. defining a thin disc which is only slightly warped by /=1000.," It is also the least spread out structure, defining a thin disc which is only slightly warped by $t=1000$." +" The innermos disc orientation does evolve with time. however. as we note already in οον, since matter infall on the cise continues throughout the simulation."," The innermost disc orientation does evolve with time, however, as we noted already in \ref{sec:overall}, since matter infall on the disc continues throughout the simulation." +" The eas coloured. in orange demonstrates à greater extent of warping. and the region outside this (2 5"") cannot even be classified into a single structure (cf."," The gas coloured in orange demonstrates a greater extent of warping, and the region outside this $> 5''$ ) cannot even be classified into a single structure (cf." + Figure 1)., Figure \ref{fig:S1overview}) ). + Nevertheless. it is clear that the inner and outer gas distributions are similarlv oriented with respect to cach other. with the majority of the outer gas angular momentum distributed in @ and © between the initial values of the cloucs.," Nevertheless, it is clear that the inner and outer gas distributions are similarly oriented with respect to each other, with the majority of the outer gas angular momentum distributed in $\theta$ and $\phi$ between the initial values of the clouds." +(1999) simulate the formation of a DII (and not a NS). and the strong disk wind is formed onlv when the collapsing core is rapidly rotating.,"(1999) simulate the formation of a BH (and not a NS), and the strong disk wind is formed only when the collapsing core is rapidly rotating." + Ixohri et al. (, Kohri et al. ( +2005) conducted a study of disk wind in CCSN. where the central object is à NS.,"2005) conducted a study of disk wind in CCSN, where the central object is a NS." + Llere again. (he wind comes from an extended region in the disk. ancl it is less efficient Chat the expected [ast jets blown from (he verv inner region of (he disk.," Here again, the wind comes from an extended region in the disk, and it is less efficient that the expected fast jets blown from the very inner region of the disk." + More over. to form (heir proposed disk wind. Ixohri et al. (," More over, to form their proposed disk wind, Kohri et al. (" +2005)Hr require the progenitors core to rotate very. rapidly. as (μον form the accretion disk earlier (han in the present model.,"2005) require the progenitor's core to rotate very rapidly, as they form the accretion disk earlier than in the present model." + start with a list of assumptions (hat has a one to one correspondence wilh the the list of assuniptions that I used in paper 2 for the explanation of SMDII-bulge masses correlation in galaxies., I start with a list of assumptions that has a one to one correspondence with the the list of assumptions that I used in paper 2 for the explanation of SMBH-bulge masses correlation in galaxies. + Dillerent are the tvpical values used. as here I deal with a CCSN.," Different are the typical values used, as here I deal with a CCSN." + Like. e.g. Couch οἱ al. (," Like, e.g., Couch et al. (" +2009). I assume that about a Chancrasekhar mass has already. collapsed and formed the almost final neutron star. will an escape velocity of e0.5e: E don't deal with (he first stage of the collapse that forms the compact object.,"2009), I assume that about a Chandrasekhar mass has already collapsed and formed the almost final neutron star, with an escape velocity of $v_{\rm esc} \simeq 0.5c$; I don't deal with the first stage of the collapse that forms the compact object." +Langer 2000. Aikawa et al.,"Langer 2000, Aikawa et al." + 2002)., 2002). + In the clisk midplane. which contains most of the mass. the combination of high densities aud low temperatures results in nearly all trace molecules sticking to grain surfaces and disappearing from the gas.," In the disk midplane, which contains most of the mass, the combination of high densities and low temperatures results in nearly all trace molecules sticking to grain surfaces and disappearing from the gas." + At the disk surface. the molecules are photo-dissociated.," At the disk surface, the molecules are photo-dissociated." + In. between. below the surface. is a laver (hat is warm and shielded from stellar radiation and activity. where molecules survive and abundances peak.," In between, below the surface, is a layer that is warm and shielded from stellar radiation and activity where molecules survive and abundances peak." + The TW Iva disk structure and chemistry has been considered in detail by van Zadelholt et al. (, The TW Hya disk structure and chemistry has been considered in detail by van Zadelhoff et al. ( +2001). whose model calculations suggest that the depletion of species like CO and results [rom a combination of photodissociation in (the warm surface lavers and Ireezing-out in the cold. dense parts of the disk.,"2001), whose model calculations suggest that the depletion of species like CO and $^+$ results from a combination of photodissociation in the warm surface layers and freezing-out in the cold, dense parts of the disk." +" In these models. the molecular emission largely originates [rom the region just below the disk surface where the — abundance climbs to a few times 10.10,"," In these models, the molecular emission largely originates from the region just below the disk surface where the $^+$ abundance climbs to a few times $10^{-10}$." +" In general. the — abundance follows the CO abundance in the disk. since its formation is primarily from CO reacting with IL,. with destruction by dissociative recombination with free electrons."," In general, the $^+$ abundance follows the CO abundance in the disk, since its formation is primarily from CO reacting with $_3^+$, with destruction by dissociative recombination with free electrons." + Figure 5 shows the visibility amplitude of the J=10 emission from TW Iva as a function of baseline length: the falloff at longer baselines demonstrates (hat the emission region is resolved., Figure \ref{fig:tw_hcop_visamp} shows the visibility amplitude of the $^+$ J=1–0 emission from TW Hya as a function of baseline length; the falloff at longer baselines demonstrates that the emission region is resolved. + A circular Gaussian FEWIIM “size” of 372 provides a crude description of the full line brightness distribution., A circular Gaussian FWHM “size” of $3\farcs2$ provides a crude description of the full line brightness distribution. + Figure 5 includes (he visibility amplitudes derived [rom four of the [avored models of van Zadelholf et al. (, Figure \ref{fig:tw_hcop_visamp} includes the visibility amplitudes derived from four of the favored models of van Zadelhoff et al. ( +2001). which provide reasonable fits to higher-J single dish observations.,"2001), which provide reasonable fits to higher-J $^+$ single dish observations." + Two models are based on the radiativelv heated accretion disk structure of D'Alessio et al. (, Two models are based on the radiatively heated accretion disk structure of D'Alessio et al. ( +1999). and two models are based on the passive (wo-laver description of Chiang Goldreich (1997).,"1999), and two models are based on the passive two-layer description of Chiang Goldreich (1997)." + Two chemical scenarios are presented for each of these physical models., Two chemical scenarios are presented for each of these physical models. + The interstellar — abundance is assumed to be 5x10.7. and in one model — is depleted by a factor of LOO with an additional order of magnitude drop when the temperature falls below 20 Ix. while in another model is depleted by a [actor of 500 throughout.," The interstellar $^+$ abundance is assumed to be $5\times10^{-9}$, and in one model $^+$ is depleted by a factor of 100 with an additional order of magnitude drop when the temperature falls below 20 K, while in another model $^+$ is depleted by a factor of 500 throughout." + Table 2. summarizes the models., Table \ref{tab:models} summarizes the models. + Figure 5. shows that all of these models. which have disk masses of 0.03. AZ. and disk radii of 200 AU. agree well with the ATCA observations. for both the size scale and the absolute intensity of the Hine enussion. (," Figure \ref{fig:tw_hcop_visamp} shows that all of these models, which have disk masses of 0.03 $M_{\odot}$ and disk radii of 200 AU, agree well with the ATCA observations, for both the size scale and the absolute intensity of the $^+$ line emission. (" +Note that. visibility amplitude is a positive definite quantity. which results in a positive bias in Figure 5..),"Note that visibility amplitude is a positive definite quantity, which results in a positive bias in Figure \ref{fig:tw_hcop_visamp}. .)" + Figure 6 provides another view of the four models in the lorm of synthetic images., Figure \ref{fig:model_images} provides another view of the four models in the form of synthetic images. + These inages were made by sampling each of the models with the same visibility distribution as obtained by the ATCA observations. taking a 0.5 km + bin centered on the line.," These images were made by sampling each of the models with the same visibility distribution as obtained by the ATCA observations, taking a 0.5 km $^{-1}$ bin centered on the line." + These images may be compared with the panel in Figure 2. [or LSR velocity 2.75 km s... where the line emission peaks.," These images may be compared with the panel in Figure \ref{fig:tw_4chan} + for LSR velocity 2.75 km $^{-1}$, where the line emission peaks." + In (liis view. 1t is not easy. to see that (the line emission is well resolved spatially. but the similarity of the models in overall brightness and spatial extent is clearly apparent.," In this view, it is not easy to see that the line emission is well resolved spatially, but the similarity of the models in overall brightness and spatial extent is clearly apparent." +Inversions of helioseismic data have shown that the solar convection zone rotates differentially. but that the radiative interior has an almost solid-body like rotation (see Schou et al.,"Inversions of helioseismic data have shown that the solar convection zone rotates differentially, but that the radiative interior has an almost solid-body like rotation (see Schou et al." + 1998, 1998 +Interestingly. the quantity A/ does not appear in Ostriker's inal expression for the subsouic force.,"Interestingly, the quantity $\Delta t$ does not appear in Ostriker's final expression for the subsonic force." + This [act indicates that the artifice of a finite time interval was unuecessary aud that a steady-state analysis is applicable., This fact indicates that the artifice of a finite time interval was unnecessary and that a steady-state analysis is applicable. + Indeed. te force attalns a steady-state value in the numerical sliiulations of Sáuclez-Salcedo&Braucdenbure{1999).," Indeed, the force attains a steady-state value in the numerical simulations of \citet{sb99}." +. The divergence at a Mach number of uuity in the analytical expression further suggests that physical uiderstaudiug of the problem is Incomplete., The divergence at a Mach number of unity in the analytical expression further suggests that physical understanding of the problem is incomplete. + Iu this paper. we revisit the subject of dynamical frictiou. conceutratiug entirely ou the less studied subsouic case.," In this paper, we revisit the subject of dynamical friction, concentrating entirely on the less studied subsonic case." + We take the perturbing body to be a point mass AZ traveling through au initially uniform gas., We take the perturbing body to be a point mass $M$ traveling through an initially uniform gas. + The previous studies cited also ostensibly dealt with potut masses. in the sense that the plivsical size of the body was Ignored.," The previous studies cited also ostensibly dealt with point masses, in the sense that the physical size of the body was ignored." + However. it was assumed. either tacitly or explicitly. that the objects radius & farexceeds the accretion radius ryee. conventionally defined ⋅ ⋅," However, it was assumed, either tacitly or explicitly, that the object's radius $R$ farexceeds the accretion radius $r_{\rm acc}$, conventionally defined as." + ⋅ ⋅ ⋜↕⊳∖∣⊲⋯⊲⋅⊲≣−≻∪⋀⊔↙∕∣⊢⋅⋅∐↓⊳∖⋃⋅⋯↵∐⋜↕↕∖∖↽∐≺↵∐∫∎≱∕≥∖∕∖∣↝⋯⊲∙⊲⋅⋅↕∐≺↵∑∸↥⋅⋜↕∖⊽∐⋜↕⋃∩∐⋜↕↥↥∩↓⋅∢∙≺↵∐⋅∩⋯↕↕≺↵∩∣∪≺↲∢∙↕↥↠∖↜∖∩ weak that mass accretiou by iufal| is negligible.," It is true that when, the gravitational force from the object is so weak that mass accretion by infall is negligible." +" Under these circumstances. however. the primary drag ou the body is not from dynauical friction. but from direct impact by the gas. a fact sometimes The couventionally assumed inequality mareinallye holds in oue situatiou Commonly euvisiouect. ealaxies"" withinη. intraclusterη gas cimm))."," Under these circumstances, however, the primary drag on the body is not from dynamical friction, but from direct impact by the gas, a fact sometimes The conventionally assumed inequality marginally holds in one situation commonly envisioned, galaxies within intracluster gas )." + However. it fails badly tu other contexts. e.g.. supermassive |lack holes within galaxiescn. 1)) or gas giant planets inside circumstellar disksem. em)).," However, it fails badly in other contexts, e.g., supermassive black holes within galaxies, ) or gas giant planets inside circumstellar disks, )." + Whenrages. as we assume here. dynamical frietion is Indeed the main drag force.," When, as we assume here, dynamical friction is indeed the main drag force." + The relative density enhancement in tle wake is uot siuall. as ueecled for linear theory (see.e.g..Ixiur&Wim2009).. and mass accretion caunot be ueplectecl.," The relative density enhancement in the wake is not small, as needed for linear theory \citep[see, e.g.,][]{kk09}, and mass accretion cannot be neglected." + Our analysis indeed pivots oi the fact that the transfer of linear momentum from the background eas to the object. which uuderlies the friction force. is closely related to the trausfer of mass.," Our analysis indeed pivots on the fact that the transfer of linear momentum from the background gas to the object, which underlies the friction force, is closely related to the transfer of mass." + The problem of gas accretion onto a moving bods was addressed in a classic series of papers by . Bondi&Hovle(19 £1).. and. Βοι(1952).," The problem of gas accretion onto a moving body was addressed in a classic series of papers by \citet{hl39}, \citet{bh44}, and \citet{b52}." +. The final result for the accretion rate. applicable Lor all Mach nunubers. is the interpolation formula offered by Boudi(1952).," The final result for the accretion rate, applicable for all Mach numbers, is the interpolation formula offered by \citet{b52}." +. While uot derived rigorotsly. the formula matches knowt results in the hypersoulc aud stationary. limits. aud is broadly cousistent with uumerical simmulatious (seeRullert1996.audreferencestherein)..," While not derived rigorously, the formula matches known results in the hypersonic and stationary limits, and is broadly consistent with numerical simulations \citep[see][and references therein]{r96}." + The strategy 1 Lour paper is to determine. usiie perturbation theory. the density aud velocity ol the gas.," The strategy in our paper is to determine, using perturbation theory, the density and velocity of the gas." + However. we focus not ou the wake. as iu previous studies. but on a regionfar from the object. where its οavity is relatively weak.," However, we focus not on the wake, as in previous studies, but on a region from the object, where its gravity is relatively weak." + Extencine the perturbation analysis into the noulinear regime. we calculate the net nonmentuim flux onto he accreting object aud derive analytically that the force from cyuamical friction is AJ V. where AZ is the mass accretion rate onto the object.," Extending the perturbation analysis into the nonlinear regime, we calculate the net momentum flux onto the accreting object and derive analytically that the force from dynamical friction is $\dot M\,V$ , where $\dot M$ is the mass accretion rate onto the object." +binary fraction in the core and Ad... is the total stellar mass contained within the core.,binary fraction in the core and $M_{core}$ is the total stellar mass contained within the core. + Mathieu&Geller(2009) also showed that at least 764 of the BSs in the old open cluster NGC 188 have binary companions., \citet{mathieu09} also showed that at least $76\%$ of the BSs in the old open cluster NGC 188 have binary companions. + Although the nature of these companions remains unknown. it is clear that binaries played. a role in the formation of these DSs.," Although the nature of these companions remains unknown, it is clear that binaries played a role in the formation of these BSs." + Blue stragelers are tvpically concentrated in the dense cores of globular clusters where the high stellar densities should. result. in a higher rate of stellar encounters. (c.g.Leonard 1989)., Blue stragglers are typically concentrated in the dense cores of globular clusters where the high stellar densities should result in a higher rate of stellar encounters \citep[e.g.][]{leonard89}. +. Whether or not this fact is cirectly related to BS formation remains unclear. since mass scerceation also acts to migrate DSs (or their progenitors) into the core (e.g.Savianeetal.1998:Cubathakurtact1998).," Whether or not this fact is directly related to BS formation remains unclear, since mass segregation also acts to migrate BSs (or their progenitors) into the core \citep[e.g.][]{saviane98, guhathakurta98}." +. Additionally. numerous BSs have been observed in. more sparsely populated: open clusters (e.g.Anclrievskyοἱal.2000) and the fields of GCs where collisions are much less likely to occur ancl mass-transfer within binary svstenis is thought to be a more likely formation scenario (e.g.Mapellietal. 2004).," Additionally, numerous BSs have been observed in more sparsely populated open clusters \citep[e.g.][]{andrievsky00} and the fields of GCs where collisions are much less likely to occur and mass-transfer within binary systems is thought to be a more likely formation scenario \citep[e.g.][]{mapelli04}." +. Several studies have provided evidence that DSs show a bimodal spatial distribution in some GC's (Ferraroetal.1997.1999:Lanzonietal. 2007).," Several studies have provided evidence that BSs show a bimodal spatial distribution in some GCs \citep{ferraro97, ferraro99, lanzoni07}." +. In these clusters. the DS numbers are the highest in the central cluster regions and decrease with increasing distance from the cluster. centre until a second rise occurs in the cluster outskirts.," In these clusters, the BS numbers are the highest in the central cluster regions and decrease with increasing distance from the cluster centre until a second rise occurs in the cluster outskirts." +" This drop in BS numbers at intermediate cluster radii is often referred to as the ""zone of avoidance"".", This drop in BS numbers at intermediate cluster radii is often referred to as the “zone of avoidance”. + Some authors have suggested that it is the result of two separate formation mechanisms occurring in the inner and outer regions of the cluster. with niass-transfer in primordial binaries dominating in the latter and. stellar collisions dominating in the former (Ferraroetal.2004:Mapelliet 2006).," Some authors have suggested that it is the result of two separate formation mechanisms occurring in the inner and outer regions of the cluster, with mass-transfer in primordial binaries dominating in the latter and stellar collisions dominating in the former \citep{ferraro04, mapelli06}." +". Conversely. mass segregation could also give rise to a ""zone of avoidance"" Lor BSs if the time-scale for dynamical friction. exceeds. the average Bs lifetime in only the outskirts of GCs that exhibit this racial trend (e.g.Leigh.Sills&WKnieee2011).."," Conversely, mass segregation could also give rise to a “zone of avoidance” for BSs if the time-scale for dynamical friction exceeds the average BS lifetime in only the outskirts of GCs that exhibit this radial trend \citep[e.g.][]{leigh11a}." + Dynamical interactions occur frequently enough in dense clusters that they are expected to be at least partly responsible for the observed. properties of Bss (e.g.Strvker1993:Leigh&Sills 2011)..," Dynamical interactions occur frequently enough in dense clusters that they are expected to be at least partly responsible for the observed properties of BSs \citep[e.g.][]{stryker93, leigh11b}." + Le follows that the current properties of BS populations should reflect. the cynamical histories of their host clusters., It follows that the current properties of BS populations should reflect the dynamical histories of their host clusters. + As a result. DSs could provide an indirect means of probing the physical processes. that drive star cluster evolution (e.g.Hegeie&Lut2003:etal.2005:Leigh&Sills 2011)..," As a result, BSs could provide an indirect means of probing the physical processes that drive star cluster evolution \citep[e.g.][]{heggie03, hurley05, leigh11b}." + In this paper. our goal is to constrain the dominant BS formation mechanism(s) operating in the dense cores of GCs bv analyzing the principal processes thought to influence their production.," In this paper, our goal is to constrain the dominant BS formation mechanism(s) operating in the dense cores of GCs by analyzing the principal processes thought to influence their production." + To this end. we use an analytic reatment to obtain predictions for the number of BSs expected to be found within one core radius of the cluster centre at the current cluster age.," To this end, we use an analytic treatment to obtain predictions for the number of BSs expected to be found within one core radius of the cluster centre at the current cluster age." + Predicted numbers [or he core are calculated: for a range of [ree parameters. and then compared to the observed: numbers in. order to ind the best-fitting model parameters.," Predicted numbers for the core are calculated for a range of free parameters, and then compared to the observed numbers in order to find the best-fitting model parameters." + In. this way. we ave able to quantify the degree to which each of the considered. formation mechanisms should. contribute to the otal predicted: numbers in. order to best. reproduce. the observations.," In this way, we are able to quantify the degree to which each of the considered formation mechanisms should contribute to the total predicted numbers in order to best reproduce the observations." + In Section 2.. we describe the BS catalogue. used for comparison to our model predictions.," In Section \ref{data}, we describe the BS catalogue used for comparison to our model predictions." + In Section 3... we present our analytic model for BS formation as well as the statistical technique we have developed to compare its predictions to the observations.," In Section \ref{method}, we present our analytic model for BS formation as well as the statistical technique we have developed to compare its predictions to the observations." + These predictions are then compared to the observations in Section 4. for a range of model parameters., These predictions are then compared to the observations in Section \ref{results} for a range of model parameters. + In Section 5.. we discuss the implications of our results for BS formation. as well as the role plaved by the eluster dynamics in shaping the current properties of BS populations.," In Section \ref{discussion}, we discuss the implications of our results for BS formation, as well as the role played by the cluster dynamics in shaping the current properties of BS populations." + The cata used in this study was taken from Leigh.Sills&Ixnigge(2011).., The data used in this study was taken from \citet{leigh11a}. + In that paper. we presented a catalogue for blue straggler. red giant branch (ROB). horizontal branch (LIB) and main-sequence turn-olf stars obtained from the colour-magnitude cliagrams of 35 Milky Way GC's taken from the ACS Survey for Globular Clusters (Sarajedinietal.2007).," In that paper, we presented a catalogue for blue straggler, red giant branch (RGB), horizontal branch (HB) and main-sequence turn-off stars obtained from the colour-magnitude diagrams of 35 Milky Way GCs taken from the ACS Survey for Globular Clusters \citep{sarajedini07}." +. The ACS Survey provides unpecedentec deep photometry in the FGOGW (~ V) and FSI4W (~ D filters that extends reliably from the IB all the way down to about 7 magnitudes below the MSTO., The ACS Survey provides unpecedented deep photometry in the F606W $\sim$ V) and F814W $\sim$ I) filters that extends reliably from the HB all the way down to about 7 magnitudes below the MSTO. + The clusters in our sample span a range of total masses (by nearly 3 orders of magnitude) and central concentrations (Harrisetal.1996)., The clusters in our sample span a range of total masses (by nearly 3 orders of magnitude) and central concentrations \citep{harris96}. + We have confirmed that the photometry is nearly complete in the BS region of the CMD for every cluster in our sample., We have confirmed that the photometry is nearly complete in the BS region of the CMD for every cluster in our sample. + ‘This was done using the results of artificial star tests taken from Andersonetal.(2008)., This was done using the results of artificial star tests taken from \citet{anderson08}. +. Each cluster was centred in the ACS Geld. which extends oul to several core radii from the cluster centre in most of the clusters in our sample.," Each cluster was centred in the ACS field, which extends out to several core radii from the cluster centre in most of the clusters in our sample." + Only the core populations provided in Leigh.Sills&Ixnigge(2011) are used in this paper., Only the core populations provided in \citet{leigh11a} are used in this paper. + We have taken estimates for the core radii and central Iuminositv densities for the clusters in our sample [from ]larrisctal.(1996)... whereas central velocity clispersions were taken from Webbink(1985).," We have taken estimates for the core radii and central luminosity densities for the clusters in our sample from \citet{harris96}, whereas central velocity dispersions were taken from \citet{webbink85}." +. Estimates for the total stellar mass contained within the core were obtained from single-mass Wine models. as described in Leigh.Sills&Ixnigge (2011)..," Estimates for the total stellar mass contained within the core were obtained from single-mass King models, as described in \citet{leigh11a}." + All of the clusters in our sample were chosen to be non-post-core collapse. and have surface. brightness profiles that. provide good fits to our Wing mocels.," All of the clusters in our sample were chosen to be non-post-core collapse, and have surface brightness profiles that provide good fits to our King models." + In this section. we present our model and outline our assumptions.," In this section, we present our model and outline our assumptions." + We also present the statistical technique used to compare the observed. number counts to. our model predictions in order to identify the best-fittine moclel parameters., We also present the statistical technique used to compare the observed number counts to our model predictions in order to identify the best-fitting model parameters. + Consider a GC core that is home to Nes. BSs at some time C — 09.," Consider a GC core that is home to $_{BS,0}$ BSs at some time t $=$ $_0$." +" At a specified time in the future. the number of BSs in the core can be approximated. by: where Noo is the number of BSs formed from collisions during single-single (1|1). sinele-binary (112) ancl binary- (2]2) encounters. Noo, is the number formed. [rom binary evolution (either partial mass-transler between the binary components or their complete coalescence). N;, is the"," At a specified time in the future, the number of BSs in the core can be approximated by: where $_{coll}$ is the number of BSs formed from collisions during single-single (1+1), single-binary (1+2) and binary-binary (2+2) encounters, $_{bin}$ is the number formed from binary evolution (either partial mass-transfer between the binary components or their complete coalescence), $_{in}$ is the" +"and variable sources may differ, and should require a different treatment when considering the rates of events.","and variable sources may differ, and should require a different treatment when considering the rates of events." +" For example, we might expect the rates of variable sources to differ from ‘one off’ explosive transients such as GRB afterglows — which have a finite lifetime and will be undetectable beforehand."," For example, we might expect the rates of variable sources to differ from `one off' explosive transients such as GRB afterglows – which have a finite lifetime and will be undetectable beforehand." +" For future surveys, a spectrum of transient and variable behaviour will be observed depending on the cadence and sensitivity."," For future surveys, a spectrum of transient and variable behaviour will be observed depending on the cadence and sensitivity." + The boundaries between the definitions will become more blurred as the cadence and sensitivity is increased., The boundaries between the definitions will become more blurred as the cadence and sensitivity is increased. +" The WJN transients summarised in Matsumuraetal.(2009) range in flux density from 1 to 4.3 Jy with characterstic timescale ~ 1 day, yielding a snapshot rate p ~3x10~% deg? (labelled ‘Mat20097” in Figure 4)."," The WJN transients summarised in \cite{Matsumura_2009} range in flux density from 1 to 4.3 Jy with characterstic timescale $\sim$ 1 day, yielding a snapshot rate $\rho\sim$ $\times10^{-3}$ $^{-2}$ (labelled $^{T}$ ' in Figure 4)." + In comparison the Croftetal.(2010) survey set a 2e upper limit on the snapshot rate of events > 40 mJy to be p «0.004 deg?; by comparing their source fluxes with those in the NVSS catalogues the characteristic timescale is ~ 15 years (labelled ‘Croft20107” in Figure 4)., In comparison the \cite{Croft} survey set a $\sigma$ upper limit on the snapshot rate of events $>$ 40 mJy to be $\rho<$ 0.004 $^{-2}$; by comparing their source fluxes with those in the NVSS catalogues the characteristic timescale is $\sim$ 15 years (labelled $^{T}$ ' in Figure 4). + The most stringent limit placed on the snapshot rate of sources is set by Gal-Yametal.(2006) to be p« 1.5x10 deg? for flux densities >6 mJy (labelled ‘GY20067’ in Figure? 4)., The most stringent limit placed on the snapshot rate of sources is set by \cite{Gal-Yam} to be $\rho<$ $\times10^{-3}$ $^{-2}$ for flux densities $>$ 6 mJy (labelled $^{T}$ ' in Figure 4). +" Note, the FIRST survey has improved angular resolution (5"") when compared with NVSS (45""), therefore correct source association effects transient identification."," Note, the FIRST survey has improved angular resolution $^{\prime\prime}$ ) when compared with NVSS $^{\prime\prime}$ ), therefore correct source association effects transient identification." + We do not state a characteristic time scale for the FIRST-NVSS comparison as both individual surveys took a number of years; specific timescales can only be considered on a source by source basis., We do not state a characteristic time scale for the FIRST-NVSS comparison as both individual surveys took a number of years; specific timescales can only be considered on a source by source basis. +pointed. relatively wide-field (30° diameter) observations of the Position-Sensitive Proportional Counter (PSPC) on board the ROSAT X-ray observatory (1990-1999).,"pointed, relatively wide-field (30' diameter) observations of the Position-Sensitive Proportional Counter (PSPC) on board the ROSAT X-ray observatory (1990-1999)." + Seventy-two X-ray clusters between z=0.3—0.7 were discovered (see Fig. 1))., Seventy-two X-ray clusters between $z=0.3-0.7$ were discovered (see Fig. \ref{sample}) ). + All have been identified and assigned redshifts (?).., All have been identified and assigned redshifts \citep{Mullis03}. + Because this survey included pointed observations that were quite long. some of these clusters are among the faintest clusters of galaxies known at these moderately high redshifts.," Because this survey included pointed observations that were quite long, some of these clusters are among the faintest clusters of galaxies known at these moderately high redshifts." +" Therefore. our new weak lensing measurements extend the X-ray luminosity limit of the mass-Z, relation by almost an order of magnitude. based on targeted observations."," Therefore, our new weak lensing measurements extend the X-ray luminosity limit of the $L_x$ relation by almost an order of magnitude, based on targeted observations." + We note that studies of the ensemble-averaged properties of clusters discovered in the SDSS (?) and X-ray groups in COSMOS (?) have pushed the limits to even lower luminosities., We note that studies of the ensemble-averaged properties of clusters discovered in the SDSS \citep{Rykoff08b} and X-ray groups in COSMOS \citep{Leauthaud10} have pushed the limits to even lower luminosities. + The structure of the paper follows., The structure of the paper follows. + In 322 we describe our data and weak lensing analysis., In 2 we describe our data and weak lensing analysis. + In particular we discuss how we correct for the effects of CTE in our ACS data and how we correct for PSF anisotropy., In particular we discuss how we correct for the effects of CTE in our ACS data and how we correct for PSF anisotropy. + The measurements of the cluster masses. and the comparison to the X-ray properties are presented in. $33.," The measurements of the cluster masses, and the comparison to the X-ray properties are presented in 3." + We compare our results to previous work and examine biases in our mass estimates that arise from uncertainties in the position of the cluster center and sample selection., We compare our results to previous work and examine biases in our mass estimates that arise from uncertainties in the position of the cluster center and sample selection. +" Throughout this paper we assume a flat ACDM cosmology with O,,20.3 and Ho=70/555 km/s/Mpe.", Throughout this paper we assume a flat $\Lambda$ CDM cosmology with $\Omega_m=0.3$ and $H_0=70h_{70}$ km/s/Mpc. + The data studied here were obtained as part of a snapshot program (PI: Donahue) to study a sample of clusters found in the 160 square degree survey (??)..," The data studied here were obtained as part of a snapshot program (PI: Donahue) to study a sample of clusters found in the 160 square degree survey \citep{Vikhlinin98,Mullis03}." + The clusters from the latter survey were selected based on the serendipitous detection of extended X-ray emission in ROSAT PSPC observations. resulting in a total survey area of 160 deg.," The clusters from the latter survey were selected based on the serendipitous detection of extended X-ray emission in ROSAT PSPC observations, resulting in a total survey area of 160 $^2$ ." + A detailed discussion of thesurvey can be found in ?.., A detailed discussion of thesurvey can be found in \cite{Vikhlinin98}. + The sample was reanalysed by 2.. which also lists spectroscopic redshifts for most of the clusters.," The sample was reanalysed by \cite{Mullis03}, which also lists spectroscopic redshifts for most of the clusters." + The X-ray luminosity as a function. of cluster redshift is plotted in Figure 1.., The X-ray luminosity as a function of cluster redshift is plotted in Figure \ref{sample}. + The HST snapshot program targeted clusters with 0.3/ such that A=/|1."," After all GMCs have emitted some number of model photons, the level populations in the GMCs are updated by assuming detailed balance: where $C_{lk}$ and $C_{kl}$ are the collisional rates, and $\beta$ only exists for transition $k\rightarrow l$ such that $k=l+1$." + Equations 22. are solved via Gauss-Jordan matrix inversion., Equations \ref{eq:tb_stateq} are solved via Gauss-Jordan matrix inversion. + This process is iterated upon until the level populations have achieved convergence., This process is iterated upon until the level populations have achieved convergence. + Here. we demand that they not vary by more than a fractional difference of 1.10.? for at least 3 iterations.," Here, we demand that they not vary by more than a fractional difference of $1\times10^{-3}$ for at least 3 iterations." + Once the level populations have been solved for. we build the formal spectrum by choosing an (arbitrary) viewing angle. and integrating along lines of sight19943: Tests of aagainst the publicly available Leiden Benchmarks are presented in(2006b).," Once the level populations have been solved for, we build the formal spectrum by choosing an (arbitrary) viewing angle, and integrating along lines of sight: Tests of against the publicly available Leiden Benchmarks are presented in." +. We obtained our coefficients from the2005)., We obtained our coefficients from the. +. We assume a fractional carbon abundance of 1.510.+. though the abundance of CO with respect to iis given by Equation 12..," We assume a fractional carbon abundance of $1.5\times10^{-4}$, though the abundance of CO with respect to is given by Equation \ref{eq:abundance}." + As we aim to compare potential variations in ΠΠ our simulated galaxy mergers to those that are actually observed. it is worth briefly comparing the physical and synthetic observational woperties of our model galaxies to real galaxies.," As we aim to compare potential variations in in our simulated galaxy mergers to those that are actually observed, it is worth briefly comparing the physical and synthetic observational properties of our model galaxies to real galaxies." + Our tiducial merger has been well-studied in the literature. and is very much an average merger simulation as far as the range of simulated SFRs. black hole aceretion rates and bolometric luminosities.," Our fiducial merger has been well-studied in the literature, and is very much an average merger simulation as far as the range of simulated SFRs, black hole accretion rates and bolometric luminosities." + While he processes described in this section generically describe gas-rich mergers. what we summarise here has been calculated and sublished previously explicitly for our tiducial model.," While the processes described in this section generically describe gas-rich mergers, what we summarise here has been calculated and published previously explicitly for our fiducial model." + The merger goes through elevated star formation rate upon first passage as tidal torques on the gas cause the gas to lose angular momentum and fall toward the centres causing high-density regions, The merger goes through elevated star formation rate upon first passage as tidal torques on the gas cause the gas to lose angular momentum and fall toward the centres causing high-density regions +ποπο) computed with (his scheme is never less (han one half of the value delivered bv the more elaborate scheme. ancl the strings of squares and circles are closely similar.,"$n_{CO}(f)/n_{C}(0)$ computed with this scheme is never less than one half of the value delivered by the more elaborate scheme, and the strings of squares and circles are closely similar." + This is witness (o tlie robustness of the first scheme., This is witness to the robustness of the first scheme. + This was further tested bv performing other runs with the first scheme. only changing one or two parameters.," This was further tested by performing other runs with the first scheme, only changing one or two parameters." + Figure 7 plots neot(f)/ne(0) (open squares) and nef)/ne(0) (lilled squares). for some of these cases. all with πο(0)=no(0)310 *.," Figure 7 plots $n_{CO}(f)/n_{C}(0)$ (open squares) and $n_{Cgr}(f)/n_{C}(0)$ (filled squares), for some of these cases, all with $n_{C}(0)=n_{O}(0)=3\,\,10^{6}$ $^{-3}$." + The integer abscissa relers (ο the sentence in the legend which describes the corresponding changes applied to the parameters., The integer abscissa refers to the sentence in the legend which describes the corresponding changes applied to the parameters. + The results are arranged so as to higlight the opposite effects of various changes in (he chemical scheme. with respect to the “standard” case. corresponding to the equations of Sec.," The results are arranged so as to higlight the opposite effects of various changes in the chemical scheme, with respect to the “standard"" case, corresponding to the equations of Sec." + 3., 3. + Some elements of (he scheme have no great impact on the final values of interest here: for instance. (he inclusion of OIL (N=3) and the initial fraction of molecular hydrogen (N=5).," Some elements of the scheme have no great impact on the final values of interest here; for instance, the inclusion of OH (N=3) and the initial fraction of molecular hydrogen (N=5)." + By contrast. the association of C and II to form CIL (reaction K1) is essential lor a high vield of carbon erains. as stated above and as evidenced by the steep reduction," By contrast, the association of C and H to form CH (reaction k1) is essential for a high yield of carbon grains, as stated above and as evidenced by the steep reduction" +where j—-Do+Af ds the flux in the size space.,where $j=-B\frac{\partial f}{\partial r}+Af$ is the flux in the size space. + D is the nuclear size diffusion coefficient aud Lis connected with 2 by a relationship. which follows from the fact that for an ecquilibrium distribution j=0.," $% + B is the nuclear size diffusion coefficient and $A$ is connected with $B$ by a relationship, which follows from the fact that for an equilibrium distribution $j=0$." + Therefore we find =—DW'(r)/T., Therefore we find $A=-BW^{\prime }(r)/T$. + In the case of a continuous stationary phase-lransilion process we have j—constant., In the case of a continuous stationary phase-transition process we have $j=$ constant. + The constant flix is just the number of nuclei passing through the critical range per unil lime per unit volume of the medium. ie. it defines (he rate of the process.," The constant flux is just the number of nuclei passing through the critical range per unit time per unit volume of the medium, i.e. it defines the rate of the process." + With the use οἱ the condition of the constant flix we obtain -Bfui.(1)—j giving ↴∏∐↲≺∢∪∐⋟∖⇁↥≀↧↴∐↥↕∐⊔∐⋟∖⊽≼↲≺⇂∏≀↧↴∐∪∐≀↧↴∐≼⇂⋮∫⋮≀↧↴↕⋅≼↲↓⋟∪∏∐≼⇂↓⋟↕⋅∪∐↓⊔∐↲∣↽≻∪∏∐≺⇂≀↧↴↕⋅⋡∖↽≺∢∪∐≺∐∐∪∐⋟∖⊽↓⋟∪↕⋅⋟∖⊽∐⋯↴↥ ≀↕↴∐≼⇂↥≀↧↴↕⋅≸↽↔↴≼↲∣⋮⋅↴∏∐↲∐∏≺∢⋯≀↧↴∐∪∐↕↽≻↕⋅∪∣↽≻≀↧↴∣↽≻∐∐," With the use of the condition of the constant flux we obtain $-Bf_{0}\frac{\partial }{\partial r}\left( \frac{f}{f_{0}}\right) +=j$ giving The constant in this equation and $j$ are found from the boundary conditions for small and large $r$." +⋡∖⇁↕∐≺∢↕⋅≼↲≀↧⊔∖⊽≼↲⋟∖⊽↕⋅≀↕↴↕↽≻↕≺∐⋡∖⇁∖∖⇁↕⊔↥≼⇂≼↲≺∢↕⋅≼↲≀↧⊔∖⊽↕∐≸≟⋟∖⊽↕∠≼↲≀↧↴∐≼⇂⋟∖⊽∐↓≀↧↴↥ nuclei have a high probability of occurrence., The fluctuation probability increases rapidly with decreasing size and small nuclei have a high probability of occurrence. + This is expressed by the boundary. condition f[/fo— las r- 0.," This is expressed by the boundary condition $f/f_{0}\rightarrow 1$ as $% +r\rightarrow 0." + The boundary condition lor large r can be established by noting that above the critical range the function fi increases without limit. whereas the true distribution [function f/(r) remains finite.," The boundary condition for large $r$ can be established by noting that above the critical range the function $f_{0}$ increases without limit, whereas the true distribution function $f(r)$ remains finite." + This situation is expressed by imposing the boundary condition fifo=O lor r—oc.," This situation is expressed by imposing the boundary condition $f/f_{0}=0$ for $% +r\rightarrow \infty." + The solution which satislies the above conditions is In theseequations the integrand has a sharp masxinnun al r=A., The solution which satisfies the above conditions is In theseequations the integrand has a sharp maximum at $r=R_{c}$. + By extending the integration will respect to r [rom —2€ to +x. one obtain for the number of viable quark nuclei formed in stationary conditions per unit time and per unit volume the expression: Above the eritical range. the distribution function is constant: having reached that point. the nucleus becomes steaclily larger. with practically no change in (he reverse direction.," By extending the integration with respect to $r$ from $-\infty $ to $+\infty $, one obtain for the number of viable quark nuclei formed in stationary conditions per unit time and per unit volume the expression: Above the critical range, the distribution function is constant: having reached that point, the nucleus becomes steadily larger, with practically no change in the reverse direction." + Accordingly we can neglect the term containing the derivative Of/Or in the flix. leading to J= Af.From the significance of the Εαν it follows that the coefficient A acts as a velocity in size space. το 1980)..," Accordingly we can neglect the term containing the derivative $\partial f/\partial r$ in the flux, leading to $% +j=A f.From the significance of the flux it follows that the coefficient $A$ acts as a velocity in size space, $A=\left( dr/dt\right) _{macro}$ ." + Therefore we find [or D:, Therefore we find for $B$ : +10? realizations of EGRET observations assuming that the distribution of Fsngr/Faarsr follows equation (11)) with the most likely values of µ and c.,"$10^5$ realizations of EGRET observations assuming that the distribution of $F_{\rm EGRET} / +F_{\rm BATSE}$ follows equation \ref{eq:eta distribution}) ) with the most likely values of $\mu$ and $\sigma$." +" By comparing the likelihood of these Monte Carlo realizations with that of the actual EGRET observations, we find that of the realizations have a lower likelihood, suggesting that equation (11)) with its most likely values isindeed consistent with the observations."," By comparing the likelihood of these Monte Carlo realizations with that of the actual EGRET observations, we find that of the realizations have a lower likelihood, suggesting that equation \ref{eq:eta distribution}) ) with its most likely values isindeed consistent with the observations." +" Given µ and c, we can obtain the distribution of fluence in EGRET band by convolving BATSE fluence distribution /(dNdFgarsg; Fig. 1))"," Given $\mu$ and $\sigma$, we can obtain the distribution of fluence in EGRET band by convolving BATSE fluence distribution $dN / dF_{\rm BATSE}$; Fig. \ref{fig:fluence}) )" +" and p(y|p,0): As representative models, we use three sets of (41,0)for both the prompt and afterglow cases."," and $p(\eta|\mu,\sigma)$: As representative models, we use three sets of $(\mu,\sigma)$for both the prompt and afterglow cases." +" These are labeled as Άγορ, Broo, and Croo (A200, Boo, and C299), and shown in Figure 2.."," These are labeled as $_{T{90}}$, $_{T{90}}$, and $_{T{90}}$ $_{\rm +200}$, $_{\rm 200}$, and $_{\rm 200}$ ), and shown in Figure \ref{fig:mu_sig}." +" In Figure 4,, we show the resulting fluence distribution corresponding to each of these models."," In Figure \ref{fig:dndf_egret}, we show the resulting fluence distribution corresponding to each of these models." +" EGRET results imply that during the prompt emission phase, 0.003<η 0.06."," EGRET results imply that during the prompt emission phase, $0.003\lesssim \eta \lesssim 0.06$ ." +" As we discussed in 2.1,, the low number of photons in the bursts detected by EGRET,"," As we discussed in \ref{sub:prompt}, , the low number of photons in the bursts detected by EGRET," +After the detection of the accelerated expansion of the universe the physical explanation of dark energy has become the major challenge of astronomy and physics.,After the detection of the accelerated expansion of the universe the physical explanation of dark energy has become the major challenge of astronomy and physics. + One way to constrain the physics behind dark energy 1s to measure the equation-of-state parameter w = p/(pe7)., One way to constrain the physics behind dark energy is to measure the equation-of-state parameter w = $\rho$ $^{2}$ ). + This requires an extremely accurate determination of the extragalactic distance scale and the Hubble Constant Hy., This requires an extremely accurate determination of the extragalactic distance scale and the Hubble Constant $_{0}$. + As is. well known (Macrietal.2006).. the determination of cosmologicall parameters from the cosmic microwave background is affected by degeneracies in parameter space and cannot provide strong constraints on the value of Hy (Spergel2006:Tegmarketal. 2004).," As is well known \citep{macri06}, the determination of cosmological parameters from the cosmic microwave background is affected by degeneracies in parameter space and cannot provide strong constraints on the value of $_{0}$ \citep{spergel06, tegmark04}." +. Only if additional assumptions are made. for instance that the universe is flat. Hy can be predicted with high precision (1.9. )) from the observations of the cosmic microwave background. baryonic acoustic oscillations and type I high redshift supernovae.," Only if additional assumptions are made, for instance that the universe is flat, $_{0}$ can be predicted with high precision (i.e. ) from the observations of the cosmic microwave background, baryonic acoustic oscillations and type I high redshift supernovae." + If these assumptions are relaxed. then much larger uncertainties are introduced (Spergeletal.2007;Komatsu2009).," If these assumptions are relaxed, then much larger uncertainties are introduced \citep{spergel07, komatsu09}." +. The uncertainty of the determination of w is related to the uncertainty of Hy through Aw/w ~ 2ΔΗΩ Ημ., The uncertainty of the determination of w is related to the uncertainty of $_{0}$ through $\Delta$ w/w $\approx$ $\Delta$ $_{0}$ $_{0}$. + Thus. an independent determination of Hy with an accuracy of will allow the uncertainty of w to be reduced to «0.1 or. even more ambitious. Hy accurate to will yield w accurate to 0.02.," Thus, an independent determination of $_{0}$ with an accuracy of will allow the uncertainty of w to be reduced to $\pm$ 0.1 or, even more ambitious, $_{0}$ accurate to will yield w accurate to 0.02." + Extremely promising steps towards this goal have been made recently by Macrietal.(2006) and by, Extremely promising steps towards this goal have been made recently by \citet{macri06} and by +continuum light.,continuum light. +" Broad permitted lines are indeed observed in the spectrum measured in polarized light, confirming that this galaxy harbours a Seyfert 1 nucleus (Antonucci Miller 1985; Antonucci, Hurt, Miller 1994; Miller, Goodrich, Mathews 1991; Inglis et al."," Broad permitted lines are indeed observed in the spectrum measured in polarized light, confirming that this galaxy harbours a Seyfert 1 nucleus (Antonucci Miller 1985; Antonucci, Hurt, Miller 1994; Miller, Goodrich, Mathews 1991; Inglis et al." +" 1995; Alexander, Ruiz Hough 1999)."," 1995; Alexander, Ruiz Hough 1999)." +" Interestingly though, this is not the region where the power-law dominates the spectra."," Interestingly though, this is not the region where the power-law dominates the spectra." +" There are peaks around 100 - 150 pc from each side of the centre, where the power-law is responsible for more than 5096 of the light."," There are peaks around 100 - 150 pc from each side of the centre, where the power-law is responsible for more than $\%$ of the light." + T'hese peaks are probably related to shocked region., These peaks are probably related to shocked region. +" In Figure 1, these regions correspond to apertures 03 and 10."," In Figure 1, these regions correspond to apertures 03 and 10." +" Aperture 03, for example, is coincident with a region where the jet seems to be changing directions, probably due to the interaction with the ISM."," Aperture 03, for example, is coincident with a region where the jet seems to be changing directions, probably due to the interaction with the ISM." +" If these are the regions where the jet encounters dense clouds, shocks might have an important contribution to the continuum."," If these are the regions where the jet encounters dense clouds, shocks might have an important contribution to the continuum." +" Another possibility is that these peaks are associated with reflected light from the BLR, due to the higher concentration of dust."," Another possibility is that these peaks are associated with reflected light from the BLR, due to the higher concentration of dust." +" In Paper I, Martins et al."," In Paper I, Martins et al." +" show that many emission lines have double peaked profiles, and the maximum of the second components are also in this region."," show that many emission lines have double peaked profiles, and the maximum of the second components are also in this region." +" As mentioned above, it is important to keep in mind that the results for the power law component might have uncertainties due to the fact that it cannot be"," As mentioned above, it is important to keep in mind that the results for the power law component might have uncertainties due to the fact that it cannot be" +order of this critical radius are located in the Oort cloud.,order of this critical radius are located in the Oort cloud. + This cloud. is assumed to be a reservoir of comets that represents the outer most material border of our Solar System and lies at a distance of about 50000AU., This cloud is assumed to be a reservoir of comets that represents the outer most material border of our Solar System and lies at a distance of about $50000~\mathrm{AU}$. + So it is convenient to consider the influence of the DM-mocification on Oort-cloud objects., So it is convenient to consider the influence of the DM-modification on Oort-cloud objects. +Lhe calculated additional racial acceleration. was included. into the used orbit integrating program that will be presented in Section ,The calculated additional radial acceleration was included into the used orbit integrating program that will be presented in Section 3. +"DUMd ? introduced a function s(2) in Newtonssecond law where 2=Ze. width the actual! acceleration e devided by some critical macceleration ay which is a universal constant z210P""msee7. derived from galactic rotation curves and turns out to be of the same order of magnitude as the Pioneer-acceleration."," \citet{10} introduced a function $\mu(z)$ in Newtonssecond law where $z=\frac{a}{a_0}$, with the 'actual' acceleration $a$ devided by some critical acceleration $a_0$ which is a universal constant $\approx 2\times10^{-10}~\mathrm{m\,sec^{-2}}$, derived from galactic rotation curves and turns out to be of the same order of magnitude as the Pioneer-acceleration." + With this function. Newton's second law is written where e is the actual acceleration of the object while QN=CM.s+ is. the strict. Newtonian. T'The function pz) is not further specified but has the limiting-values The second. case corresponds to an actual acceleration e that is much smaller than the critical acceleration eo., With this function Newton's second law is written where $a$ is the actual acceleration of the object while $g_N=-\frac{GM_{\odot}}{r^2}$ is the strict Newtonian The function $\mu(z)$ is not further specified but has the limiting-values The second case corresponds to an actual acceleration $a$ that is much smaller than the critical acceleration $a_0$. + “Phis leads to an expression for e such that This expression does not describe a continuous transition from the pure Newtonian regime (e77 ao) to the pure MONDian regime (e«« ag)., This leads to an expression for $a$ such that This expression does not describe a continuous transition from the pure Newtonian regime $a>>a_0$ ) to the pure MONDian regime $a<25$: The detection of the jet break was observed in X-ray only (Soderberg et al." + 2006)., 2006). + A jet-break is clearly visible in the light curve at about 5 days We note that determination of the jet opening angle from the break-time is strongly sensitive on the model parameters used., A jet-break is clearly visible in the light curve at about 5 days We note that determination of the jet opening angle from the break-time is strongly sensitive on the model parameters used. + In the previous cases. the mocel was always the same(a forward shock fireball espandi with kinetic energy. in a medium of constant density 2)).M where 0x(nfE):," In the previous cases, the model was always the same(a forward shock fireball expanding with kinetic energy in a medium of constant density ), where $\theta \propto (n/E)^{1/8}$." +" mna n and ££ are uncertain in bursts (see e.g. =anaitescu 2 for the values of n in the cases of GAB 050709 nu and€ ""m00724)."," However, $n$ and $E$ are uncertain in all bursts (see e.g. Panaitescu 2006 for the values of $n$ in the cases of GRB 050709 and GRB 050724)." + Lenee. opening15 angle5 values reportedin papers are taken as indicative values. and we use them as a guide (this is why we do not perform a k- for cosmological elfects. as the correction is small compared to the uncertainties of the beaming angles).," Hence, opening angle values reported in these papers are taken as indicative values, and we use them as a guide (this is why we do not perform a k-correction for cosmological effects, as the correction is small compared to the uncertainties of the beaming angles)." + For CRB 050724. CRB meg050709 and GRB051221. we define Pia using /-banel αἲ 11 hr from NysewancderFruchter&Peer. (2009).. but scaled to a source clistance of ) MIpe (the mean sensitivity distance of the CAV search).," For GRB 050724, GRB 050709 and GRB 051221, we define $F_{11 \mathrm{hr}}$ using $R$ -band fluxes at 11 hr from \citet{Nys09}, , but scaled to a source distance of 300 Mpc (the mean sensitivity distance of the GW search)." +" Equation (1) scales the Dux using a power law index a, until jet-break time /xfio. when the beamed emission. starts to expand sideways. and by the Luminosity distance to the source αν) The above equation can be used to estimate the ZI-band Hux at times before the jet break."," Equation (1) scales the flux using a power law index $\alpha_1$ until jet-break time $t\le t_{j,0}$, when the beamed emission starts to expand sideways, and by the luminosity distance to the source $d_{\mathrm{L}}(z)$: The above equation can be used to estimate the $R$ -band flux at times before the jet break." + To model the SCRB light curve at post jet-break times. we employ a smoothly.joined broken power law (Beuermann et al.," To model the SGRB light curve at post jet-break times, we employ a smoothly joined broken power law (Beuermann et al." +" 1999) where £) is the Hux at the jet break time /;. a, and as are thepre-break and post-break light-curve slopes. anc scales the sharpness of the break."," 1999), where $F_j$ is the flux at the jet break time $t_{j}$ , $\alpha_1$ and $\alpha_2$ are thepre-break and post-break light-curve slopes, and scales the sharpness of the break." + The beaming angles and break, The beaming angles and break +as the square of the distance to the source.,as the square of the distance to the source. + It is also known that the jet pressure (Pi) and density satisfy the relation P;Ip- C. where E is the adiabatic exponent and C» a constant.," It is also known that the jet pressure $P_{\rm j}$ ) and density satisfy the relation $P_{\rm +j}/\rho_{\rm j}^{\Gamma}=C_2$ , where $\Gamma$ is the adiabatic exponent and $C_2$ a constant." +" Thus. Pix{σι which implies (7= 5/3): A minimum distance for the position of a recollimation shock can be given as the place where the pressure in the Jet is the same as the pressure of the ambient (z,)."," Thus, $P_{\rm j}\propto 1/z^{2\Gamma}$, which implies $\Gamma=5/3$ ): A minimum distance for the position of a recollimation shock can be given as the place where the pressure in the jet is the same as the pressure of the ambient $z_{\rm eq}$)." + We can express, We can express +"For the beta-inodell applied in the previous section. the eas density distribution is given by This iuplics a central densitv ny = "" "" and a gas lass within 1MMpe of A, = 131107 M.","For the beta-modell applied in the previous section, the gas density distribution is given by This implies a central density $n_0$ = $^{-3}$ $^{-3}$ and a gas mass within Mpc of $M_{\rm gas}$ = $^{13}$ $_{\odot}$." +" Asstuning spherical svinmetry aud the eroup to be approximately in lydrostatic equilibrium. the total eravitating mass follows the relation With the observed paramicters this results in an integrated total mass of AM = 63110 NE, within 1 Mpe radius and a eas mass fraction of21%."," Assuming spherical symmetry and the group to be approximately in hydrostatic equilibrium, the total gravitating mass follows the relation With the observed parameters this results in an integrated total mass of $M_{\rm total}$ = $^{13}$ $_{\odot}$ within 1 Mpc radius and a gas mass fraction of." +.. Using instead the galaxy velocity dispersion as derived from optical observations. σ = 166 kin/s (Lecdlow ct al.," Using instead the galaxy velocity dispersion as derived from optical observations, $\sigma$ = 466 km/s (Ledlow et al." + 1996: see also Sakai et al., 1996; see also Sakai et al. + 1991). and a core radius of 73 kpc we ect a mass of ~7 11018 AL. within 1 Mpc. which is well consistent with the value obtained purely from the X-ray data.," 1994), and a core radius of 73 kpc we get a mass of $\sim$ $^{13}$ $_{\odot}$ within 1 Mpc, which is well consistent with the value obtained purely from the X-ray data." + The profile of total and eas mass is displaved in Fie. 3Se, The profile of total and gas mass is displayed in Fig. \ref{mass}. +" Errors on the amass απο obtainec from the temperature range allowed by the N-ray spectral analysis. KT = 1540.2 keV. aud a temperature profile for a fauuly of 5 models with polvtropic index + in the range 0.9 19,"," Errors on the mass $M_{\rm total}$ are obtained from the temperature range allowed by the X-ray spectral analysis, $kT$ = $\pm{0.2}$ keV, and a temperature profile for a family of $\gamma$ models with polytropic index $\gamma$ in the range 0.9 – 1.3." + Iu the polvtropic mocels the nominal temperature is fixed at the core radius., In the polytropic models the nominal temperature is fixed at the core radius. + There are sole) spectacular examples of pressure interaction between the radio aud X-ray eas in clusters of galaxies (c.g... Bohringer ct al.," There are some spectacular examples of pressure interaction between the radio and X-ray gas in clusters of galaxies (e.g., Böhhringer et al." + 1993. 1995. Tlarris ct al.," 1993, 1995, Harris et al." + 1991. Clarke et al.," 1994, Clarke et al." + 1997. Otani et al.," 1997, Otani et al." + 1998)., 1998). + In. the present case. we do not fud conspicuous morphological correlations between radio- and N-ray cussion (Fig. 1)).," In the present case, we do not find conspicuous morphological correlations between radio- and X-ray emission (Fig. \ref{over_rx}) )." + This mav be partly due to the narrowness of the jet. the still limited spatial resolution of the PSPC. aud the 2D view of the 3D source structure.," This may be partly due to the narrowness of the jet, the still limited spatial resolution of the PSPC, and the 2D view of the 3D source structure." + Changes of the jet orientation angle near the locations of some optical chain galaxies. now also cletected as strong N-rayv sources. were already noted by Strom ot al. (," Changes of the jet orientation angle near the locations of some optical chain galaxies, now also detected as strong X-ray sources, were already noted by Strom et al. (" +1983).,1983). + As background we close (1) à ποιαοςπου ring around the arect source. and (11) a source-free circular region near the arect source.," As background we chose (i) a source-free ring around the target source, and (ii) a source-free circular region near the target source." + This allows to check for scusitivity against he backeround correction., This allows to check for sensitivity against the background correction. + All majour fits were repeated or both background geometries., All majour fits were repeated for both background geometries. + Further. we note that the source enussion m the first bin (below 0.1 keV) is weak.," Further, we note that the source emission in the first bin (below 0.4 keV) is weak." + We repeated all fits after having removed he first bin from he spectrum., We repeated all fits after having removed the first bin from the spectrum. + Tn all cases. the results preseuted below are ound to be robust.," In all cases, the results presented below are found to be robust." + First. several single component models were fit to the N-rayv spectrum. starting with à powerlaw (pl).," First, several single component models were fit to the X-ray spectrum, starting with a powerlaw (pl)." + Although lis model fits the N-vay spectrum (A44 = 13). the derived parameters are unusual.," Although this model fits the X-ray spectrum $\chi{^{2}}_{\rm red}$ = 1.3), the derived parameters are unusual." + The slope is extremely steep = 5. and there is evidence for strong excess absorption (about & times the Galactic value).," The slope is extremely steep $\simeq$ –5, and there is evidence for strong excess absorption (about 8 times the Galactic value)." + A single steep pl amav be minuicked by a fat pl plus soft excess., A single steep pl may be mimicked by a flat pl plus soft excess. + DPariuneterizing the excess as black body auc fixing 1.9. we do not find a successtul fit.," Parameterizing the excess as black body and fixing –1.9, we do not find a successful fit." + This also holds for a sinele pl iu which absorption is fixed to the Galactic value ud = 33)., This also holds for a single pl in which absorption is fixed to the Galactic value $\chi{^{2}}_{\rm red}$ = 3.3). +" A sinele rs model with mctal abundances of 0.35 « solar does not eive an acceptable fit. either (N, = 2.1)."," A single rs model with metal abundances of 0.35 $\times$ solar does not give an acceptable fit, either $\chi{^{2}}_{\rm red}$ = 2.4)." + Lowering the abundances up to = 0.1 s solar vielcds, Lowering the abundances up to $\approxlt$ 0.1 $\times$ solar yields +ages between 63 Myr and 315 Myr (third suapshot).,ages between 63 Myr and 315 Myr (third snapshot). + Moreover. the northern part of the SAIC body is covered with clusters in this age rauge.," Moreover, the northern part of the SMC body is covered with clusters in this age range." + Finally. the last suapshot displavs clusters older than 315 Myr (up to ~ 1 C).," Finally, the last snapshot displays clusters older than 315 Myr (up to $\sim$ 1 Gyr)." + These clusters inauly populate the western part of the SAIC iain body aud ouly a few are found in the north or in the east., These clusters mainly populate the western part of the SMC main body and only a few are found in the north or in the east. + Supershell 301 A contains fewer of these older objects than 37 A aud they are mainly located at the western rimi of the shell. while iu 27 A they ave widely distributed.," Supershell 304 A contains fewer of these older objects than 37 A and they are mainly located at the western rim of the shell, while in 37 A they are widely distributed." +" Generally. the cluster distribution in 301 A lndicates a continuous cluster formation from a few Myr to 1 αντ,"," Generally, the cluster distribution in 304 A indicates a continuous cluster formation from a few Myr to 1 Gyr." + According to the standard model of shell formation (MeCvay&ἹναατοςL987) the older objects are supposed to be found iu the ceuter of the shell while vounger objects are distributed around the edge., According to the standard model of shell formation \citep{mccray87} the older objects are supposed to be found in the center of the shell while younger objects are distributed around the edge. + As ienutioned above. the vounger objects in 37 A and 301 A are clustered. toward the eastern anc the western run of the shells. respectively.," As mentioned above, the younger objects in 37 A and 304 A are clustered toward the eastern and the western rim of the shells, respectively." + Shell interaction due to collisions following shell expansion has probably triggered the cluster formation iu the inter-shell region as well as at the two opposing rims., Shell interaction due to collisions following shell expansion has probably triggered the cluster formation in the inter-shell region as well as at the two opposing rims. + The reason might be that the shell is surrounded by an interstellar mediuu with differiug densities., The reason might be that the shell is surrounded by an interstellar medium with differing densities. + Shell expausiou iuto hieher-densitv reeious leads to slower expausion: the correspondiueg strong gas conrpressionu leads to cuhanced star formation in that region., Shell expansion into higher-density regions leads to slower expansion; the corresponding strong gas compression leads to enhanced star formation in that region. + On the other laud. if the shell expands iuto a region with lower deusitv the star formation rate will be lower since there is less compression and less material to be swept up.," On the other hand, if the shell expands into a region with lower density the star formation rate will be lower since there is less compression and less material to be swept up." + We confirm C06's finding that the location of the voune SMC clusters is correlated with III intensities. which decrease with increasing age.," We confirm C06's finding that the location of the young SMC clusters is correlated with HI intensities, which decrease with increasing age." + Mizunoctal.(2001a) found that vouug emission objects are positionallv well correlated with CO clouds. while emissiouless objects of ages ~6-L00 Myr. do not show any correlation to the CO clouds.," \citet{mizuno01a} found that young emission objects are positionally well correlated with CO clouds, while emissionless objects of ages $\sim$ 6-100 Myr do not show any correlation to the CO clouds." + Emission objects were excluded from our sample and therefore we cannot investigate their possible association with CO clouds., Emission objects were excluded from our sample and therefore we cannot investigate their possible association with CO clouds. + The youngest star clusters are found mostly in the LMC III supereiant shells (SCSs) 30. Doradus.4. SCS 7 (LAIC 5). SCS 11 (LAIC 1). SCS 12 (LAIC 3). aud SCS 19 (LAIC 2) and in the 103 eiaut shells published by Teametal.(1999.2003). (seealsoDaviesctal.1976:Meaburn 1980).," The youngest star clusters are found mostly in the LMC HI supergiant shells (SGSs) 30 Doradus, SGS 7 (LMC 5), SGS 11 (LMC 4), SGS 12 (LMC 3), and SGS 19 (LMC 2) and in the 103 giant shells published by \citet{kim99,kim05} \citep[see also][]{davies76,meaburn80}." +. The authors classified the shells iuto three categories: the are simple expanding stalled shells (solid). consist of sinaller interlocked shells aud their rius often contain sinaller shells (SCS 1. 9. 10. 12. 17. 18. 20: dashed). aud. aye surrounded by another SCS (SGS 11. 19: dash-dotted).," The authors classified the shells into three categories; the are simple expanding stalled shells (solid), consist of smaller interlocked shells and their rims often contain smaller shells (SGS 4, 9, 10, 12, 17, 18, 20; dashed), and are surrounded by another SGS (SGS 11, 19; dash-dotted)." + Ii most of the complex SCSs (see Fig. 94) , In most of the complex SGSs (see Fig. \ref{fig:lmcageall}) ) +star clusters are located along the rius aud lack the vouugest clusters., star clusters are located along the rims and lack the youngest clusters. + The sinaller shells along their rims nuelt iudicate that trigecred star formation occurred recently., The smaller shells along their rims might indicate that triggered star formation occurred recently. + The propagated SOGSs may have formed bv sequential star formation., The propagated SGSs may have formed by sequential star formation. + De Doer et al. (, De Boer et al. ( +1998). proposed a scenario in which star formation in the LMC is tigeered by the eas bene compressed at the leading edge due to the bow-shocks as the LMC inoves through. the gaseous. Galactic halo around the Milkv. Way.,1998) proposed a scenario in which star formation in the LMC is triggered by the gas being compressed at the leading edge due to the bow-shocks as the LMC moves through the gaseous Galactic halo around the Milky Way. + The bow-shock compresses large areas Which leads to star formation ou a large scale., The bow-shock compresses large areas which leads to star formation on a large scale. + Due to the LAIC’s rotation. the material at the leading edge will move away clockwise ancl distribute itself around the LAIC’s riu.," Due to the LMC's rotation, the material at the leading edge will move away clockwise and distribute itself around the LMC's rim." + Iu this scenario oue would expect to find a progression in the age of star clusters along the ivection of the rotation Gu Fie., In this scenario one would expect to find a progression in the age of star clusters along the direction of the rotation (in Fig. + 9 the ealaxy rotates clockwise)., \ref{fig:lmcageall} the galaxy rotates clockwise). + The LAIC dise shows solid-body rotation aud has an approximate full rotation velocity for a simall inclination of ~L50 lans| at 1.5 kpe (deBoer1998)., The LMC disc shows solid-body rotation and has an approximate full rotation velocity for a small inclination of $\sim$ 150 $^{-1}$ at 1.5 kpc \citep{deBoer98}. +. The time of one full rotation period is ~250 Myr., The time of one full rotation period is $\sim$ 250 Myr. + If present the progression of age along the galaxys rim should be detectable., If present the progression of age along the galaxy's rim should be detectable. + The vouugest shell structures le in the proximity of 30 Doradus. the largest star forming reeion of the LMC.," The youngest shell structures lie in the proximity of 30 Doradus, the largest star forming region of the LMC." + 30 Doradus lies close to the leading edge of the LMC., 30 Doradus lies close to the leading edge of the LMC. + It is the largest star forming region oei the galaxy and may very well be related to the bow shock., It is the largest star forming region in the galaxy and may very well be related to the bow shock. + Grebel&Drauduer(1998) used Cepheids aud other superelant stars to study the recent star formation listory of the LMC., \citet{grebel98} used Cepheids and other supergiant stars to study the recent star formation history of the LMC. + They found that the majority of objects vounger than 30 Myr are concentrated ou the south-eastern border. while others are widely distributed across the entire disk which cannot be explained with the bow-shock star formation model.," They found that the majority of objects younger than 30 Myr are concentrated on the south-eastern border, while others are widely distributed across the entire disk which cannot be explained with the bow-shock star formation model." +" A progression of age was found iu several giant shells along the LMC rmi moving from the south-east (LMC 2) to the north (NGC ISIN at a = ο""00, 6 = 6626'00""3 (de"," A progression of age was found in several giant shells along the LMC rim moving from the south-east (LMC 2) to the north (NGC 1818 at $\alpha$ = $5^h04^m03^s$, $\delta$ = $-66^{\circ}26'00''$ ) \citep{deBoer98}." + 30 Doradus has an age of 3-5 Myr. LMC | of 9-16 Myr. and NGC I818 of 25-30 Myr (ParkerCiyebel1997).," 30 Doradus has an age of 3-5 Myr, LMC 4 of 9-16 Myr, and NGC 1818 of 25-30 Myr \citep{Parker93,Will95,Braun97,Grebel97}." +. The difference in age between these shells corresponds to their distance aloug the border of the disk divided by the ealaxw’s rotation velocity (Mastropietroetal.2009)., The difference in age between these shells corresponds to their distance along the border of the disk divided by the galaxy's rotation velocity \citep{mastropietro09}. +. We find no evidence for such a cluster age distribution or the LMC., We find no evidence for such a cluster age distribution for the LMC. + The older clusters are mostly located iu he bar region and a few are located along the rim., The older clusters are mostly located in the bar region and a few are located along the rim. + Most clusters populating the LALIC bar were adopted roni the sample published by PUOO0., Most clusters populating the LMC bar were adopted from the sample published by PU00. + Ages of clusters older than ~1 Cyr cannot be derived due to the mated photometric depth of the MCTPSs. which docs not resolve MSTOs of older clusters.," Ages of clusters older than $\sim$ 1 Gyr cannot be derived due to the limited photometric depth of the MCPSs, which does not resolve MSTOs of older clusters." + Overall our spatial cluster age distribution does not support ran pressure as the Παν ageut of cluster formation iu the LMC.," Overall, our spatial cluster age distribution does not support ram pressure as the primary agent of cluster formation in the LMC." +" As mentioned above. the highest concentration of voung clusters can be found in the 30 Doradus region 22070) in the southeastern part of the LMC at roughly a = 538"". 8 = 69°06"""," As mentioned above, the highest concentration of young clusters can be found in the 30 Doradus region 2070) in the southeastern part of the LMC at roughly $\alpha$ = $5^h38^m$, $\delta$ = $-69^{\circ}06'$." + In this laree star {ωντις complex nauy ος are interlocking. where active star formation occurred simultaneously (simetal. 1999).," In this large star forming complex many SGSs are interlocking, where active star formation occurred simultaneously \citep{kim99}." +. A number of smaller shells have formed- along the tims of the supershells. as expected for seltf-propagatiugπι star formation (e.e.. MeCvrayv&Ἱναίαῖος1987).," A number of smaller shells have formed along the rims of the supershells, as expected for self-propagating star formation \citep[e.g., ][]{mccray87}." +. The IIT regions are sometimes associated with the IIT shells and the largest coucentration can be found iu the 30 Doradus region as well as iu SCSs hosting the vouneest star clusters., The HII regions are sometimes associated with the HI shells and the largest concentration can be found in the 30 Doradus region as well as in SGSs hosting the youngest star clusters. + Fie., Fig. + 10. displays six snapshots showiug the spatial distribution of LAIC star clusters within differeut age bins., \ref{fig:lmcageslides} displays six snapshots showing the spatial distribution of LMC star clusters within different age bins. + The first snapshot shows onlv clusters vounecr than 20 My., The first snapshot shows only clusters younger than 20 Myr. + The star clusters are located iu the 30 Doradus region. LMC Ll. in the western part of the bar. aud along the rim iu the soutlwestern part of the ealaxy.," The star clusters are located in the 30 Doradus region, LMC 4, in the western part of the bar, and along the rim in the southwestern part of the galaxy." + Star clusters within the ageo range of 20 Myr, Star clusters within the age range of 20 Myr +Basically two intervening effects modulate the integrated SED of spherical models with respect to their correspoudiug plane-parallel cases.,Basically two intervening effects modulate the integrated SED of spherical models with respect to their corresponding plane-parallel cases. + First. as a eeneral trend for fixed aandg.. spherical model atmospheres tend to display a lower clectromic pressure aud a cooler temperature profile sstellu spatial coordinate (ic.radiusoropticaldepth.cf.e.g.Scholz&Tsuji 1981).," First, as a general trend for fixed and, spherical model atmospheres tend to display a lower electronic pressure and a cooler temperature profile stellar spatial coordinate \citep[i.e.\ radius or optical depth, +cf. e.g.][]{st84}." + To some extent. this is the physical consequence of the decreasing eravity when moving outward of stellar plotosphere: with a lower eravitv. i fact. thermodvuauuical equilibriun in the external lavers readjusts such as to allow a lower pressure of the electronic plasma (because of an iucreased mean distance between atoms and a higher dumping potential for the bouud-bouud aud bouud-free ο transitions) aud a cooler temperature. still sufficient however to “sustain” the atimosphere structure.," To some extent, this is the physical consequence of the decreasing gravity when moving outward of stellar photosphere; with a lower gravity, in fact, thermodynamical equilibrium in the external layers readjusts such as to allow a lower pressure of the electronic plasma (because of an increased mean distance between atoms and a higher dumping potential for the bound-bound and bound-free $e^-$ transitions) and a cooler temperature, still sufficient however to “sustain” the atmosphere structure." + As a result. for fixed aandlogg.. the SED of a “spherical” star ds therefore expected to display sharper absorption lines and a redde? coutimmun.," As a result, for fixed and, the SED of a “spherical” star is therefore expected to display sharper absorption lines and a “redder” continuum." + Amoue others. this should also reflect iu a less severe blauketiug absorption (seeinthisscusetheexperimentsofTauschildtcetal.1999)) as a consequence of a reduced lend of metal absorption lines at shor waveloneth.," Among others, this should also reflect in a less severe blanketing absorption \citep[see in this sense the experiments of][]{hau99b} as a consequence of a reduced blend of metal absorption lines at short wavelength." + A second related effect that should be deal with. when comparing plane-parallel aud spherical model atinosphlieres. coucerns Bub darkening.," A second related effect that should be dealt with, when comparing plane-parallel and spherical model atmospheres, concerns limb darkening." +" Due to the geometry. in fact. he integrated flux tha emerges frou a ""spherical star receives a more Huportant contribution from low-eravity cooler lavers. and appears therefore in average “cooley” with respect to its correspouding plane-parallel"," Due to the geometry, in fact, the integrated flux that emerges from a “spherical” star receives a more important contribution from low-gravity cooler layers, and appears therefore in average “cooler” with respect to its corresponding plane-parallel" +"""So on observations.",do on observations. + The quality and size of the Images is chosen to match that of the PC chip in WFPC? or the HRC channel 1 ACS., The quality and size of the images is chosen to match that of the PC chip in WFPC2 or the HRC channel in ACS. + In this way. we can make a proper comparison with observed clusters contained on NGO6.," In this way, we can make a proper comparison with observed clusters contained on NG06." +" The procedure to create images ts like the one described in ""Setail in NGO6 and NGO7.", The procedure to create images is like the one described in detail in NG06 and NG07. + Wetse DAOPHOT (Stetson to add stars from a list of positions and magnitudes onto a base image., We use DAOPHOT \citep{ste87} to add stars from a list of positions and magnitudes onto a base image. + With the goal of 1neluding realistic background noise. we use as a base a WFPC? image of a sparse field with the few present stars cleanly subtracted.," With the goal of including realistic background noise, we use as a base a WFPC2 image of a sparse field with the few present stars cleanly subtracted." + We modify the base nage to have a lareer number of pixels than the PC chip on ΜΕΡΟΣ. and we locate the center of the cluster at the center of the base image.," We modify the base image to have a larger number of pixels than the PC chip on WFPC2, and we locate the center of the cluster at the center of the base image." + The utilized point spread function (PSF) ts obtained from observed data and it does not include variations across the chip., The utilized point spread function (PSF) is obtained from observed data and it does not include variations across the chip. + Since the center of observed clusters is not known a priori. we made a blind test. in which the center of the models were given an arbitrary shift in the three spatial coordinates. and the new center was calculated using the octants method described in detail on NGO6.," Since the center of observed clusters is not known a priori, we made a blind test, in which the center of the models were given an arbitrary shift in the three spatial coordinates, and the new center was calculated using the octants method described in detail on NG06." +" We choose a guess center and a radius. we count the stars present in eight ""pie slices” segments defined by the chosen center and radius and we calculate the standard deviation of the eight numbers."," We choose a guess center and a radius, we count the stars present in eight 'pie slices' segments defined by the chosen center and radius and we calculate the standard deviation of the eight numbers." + Using the same radius. we move to a new guess center and repeat the procedure several times around the initial guess center.," Using the same radius, we move to a new guess center and repeat the procedure several times around the initial guess center." + In the end we have a map of center locations and a standard deviation value associated to each of them., In the end we have a map of center locations and a standard deviation value associated to each of them. + We fit a smoothing spline to the resulting surface and find the location of the minimum defined by the erid of guess centers. which we take as the true center.," We fit a smoothing spline to the resulting surface and find the location of the minimum defined by the grid of guess centers, which we take as the true center." + For this procedure. we used every star in the list. which implies using many more stars than the ones that would be available to an observer.," For this procedure, we used every star in the list, which implies using many more stars than the ones that would be available to an observer." + Our goal is to test the method for a complete dataset. not to test the observed accuracy of the measurement. since this has already been tested in NGO6 and NGO7.," Our goal is to test the method for a complete dataset, not to test the observed accuracy of the measurement, since this has already been tested in NG06 and NG07." + The centers were calculated for three projections on the x-y. x-z. and y-z planes.," The centers were calculated for three projections on the x-y, x-z, and y-z planes." + In the end we found that the method is able to recover the center with an accuracy of 0.01pe (—0.005/.)., In the end we found that the method is able to recover the center with an accuracy of 0.01pc $\sim$ $r_c$ ). + The tests performed in NGO6 yield an error for the observed center location that corresponds to «0.051..., The tests performed in NG06 yield an error for the observed center location that corresponds to $\sim$ $r_c$. + In general. the effect of measuring a density profile using the wrong radius is not necessarily to change the central surface brightness slope. but instead. a drop 1n the central measurement point is created.," In general, the effect of measuring a density profile using the wrong radius is not necessarily to change the central surface brightness slope, but instead, a drop in the central measurement point is created." + Seeing such a drop is actually an indication. of having the wrong center. ?. use this fact as a test for correct centering in their work. for example.," Seeing such a drop is actually an indication of having the wrong center, \citet{lan08} use this fact as a test for correct centering in their work, for example." + Despite that drop. the slope of the other points up to the core radius is normally the same as the one using the correct radius.," Despite that drop, the slope of the other points up to the core radius is normally the same as the one using the correct radius." + This is clearly seen comparing the profiles for omega Centauri between Noyolaetal.(2008) and Anderson&vanderMarel(2010)., This is clearly seen comparing the profiles for omega Centauri between \citet{noy08} and \citet{and10}. +". Despite using very different centers. and getting density profiles with different shapes. the slope of the profile between 15"" and the core radius is consistent in both cases."," Despite using very different centers, and getting density profiles with different shapes, the slope of the profile between 15"" and the core radius is consistent in both cases." +citelivperz)).,). +" Only few objects are erroneously attributed o high redshitts: these objects are very fait salaxies. ron detected iu the C,ijo ald Viso filters. determine a confusion in the location of the Lyman break."," Only few objects are erroneously attributed to high redshifts: these objects are very faint galaxies, non detected in the $U_{300}$ and $V_{450}$ filters, determining a confusion in the location of the Lyman break." + Iu Fig., In Fig. + 12 he input absolute magnitude is compared o the absolute maenitude computed byAgperz. usiug he redshift and the spectral type best fit.," \ref{mmsimul} the input absolute magnitude is compared to the absolute magnitude computed by, using the redshift and the spectral type best fit." + The objects represented iu hese two paucls have been selected. using heir photometric aud their input redshifts. in the two redshift bins shown in Fie. 10..," The objects represented in these two panels have been selected using their photometric and their input redshifts, in the two redshift bins shown in Fig. \ref{lfKsimul}." + We considered oulv objects with A«x2]. ie the same objects used iu the LF estimate.," We considered only objects with $K \le 24$, i.e. the same objects used in the LF estimate." + The agreement is very good. with very few outliers.," The agreement is very good, with very few outliers." + Iu the eft pauecl. we cau notice the rapid decrease of galaxies with My&16. producing large error bars iu the binned estimate ofthe LF.," In the left panel, we can notice the rapid decrease of galaxies with $M_K \ga -16$, producing large error bars in the binned estimate ofthe LF." + In the range between :=1 aud 2. the ack of faint objects due to observational limits prevents a good estimate of the faint-eud slope α using the STY uecthod.," In the range between $z=1$ and $2$, the lack of faint objects due to observational limits prevents a good estimate of the faint-end slope $\alpha$ using the STY method." + Nevertheless. the right end is well reproduced x the binned methods.," Nevertheless, the bright end is well reproduced by the binned methods." + Siuilar analysis comparing methods for LE estimate woueh simulations have been carried out bw other uthors., Similar analysis comparing methods for LF estimate through simulations have been carried out by other authors. + Willner (1997)) found that the STY method ends to slightly underestimate the faiut-eud compared to 1e input value., Willmer \cite{willmer}) ) found that the STY method tends to slightly underestimate the faint-end compared to the input value. + Iun our case. we found a sill overestimate of a. but the large error bars are consistent with the oeiput value.," In our case, we found a small overestimate of $\alpha$, but the large error bars are consistent with the input value." + Concerning the non parametric methods. the y.πάν of Takeuchi et ((2000)) demonstrated that for large and spatially homogeneous samples the LF estimate is not biased. whereas the fant-end is subject to large fluctuations when the sample is small.," Concerning the non parametric methods, the study of Takeuchi et \cite{take}) ) demonstrated that for large and spatially homogeneous samples the LF estimate is not biased, whereas the faint-end is subject to large fluctuations when the sample is small." + The overestimate of the low redshift LF ou the faintest dus ds simular to ours. according to their figures. aud still consistent with the iuput LF due to the large error bars.," The overestimate of the low redshift LF on the faintest bins is similar to ours, according to their figures, and still consistent with the input LF due to the large error bars." + Ou the coutrary. at higher redshift we see a decline iu the faintest bins. that is also been shown by Liu et ((1998)).," On the contrary, at higher redshift we see a decline in the faintest bins, that is also been shown by Liu et \cite{liu}) )." + Iu sunmuary. the procedure used to recover the LF iu the range 2=0. 1 can be considered as reliable. aud we did not try to take iuto account the snall svstematic effects iieutioned above.," In summary, the procedure used to recover the LF in the range $z=0$ – $1$ can be considered as reliable, and we did not try to take into account the small systematic effects mentioned above." + Inthe range :=1 2. the results of the STY inethod have to be taken with care. but the nol parametric estimate of the LF still provides a good fit of the bright-cucl.," In the range $z=1$ – $2$, the results of the STY method have to be taken with care, but the non parametric estimate of the LF still provides a good fit of the bright-end." + We compute the LEs using the three methods described iu Sect. {τιν, We compute the LFs using the three methods described in Sect. \ref{lf_estim}. + Iun particular. for the non-paraimioetric methods we adopt a biuniug of l magnitude or 2 maguitudes at the faint eund to have a conspicuous uunuber of objects in each biu.," In particular, for the non-parametric methods we adopt a binning of $1$ magnitude or $2$ magnitudes at the faint end to have a conspicuous number of objects in each bin." + To compute the hunuinositv functions we divide the sample in redshift slices. larger than the typica errors of photometric redshifts. to minimize the chanec of redshift bin aud to studv the redshift evolution of the LFs.," To compute the luminosity functions we divide the sample in redshift slices, larger than the typical errors of photometric redshifts, to minimize the change of redshift bin and to study the redshift evolution of the LFs." +" The adopted limiting maguitude is A,=2 in both he IIDE-N aud IIDE-S. Following the xocedure described above. we iterate he computation of the biuue or paraiuetrized LE."," The adopted limiting magnitude is $K_s = 24$ in both the HDF-N and HDF-S. Following the procedure described above, we iterate the computation of the binned or parametrized LF." + We choose to realize 100 iterations. sufficient to estimate the effect of random selection of redshifts.," We choose to realize $100$ iterations, sufficient to estimate the effect of random selection of redshifts." + During the photometric redshift calculation we inpose a rauge of absolute D magnitudes: solutions with Mp outside the range |.28.9| are considered forbidden also when estimating he LF.," During the photometric redshift calculation we impose a range of absolute $B$ magnitudes: solutions with $M_B$ outside the range $[-28,-9]$ are considered forbidden also when estimating the LF." +" Because the A -bau is the reddest one. the absolute magnitudes have been computed using abways the A, apparent magnitudes."," Because the $K_s$ -band is the reddest one, the absolute magnitudes have been computed using always the $K_s$ apparent magnitudes." + Studvine the A-band at redshifts Doc2 ineans to map the rest-frame Z-baund cussion: in Fie., Studying the $K$ -band at redshifts $z\sim 2$ means to map the rest-frame $I$ -band emission: in Fig. + 13 we show that these magnitudes are strictly correlated arc thus they basically map the same stellar population., \ref{ikij} we show that these magnitudes are strictly correlated and thus they basically map the same stellar population. +" This behaviour can be explained considering the enmüttiug stellar population: even at :~2 the huninosity at the wavelengths covered by the A, filter is always produced by the old star population. the £000 bbreak still being insicle the J filter."," This behaviour can be explained considering the emitting stellar population: even at $z \sim 2$ the luminosity at the wavelengths covered by the $K_s$ filter is always produced by the old star population, the $4000$ break still being inside the $J$ filter." + Furthermore. A. magnitudes are not affected by receut bursts of star formation.," Furthermore, $K_s$ magnitudes are not affected by recent bursts of star formation." + For this reason. and because of the characteristics of the A-correction discussed in Sect. 123..," For this reason, and because of the characteristics of the $k$ -correction discussed in Sect. \ref{kcorr}," + we cousidered that we can sately compute A.-baud absolute magnitudes at least up to a redshift of 2., we considered that we can safely compute $K_s$ -band absolute magnitudes at least up to a redshift of $2$ . + We have also estimated the -baud LF in the redshift range ;=[0.1] from the J-sclected subsample. aud in the redshift range |1.2| by selecting the objects iu the Άν ατα sample that better approximate the J filter rest frame.," We have also estimated the $J$ -band LF in the redshift range $z=[0,1]$ from the $J$ -selected subsample, and in the redshift range $[1,2]$ by selecting the objects in the $K_s$ -band sample that better approximate the $J$ filter rest frame." +suddenly changed around 1999 and (he step function fit appears to support this hypothesis.,suddenly changed around 1999 and the step function fit appears to support this hypothesis. + The large 4? is to be expected as Eq. (, The large $\chi^2$ is to be expected as Eq. ( +1) that is used to caleulate 42. does not really fit the observed data at all times.,"1) that is used to calculate $\Delta R$, does not really fit the observed data at all times." + Ideally. one should remove the oscillatory component in frequency variation before considering longer period variations. but for simplicitw. P consider fits at interval of 1 vear which will be at the same phase of oscillatory component and further. select the phase such that the fits are the best in some sense.," Ideally, one should remove the oscillatory component in frequency variation before considering longer period variations, but for simplicity, I consider fits at interval of 1 year which will be at the same phase of oscillatory component and further, select the phase such that the fits are the best in some sense." + These points are marked by filled squares in Fie., These points are marked by filled squares in Fig. + 2., 2. + Table 1 gives the results obtained [or these sets. which includes the 4? per degree of [reedom as well as (he average 10.7 cm radio flux during the Gime interval covered by the data set. which is a measure of solar activity.," Table 1 gives the results obtained for these sets, which includes the $\chi^2$ per degree of freedom as well as the average 10.7 cm radio flux during the time interval covered by the data set, which is a measure of solar activity." + Looking at this table it is clear that the radius is nol changing continuously., Looking at this table it is clear that the radius is not changing continuously. + In fact. most of the radius variation has occurred between 1993.4 and 1999.4.," In fact, most of the radius variation has occurred between 1998.4 and 1999.4." + Possible radius variation during 1996.41998.4 and 1999.42002.4 is less than 1 km., Possible radius variation during 1996.4–1998.4 and 1999.4–2002.4 is less than 1 km. + The solar activity. did increase signilicantly during the period 1998.41999.4. but there has been comparable change in activity during other periods too.," The solar activity did increase significantly during the period 1998.4–1999.4, but there has been comparable change in activity during other periods too." + Ilence that cannot explain (he variation seen in Table 1., Hence that cannot explain the variation seen in Table 1. + This happens to be the period during which contact with SOLO satellite was lost and it is most likely that this variation reflects svstematic errors arising from changes in the MDI instrument that may have occurred. curing recovery. of the satellite., This happens to be the period during which contact with SOHO satellite was lost and it is most likely that this variation reflects systematic errors arising from changes in the MDI instrument that may have occurred during recovery of the satellite. + Even if we assume that (his variation is real. the rate of shrinking is not 1.5 km tas claimed by DCS. but something like 3 kan | during 1998.41999.4 and essentially no variation al other times.," Even if we assume that this variation is real, the rate of shrinking is not 1.5 km $^{-1}$ as claimed by DGS, but something like 3 km $^{-1}$ during 1998.4–1999.4 and essentially no variation at other times." + Thus. anv model to explain this [requency change by a radius variation must explain why there is little radius variation during most of the time and why all variation is confined to less than 1 vr αἱ some intermediate phase of solar cvele.," Thus, any model to explain this frequency change by a radius variation must explain why there is little radius variation during most of the time and why all variation is confined to less than 1 yr at some intermediate phase of solar cycle." + In order to study the robustuess of the inferred radius variation. I attempt the fits bv restricting the mode set or the data sets and the results are summarized in Table 2.," In order to study the robustness of the inferred radius variation, I attempt the fits by restricting the mode set or the data sets and the results are summarized in Table 2." + If high degree modes are neglected. then the fits to data using Eq. (," If high degree modes are neglected, then the fits to data using Eq. (" +1) improve to some extent. which is mainlv because the total variation in frequencies reduces with degree.,"1) improve to some extent, which is mainly because the total variation in frequencies reduces with degree." + Nevertheless. the fit to linear variation in AJ? is still bad and its slope keeps reducing as the upper limit on (is reduced.," Nevertheless, the fit to linear variation in $\Delta R$ is still bad and its slope keeps reducing as the upper limit on $\ell$ is reduced." + Thus if only modes with 140«6<250 are used the radius variation comes out to be —0.57£0.08 km | (with a 4?= 2.6). while if the upper limit on ( is reduced to 200. it becomes —0.4720.17 km ! (4?= 5)2).," Thus if only modes with $140<\ell<250$ are used the radius variation comes out to be $-0.57\pm0.08$ km $^{-1}$ (with a $\chi^2=2.6$ ), while if the upper limit on $\ell$ is reduced to 200, it becomes $-0.47\pm0.17$ km $^{-1}$ $\chi^2=2$ )." + In these cases if a step function is fitted the 4? comes out to be 2.1., In these cases if a step function is fitted the $\chi^2$ comes out to be 2.1. + Figure 3 shows the fits in these cases., Figure 3 shows the fits in these cases. + It can be seen that the magnitude of possible discontnuity. around 1999 reduces as the upper limit on (£ is reduced and is hardlv visible when the upper limit is reduced (o £6=200., It can be seen that the magnitude of possible discontinuity around 1999 reduces as the upper limit on $\ell$ is reduced and is hardly visible when the upper limit is reduced to $\ell=200$. + In this case (he errors in inlerred radius ave rather large and (he one vear oscillations are essentially wiped out by statistical fluctuations., In this case the errors in inferred radius are rather large and the one year oscillations are essentially wiped out by statistical fluctuations. + The reduction in 4? is mainly due to increase in estimated errors in AR., The reduction in $\chi^2$ is mainly due to increase in estimated errors in $\Delta R$. + Antia et al. (, Antia et al. ( +2001) have shown that the amplitude of oscillatory term reduces with decreasing £6 and that also contributes to improvement in fits.,2001) have shown that the amplitude of oscillatory term reduces with decreasing $\ell$ and that also contributes to improvement in fits. + If the £ range is reduced still, If the $\ell$ range is reduced still +In this paper. we have analyzed (he rotational properties of dense molecular cloud cores [formed in (wo magnetized. sell-eravitating molecular cloud simulations with a decaving turbulence.,"In this paper, we have analyzed the rotational properties of dense molecular cloud cores formed in two magnetized, self-gravitating molecular cloud simulations with a decaying turbulence." + The two simulations differ bv the strength of the magnetic field in the clouds with one cloud being mildly magnetically supercritical and the other being strongly maenetically supercritical., The two simulations differ by the strength of the magnetic field in the clouds with one cloud being mildly magnetically supercritical and the other being strongly magnetically supercritical. + Our results show Chat the formation elliciency of dense cores is strongly reduced with increasing importance of (he maenetic field in the cloud (going down [rou 33 percent per lree-fall Gime in (he strongly. supercritical cloud to 6 percent for the mildly supercritical cloud)., Our results show that the formation efficiency of dense cores is strongly reduced with increasing importance of the magnetic field in the cloud (going down from 33 percent per free-fall time in the strongly supercritical cloud to 6 percent for the mildly supercritical cloud). + We also observe that the median value of the specific angular momentum of the hieh densitv cores in the mildly supercritical simulation is smaller than the values derived for cores in the strongly supercritical simulation., We also observe that the median value of the specific angular momentum of the high density cores in the mildly supercritical simulation is smaller than the values derived for cores in the strongly supercritical simulation. + This result is consistent with the fact that magnetic braking which leads to angular momentum loss is plaving a more important role in the cloud where the magnetic field is stronger., This result is consistent with the fact that magnetic braking which leads to angular momentum loss is playing a more important role in the cloud where the magnetic field is stronger. + We have focused our attention on the discrepancies (hat may arise between estimates of the specilic angular momentum of the cores derived from the elobal velocity exadient method commonly. used in the observations and its the true value measured in the intrinsic space., We have focused our attention on the discrepancies that may arise between estimates of the specific angular momentum of the cores derived from the global velocity gradient method commonly used in the observations and its the true value measured in the intrinsic three-dimensional space. + In order to derive (he specific auigular momentum of the cores following the observational procedure. we generate synthetic velocity maps of the cores along three different projections.," In order to derive the specific angular momentum of the cores following the observational procedure, we generate synthetic velocity maps of the cores along three different projections." + The elobal velocity gradient. of (hie. cores is measured from (he velocity. map using (he VEIT routine emploved initially by Goodman et al. (, The global velocity gradient of the cores is measured from the velocity map using the VFIT routine employed initially by Goodman et al. ( +1993).,1993). + The specific angular momentum is then calculated using the elobal velocity gradient value uider (he assumption of uniform rotation of the cores., The specific angular momentum is then calculated using the global velocity gradient value under the assumption of uniform rotation of the cores. + We find. in the two simulations. that the distributions of the ratio of the specific angular momentum determined in the intrinsic 3D space to the one derived [rom projected velocity maps peaks al values around ~0.1.," We find, in the two simulations, that the distributions of the ratio of the specific angular momentum determined in the intrinsic 3D space to the one derived from projected velocity maps peaks at values around $\sim 0.1$." +" This may well explain the dilference by a factor ~10 that is observed between the distribution of specific angular momentum derived [rom (he intrinsic data in our simulations and the corresponding real observations using (he NIL, and Noll molecules of roughly similar excitation density than the density thresholds used to identify (he cores in the simulations.", This may well explain the difference by a factor $\sim 10$ that is observed between the distribution of specific angular momentum derived from the intrinsic data in our simulations and the corresponding real observations using the $_{3}$ and $_{2}$ $^{+}$ molecules of roughly similar excitation density than the density thresholds used to identify the cores in the simulations. + We suggest (hat the origin of this discrepency (between 2D and 3D) lies in the fact that contrary to the intrinsic determination of j which sums up the individual gas parcels contributions to the angular momentum. (he observational determination of j is based on a measurement on the global velocity gradient under (he hypothesis of uniform rotation which smoothes out the complex fluctuations present in the three-dimensional velocity field.," We suggest that the origin of this discrepency (between 2D and 3D) lies in the fact that contrary to the intrinsic determination of $j$ which sums up the individual gas parcels contributions to the angular momentum, the observational determination of $j$ is based on a measurement on the global velocity gradient under the hypothesis of uniform rotation which smoothes out the complex fluctuations present in the three-dimensional velocity field." + We therefore suggest (hat previous measurements of the specilic angular momentum of the cores overestimate ils (rue value and that a correction [actor of ~10 should be applied to these nmeasurenienis as well as to new determinations of the specific angular momentum when using the global gradient method adopted so far in the observations., We therefore suggest that previous measurements of the specific angular momentum of the cores overestimate its true value and that a correction factor of $\sim 10$ should be applied to these measurements as well as to new determinations of the specific angular momentum when using the global gradient method adopted so far in the observations. + As already. stressed bv other eroups (e.g.. Padoan et al.," As already stressed by other groups (e.g., Padoan et al." + 1998.2000: Pichardo οἱ al.," 1998,2000; Pichardo et al." + 2000; Ostriker et al., 2000; Ostriker et al. + 2001:, 2001; +the parameter space volume constrained by the different configurations. we find that with respect to EC2. EC3 reduces the volume by a factor 4.6. and ECS by a factor 27 (with the 8 keV prior).,"the parameter space volume constrained by the different configurations, we find that with respect to EC2, EC3 reduces the volume by a factor 4.6, and EC5 by a factor 27 (with the 8 keV prior)." + The balloon-borne warm spectrometer EC? ts still limited at high frequencies by radiative background fluctuations., The balloon-borne warm spectrometer EC2 is still limited at high frequencies by radiative background fluctuations. + For this reason ΑΤοΜΗ 18 basically not constrained (see fig. 11))., For this reason $\Delta T_{CMB}$ is basically not constrained (see fig. \ref{fig8}) ). + However. the other parameters are unbiased and well constrained even with the very weak prior on Το.," However, the other parameters are unbiased and well constrained even with the very weak prior on $T_e$." +" An experiment like OLIMPO. which combines photometric measurements (as in Ες}aad spectroscopic measurements (as EC2). performing both during the same flight. can use the first measurement to optimally constrain AZ, and ΑΤομ. and the second to better constrain v, and 7,."," An experiment like OLIMPO, which combines photometric measurements (as in EC1) spectroscopic measurements (as EC2), performing both during the same flight, can use the first measurement to optimally constrain $\Delta I_d$ and $\Delta T_{CMB}$, and the second to better constrain $\tau_t$ and $T_e$." +" Note that even rj, Is close to be detected (and can be detected with an integration time longer than the 3 hours considered here) and p, is also constrained (still with a bimodal distribution).", Note that even $\tau_{nt}$ is close to be detected (and can be detected with an integration time longer than the 3 hours considered here) and $p_1$ is also constrained (still with a bimodal distribution). + Finally note that the spectroscopic capabilities allow the user to remove the contamination of Galactic CO and other cooling lines within the photometric bands unambiguously., Finally note that the spectroscopic capabilities allow the user to remove the contamination of Galactic CO and other cooling lines within the photometric bands unambiguously. + The low-Earth-orbit case EC3 improves over the balloon spectrometer EC2., The low-Earth-orbit case EC3 improves over the balloon spectrometer EC2. + Cooling the spectrometer results in a significant unbiased measurement of all six parameters. including the elusive ATc4;5 (see fig. 12)).," Cooling the spectrometer results in a significant unbiased measurement of all six parameters, including the elusive $\Delta T_{CMB}$ (see fig. \ref{fig9}) )." + Because the noise is reduced. the effect of degeneracies is more evident.," Because the noise is reduced, the effect of degeneracies is more evident." + The 3 keV prior is needed to fully exploit the. potential of this configuration., The 3 keV prior is needed to fully exploit the potential of this configuration. +" Experimental configuration ECS. where both the spectrometer and the telescope are cold. results in an improved precision of the determination of all parameters. and little sensitivity to the prior on 7, (see fig."," Experimental configuration EC5, where both the spectrometer and the telescope are cold, results in an improved precision of the determination of all parameters, and little sensitivity to the prior on $T_e$ (see fig." + 13 and table 1))., \ref{fig10} and table \ref{tab1}) ). + We have investigated the possibility of extending the frequency coverage of ECS up to | THz., We have investigated the possibility of extending the frequency coverage of EC5 up to 1 THz. + Keeping the same, Keeping the same +"smaller k, roughly doubles from its smaller-scale value; unsurprisingly,CxS other effects take over on the largest scales.","smaller $k$ , $\cngij$ roughly doubles from its smaller-scale value; unsurprisingly, other effects take over on the largest scales." +" As in the Coyote Universe results, at BAO scales there are interesting depressions in the covariance near the diagonal, where the covariance even dips slightly negative."," As in the Coyote Universe results, at BAO scales there are interesting depressions in the covariance near the diagonal, where the covariance even dips slightly negative." + In reffig:tak there is also a suggestion of periodic BAO bumps along the axes., In \\ref{fig:tak} there is also a suggestion of periodic BAO bumps along the axes. +" In redshift space, we found empirically that CNS instead falls off roughly as (k;k;)1/3."," In redshift space, we found empirically that $\cngij$ instead falls off roughly as $(k_ik_j)^{-1/2}$." +" We do not speculate here on why it has this form, but the reduced redshift-space covariance on small scales, noted by Τ09, is not surprising given the more-Gaussian redshift- density 1-point distribution, smeared by redshift distortions (?).."," We do not speculate here on why it has this form, but the reduced redshift-space covariance on small scales, noted by T09, is not surprising given the more-Gaussian redshift-space density 1-point distribution, smeared by redshift distortions \citep{nss11}." +" reffig:coyoteinfo shows signal-to-noise,(S/N)?,, curves for the various power spectra."," \\ref{fig:coyoteinfo} shows signal-to-noise, curves for the various power spectra." + This ccan be thought of as the effective number (S/N)?of independent modes over a range of wavenumber bins R., This can be thought of as the effective number of independent modes over a range of wavenumber bins $\R$ . + where Cr is the covariance matrix over R., where $\bssC_\R$ is the covariance matrix over $\R$. +" Here, the bins in R vary from kin, the largest modes not directly modulated by the sinusoidal weightings, to kmax."," Here, the bins in $\R$ vary from $k_{\rm min}$, the largest modes not directly modulated by the sinusoidal weightings, to $k_{\rm max}$." +" Compared to NSS09, the range of k plotted here is shifted smaller by a factor of 2 by the double box size, and there is reduced noise, but the trends are the same as found there."," Compared to NSS09, the range of $k$ plotted here is shifted smaller by a factor of 2 by the double box size, and there is reduced noise, but the trends are the same as found there." +" In fact, Ps/o2,, is comparable to Pgs), the power spectrum of the Gaussianized density."," In fact, $P_\delta/\varc$ is comparable to $P_{G(\delta)}$, the power spectrum of the Gaussianized density." +" The iin Ps/o2,, ramps up quickly at the smallest scales, because the power spectra are effectively pinned together there when they are divided by o2,,, resulting in tiny (co)variance."," The in $P_\delta/\varc$ ramps up quickly at the smallest scales, because the power spectra are effectively pinned together there when they are divided by $\varc$, resulting in tiny (co)variance." +" We also show the ccurve for our CNS=a model, which approximates the Ps curve well."," We also show the curve for our $\cngij=\alpha$ model, which approximates the $P_\delta$ curve well." +" iis a (S/N)?good single measure of intrinsic Fisher information, but without derivative terms of the power spectrum with respect to cosmologicalparameters, the connection with parameter estimation is vague."," is a good single measure of intrinsic Fisher information, but without derivative terms of the power spectrum with respect to cosmologicalparameters, the connection with parameter estimation is vague." +" For P5, iis roughly the information in lnog, unmarginalized over other parameters, since on linear scales =1, and it stays of order unity OP5(k)/(OInoz)on non-linear scales, reaching ~2 (?).."," For $P_\delta$, is roughly the information in $\ln +\sigma_8^2$ , unmarginalized over other parameters, since on linear scales $\partial P_\delta(k)/(\partial \ln \sigma_8^2) =1$, and it stays of order unity on non-linear scales, reaching $\sim 2$ \citep{ns07}." +" However, at least for ccells, Ps/o2,, contains little information about o2. ("," However, at least for cells, $P_\delta/\varc$ contains little information about $\sigma_8^2$. (" +"If the measured power spectrum were linear, obviously all sensitivity to o2 would be lost in dividing by it.)","If the measured power spectrum were linear, obviously all sensitivity to $\sigma_8^2$ would be lost in dividing by it.)" +" For Pes), too, a free parameter is the variance in the Gaussianized density."," For $P_{G(\delta)}$, too, a free parameter is the variance in the Gaussianized density." +" In the present measurements, as in ?,, the G(d) variance is fixed, pinning down the power spectrum at small scales in a similar manner as with Ps5/o2,,."," In the present measurements, as in \citet{nss11}, the $G(\delta)$ variance is fixed, pinning down the power spectrum at small scales in a similar manner as with $P_\delta/\varc$." +" The situation with Pj(1,5) is in-between; on small scales it is allowed to fluctuate as it pleases (which is to a much lesser degree than Ps), but on large scales, 0«<1 because of large-scale bias producedOPu45/(01no$) by the log transform."," The situation with $P_{\ln(1+\delta)}$ is in-between; on small scales it is allowed to fluctuate as it pleases (which is to a much lesser degree than $P_\delta$ ), but on large scales, $0<\partial P_{\ln(1+\delta)}/(\partial \ln \sigma_8^2)<1$ because of large-scale bias produced by the log transform." + An analysis of these issues (?) is essential for these modified power spectra to be used for cosmological constraints., An analysis of these issues \citep{nprep} is essential for these modified power spectra to be used for cosmological constraints. +" One might think that the insight that P;’s covariance is largely from fluctuations in a multiplicative bias might imply that this covariance is unimportant for parameters that depend on the power-spectrum shape, such as the tilt, or the BAO scale."," One might think that the insight that $P_\delta$ 's covariance is largely from fluctuations in a multiplicative bias might imply that this covariance is unimportant for parameters that depend on the power-spectrum shape, such as the tilt, or the BAO scale." +" However, as shown in reffig:tak,, the form we have found for the translinear covariance does not really extend to fully linear scales, leaving some room for shape fluctuations at the interface (occupied by BAO at z—0) between the linear and translinear regimes."," However, as shown in \\ref{fig:tak}, the form we have found for the translinear covariance does not really extend to fully linear scales, leaving some room for shape fluctuations at the interface (occupied by BAO at $z=0$ ) between the linear and translinear regimes." + We show that a fluctuating scale-independent multiplicative bias provides quite an accurate model for the covariance matrix of the real-space dark-matter power spectrum on translinear scales., We show that a fluctuating scale-independent multiplicative bias provides quite an accurate model for the covariance matrix of the real-space dark-matter power spectrum on translinear scales. +" The non-Gaussian part of the covariance CNS&a=Var(o2,))/o4y, a constant measure of the variance (among of the variance (within a realization) of therealizations) measured nonlinear density field."," The non-Gaussian part of the covariance $\cngij\approx\alpha=\Var(\varc)/\varcs$, a constant measure of the variance (among realizations) of the variance (within a realization) of the measured nonlinear density field." +" o is rather insensitive to the cell size used to measure it, at least within a range of"," $\alpha$ is rather insensitive to the cell size used to measure it, at least within a range of." +"Mpc.. a is not entirely trivial to measure, but it is much easier than the full covariance."," $\alpha$ is not entirely trivial to measure, but it is much easier than the full covariance." +" For example, it could be estimated using sufficiently large simple sub-volumes, with little worry about edge effects."," For example, it could be estimated using sufficiently large simple sub-volumes, with little worry about edge effects." +" Furthermore, at least in real space, this translinear covariance can largely be removed, or modeled out, by dividing the power spectrum by o2."," Furthermore, at least in real space, this translinear covariance can largely be removed, or modeled out, by dividing the power spectrum by $\varc$." + This is equivalent to measuring the power spectrum of 6/ocen., This is equivalent to measuring the power spectrum of $\delta/\sigma_{\rm cell}$. +" However, this changes the sensitivity to cosmology, for example giving up information on the power-spectrum amplitude."," However, this changes the sensitivity to cosmology, for example giving up information on the power-spectrum amplitude." +" The simplicity of this model suggests that it may be applicable not only to dark matter, but perhaps to galaxies, or even to CMB anisotropies, where pushingto smaller scales dredges up somenon-Gaussian covariance in the power spectrum of Sunyaev-Zeldovich effect anisotropies "," The simplicity of this model suggests that it may be applicable not only to dark matter, but perhaps to galaxies, or even to CMB anisotropies, where pushingto smaller scales dredges up somenon-Gaussian covariance in the power spectrum of Sunyaev-Zel'dovich effect anisotropies \citep{shaw09}. ." +"Shot noisewould complicate the situation for galaxies,(?). but possibly this component could be accurately approximated with a Poisson term and subtracted."," Shot noisewould complicate the situation for galaxies, but possibly this component could be accurately approximated with a Poisson term and subtracted." +" We thank Istvánn Szapudi, Alex Szalay, Martin White"," We thank Istvánn Szapudi, Alex Szalay, Martin White" +along the orbit would. decrease.,along the orbit would decrease. + OL course. the orbits are not initially circular. ancl thew potential is not. Ixeplerian so the net. result is to diminish the effect (ancl not reverse i.," Of course, the orbits are not initially circular and thew potential is not Keplerian so the net result is to diminish the effect (and not reverse it)." + The reduction is more dramatic for the loosely bound stars because a modest increase in the velocity can greatly increase the size of the orbit and. possibly unbind the star from the cluster: therefore. the stars that remain bound to the cluster will necessarily have lower velocities the loosely bound. stars are more strongly allected by evaporative cooling.," The reduction is more dramatic for the loosely bound stars because a modest increase in the velocity can greatly increase the size of the orbit and possibly unbind the star from the cluster; therefore, the stars that remain bound to the cluster will necessarily have lower velocities --- the loosely bound stars are more strongly affected by evaporative cooling." + The orbits of the stars change in a second wav., The orbits of the stars change in a second way. + The orbits after the kick and orbit averaging are twpically more eccentric that before., The orbits after the kick and orbit averaging are typically more eccentric that before. + Ehe distribution of velocities according o Eq. (13) , The distribution of velocities according to Eq. \ref{eq:1}) ) +is spherically symmetric., is spherically symmetric. + Furthermore. the kicks are cistributed svmmoetricallvy: therefore. the distribution of he angle between the proper motions and the projection direction to the centre of the cluster is uniform.," Furthermore, the kicks are distributed symmetrically; therefore, the distribution of the angle between the proper motions and the projection direction to the centre of the cluster is uniform." + However. after the kiekecl stars have mixed in phase. it is more likely o lind stars moving within forty-five degrees of the radial direction than within forty-five degrees of the tangential direction the orbits are typically more eccentric. than odore.," However, after the kicked stars have mixed in phase, it is more likely to find stars moving within forty-five degrees of the radial direction than within forty-five degrees of the tangential direction – the orbits are typically more eccentric than before." + Fie., Fig. + 2 shows the cumulative distribution of this anele (8) for various sizes of kick with a uniform clistribution subtracted away., \ref{fig:angle} shows the cumulative distribution of this angle $\theta$ ) for various sizes of kick with a uniform distribution subtracted away. + First. the elect weakens with the size of he kick and vanishes for no kick.," First, the effect weakens with the size of the kick and vanishes for no kick." + Second. for large kicks he effect is weaker for the more loosely bound stars.," Second, for large kicks the effect is weaker for the more loosely bound stars." + Again his is because the loosely bound stars are more likely to eet eccentricities greater than unity and leave the system., Again this is because the loosely bound stars are more likely to get eccentricities greater than unity and leave the system. + Although these differences in the distributions are apparent when many thousands of stars are use as probes. in reality one tvpically has only several tens of stars to characterise the distribution of voung white cwarls (the. kicked. stars) ancl possibly a factor of ten more stars to estimate the distribution. of the progenitors.," Although these differences in the distributions are apparent when many thousands of stars are use as probes, in reality one typically has only several tens of stars to characterise the distribution of young white dwarfs (the kicked stars) and possibly a factor of ten more stars to estimate the distribution of the progenitors." + To estimate the typical sensitivity of measurements to the effects of white dwarl kicks. smaller samples were generated with various numbers of kicked. stars and a factor of ten more progenitors for comparison.," To estimate the typical sensitivity of measurements to the effects of white dwarf kicks, smaller samples were generated with various numbers of kicked stars and a factor of ten more progenitors for comparison." + A total of one thousand samples were generated in each group with epo=0.5o and 0.Se and eg=ero., A total of one thousand samples were generated in each group with $\sigma_\rmscr{TO}=0.5\sigma$ and $0.8\sigma$ and $\sigma_k=\sigma_\rmscr{TO}$. + For each pair of samples the likelihood that they were drawn from the same underlving distribution was calculated. using 1e Ixolmogorov-Smirnov test and the Wileoxon rank-sum test., For each pair of samples the likelihood that they were drawn from the same underlying distribution was calculated using the Kolmogorov-Smirnov test and the Wilcoxon rank-sum test. + the final result is the median likelihood over the one thousand realisations., the final result is the median likelihood over the one thousand realisations. + For the sake of clarity and deliniteness observational errors have not been included in the samples generated — such errors would reduce the significance of the etections., For the sake of clarity and definiteness observational errors have not been included in the samples generated – such errors would reduce the significance of the detections. + The statistical likelihoods depicted. in Fig., The statistical likelihoods depicted in Fig. + 3/— of etecting the change in the distributions support what is apparent from the distributions themselves., \ref{fig:significance_perp} of detecting the change in the distributions support what is apparent from the distributions themselves. + Finding a change in the racial distribution is much more straightforward than finding changes in the velocity distribution (even with perfect data)., Finding a change in the radial distribution is much more straightforward than finding changes in the velocity distribution (even with perfect data). + Furthermore. for the loosely bound. progenitors (lower panel of Fig. 3)).," Furthermore, for the loosely bound progenitors (lower panel of Fig. \ref{fig:significance_perp}) )," + if it is impossible to distinguish the proper motion clistribution of the voung white dwarfs with kicks from their. progenitors with fewer than one white chvarls in the sample (ancl 1.000 turn-oll stars).," if it is impossible to distinguish the proper motion distribution of the young white dwarfs with kicks from their progenitors with fewer than one white dwarfs in the sample (and 1,000 turn-off stars)." + The kev to finding these changes is building up a sample of many stars., The key to finding these changes is building up a sample of many stars. + For à kick comparable to the initial velocity. dispersion. at least one hundred: stars are required even in the best case for tightly bound. progenitor stars (upper panel of Fig. 3)).," For a kick comparable to the initial velocity dispersion, at least one hundred stars are required even in the best case for tightly bound progenitor stars (upper panel of Fig. \ref{fig:significance_perp}) )." + ? reported a significant dillerence between the distribution of voung white cbwarfs and turn-oll stars and between voung white dwarls anc older white chwarls., \citet{2007Davis} reported a significant difference between the distribution of young white dwarfs and turn-off stars and between young white dwarfs and older white dwarfs. + Furthermore. they estimated that the distribution of voung white cwarks was most similar to that of main-sequence stars whose mass was half that of stars near the turn-olf.," Furthermore, they estimated that the distribution of young white dwarfs was most similar to that of main-sequence stars whose mass was half that of stars near the turn-off." + ? found that such a large change in the stellar distribution would require a Kick with σι29ops., \citet{Heyl07kickgc} found that such a large change in the stellar distribution would require a kick with $\sigma_k>\sigma_\rmscr{TO}$. + Lone starts with ope=0.50. a kick of 1.520*p0 is required to make the final distribution of projected radii look like a population with dispersion of 0.70: that is one that corresponds to one-half the mass of the progenitors.," If one starts with $\sigma_\rmscr{TO}=0.5\sigma$, a kick of $1.82\sigma_\rmscr{TO}$ is required to make the final distribution of projected radii look like a population with dispersion of $0.7\sigma$; that is one that corresponds to one-half the mass of the progenitors." + The dilference between the initial and final distribution of radii is detectable with a median likelihood of the null hypothesis of less than one part in one thousand with only twenty voung white chvarls in the sample. comparable to the probability quoted by 2..," The difference between the initial and final distribution of radii is detectable with a median likelihood of the null hypothesis of less than one part in one thousand with only twenty young white dwarfs in the sample, comparable to the probability quoted by \citet{2007Davis}." + With about forty voung white cwarfs. the dillerence between the initial and final proper motion distributions in Fig.," With about forty young white dwarfs, the difference between the initial and final proper motion distributions in Fig." + 4 is detectable with the likelihood of the null hypothesis of less than two percent., \ref{fig:bigkick} is detectable with the likelihood of the null hypothesis of less than two percent. + Lowever. the systematics of detecting an increase in the tvpical proper motion of the faint voung white chvarls relative to the much brighter main sequence stars is problematic because the expected errors in," However, the systematics of detecting an increase in the typical proper motion of the faint young white dwarfs relative to the much brighter main sequence stars is problematic because the expected errors in" +wavelength dependence is the same.,wavelength dependence is the same. + As the disk becomes more inclined the warp is ποσα closer to face-on. creating more significant variations as it rotates m and out of view.," As the disk becomes more inclined the warp is seen closer to face-on, creating more significant variations as it rotates in and out of view." + Creating a warp iu the muddle of the disk is possible with a (subjstellar companion enmibedded in the disk., Creating a warp in the middle of the disk is possible with a (sub)stellar companion embedded in the disk. + If the companion is not coplanar with the disk then the eravitational perturbation from the companion can drive material out of the uudplaue., If the companion is not coplanar with the disk then the gravitational perturbation from the companion can drive material out of the midplane. + The disk around ./ Pic displays a warp in tle middle of the disk due to an uuiseeu colmpanion (Augercanetal.2001)., The disk around $\beta$ Pic displays a warp in the middle of the disk due to an unseen companion \citep{aug01}. +. The variable star WL Ll displavs periodic variability in the ucar-intrared. indicative of a multiple svstem. as well as imiddufrared variability. indicative of a change in the dust structure near the star (Plavchauetal.2008).," The variable star WL 4 displays periodic variability in the near-infrared, indicative of a multiple system, as well as mid-infrared variability, indicative of a change in the dust structure near the star \citep{pla08}." +.. Roughly of stellar svstenis have a binary companion within 1 AU (Mathieu1991)., Roughly of stellar systems have a binary companion within 1 AU \citep{mat94}. +. Tf the companion is within one AU of the ceutral star then the precession period of such a configuration is vears to decades. depending on the exact configuration of the system (Capranictal.2006).," If the companion is within one AU of the central star then the precession period of such a configuration is years to decades, depending on the exact configuration of the system \citep{cap06}." +. The conibination of the sinall fiux chauge aud long timescale would make precession difficult to observe., The combination of the small flux change and long timescale would make precession difficult to observe. + We next consider the effect of changing the height of he warp., We next consider the effect of changing the height of the warp. + As the warp height increases the disk will ect jeated to a higher temperature since it is more directly iliuuinated by the radiation field., As the warp height increases the disk will get heated to a higher temperature since it is more directly illuminated by the radiation field. + This is the same reason hat a flared disk ects heated to a ligher temperature and has a higher flux than a flat passive disk., This is the same reason that a flared disk gets heated to a higher temperature and has a higher flux than a flat passive disk. + The Iareer warp will also cast a larger shadow ou the outer disk which will decrease its temperature and lower its fux., The larger warp will also cast a larger shadow on the outer disk which will decrease its temperature and lower its flux. + If jio warp chauges substantially enough then the chauge in the temperature structure would be evident iu the SED., If the warp changes substantially enough then the change in the temperature structure would be evident in the SED. + The hot surface lavers of the disk that are secu 1i the middntrared respond almost iustantaucouslv to a eothanee in the stellar radiation field (Chiang&Coldreich 997)., The hot surface layers of the disk that are seen in the mid-infrared respond almost instantaneously to a change in the stellar radiation field \citep{chi97}. +. This means that the timescale for the SED to change will depend on how quickly the disk can chanec its structure. which is the cwuaimical timescale.," This means that the timescale for the SED to change will depend on how quickly the disk can change its structure, which is the dynamical timescale." + For the central star considered here the dynamical timescale can be as low as one week within 0.1 AU., For the central star considered here the dynamical timescale can be as low as one week within 0.1 AU. +" Iu order to examine this effect we take the disk we used to study precession (Rivage,= 0.5AU) and vary its scale height. parameterized by the factor g. from 0.01-0.1."," In order to examine this effect we take the disk we used to study precession $R_{warp}=0.5$ AU) and vary its scale height, parameterized by the factor $g$, from 0.01-0.1." + This corresponds to a physical height of 0.005-0.05 AU., This corresponds to a physical height of 0.005-0.05 AU. + The results are shown in figure L., The results are shown in figure \ref{warp_grow_i60}. + We find that as the height of the warp increases the flax at A«154a increases while the flux lougward of ddecreases., We find that as the height of the warp increases the flux at $\lambda<15\micron$ increases while the flux longward of decreases. + The fiux variatious is siiall but the unique wavelength dependence would make intrarecd variability due to a changing scale height at the inner edge of the disk easy to diagnose., The flux variations is small but the unique wavelength dependence would make infrared variability due to a changing scale height at the inner edge of the disk easy to diagnose. + The same mechanisin that drove the disk to become warped mav also cause it to change the height of the warp., The same mechanism that drove the disk to become warped may also cause it to change the height of the warp. + If the warp is caused by a companion. then this object could drag material as its orbit takes it out of the midplane (Fraguer&Nelsou2009).," If the warp is caused by a companion, then this object could drag material as its orbit takes it out of the midplane \citep{fra09}." +. For a binary companion whose orbit is misaligned with the disk. the plane of the disk will equilibrate with the plane of orbit over thousands of vears. but on the timescale of a suele orbit dust will be shifted by the passing of the companion.," For a binary companion whose orbit is misaligned with the disk, the plane of the disk will equilibrate with the plane of orbit over thousands of years, but on the timescale of a single orbit dust will be shifted by the passing of the companion." + As the companion’s orbit takes it out of the plane of the disk it will drag material with it. but when the companions orbit takes it back iuto the midplane of the disk this dust will quickly settle down.," As the companion's orbit takes it out of the plane of the disk it will drag material with it, but when the companion's orbit takes it back into the midplane of the disk this dust will quickly settle down." + This would cad to periodic variations in the scale height of the warp ou top of the long term variations., This would lead to periodic variations in the scale height of the warp on top of the long term variations. + It may also be possible hat a long-lived asvuunetric structure within the disk. such as a warp caused by a companion. ix experieuciug variable ilhunination from the ceutral source.," It may also be possible that a long-lived asymmetric structure within the disk, such as a warp caused by a companion, is experiencing variable illumination from the central source." + This is xossible if the accretion flow is localized iuto hot spots hat rotate around the stay., This is possible if the accretion flow is localized into hot spots that rotate around the star. + As the hot spot ilhuninates he warp. it will heat the side facing the star. causing its scale height to iucreasc.," As the hot spot illuminates the warp, it will heat the side facing the star, causing its scale height to increase." + The scale height of the warp will decrease as the hot spot rotates around to the far side of he star., The scale height of the warp will decrease as the hot spot rotates around to the far side of the star. + As the warp moves closer to the star. the deviation in the SED from a flat passive disk moves to shorter wavelengths.," As the warp moves closer to the star, the deviation in the SED from a flat passive disk moves to shorter wavelengths." + To affect the flux at οSyau we need to nove the warp alinost to the inner edge of the disk., To affect the flux at $5-8\micron$ we need to move the warp almost to the inner edge of the disk. + We could also consider a warp that reaches its maxima weight above the midplane at the imuer. rather than the outer. edge of the disk.," We could also consider a warp that reaches its maximum height above the midplane at the inner, rather than the outer, edge of the disk." + An inner warp has been invoked o explain the variability observed in AA Tau (Bouvieretal.2003) in which the stellar magnetic field is musaligned with the disk causing it to warp as material flows onto he field lines., An inner warp has been invoked to explain the variability observed in AA Tau \citep{bou03} in which the stellar magnetic field is misaligned with the disk causing it to warp as material flows onto the field lines. +" A inner warp can be described bv the ΠΙΟΠΟ: The temperature distribution for disks with g=405.0.01. ta,=SR. are shown in figure 5.."," A inner warp can be described by the function: The temperature distribution for disks with $g=0.05,0.01$ , $r_{min}=8R_*$ are shown in figure \ref{warp2}." + The exponent for the power law was chosen to match the widdle warp aud depends ou the exact plysical cause of the warp., The exponent for the power law was chosen to match the middle warp and depends on the exact physical cause of the warp. + The inner warp cau be split into two jueces. a convex piece which directly faces the star aud a concave piece which is turned away from the star.," The inner warp can be split into two pieces, a convex piece which directly faces the star and a concave piece which is turned away from the star." + Iu he schematic dvawing of the ΠΙΟ warp in figure 1bb on he welt side the convex piece is on the bottoni while he concave piece is on the top., In the schematic drawing of the inner warp in figure \ref{drawing}b b on the right side the convex piece is on the bottom while the concave piece is on the top. + The inner edee of the convex side reaches a very high teniperature and departs sienificautly frou a flat passive disk., The inner edge of the convex side reaches a very high temperature and departs significantly from a flat passive disk. + The concave side just belund the warp has a low temperature because he warp completely blocks the star and the disk is oulv heated by viscous dissipation., The concave side just behind the warp has a low temperature because the warp completely blocks the star and the disk is only heated by viscous dissipation. + Moving outwards. a out on the disk will be able to see some of the star. although it is still partially blocked.," Moving outwards, a point on the disk will be able to see some of the star, although it is still partially blocked." + The temperature ou he concave side far from the warp will be between that of a flat passive disk which experiences no shadowing aud a fully shadowed disk which is only heated by viscous dissipation., The temperature on the concave side far from the warp will be between that of a flat passive disk which experiences no shadowing and a fully shadowed disk which is only heated by viscous dissipation. + As the warp grows the temperature on the convex side increases and on the concave side it decreases., As the warp grows the temperature on the convex side increases and on the concave side it decreases. + Tn anit of a very large warp the concave side will be completely shadowed while the convex side will be much warlucr than a flat passive disk., In limit of a very large warp the concave side will be completely shadowed while the convex side will be much warmer than a flat passive disk. + Figure 5. compares the SED of the iuner warp disk to that of a fat passive disk aud a disk heated bv viscous dissipation., Figure \ref{warp2} compares the SED of the inner warp disk to that of a flat passive disk and a disk heated by viscous dissipation. + The warped disk siguificautly departs from the flat passive disk at short waveleneths because of the lieh temperature on the convex side while it» SED is lower at long wavelengths because of the shadowing ou the concave side., The warped disk significantly departs from the flat passive disk at short wavelengths because of the high temperature on the convex side while its SED is lower at long wavelengths because of the shadowing on the concave side. + The warp drops below the midplane for 90«0<270° (the left side of the top half of the disk shown in figure 1bb) aud onlv half of the disk is shadowed., The warp drops below the midplane for $90<\theta<270^{\circ}$ (the left side of the top half of the disk shown in figure \ref{drawing}b b) and only half of the disk is shadowed. + Since at most of halfthe disk can be shadowed.," Since at most half of the disk can be shadowed," +necessary (o deredden (he Oph 51 spectrum to correct for the known 10 magnitudes οἱ visual absorption (Gagneetal.2004).,necessary to deredden the Oph S1 spectrum to correct for the known 10 magnitudes of visual absorption \citep{gag04}. +. For telluric correction we also utilized an observation of NGC! 4361. a planetary nebula whose //A spectrum is dominated by the continuum of the hot central star.," For telluric correction we also utilized an observation of NGC 4361, a planetary nebula whose $HK$ spectrum is dominated by the continuum of the hot central star." + Wavelength calibration was accomplished using a cubic fit to a set of atmospheric OIL lines identified in skv observations based on Rousselotetal.(2000)... and a set of nebular lines [rom an observation of another planetary nebula. 049.34-38.1.," Wavelength calibration was accomplished using a cubic fit to a set of atmospheric OH lines identified in sky observations based on \citet{rous2000}, and a set of nebular lines from an observation of another planetary nebula, G049.3+88.1." + The maxinmumn likelihood estimate of the spectrum of each program object was obtained using all available observations for that object simultaneously., The maximum likelihood estimate of the spectrum of each program object was obtained using all available observations for that object simultaneously. + This necessitated spatial co-registration of the individual subtracted nods. accomplished by adjusting the image offset parallel to the slit based on maximum correlation of the signal with the wavelength-dependent spatial point spread. function (PSF).," This necessitated spatial co-registration of the individual subtracted nods, accomplished by adjusting the image offset parallel to the slit based on maximum correlation of the signal with the wavelength-dependent spatial point spread function (PSF)." + The latter was estimated using observations of strong calibrators., The latter was estimated using observations of strong calibrators. +" The program star spectrum was then obtained from a series of maximum likelihood fIux estimates as a function of wavelength using all observations which fell within a rectangular Παπ window of width tvpicallvy 9 pixels in both the spatial and spectral directions. where 1 pixel corresponds to 0.15"" and ~0.005 jan. respectivelv: the spectral boxcar width was. however. increased (o 21 pixels for #44450. the object with lowest S/N."," The program star spectrum was then obtained from a series of maximum likelihood flux estimates as a function of wavelength using all observations which fell within a rectangular “fitting"" window of width typically 9 pixels in both the spatial and spectral directions, where 1 pixel corresponds to $0.15''$ and $\sim0.005$ $\mu$ m, respectively; the spectral boxcar width was, however, increased to 21 pixels for 4450, the object with lowest $S/N$." + The estimation procedure involved knowledge of the measurement noise. estimated [rom adjacent strips on the image. external to the strip containing the signal.," The estimation procedure involved knowledge of the measurement noise, estimated from adjacent strips on the image, external to the strip containing the signal." + In order to minimize the effect of spikes due to cosmic rav. hits. il was necessary to use Urimmed averaging during noise estimation. and 36 outlier rejection during spectral estimation.," In order to minimize the effect of spikes due to cosmic ray hits, it was necessary to use trimmed averaging during noise estimation, and $3\sigma$ outlier rejection during spectral estimation." + The estimated spectra of our seven program objects are shown by the solid lines in Figures 1 and 2.., The estimated spectra of our seven program objects are shown by the solid lines in Figures \ref{fig1} and \ref{fig2}. + Also included in Figure 2.. for comparison. are our spectra of two known T chwarls. SDSS 1254-0122 (T2) and 2MAÀSS 15034-2525 (5.51.," Also included in Figure \ref{fig2}, for comparison, are our spectra of two known T dwarfs, SDSS 1254-0122 (T2) and 2MASS 1503+2525 (T5.5)." +"Therefore: If we define 7, as the Thompson optical depth of a photon moving toward the upstream then τι©7; rg, where στ is the Thomson cross-section and aN(I?) is the Klein-Nishina cross section of electron at rest and photon with energy I?m,c?.","Therefore: If we define $\tau_*$ as the Thompson optical depth of a photon moving toward the upstream then $\tau_* \approx \tau_s +\frac{\sigma_T}{\sigma_{KN}(\G^2)}$ , where $\sigma_T$ is the Thomson cross-section and $\sigma_{KN}(\G^2)$ is the Klein-Nishina cross section of electron at rest and photon with energy $\G^2 m_e c^2$." +" Therefore Integrating this equation starting at the end of the transition layer, i.e., [(7,=0)1 results in the structure of the transition layer."," Therefore Integrating this equation starting at the end of the transition layer, i.e., $\G(\tau_s=0)=1$ results in the structure of the transition layer." + Comparison of this structure to the numerical results of Budniketal.(2010) is presented in figure 2.., Comparison of this structure to the numerical results of \cite{Budnik10} is presented in figure \ref{fig2}. + In order to find the width of the shock in the upstream frame we use the relation where 2’ is the length coordinate (positive towards theupstream) in the shock frame., In order to find the width of the shock in the upstream frame we use the relation where $z'$ is the length coordinate (positive towards theupstream) in the shock frame. + Therefore, Therefore +In the absence of large spectroscopic surveys. the DES and VILIS datasets. when combined. will prove extremely ellective in constraining dark οποίον through large scale structure signals like barvon acoustic oscillations.,"In the absence of large spectroscopic surveys, the DES and VHS datasets, when combined, will prove extremely effective in constraining dark energy through large scale structure signals like baryon acoustic oscillations." + ὃν clipping photometric redshift catalogues aid: carefully removing a suitable number of outliers. one can achieve reasonably precise measurements of the galaxy power spectrum out to a redshift of 2.," By clipping photometric redshift catalogues and carefully removing a suitable number of outliers, one can achieve reasonably precise measurements of the galaxy power spectrum out to a redshift of 2." + We are very grateful. to Peter Capak for. providing the JPLOAT simulations., We are very grateful to Peter Capak for providing the JPLCAT simulations. + We thank members of the DIES photometric redshift ancl large scale. structure working eroups for useful discussions. in. particular Josh Fricmann. Enrique Caztanaga anc Will Percival.," We thank members of the DES photometric redshift and large scale structure working groups for useful discussions, in particular Josh Friemann, Enrique Gaztanaga and Will Percival." + We also. thank Richard AleMahon and Will Sutherland. for information regarding the VISTA public surveys., We also thank Richard McMahon and Will Sutherland for information regarding the VISTA public surveys. + ALB is supported. by an STC studentship., MB is supported by an STFC studentship. + EBA acknowledges support from the Leverhulme Foundation. through an Early Careers Fellowship., FBA acknowledges support from the Leverhulme Foundation through an Early Careers Fellowship. + , +"age and uctallicitv. eive in Table aud the observed values of DB aud V usec to cousty""uet the SEDs (see subsectio1 12 and Tabe 2)). the extinctions £(BY) obtained are 0.0 for IID :282 and 1.06 for ΠΟ 111569.","age and metallicity given in Table \ref{STARS} and the observed values of $B$ and $V$ used to construct the SEDs (see subsection \ref{PHOT} and Table \ref{TablePHOT}) ), the extinctions $E(B\!-\!V)$ obtained are 0.04 for HD 34282 and 0.06 for HD 141569." + The former value especialv is in excelent agreement with that eivei by the 47P analvsis., The former value especially is in excellent agreement with that given by the $\chi^2$ analysis. +: TheY :vbsolute magnitudes Ady: provided by he tracsS are 2.0Laid 1.37 respectively: these. combined with the observed values of V. corrected with the above extinctions. vield disances of 317 pe for IID 31282 aud 129 pe for IID 111569. again in good agreement with tιο results shown in Table 1.," The absolute magnitudes $M_{\rm V}$ provided by the tracks are 2.04 and 1.37 respectively; these, combined with the observed values of $V$ corrected with the above extinctions, yield distances of 347 pc for HD 34282 and 129 pc for HD 141569, again in good agreement with the results shown in Table \ref{STARS}." + The origin of the IR excess in WAcBe stars has σοι a matter of intense debate (see c.g. Waters Wacellecus 1998)., The origin of the IR excess in HAeBe stars has been a matter of intense debate (see e.g. Waters Waelkens 1998). + Some authors argued in favor of models with au approximately spherical dusty euvelope of low optical depth (Berrilli et al., Some authors argued in favor of models with an approximately spherical dusty envelope of low optical depth (Berrilli et al. + 1992: di Francesco et al., 1992; di Francesco et al. + 199I: Pezzuto et al., 1994; Pezzuto et al. + 1997: Mirosinichenuko et al., 1997; Miroshnichenko et al. + 1997). 0thers considered cireunistellu disss (Illleubraud et al.," 1997), others considered circumstellar disks (Hillenbrand et al." + 1992: Cliane ct al., 1992; Chiang et al. + 2001: Natta «ft al., 2001; Natta et al. + 2001) or proposed the existence of both (Natta e al., 2001) or proposed the existence of both (Natta et al. + 1993: Miroshnicheuko et al., 1993; Miroshnichenko et al. + 1999)., 1999). + Ultimately the existence of disks around IWAceBe stars was firmly estabished by direct tuaging at millimetre wavelengths (Mainines et al., Ultimately the existence of disks around HAeBe stars was firmly established by direct imaging at millimetre wavelengths (Mannings et al. + 1997: Mauvines Sarecut 1997. 2000: Testi et al.," 1997; Mannings Sargent 1997, 2000; Testi et al." + 2001: Piéttu ct :d., 2001; Piéttu et al. + 2003). in the optical (Caady ο al.," 2003), in the optical (Grady et al." + 1999. 2000) aud 1 the IR. (Close et al.," 1999, 2000) and in the IR (Close et al." + 1997: Javawardhana et al., 1997; Jayawardhana et al. + 1998: Weinberger et al., 1998; Weinberger et al. + 1999)., 1999). + Some authors have been able to fit the complete SEDs of TAcBe stars with passive irradiated disk models from Chiang Goldreich (Chiang et al., Some authors have been able to fit the complete SEDs of HAeBe stars with passive irradiated disk models from Chiang Goldreich (Chiang et al. + 2O1: Natta et al., 2001; Natta et al. + 2001)., 2001). +(Jaunary 99) and ΠΟ 111560 (Alay 98) where some lines are identified.,(January 99) and HD 141569 (May 98) where some lines are identified. + In the following. we describe the CS spectrum of both objects.," In the following, we describe the CS spectrum of both objects." +3412852: The CES cchelle spectra show ai CS contribution in the Ca EK line aud iu the Baluer ines ID} and IH., The UES echelle spectra show a CS contribution in the Ca K line and in the Balmer lines $\beta$ and $\gamma$. + The line He at Ss76 is seen in absorption: it is uulikelv to be of photospheric origin since ΠΟ 31282 has an ~A3 spectral type., The line He at 5876 is seen in absorption; it is unlikely to be of photospheric origin since HD 34282 has an $\sim$ A3 spectral type. + Its streneth iux xofile might show sinall variations (after a comparison of all the INT spectra). but this should be confined with eher resolution spectra.," Its strength and profile might show small variations (after a comparison of all the INT spectra), but this should be confirmed with higher resolution spectra." + Te 15876 has been observe with laree variations in WAcBe and T Tauri stars (6.9. Bolin Catala 1995. Jolus Dasi 1995) aud it has beeu explained in terms of naguctospleric accretion in the low-mass PAIS stars (6.8. Oliveira et al.," He 5876 has been observed with large variations in HAeBe and T Tauri stars (e.g. Böhhm Catala 1995, Johns Basri 1995) and it has been explained in terms of magnetospheric accretion in the low-mass PMS stars (e.g. Oliveira et al." + 2000). but in the case of ILAeDe stars its origin is controversial (c.g. Bouret Catala 2000).," 2000), but in the case of HAeBe stars its origin is controversial (e.g. Bouret Catala 2000)." + a always preseuts a variable double-peaked. cussion with a central absorption., $\alpha$ always presents a variable double-peaked emission with a central absorption. + Fig., Fig. + 2. shows the observed Ia profiles after the subtraction of a spectrum of a standard of the same spectral type broadened to the rotational velocity of ΠΟ 21282., \ref{HALPHA} shows the observed $\alpha$ profiles after the subtraction of a spectrum of a standard of the same spectral type broadened to the rotational velocity of HD 34282. + The depth of the central absorption varices and its radial velocity. micasured with respect to the stellar photosphere. shifts from an average value of 21.5435.5 Dodknos lod October 98 το G3IBELLG lau ! in Jannary 99.," The depth of the central absorption varies and its radial velocity, measured with respect to the stellar photosphere, shifts from an average value of $\pm$ 5.5 km $^{-1}$ in October 98 to $\pm$ 14.6 km $^{-1}$ in January 99." + The radial velocities of the viole andl red chussion peaks aud their separation also chauge from October 98 to Jauuary 99 (the ΜΑΝΤΗ peak separation is 319 kiu 1 on 28 Oct 98 and the miuinuuu is 117 lan lon 30 Jan 99)., The radial velocities of the violet and red emission peaks and their separation also change from October 98 to January 99 (the maximum peak separation is 319 km $^{-1}$ on 28 Oct 98 and the minimum is 117 km $^{-1}$ on 30 Jan 99). + The relative intensity of the euissiou ροκ» Chauges from dav to day aud a flip is observed from October 98. when the violet peak is stronger. to Jauuuy 99. when the read peak is the strouger one.," The relative intensity of the emission peaks changes from day to day and a flip is observed from October 98, when the violet peak is stronger, to January 99, when the read peak is the stronger one." + Furthermore. he blue wing shows a shoulder on 28 October 98 which could be due to a third velocity component.," Furthermore, the blue wing shows a shoulder on 28 October 98 which could be due to a third velocity component." + Finally. the otal equivalent width varies from 3.0 to 5.7A.," Finally, the total equivalent width varies from –3.0 to –5.7." +" Using he R baud flux from simultancous optical photometry ou 27 October 98 aud 30 Jaunary 99 we estimate a Πα ine chussion flux of τι«10154 and ↽⋅↽1.6«105P cre Dos 1 respectively,"," Using the $R$ band flux from simultaneous optical photometry on 27 October 98 and 30 January 99 we estimate a $\alpha$ line emission flux of $7.4\times 10^{-13}$ and $1.6\times 10^{-12}$ erg $^{-2}$ $^{-1}$, respectively." +" The variability iu the emission Hux and shape of Πα proves the changiug couditious in the CS region where this line originates,", The variability in the emission flux and shape of $\alpha$ proves the changing conditions in the CS region where this line originates. + Cuiuin Rostopchina (1996) studied a sample of WAcBe stars and ound that double-peaked Πα cinission likely arises iu regular gaseous cireuiistellar disks rotating close o the stars and seen nearly edge on., Grinin Rostopchina (1996) studied a sample of HAeBe stars and found that double-peaked $\alpha$ emission likely arises in irregular gaseous circumstellar disks rotating close to the stars and seen nearly edge on. + We notice that Piéttu et al. (, We notice that Piéttu et al. ( +2003) find an inclination ofthe CO kepleriau disk of {ΠΩΣ with respect to the plane of the slaw.,2003) find an inclination of the CO keplerian disk of $i\!=\!56^\circ$ with respect to the plane of the sky. + The change of, The change of +have double values with respect to the average ratio obtained from terrestrial water.,have double values with respect to the average ratio obtained from terrestrial water. + A third potential source for Earth water. different from long-period and. short-period comets. could solve the problem. if the D/H ratio in MBCs will prove to be more similar to the terrestrial one.," A third potential source for Earth water, different from long-period and short-period comets, could solve the problem, if the D/H ratio in MBCs will prove to be more similar to the terrestrial one." + Dust ejection due to sublimation implies the existence of both ice and dust particles., Dust ejection due to sublimation implies the existence of both ice and dust particles. + This leads us to imagine that MBCs are comet-like bodies. that means intimate mixtures of ice and dust. and not rubble-pile rocky objects with some ice filling the interstices.," This leads us to imagine that MBCs are comet-like bodies, that means intimate mixtures of ice and dust, and not rubble-pile rocky objects with some ice filling the interstices." + If this assumption is coupled with the further assumption that the activity is driven by sublimation. then we can simulate and study the activity of MBCs through the thermal modeling codes used for comets. KBOs and icy bodies in Prialnik and Rosenberg (2009)) applied their comet nuclei thermal evolution model to 177P/Elst-Pizarro.," If this assumption is coupled with the further assumption that the activity is driven by sublimation, then we can simulate and study the activity of MBCs through the thermal modeling codes used for comets, KBOs and icy bodies in Prialnik and Rosenberg \cite{prialnik}) ) applied their comet nuclei thermal evolution model to 177P/Elst-Pizarro." + In their paper the authors demonstrate that deep-buried tice could have survived since the Main Belt formation time. and that this ice is most probably composed. at least nowadays. of water crystalline ice.," In their paper the authors demonstrate that deep-buried ice could have survived since the Main Belt formation time, and that this ice is most probably composed, at least nowadays, of water crystalline ice." + It would have been almost impossible. for ices sublimating at temperatures well under 130 K. to survive even under an insulating mantle.," It would have been almost impossible, for ices sublimating at temperatures well under 130 K, to survive even under an insulating mantle." + Schorghofer too (2008)) in his paper assumes that the ice. in order to survive for such a long time. must have been buried under an insulating mantle. and gives estimations of the thickness of this dust layer.," Schorghofer too \cite{schorghofer}) ) in his paper assumes that the ice, in order to survive for such a long time, must have been buried under an insulating mantle, and gives estimations of the thickness of this dust layer." + The same author argues against the possibility that the ice be mixed with rocky material rather than dusty material., The same author argues against the possibility that the ice be mixed with rocky material rather than dusty material. + Rocky surfaces are seldom able to retain ice. due to the larger thermal conductivity and the larger molecular free path of rocks with respect to dust grains.," Rocky surfaces are seldom able to retain ice, due to the larger thermal conductivity and the larger molecular free path of rocks with respect to dust grains." + Being obvious that exposed ice cannot last for a long time at this distance from the Sun. we make the hypothesis that buried ice has been exposed in recent times.," Being obvious that exposed ice cannot last for a long time at this distance from the Sun, we make the hypothesis that buried ice has been exposed in recent times." + The most probable explanation is that of an impact excavating à crater in à dust mantle., The most probable explanation is that of an impact excavating a crater in a dust mantle. + This hypothesis. and if the present-days impact frequency in the Main Belt ts compatible with it. will be discussed in a following section.," This hypothesis, and if the present-days impact frequency in the Main Belt is compatible with it, will be discussed in a following section." + Starting from the assumptions stated above. we apply our thermal evolution model to simulate MBCs activity in the hypothesis that an impact has recently happened and that a crater has been excavated in the dust mantle.," Starting from the assumptions stated above, we apply our thermal evolution model to simulate MBCs activity in the hypothesis that an impact has recently happened and that a crater has been excavated in the dust mantle." + The effect of the impact could have been to directly expose a fresh ice-rich layer or. if the crater is not deep enough. bring an ice-rich layer closer to the surface. making it reachable by the the diurnal/seasonal heat wave.," The effect of the impact could have been to directly expose a fresh ice-rich layer or, if the crater is not deep enough, bring an ice-rich layer closer to the surface, making it reachable by the the diurnal/seasonal heat wave." + The aim of the simulation is to investigate the activity of MBCs in à more general way and under different hypotheses. and study how long can the activity last. on which parameters it depends. and which are the characteristics of this activity when a thin mantle is still covering an active layer.," The aim of the simulation is to investigate the activity of MBCs in a more general way and under different hypotheses, and study how long can the activity last, on which parameters it depends, and which are the characteristics of this activity when a thin mantle is still covering an active layer." + The thermal evolution model that has been applied to simulate the activity of MBCs ts described in this subsection (Capria et al. 2000a::, The thermal evolution model that has been applied to simulate the activity of MBCs is described in this subsection (Capria et al. \cite {capria}; + Capria et al. 2000b:: , Capria et al. \cite{capria1}; ; +Capria et al. 2001:: , Capria et al. \cite{capria2}; ; +De Sanctis et al. 2003.. 2005)).," De Sanctis et al. \cite{desanctis}, \cite{desanctis1}) )." + In the next subsection. the simulation of dust component. dust flux and mantle structure are explained in greater detail. because these features have been recently improved in this continuously evolving The model is one-dimensional.," In the next subsection, the simulation of dust component, dust flux and mantle structure are explained in greater detail, because these features have been recently improved in this continuously evolving The model is one-dimensional." + The spherical nucleus is porous and composed of ices (water and up to two different species. typically CO and CO») and a refractory component.," The spherical nucleus is porous and composed of ices (water and up to two different species, typically CO and $_2$ ) and a refractory component." + Water ice can be initially amorphous. and in this case a fraction of gases such as CO can be trapped in the amorphous matrix and released during the transition to ervstalline phase.," Water ice can be initially amorphous, and in this case a fraction of gases such as CO can be trapped in the amorphous matrix and released during the transition to crystalline phase." + In this work. anyway. we will deal only with water ice in its crystalline status.," In this work, anyway, we will deal only with water ice in its crystalline status." + Together with Prialnik and Rosenberg (2009)). we deem extremely improbable. for ices sublimating at temperatures well under 130 K. to have survived till now. even under an insulating mantle.," Together with Prialnik and Rosenberg \cite{prialnik}) ), we deem extremely improbable, for ices sublimating at temperatures well under 130 K, to have survived till now, even under an insulating mantle." + Energy and mass conservation. is expressed. by the following system of coupled differential equations. solved forthewhole nucleus:," Energy and mass conservation is expressed by the following system of coupled differential equations, solved forthewhole nucleus:" +spectra cover the wavelength range from 4400 tto 9265 with a resolution of 0.2 and 0.3 bbetween 4700 and 8450 aand signal-to-noise ratio S/N=15/—GO per resolution element.,spectra cover the wavelength range from 4400 to 9265 with a resolution of 0.2 and 0.3 between 4700 and 8450 and signal-to-noise ratio $=15-60$ per resolution element. + The data were reduced and analysed by Savaglioetal.(1997) to which we refer the reader for a detailed description of the observations and data reduction procedure., The data were reduced and analysed by \cite*{Savaglio97} to which we refer the reader for a detailed description of the observations and data reduction procedure. + In the spectrum of 2610. SOM have identified nine metal absorption systems; among these two are known damped systems at redshifts 3.054 and 3.390.," In the spectrum of $-$ 2619, SOM have identified nine metal absorption systems; among these two are known damped systems at redshifts 3.054 and 3.390." + Eight of the nine systems have redshift greater than. 3., Eight of the nine systems have redshift greater than 3. + We carefully inspected the spectrum looking for absorption from the and ground. state multiplet., We carefully inspected the spectrum looking for absorption from the and ground state multiplet. + For all systems at redshifts greater than 3. the absorption from the ground state multiplet would land redwards of the Lyman-o emission.," For all systems at redshifts greater than 3, the absorption from the ground state multiplet would land redwards of the $\alpha$ emission." + No absorption from is detectable in the spectrum., No absorption from is detectable in the spectrum. + absorption was detected for both the damped systems at ;=051] and 2=3.390 (SOM)., absorption was detected for both the damped systems at $z=3.054$ and $z=3.390$ (SOM). + For these systems the (A1331) absorption line lands bluewards of the Ένα emission., For these systems the $\lambda1334$ ) absorption line lands bluewards of the $\alpha$ emission. + The at 2=3.3913 is heavily blended. while the at redshift +=3.0513 is reasonably clean. despite falling in the Lyman forest at A=5110.6.," The at $z = 3.3913$ is heavily blended, while the at redshift $z = 3.0543$ is reasonably clean, despite falling in the Lyman forest at $\lambda = 5410.6$." + At A=5115.1 we detect a weak absorption line (3.50 confidence) consistent with absorption from the excited fine-structure level of at redshift ;=3.05 13., At $\lambda = 5415.4$ we detect a weak absorption line $\sigma$ confidence) consistent with absorption from the excited fine-structure level of at redshift $z = 3.0543$ . +" Table 1. summarizes the data on the absorption lines detected for the system at +=3.0513,", Table \ref{tab:lines} summarizes the data on the absorption lines detected for the system at $z =3.0543$. + At a redshift of 3.0543. the J=1/2 (\1334.53 An and J=3/2 (\\1335.66.1335.71 A)) absorption lines land respectively at 5410.54 aand 5415.17.5415.37Α," At a redshift of 3.0543, the $J = 1/2$ $\lambda$ 1334.53 ) and $J = 3/2$ $\lambda\lambda$ 1335.66,1335.71 ) absorption lines land respectively at 5410.54 and 5415.17,5415.37." +.. reffig:Cir. shows the spectrum of 2619 in the vicinity of the multiplet., \\ref{fig:Cii} shows the spectrum of $-$ 2619 in the vicinity of the multiplet. + In this wavelength range the spectral resolution is of 0.2 aand the S/N per resolution element is about 15., In this wavelength range the spectral resolution is of 0.2 and the S/N per resolution element is about 15. + The multiplet lands in the Lyman forest and in the damping wing of the Ενα absorption of the >=3.590 damped system. at ~ 5337Α..," The multiplet lands in the Lyman forest and in the damping wing of the $\alpha$ absorption of the $z = 3.390$ damped system, at $\sim$ 5337." + The ground state absorption line is slightly blended., The ground state absorption line is slightly blended. + We used a multiple Gaussian fit to deblend the line and measured an equivalent width of I4=1.16+0.02Α., We used a multiple Gaussian fit to deblend the line and measured an equivalent width of $W_{\lambda} = 1.16 \pm 0.02$. +. The absorption line is detected at 3.50., The $^*$ absorption line is detected at $3.5\sigma$ . + For Wy=0.077+0.02., For $^*$ $W_{\lambda} = 0.077 \pm 0.02$. + The Gaussian fit to the line has a FWHM of 0.29 wwhich is consistent with the instrument resolution., The Gaussian fit to the line has a FWHM of 0.29 which is consistent with the instrument resolution. +" The two equivalent widths correspond respectively to ΙονΑλ).=3.67 and Lash, ", The two equivalent widths correspond respectively to $\log(W_\lambda/\lambda) = -3.67$ and $-4.85$ . +In both cases a local continuum level corresponding to the damping wing of the Ένα absorption at >=3.390 has been used., In both cases a local continuum level corresponding to the damping wing of the $\alpha$ absorption at $z = 3.390$ has been used. + The absorption line is well fitted by a Gaussian having a FWHM of 53+5 kms +. which given the instrumental resolution in this range of 11 kms. 1 corresponds to an intrinsic } parameter of3l-c3kms +.," The absorption line is well fitted by a Gaussian having a FWHM of $53\pm5$ km $^{-1}$, which given the instrumental resolution in this range of 11 km $^{-1}$ corresponds to an intrinsic $b$ parameter of $31 \pm 3$ km $^{-1}$." + In reffig:ce the theoretical curve of growth of is plotted for three values of b: 28. 31 and 34 km +.," In \\ref{fig:cg} the theoretical curve of growth of is plotted for three values of $b$ : 28, 31 and 34 km $^{-1}$." + The two values of log(T4/A) are also shown., The two values of $\log(W_\lambda/\lambda)$ are also shown. + The corresponding column density values derived for Hand are summarized in Table 2.., The corresponding column density values derived for and $^*$ are summarized in Table \ref{tab:CII}. . +" According to the Boltzmann equation. an excitation temperature 7;.. can be expressed in terms of the column densities Vy and Ny in the excited and the ground-state level: where AT}, is the energy difference between the excited level (1) and the ground level (0)."," According to the Boltzmann equation, an excitation temperature $T_{\rm ex}$ can be expressed in terms of the column densities $N_1$ and $N_0$ in the excited and the ground-state level: where $k\Delta T_{10}$ is the energy difference between the excited level (1) and the ground level (0)." + For the fine structure levels J=3/2 and J=1/2 ofCin. ATi=91.2 K. The weights gj are given by 2.7|1.," For the fine structure levels $J= 3/2$ and $J=1/2$ of, $\Delta T_{10} = 91.2$ K. The weights $g_J$ are given by $2J + 1$." + The derived ratio of column densities. ΑΙ=3/2)/N4(7.1/2) corresponds to an excitation temperature of 19.6 K (for)=28 kms. 1). 20.5 K (for=31 km !) and 21.6 K (for b.=3. km 1).," The derived ratio of column densities, $N_1(J=3/2)/N_0(J=1/2)$ corresponds to an excitation temperature of 19.6 K (for $b=28$ km $^{-1}$ ), 20.5 K (for $b=31$ km $^{-1}$ ) and 21.6 K (for $b=34$ km $^{-1}$ )." + The excitation temperature of 21.6 Kprovides a strict upper limit on the temperature of the CMB at the absorberredshift of 3.0543: thisupper limit would hold even if the absorption were aspurious effect of theLyman forest., The excitation temperature of 21.6 Kprovides a strict upper limit on the temperature of the CMB at the absorberredshift of 3.0543; thisupper limit would hold even if the $^*$ absorption were aspurious effect of theLyman forest. + The CMB temperature at this redshift is predicted to be 11.05 K by the Big Bang model., The CMB temperature at this redshift is predicted to be 11.05 K by the Big Bang model. +"The variation of concentration with mass (upper panel) suggests that this relation may be steeper in cosmologies with shallower spectral indices, which in turn may reflect the importance of merging for the growth of the most massive haloes in these cosmologies.","The variation of concentration with mass (upper panel) suggests that this relation may be steeper in cosmologies with shallower spectral indices, which in turn may reflect the importance of merging for the growth of the most massive haloes in these cosmologies." +" Although the trends are tentative, we believe that this is an extremely interesting figure and one that may allow to better understand the physical origin of the density profile."," Although the trends are tentative, we believe that this is an extremely interesting figure and one that may allow to better understand the physical origin of the density profile." +" We shall return to this issue, albeit briefly, in H]."," We shall return to this issue, albeit briefly, in \ref{sec:conclusions}." +" The trend for concentration to decrease with steeper spectral index is more robust, and we show this explicitly by plotting the mean concentration of haloes in the M. sample versus spectral index (lower panel)."," The trend for concentration to decrease with steeper spectral index is more robust, and we show this explicitly by plotting the mean concentration of haloes in the $M_{*}$ sample versus spectral index (lower panel)." + This makes clear our assertion that it is the concentration that depends strongly on the spectral index., This makes clear our assertion that it is the concentration that depends strongly on the spectral index. +" The primary motivation for this paper has been to establish what dependence, if any, the logarithmic slope a of the inner mass density profile of dark matter haloes has on the spectral index n of the linear matter power spectrum."," The primary motivation for this paper has been to establish what dependence, if any, the logarithmic slope $\alpha$ of the inner mass density profile of dark matter haloes has on the spectral index $n$ of the linear matter power spectrum." + For this purpose we have runa series of high resolution cosmological N-body simulations of scale-free models (i.e. P(k)~Ak”) with values of the spectral index n varying between —0.5>n—2.75., For this purpose we have run a series of high resolution cosmological $N$ -body simulations of scale-free models (i.e. $P(k) \sim Ak^n$ ) with values of the spectral index $n$ varying between $-0.5 \geqslant n \geqslant -2.75$. +" By using scale-free models and fixing n in this manner, the problem of identifying correlations between a and n becomesa relatively straightforward one."," By using scale-free models and fixing $n$ in this manner, the problem of identifying correlations between $\alpha$ and $n$ becomes a relatively straightforward one." +" Relatively, because there is some freedom in the choice of criteria one can use to determine when to start and when to finish scale-free simulations."," Relatively, because there is some freedom in the choice of criteria one can use to determine when to start and when to finish scale-free simulations." +" To address this, we have derived clear, reproducible and physically motivated criterion that allows us to set up scale-free simulations and that is presented in Zi."," To address this, we have derived clear, reproducible and physically motivated criterion that allows us to set up scale-free simulations and that is presented in \ref{sec:starting}." +" In short, we start the simulations with the same integral power in the k-range defined by the the total number of particles N; it is especially important to have an objective criterion for starting simulations when studying mass profiles."," In short, we start the simulations with the same integral power in the $k$ -range defined by the the total number of particles $N$; it is especially important to have an objective criterion for starting simulations when studying mass profiles." +" To determine when to stop our simulations, we follow ? and use the evolution of the typical collapsing mass M..."," To determine when to stop our simulations, we follow \citet{1997ApJ...490..493N} and use the evolution of the typical collapsing mass $M_{*}$." + We do so once the mass in a typical M.. halo corresponds to approximately 42000 particles., We do so once the mass in a typical $M_{*}$ halo corresponds to approximately $42000$ particles. +" Having established a set of well-defined criteria to set up and run cosmological simulations of scale-free models, we performed a sequence of high resolution runs (1h~Mpc boxes, 512? particles) that we used to investigate the dependence of the central logarithmic slope of the dark matter halo density profile a on the spectral indexn."," Having established a set of well-defined criteria to set up and run cosmological simulations of scale-free models, we performed a sequence of high resolution runs $1 h^{-1} \rm Mpc$ boxes, $512^3$ particles) that we used to investigate the dependence of the central logarithmic slope of the dark matter halo density profile $\alpha$ on the spectral index$n$." + We varied n between —0.5 and —2.75 and selected samples of well resolved haloes (Nyir>3.15x 103) in dynamical equilibrium in each run (ranging from ~270 haloes in the n=—0.5 run to ~40 haloes in the n=—2.75 run)., We varied $n$ between $-0.5$ and $-2.75$ and selected samples of well resolved haloes $N_{\rm vir} \geqslant 3.15 \times 10^4$ ) in dynamical equilibrium in each run (ranging from $\sim 270$ haloes in the $n=-0.5$ run to $\sim 40$ haloes in the $n=-2.75$ run). +" Using x? fits to a generalised NFW profile, we identified preferred values of the inner slope o and indeed, we found a trend for the inner slope to become shallower with steeper spectral index — from a~1.6 for n=—0.5 to oc1.2 for n=—2.75."," Using $\chi^2$ fits to a generalised NFW profile, we identified preferred values of the inner slope $\alpha$ and indeed, we found a trend for the inner slope to become shallower with steeper spectral index – from $\alpha \simeq 1.6$ for $n=-0.5$ to $\alpha \simeq 1.2$ for $n=-2.75$." +" However, we argue that it is not the central slope o that depends on spectral index; rather, it is the scale radiusof the halo, Το, or our preferred measure r_2, the radius at which the differential mass profile pr? reaches its maximum value."," However, we argue that it is not the central slope $\alpha$ that depends on spectral index; rather, it is the scale radiusof the halo, $r_s$, or our preferred measure $r_{-2}$, the radius at which the differential mass profile $\rho\,r^2$ reaches its maximum value." + We have shown that haloes in different n models have similar radial profiles of the maximum slope y=3(1—p/p) when normalised to r_2., We have shown that haloes in different $n$ models have similar radial profiles of the maximum slope $\gamma=3(1-\rho/\bar{\rho})$ when normalised to $r_{-2}$. +" However, as already shown by ?,, haloes that form in models with steeper n tend to be less centrally concentrated than haloes forming in models with shallower m, and so their mass profiles can be resolved to smaller fractions of T5, where the flattening of the profile is more apparent."," However, as already shown by \citet{1997ApJ...490..493N}, haloes that form in models with steeper $n$ tend to be less centrally concentrated than haloes forming in models with shallower $n$, and so their mass profiles can be resolved to smaller fractions of $r_{-2}$, where the flattening of the profile is more apparent." +" Haloes in these modelswould then appear to have shallower central We noted in the introduction that using scale-free simulations to study the effect of the spectral index of the power spectrum on the central structure of dark matter haloes was preferable to the approach taken by ?,, ?,, ?,, and ?,, in which the box size and analysis redshift were varied to capture the behaviour of different spectral indices."," Haloes in these modelswould then appear to have shallower central We noted in the introduction that using scale-free simulations to study the effect of the spectral index of the power spectrum on the central structure of dark matter haloes was preferable to the approach taken by \citet{2003MNRAS.344.1237R}, \citet{2004astro.ph..3352C}, \citet{2004ApJ...612...50C}, and \citet{2007ApJ...663L..53R}, in which the box size and analysis redshift were varied to capture the behaviour of different spectral indices." + The claims of ? are of particular interest; these authors argue that halo concentration is a universal constant and that dwarf galaxies identified at z=10 have logarithmicslopes shallower than 0.5., The claims of \citet{2007ApJ...663L..53R} are of particular interest; these authors argue that halo concentration is a universal constant and that dwarf galaxies identified at $z$ =10 have logarithmicslopes shallower than $0.5$. + Our results strongly disagree with these claims., Our results strongly disagree with these claims. +" Although the central slope a that we obtain by fitting a generalised NFW profile does vary with n, this does not imply that the shape of the profile is sensitive to n, for the reasons presented above."," Although the central slope $\alpha$ that we obtain by fitting a generalised NFW profile does vary with $n$ , this does not imply that the shape of the profile is sensitive to $n$ , for the reasons presented above." +" Moreover,as we show in Figure B], density profiles normalised by r_2, which"," Moreover,as we show in Figure \ref{fig:maxslope_rr2}, , density profiles normalised by $r_{-2}$ , which" +density is also high.,density is also high. + The differences m average charge state between the low and lieh density models are thus viewed as a result of the temperatures in the low density model generally beiug higher than iu the lieh deusity mioclel., The differences in average charge state between the low and high density models are thus viewed as a result of the temperatures in the low density model generally being higher than in the high density model. + Based on our results. we conclude that it is not sufficient to calculate the ionization state of the plasma as a “post-processing” step.," Based on our results, we conclude that it is not sufficient to calculate the ionization state of the plasma as a “post-processing” step." + While iu lower density models the cditfereuces are small at higher densities. the caleulation will underpredict the cuission from intermediate charge states; particularly cussion from Fe-L. We speculate that these differences might be even larger in etal rich ejecta where the number of free electrons will be large.," While in lower density models the differences are small, at higher densities, the calculation will underpredict the emission from intermediate charge states, particularly emission from Fe-L. We speculate that these differences might be even larger in metal rich ejecta where the number of free electrons will be large." + Finally. we note that the shape of the enütted spectrin in an efficient model. even when folded through a CCD-resolution response. is fundamentally differcut than the emitted spectrum from a test-particle model.," Finally, we note that the shape of the emitted spectrum in an efficient model, even when folded through a CCD-resolution response, is fundamentally different than the emitted spectrum from a test-particle model." + D. J. P. acknowledges support from Theory evant TAIO-LIOOGA. and P. O. S. and D. J.P. acknowledge support from NASA contract NAS®-03060.," D. J. P. acknowledges support from Theory grant TM0-11006A, and P. O. S. and D. J. P. acknowledge support from NASA contract NAS8-03060." + D.CLE. acknowledges support from NASA contracts ATPO2-0012-0006. NNTTOLZss001N-LTSA. aud 06-ATPO06-21.," D.C.E. acknowledges support from NASA contracts ATP02-0042-0006, NNH04Zss001N-LTSA, and 06-ATP06-21." + The authors are erateful to the KITP in Santa Barbara where part of this work was done when the authors were participating iu a KITP program., The authors are grateful to the KITP in Santa Barbara where part of this work was done when the authors were participating in a KITP program. +ο these sizes are plotted in the top-right. corner of each map.,to these sizes are plotted in the top-right corner of each map. + The erev-scale bar describes the magnification., The grey-scale bar describes the magnification. + Fig., Fig. + 1 demonstrates that even à source several ER in extent can microlensed. by. an pps .factor (see⋅ for example⋅ Ha e. ., \ref{magmap} demonstrates that even a source several ER in extent can be microlensed by an appreciable factor (see for example Refsdal Stabell 1993). + PiplTB )etween the caustic⋅⋠ regions of .highest densityi ancl the ugherlohor magnification≱ regions−⋅≱⋪ for‘or the Iaroorlarger sources.," In addition, there is a correlation between the caustic regions of highest density and the higher magnification regions for the larger sources." +"""(gn However(Ver he figures demonstrate that there is significant loss οἱ correlationqarppls betweenoolwee the. magnilications“yeTend]‘ of a ""acsourcece which isi: . LolNET laren rCo-positional ""lareercsources.", However the figures demonstrate that there is significant loss of correlation between the magnifications of a source which is $\ll\eta_o$ and of larger co-positional sources. +"siti al:InCOS, particular larenarticular. rlareerand ""σοςΝshow Lieht-curyvesD witursM aOWCE event\ :ampulu aituclesanc via.. longer event curations (see the light-curves ancl correlation functions for various source sizesin Wambsganss. Paczvuski [satz 1990)."," In particular, larger sources show light-curves with lower event amplitudes and longer event durations (see the light-curves and correlation functions for various source sizes in Wambsganss, Paczynski Katz 1990)." +" uPhe cumulative. probabilityu for. the mid-LR. flux. ratio. RifACTUMoHg ‘or ciere icl-1IR ""CÓ «ον ""p ο]νο ↙∡⊳⇂∪↓∠⊔∐⋖⊓⊔∣⊔∐∠⇂∐↘⊳∖∪⊔↓⊓⊳∖↓∠⋖⊳∖⊽↔⊓∣⋏∙≟↓∖∢⊔↿↓∐, measurecl optical ratio is punT.vhs) mis. the probabilityMN for⋅ the observed optica. [lux ratios. we have assumed to be Gaussian. with a mean and healt2. (7) vnl to the observed value uncerta iy."," The cumulative probability for the mid-IR flux ratio $R_{BA}^{IR}=\frac{\mu_B^{IR}}{\mu_A^{IR}}$, for different mid-IR source sizes $S_{IR}$ given the measured optical ratio is $p(R_{BA}^{OPT,obs})$ is the probability for the observed optical flux ratios, which we have assumed to be Gaussian with a mean and halfwidth $\sigma$ ) equal to the observed value and uncertainty." +". .tegral ihove [> ;AenTabswas perfor ""⋅SC Monte-C'arlo."," The integral over $R_{BA}^{OPT,obs}$ was performed via Monte-Carlo." +] e. oweobserved optica Ux ipactions .aunt ratios ape in Tab. 3.., The observed optical flux fractions and ratios are summarised in Tab. \ref{flux_fractions}. + In the V-hanel (Wozniak et al., In the V-band (Wozniak et al. + 2000b3. the de-reddened. Dux. ratios (AJBOO) were HisOSxOON on the Ist August 1909 ane 0.26£0.07 on the 26th September 1999.," 2000b), the de-reddened flux ratios (AJB00) were $R_{BA}^{OPT,obs}=0.28\pm0.08$ on the 1st August 1999 and $0.26\pm0.07$ on the 26th September 1999." + In the remainder of this paper we use the V-band. Duxes from the 26th of September; 1999., In the remainder of this paper we use the V-band fluxes from the 26th of September 1999. + Fig., Fig. +" --2. shows the cumulative. probabilityuM ⇂⊓↓↓↓↓↓⊥⇂∐↘∐∏∖↓∡⊓↓⊓∫∆Rie,;—δινω)] Dor⋅ four"," \ref{probfns} shows the cumulative probability for mid-IR flux ratio $P_R(R_{BA}^{IR}1.3Mo are all younger than GGyr.," It can be affirmed there is tentative evidence of a pattern in the We see that stars with masses $\geq 1.3\,M_\odot$ are all younger than Gyr." +" Thus, when observing few aligned systems on stars with Teg>6250K, ? were in fact detecting an effect due to stellar age, or rather, time since planet formation."," Thus, when observing few aligned systems on stars with $T_\mathrm{eff} > 6250\,K$, \citet{Winn:2010p7311} were in fact detecting an effect due to stellar age, or rather, time since planet formation." +" Like for all multivariate problems, figure 2 offers an incomplete picture: it only shows two quantities in relation with time."," Like for all multivariate problems, figure \ref{fig:betaAge} offers an incomplete picture: it only shows two quantities in relation with time." + At the moment orbital separations and mass ratios are quite similar since the bulk of the discoveries have been done by ground-based transit search programs., At the moment orbital separations and mass ratios are quite similar since the bulk of the discoveries have been done by ground-based transit search programs. + With increasing numbers of measurements over a larger parameter space we will eventually need to account for those extra parameters., With increasing numbers of measurements over a larger parameter space we will eventually need to account for those extra parameters. + The large variety of angles around the younger stars suggests that some misaligning mechanism happens during the youth of planetary systems., The large variety of angles around the younger stars suggests that some misaligning mechanism happens during the youth of planetary systems. +" Notably, in combination with results by ? showing no evidence for misaligned protoplanetary discs, it lends strong support to a planet-planet scattering scenario occurring during the last stages of planet formation or soon in the aftermath of the disc dispersal like described in ?.."," Notably, in combination with results by \citet{Watson:2011p11844} showing no evidence for misaligned protoplanetary discs, it lends strong support to a planet-planet scattering scenario occurring during the last stages of planet formation or soon in the aftermath of the disc dispersal like described in \citet{Matsumura:2010p8930}." +" When preparing figure 2,, reason dictated that a dearth of old, misaligned systems was expected, not an absence."," When preparing figure \ref{fig:betaAge}, reason dictated that a dearth of old, misaligned systems was expected, not an absence." + The complete lack of misaligned planets orbiting stars older than 2.5GGyr in the current sample came somewhat as a surprise as secular interactions could place planets on inclined orbits well after the disc dissipated., The complete lack of misaligned planets orbiting stars older than Gyr in the current sample came somewhat as a surprise as secular interactions could place planets on inclined orbits well after the disc dissipated. +" A system presenting such characteristics can be found among the ""older"" systems: HAT-whose current configuration may have originated from secular interactions (?).."," A system presenting such characteristics can be found among the ""older"" systems: HAT-P-13,whose current configuration may have originated from secular interactions \citep{Mardling:2010p12652}." +" If that history is right, its observed coplanarity may be a chance alignment."," If that history is right, its observed coplanarity may be a chance alignment." +" Chance alignments can occur easily since firstly, we observe a projected angle, 6, and not the real obliquity v and secondly, theoretical predictions such as ?,, ? and ? predict very high orbital inclinations, but also a number of aligned systems."," Chance alignments can occur easily since firstly, we observe a projected angle, $\beta$ , and not the real obliquity $\psi$ and secondly, theoretical predictions such as \citet{Wu:2007p4179}, \citet{Fabrycky:2007p3141} and \citet{Nagasawa:2008p2997} predict very high orbital inclinations, but also a number of aligned systems." +" There is great interest in matching those theoretical distributions to observations (notably for young hot Jupiters), but the evolving nature of the spin/orbit angle distribution makes this a tricky task."," There is great interest in matching those theoretical distributions to observations (notably for young hot Jupiters), but the evolving nature of the spin/orbit angle distribution makes this a tricky task." + Multi-body dynamics are less concerned about absolute masses than about mass ratio., Multi-body dynamics are less concerned about absolute masses than about mass ratio. +" In systems where no Jupiter has formed, we would expect planet-planet scattering between Neptune-mass planets producing an inclined hot Neptune population."," In systems where no Jupiter has formed, we would expect planet-planet scattering between Neptune-mass planets producing an inclined hot Neptune population." +" If the inital stages will be similar, the later ones will not: tidal circularisation and realignment timescales will be different."," If the inital stages will be similar, the later ones will not: tidal circularisation and realignment timescales will be different." + Spin/orbit angles for planets of masses «0.1Mjyp will be less affected by tidal realignment and offer a closer picture of the initial spin/orbit angle distribution than hot Jupiters.," Spin/orbit angles for planets of masses $< 0.1 \,M_\mathrm{Jup}$ will be less affected by tidal realignment and offer a closer picture of the initial spin/orbit angle distribution than hot Jupiters." +" A hot Neptune, P-11bb has been recently detected misaligned by ? and confirmed by ?.."," A hot Neptune, b has been recently detected misaligned by \citet{Winn:2010p8446} and confirmed by \citet{SanchisOjeda:2011p12868}." + This work has focused on stars with masses >1.2Mo.," This work has focused on stars with masses $\geq 1.2\,M_\odot$." +" If age is what determines primarily whether a hot Jupiter is observed aligned or misaligned, since solar mass stars are detected in average older than more massive stars, it is not surprising that their planets are coplanar."," If age is what determines primarily whether a hot Jupiter is observed aligned or misaligned, since solar mass stars are detected in average older than more massive stars, it is not surprising that their planets are coplanar." +" There nevertheless is an interest in looking at that population carefully which stems from work by ?,, ? and ? who argue that discs around the more massive stars are not long lived enough to produce an aligned hot Jupiter population via disc migration."," There nevertheless is an interest in looking at that population carefully which stems from work by \citet{Burkert:2007p12867}, \citet{Currie:2009p12859} and \citet{Alibert:2011p11846} who argue that discs around the more massive stars are not long lived enough to produce an aligned hot Jupiter population via disc migration." +" In the mean time, if planet formation is more efficient in more massive discs (found around more massive stars), then one could expect a higher occurrence of planet-planet scattering around such stars."," In the mean time, if planet formation is more efficient in more massive discs (found around more massive stars), then one could expect a higher occurrence of planet-planet scattering around such stars." +" If this is true, it could point towards two pathways for bringing hot Jupiters to their observed location which would be dependent on stellar mass."," If this is true, it could point towards two pathways for bringing hot Jupiters to their observed location which would be dependent on stellar mass." + Unfortunately stellar ages are less precisely determined for solar mass stars as illustrated by the isochrone on figure 1.., Unfortunately stellar ages are less precisely determined for solar mass stars as illustrated by the isochrone on figure \ref{fig:tracks}. +" The change in the shape of the distribution of spin/orbit angles with time is indicative of some orbital evolution, presumably through tidal interactions between the star and the planet."," The change in the shape of the distribution of spin/orbit angles with time is indicative of some orbital evolution, presumably through tidal interactions between the star and the planet." +" ? show that retrograde planets decay into their star on timescales two to three times shorter than prograde planets would do, for given initial conditions."," \citet{Barker:2009p11693} show that retrograde planets decay into their star on timescales two to three times shorter than prograde planets would do, for given initial conditions." +" Their infall timescale for a typical, retrograde, hot Jupiter are of order of a few Gyrs."," Their infall timescale for a typical, retrograde, hot Jupiter are of order of a few Gyrs." + ? present similar behaviour., \citet{Winn:2010p7311} present similar behaviour. +" In addition they show that, for a given stellar mass, a more massive planet will realign and in-spiral faster than a lighter one?.."," In addition they show that, for a given stellar mass, a more massive planet will realign and in-spiral faster than a lighter ." + Inboth papers the retrograde planets realign with the star but only shortly before, Inboth papers the retrograde planets realign with the star but only shortly before +of in these runs and that all high-mass stars reside in binaries.,of in these runs and that all high-mass stars reside in binaries. +" Binary masses were chosen such that stars were ordered according to their mass and the components of each binary were drawn from consecutive stars in this list, i.e. the first binary contained the two most massive stars."," Binary masses were chosen such that stars were ordered according to their mass and the components of each binary were drawn from consecutive stars in this list, i.e. the first binary contained the two most massive stars." +" Hence, the stellar binary fraction is for the high-mass stars, while all low mass stars are single."," Hence, the stellar binary fraction is for the high-mass stars, while all low mass stars are single." +" Although being a strong simplification, our adopted binary distribution reflects the drop in binary fraction towards late spectral types seen for stars in the galactic disc (Lada 2006)."," Although being a strong simplification, our adopted binary distribution reflects the drop in binary fraction towards late spectral types seen for stars in the galactic disc (Lada 2006)." + The semi-major axis of the binaries were chosen randomly in logr between à minimum radius three times as large as the sum of the radii reached at the end of the accretion phase and a maximum radius which was set equal to 100 AU., The semi-major axis of the binaries were chosen randomly in $\log r$ between a minimum radius three times as large as the sum of the radii reached at the end of the accretion phase and a maximum radius which was set equal to 100 AU. +" For simplicity, we assumed in our runs that the semi-major axis of each binary remains constant during the accretion phase and increased the stellar velocities of the components to avoid a shrinkage of the binary."," For simplicity, we assumed in our runs that the semi-major axis of each binary remains constant during the accretion phase and increased the stellar velocities of the components to avoid a shrinkage of the binary." + Fig., Fig. + 9 shows the resulting number of collisions in runs with binary stars., \ref{fig:bin} shows the resulting number of collisions in runs with binary stars. + The number of collisions is large in very compact clusters with Τη=0.33 pc., The number of collisions is large in very compact clusters with $r_h = 0.33$ pc. + The projected half-light radii of these clusters after 10 Myrs are similar to those of clusters without binaries and still smaller than about 0.3 pc (see Table 1)., The projected half-light radii of these clusters after 10 Myrs are similar to those of clusters without binaries and still smaller than about 0.3 pc (see Table 1). + Such clusters therefore still end up too compact compared to observed open clusters., Such clusters therefore still end up too compact compared to observed open clusters. + In more extended clusters the number of collisions is still not high enough to allow the build-up of a complete main sequence of massive stars., In more extended clusters the number of collisions is still not high enough to allow the build-up of a complete main sequence of massive stars. +" It is therefore likely that even in the presence of binaries, stellar collisions do not play a significant role for the formation of massive stars."," It is therefore likely that even in the presence of binaries, stellar collisions do not play a significant role for the formation of massive stars." +" A definite answer to this question can, however, only be made if a wider range of binary distributions is explored."," A definite answer to this question can, however, only be made if a wider range of binary distributions is explored." +" We have performed N-body simulations of the pre-main sequence evolution of stars in stellar clusters, taking account gas accretion, primordial gas expulsion, and collisions between stars."," We have performed $N$ -body simulations of the pre-main sequence evolution of stars in stellar clusters, taking account gas accretion, primordial gas expulsion, and collisions between stars." + Our simulations show that it is very unlikely that all high-mass stars with masses m>20 Mo form from the collisions of lower mass stars., Our simulations show that it is very unlikely that all high-mass stars with masses $m>20$ $_\odot$ form from the collisions of lower mass stars. +" The reason for this is twofold: First, the necessary number of collisions between massive stars only occurs for central densities around 105 Mo/pc?, implying initial half-mass radii rj«0.1 pc for clusters of a few thousand stars."," The reason for this is twofold: First, the necessary number of collisions between massive stars only occurs for central densities around $10^8$ $_\odot$ $^3$, implying initial half-mass radii $r_h<0.1$ pc for clusters of a few thousand stars." +" Such clusters remain highly concentrated within the first 10 Myr of their evolution, despite expansion due to gas expulsion and stellar evolution mass loss, and therefore lead to clusters which are significantly more concentrated than known open clusters with O and B type stars which generally have radii around 1 pc."," Such clusters remain highly concentrated within the first 10 Myr of their evolution, despite expansion due to gas expulsion and stellar evolution mass loss, and therefore lead to clusters which are significantly more concentrated than known open clusters with O and B type stars which generally have radii around 1 pc." + Our simulations show that the observed radii of young open clusters imply initial radii in the range 0.2 to 1 pc for most of them., Our simulations show that the observed radii of young open clusters imply initial radii in the range 0.2 to 1 pc for most of them. +" Second, even if a sufficient number of collisions occurs, this will normally lead to the formation of single runaway stars with extremely large masses instead of the build-up of the observed high-mass IMF, a result that was recently also obtained by Moeckel&Clarke(2010) through direct N-body simulations."," Second, even if a sufficient number of collisions occurs, this will normally lead to the formation of single runaway stars with extremely large masses instead of the build-up of the observed high-mass IMF, a result that was recently also obtained by \citet{mc10} through direct $N$ -body simulations." + The reason is the large cross section for collisions and gravitational focusing of massive stars., The reason is the large cross section for collisions and gravitational focusing of massive stars. + 'The number of collisions cannot be increased sufficiently by considering different mass accretion rates or binary stars., The number of collisions cannot be increased sufficiently by considering different mass accretion rates or binary stars. +comparing the maxima in the asymmetry map with those from the COBE data (Bissantzetal.1997;Bissantz&Gerhard 2002).,"comparing the maxima in the asymmetry map with those from the COBE data \citep{Bissantz+97,Bissantz+Gerhard02}." +. Also both the boxy bulge and the disk are vertically more extended in the model., Also both the boxy bulge and the disk are vertically more extended in the model. + The Sun is placed at 8 kpc., The Sun is placed at $8$ kpc. + In the face-on view we can easily identify theleading ends of the stellar bar., In the face-on view we can easily identify the ends of the stellar bar. +" Over a period of 1.2 Gyr, the model shows oscillations from leading through straight to trailing ends and back."," Over a period of 1.2 Gyr, the model shows oscillations from leading through straight to trailing ends and back." + The bar spends of this time in the leading phases., The bar spends of this time in the leading phases. +" Similar morphology can be seen in other barred simulations in the literature (e.g.Fux1997,modelm08) and also in some observed galaxies such as NGC 3124 (Efremov2011) and NGC 3450 (Butaetal.2007).", Similar morphology can be seen in other barred simulations in the literature \citep[e.g.][model m08]{Fux97} and also in some observed galaxies such as NGC 3124 \citep{Efremov11} and NGC 3450 \citep{Buta+07}. +. The oscillations between trailing and leading ends of the bar could be related to the oscillations seen in the bar growth in N-body simulations (e.g.Dubinskietal.2009) and may be due to non-linear coupling modes between the bar and spiral arms (Taggeretal., The oscillations between trailing and leading ends of the bar could be related to the oscillations seen in the bar growth in N-body simulations \citep[e.g.][]{Dubinski+09} and may be due to non-linear coupling modes between the bar and spiral arms \citep{Tagger+87}. + This topic is beyond the scope of this paper., This topic is beyond the scope of this paper. + For comparison1987).. we show a snapshot at a later time in this simulation where the ends of the bar are straight and the spiral arms appear to emerge from them (Figure 2))., For comparison we show a snapshot at a later time in this simulation where the ends of the bar are straight and the spiral arms appear to emerge from them (Figure \ref{fig:snapshot2}) ). +" We apply a similar technique as was used to identify two different barred structures in the MW from star count data (B05,C07,C08,C09)."," We apply a similar technique as was used to identify two different barred structures in the MW from star count data (B05,C07,C08,C09)." + We view the projected model as an observer in the disk at 8 kpc distance from the center would see it., We view the projected model as an observer in the disk at $8$ kpc distance from the center would see it. +" To increase the particle resolution, we symmetrize the model vertically and divide the latitude)-(l,b)-space into bins of ól=3? and 6b=2°, respectively."," To increase the particle resolution, we symmetrize the model vertically and divide the $l,b$ )-space into bins of $\delta +l=3^\circ$ and $\delta b=2^\circ$, respectively." +" Then we count particles in each of the corresponding cones and bin these particles in distance modulus, with ὃμ=0.1."," Then we count particles in each of the corresponding cones and bin these particles in distance modulus, with $\delta\mu = 0.1$." + The distance modulus is given by 4=—5.+5.xlog(D[pc])., The distance modulus is given by $\mu=-5.+5.\times\log(D[pc])$. + In Figure 3 we show histograms in j for several lines-of-sight., In Figure \ref{fig:histograms} we show histograms in $\mu$ for several lines-of-sight. +" To quantify the distribution of particles with j| and to assign a distance value to the maximum number counts, we fit a Gaussian to the left-most peak, i.e., the one nearest to the observer."," To quantify the distribution of particles with $\mu$ and to assign a distance value to the maximum number counts, we fit a Gaussian to the left-most peak, i.e., the one nearest to the observer." +" In the histogram obtained when looking towards the ends of the bar in the Galactic plane 3a) we can identify three main peaks, one corresponding(Figure to the bar, one to a spiral arm in the back, and one to the end of the disk."," In the histogram obtained when looking towards the ends of the bar in the Galactic plane (Figure \ref{fig:histograms}{ ) we can identify three main peaks, one corresponding to the bar, one to a spiral arm in the back, and one to the end of the disk." +" The p-value of the fitted maximum corresponds to the end of the bar, where the bar is flat."," The $\mu$ -value of the fitted maximum corresponds to the end of the bar, where the bar is flat." +" The second histogram for (1,ϐ)=(99,53) (Figure 3b) shows the distribution of stars in a field well above the plane where the boxy bulge dominates."," The second histogram for $(l,b)=(9^\circ,8^\circ)$ (Figure \ref{fig:histograms}{ ) shows the distribution of stars in a field well above the plane where the boxy bulge dominates." + The fitted maximum corresponds to a position on the thick line in Figure 1 at @=25°., The fitted maximum corresponds to a position on the thick line in Figure \ref{fig:snapshot1} at $\alpha=25^\circ$. +" In the first panel we can clearly identify the particles in the disk, but in the second showing the higher latitude field, disk particles are absent."," In the first panel we can clearly identify the particles in the disk, but in the second showing the higher latitude field, disk particles are absent." +" We also show the histogram for (9°,0°) (Figure 3c), where we can see the increment in the number of particles with respect to those at (27°, 2?),"," We also show the histogram for $(9^\circ,0^\circ)$ (Figure \ref{fig:histograms}{ ), where we can see the increment in the number of particles with respect to those at $(27^\circ,2^\circ)$ ," +"were divided by the combined errors op. and epgc. where στι—|a2, and Thee=στι|To with σενσοι051 and σου from Equations 3 and 4.","were divided by the combined errors $\sigma_{RA}$ and $\sigma_{DEC}$ , where $\sigma^2_{RA}=\sigma^2_{\alpha 1}+\sigma^2_{\alpha 2}$ and $\sigma^2_{DEC}=\sigma^2_{\delta 1}+\sigma^2_{\delta 2}$ with $\sigma_{\alpha 1}, \sigma_{\alpha 2}, \sigma_{\delta 1}$ and $\sigma_{\delta 2}$ from Equations 3 and 4." + As shown in Figure 13.. also these error distributions for faint sources agree with the expected Gaussians (smoothed curves)," As shown in Figure \ref{histo_weak}, also these error distributions for faint sources agree with the expected Gaussians (smoothed curves)." + In conclusion the positional uncertainties: obtained using Equations 3 and 4 are accurate also for sources down to the limit of our survey (~ 0.135 mv) and they can be used. to estimate the reliability of the optical and infrared identifications., In conclusion the positional uncertainties obtained using Equations 3 and 4 are accurate also for sources down to the limit of our survey $\sim$ 0.135 mJy) and they can be used to estimate the reliability of the optical and infrared identifications. + The typical rms position uncertainties σι and as are plotted as function of the Dux density in Figure 14.., The typical rms position uncertainties $\sigma_{\alpha}$ and $\sigma_{\delta}$ are plotted as function of the flux density in Figure \ref{ra_dec_error}. + Phe positional errors of the radio sources are 2 aresee for the fainter sources (0.13mJy) and ~ 0.6 aresee for the brighter sources (2 LO mv)., The positional errors of the radio sources are $\sim$ 2 arcsec for the fainter sources $\sim$ 0.13mJy) and $\sim$ 0.6 arcsec for the brighter sources $>$ 10 mJy). +DR rate coefficients were computed from the resonant photoionization cross sections with the ADASDR code. and the output files are available at the CDS (see?.foradetaileddescriptionofthestructurethese files).,"DR rate coefficients were computed from the resonant photoionization cross sections with the ADASDR code, and the output files are available at the CDS \citep[see][for a detailed description of the structure of these files]{summers05}." + The rate coefficients were fitted with functions of the form Equation 3.. with # ranging between 5 and 7 (see Table 3)).," The rate coefficients were fitted with functions of the form Equation \ref{dreq}, with $n$ ranging between 5 and 7 (see Table \ref{drfits}) )." + The fits for most ions are accurate to within over the temperature range (10!— 10) Κ. and reproduce the correct asymptotic behavior outside of this temperature range.," The fits for most ions are accurate to within over the temperature range $^1-10^7$ $z^2$ K, and reproduce the correct asymptotic behavior outside of this temperature range." + The fitting algorithm was not able to accurately reproduce the rate coefficient behavior over the full temperature range for DR onto level 4 (the third excited state) of the Se target., The fitting algorithm was not able to accurately reproduce the rate coefficient behavior over the full temperature range for DR onto level 4 (the third excited state) of the $^{2+}$ target. + That fit is not valid below 80 K. and is only accurate to within near 20000 and 400000 K (but to better tha1 at other temperatures).," That fit is not valid below 80 K, and is only accurate to within near 000 and 000 K (but to better than at other temperatures)." + DR onto level 2 of Se is also fit less accurately. to within6%.," DR onto level 2 of $^{+}$ is also fit less accurately, to within." +. Fig., Fig. + 7 illustrates the DR. rate coefficients over the temperattre range (10!— 10ης Κ. This figure reveals that while the rate coefficients exhibit similar behavior at high temperattres (>10° K). there are marked differences in their magnitudes and behavior at lower temperatures due to the differing resonance structure near their ronization thresholds.," \ref{drfig} illustrates the DR rate coefficients over the temperature range $^1-10^7$ $z^2$ K. This figure reveals that while the rate coefficients exhibit similar behavior at high temperatures $>10^6$ K), there are marked differences in their magnitudes and behavior at lower temperatures due to the differing resonance structure near their ionization thresholds." + Fig., Fig. + 8 compares the RR. DR. and total recombination rate coefficients for each of the first six Se ions.," \ref{totfig} compares the RR, DR, and total recombination rate coefficients for each of the first six Se ions." + From this plot. it is apparent that DR dominates RR for each ion at 107 K. with rate coefficients larger by as much às two orders of magnitude (and occasionally even more at other temperatures).," From this plot, it is apparent that DR dominates RR for each ion at $^4$ K, with rate coefficients larger by as much as two orders of magnitude (and occasionally even more at other temperatures)." + The RR rate coefficient becomes comparable to that of DR at temperatures higher than 107 K for some ions. though this is likely due to the fact that we did not consider DR from An>0 core excitations. which become important at high temperatures.," The RR rate coefficient becomes comparable to that of DR at temperatures higher than $10^7$ K for some ions, though this is likely due to the fact that we did not consider DR from $\Delta n>0$ core excitations, which become important at high temperatures." + RR dominates DR only at low temperatures (less than 0000. K) for Se. Se. and Se.," RR dominates DR only at low temperatures (less than 000 K) for $^+$, $^{3+}$, and $^{6+}$." + This highlights the importance of obtaining accurate DR rate coefficients. as it is the principal recombination process for low-charge Se ions," This highlights the importance of obtaining accurate DR rate coefficients, as it is the principal recombination process for low-charge Se ions" +Between 2001 September and December the temperature of the white cwarl dropped from ~30.000 Ix to ~18.000 IX (Sion οἱ al.,"Between 2001 September and December the temperature of the white dwarf dropped from $\sim$ 30,000 K to $\sim$ 18,000 K (Sion et al." + 2003)., 2003). + We argue that by analogy with the ZZ Celi stars. the white dwarl nonracial g mode pulsation model for the origin of the οτιδι s and 28.96 s perlocicities (Robinson et al.," We argue that by analogy with the ZZ Ceti stars, the white dwarf non–radial $g$ –mode pulsation model for the origin of the 27.87 s and 28.96 s periodicities (Robinson et al." + 1976) demands a laree change in the pulsation period as the white dwarl’s temperature changes., 1976) demands a large change in the pulsation period as the white dwarf's temperature changes. + However. these observations do not support this prediction: the 29 s oscillation period 1s observed to be independent of the white dwarls temperature.," However, these observations do not support this prediction: the 29 s oscillation period is observed to be independent of the white dwarf's temperature." + We consider (his thegrace of the nonradial g mode pulsation hypothesis as (he origin of both the 28 s and 29 5 pulsations., We consider this the of the non–radial $g$ –mode pulsation hypothesis as the origin of both the 28 s and 29 s pulsations. + In light of (hese observations. the alternative hvpotheses for the origin of the periodicities. ihe venerable DQ Her magnetic rotator model (Patterson 1973) and the LIMA model of Warner Woudt. (2002). do not fare particularly well either.," In light of these observations, the alternative hypotheses for the origin of the periodicities, the venerable DQ Her magnetic rotator model (Patterson 1978) and the LIMA model of Warner Woudt (2002), do not fare particularly well either." + In. these models the 25 s periodicity is related. to rotation of either the entire white dwarl or an accretion bell on the white cdwarl, In these models the 28 s periodicity is related to rotation of either the entire white dwarf or an accretion belt on the white dwarf. + The 28 s modulation is ultimatelv responsible for driving all the other periodicities including the 29 s modulation., The 28 s modulation is ultimately responsible for driving all the other periodicities including the 29 s modulation. + The presence of a relatively strong 29 s periodicity in (he total absence of the 28 s periodicity is a problem for the models., The presence of a relatively strong 29 s periodicity in the total absence of the 28 s periodicity is a problem for the models. + While the models remain viable. they must be considered incomplete.," While the models remain viable, they must be considered incomplete." + Finally. we remark that while g mode pulsations cannot be responsible for the oscillations in WZ See. this does nol necessarily imply that other modes of white dwarl pulsation are ruled out.," Finally, we remark that while non--radial $g$ –mode pulsations cannot be responsible for the oscillations in WZ Sge, this does not necessarily imply that other modes of white dwarf pulsation are ruled out." + In particular. the periods of non.radial y modes (Papaloizou Prinele 1973) can be near those of WZ See ancl are nol very temperature sensitive so {μον may play a role in WZ See's puzzling behavior.," In particular, the periods of non–radial $r$ –modes (Papaloizou Pringle 1978) can be near those of WZ Sge and are not very temperature sensitive so they may play a role in WZ Sge's puzzling behavior." + This work was supported by NASA through grants GO-09304 and GO-09159 [rom the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. Inc.. under NASA Contract NAS 5-26555.," This work was supported by NASA through grants GO-09304 and GO-09459 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA Contract NAS 5-26555." + Support was also provided in part by NSF erant. 99-01195. NASA ADP erant. NAG5-8388 (EMS). and from NASA through STSel grant. HST-GO-08156 (WEW).," Support was also provided in part by NSF grant 99-01195, NASA ADP grant NAG5-8388 (EMS), and from NASA through STScI grant HST-GO-08156 (WFW)." + D'TG acknowledges support [rom a PPARC Advanced Fellowship., BTG acknowledges support from a PPARC Advanced Fellowship. +We have determined the SED of IID 81032 using broad baud UBVRI (present photometry). 2\TASS JI (Cutri et al.,"We have determined the SED of HD 81032 using broad band UBVRI (present photometry), 2MASS JHK (Cutri et al." + 2003) and 12. 25. 60 and 100 IRAS (Moshir 1989) fluxes.," 2003) and 12, 25, 60 and 100 $\mu$ IRAS (Moshir 1989) fluxes." + However. ouly upper limits are available at 25. (XO aud 100 4/42.," However, only upper limits are available at 25, 60 and 100 $\mu m$." + The observed SED of ΠΕ 51032 aloug with the svuthetic SED is shown in Figure 8.., The observed SED of HD 81032 along with the synthetic SED is shown in Figure \ref{sed.fig}. + The svuthetic SED is expected from the intrinsic properties of the star (INiucz 1995)., The synthetic SED is expected from the intrinsic properties of the star (Kurucz 1993). + The uodel SED shown in Fig., The model SED shown in Fig. + 8 has been adjusted to coincide with the observed SED of the star ITD 81032 at the V-baud wavelength of 0.55 jj., \ref{sed.fig} has been adjusted to coincide with the observed SED of the star HD 81032 at the V-band wavelength of 0.55 $\mu$. + We have overplotted the svuthetic SED for the different ερ ae οσο combinations., We have overplotted the synthetic SED for the different $T_{eff}$ and $\rm{log} g$ combinations. + The values of T;4 and logeoo which best match the observed SED are 5000+250 Is and 3.5+0.5. respectively. and are consistent within one subclass of the inferred IKOIV. spectral type of he star IID 81032 (sce 0)).," The values of $T_{eff}$ and $\rm{log}g$ which best match the observed SED are $5000\pm250$ K and $3.5\pm0.5$, respectively, and are consistent within one subclass of the inferred K0IV spectral type of the star HD 81032 (see \ref{physical.sec}) )." + The coutimmun of WD 81032 is in good agrecment with the normal values or the spectral type of KOTV up to JUN baud but deviates in all bauds longer than 25400 (sec Fig. 8))., The continuum of HD 81032 is in good agreement with the normal values for the spectral type of K0IV up to JHK band but deviates in all bands longer than $25 \mu m$ (see Fig. \ref{sed.fig}) ). + The ciffereuce between he observed and the expected (J-Is) aud (11:19) colours are 0.064:0.0E and 0.005£0.03 mae. respecively.," The difference between the observed and the expected (J-K) and (H-K) colours are $0.06 \pm 0.04$ and $0.005 \pm 0.03$ mag, respectively." + This indicates that there is no significant colour excess iu J. ID and IS band.," This indicates that there is no significant colour excess in J, H and K band." + The expected (J-Is) ae (II-IS) colours were taken from the spectral type of the star (IKooruecf. 1983).," The expected (J-K) and (H-K) colours were taken from the spectral type of the star (Koorneef, 1983)." + The 12 jan magnitude Gayo) of the star TD 81032 was found to be 6.09+0.17 mag using the relation mq»=25loefy|3.63 (Mitrou et al., The 12 $\mu m$ magnitude $m_{12}$ ) of the star HD 81032 was found to be $6.09 \pm 0.17$ mag using the relation $m_{12} = -2.5 \rm{log} f_{12} + 3.63$ (Mitrou et al. + 1996)., 1996). + The iutrinsic [A12] colour of the star ITD 81032 is determined to be 0.03+0.17 mag., The intrinsic $[K-12]$ colour of the star HD 81032 is determined to be $0.03\pm 0.17$ mag. + The expected [A12] colour of 0.11 mag for the IKOIV. type star (Verma ct al., The expected $[K-12]$ colour of 0.14 mag for the K0IV type star (Verma et al. + 1987). give* the colour excess of 0.17 mag. which is cousisteut with the ideal value of 0.00.2 mag (Mitrou et al.," 1987) gives the colour excess of 0.17 mag, which is consistent with the ideal value of $0.0\pm0.2$ mag (Mitrou et al." + |996)., 1996). + The licht curve for the sotree and were extracted using the xselect package for the PSPC 0.1 -2.L keV energy baud which couaius all the backgroundN-rav photous., The light curve for the source and background were extracted using the xselect package for the PSPC 0.1 - 2.4 keV energy band which contains all the X-ray photons. + The backerouud-subtracted ταν light curve of TD 81032 is shown in Figure 9 plotted with a time bin size of GL s. It appears from the Leht curve that a moderate fare occtired during the RASS observations. with a peak of about 0.6 ct © (compared to a pre-flare level of 0.2 - 0.3 ¢ l)at approximately JD = 2118206.95 (1990/11/11 10:18:0.0) and a time of 2.6ς1 Hx The halt-decayX-ray προςπα of IID 8]032 as observed with the ROSAT PSPC is show rin Figure 10..," The background-subtracted X-ray light curve of HD 81032 is shown in Figure \ref{xlc.fig} plotted with a time bin size of 64 s. It appears from the light curve that a moderate flare occurred during the RASS observations, with a peak of about 0.6 ct $^{-1}$ (compared to a pre-flare level of 0.2 - 0.3 ct $^{-1}$ ) at approximately JD = 2448206.95 (1990/11/11 10:48:0.0) and a half-decay time of $2.6 \times 10^{4}$ s. The X-ray spectrum of HD 81032 as observed with the ROSAT PSPC is shown in Figure \ref{xspec.fig}." + Response matrices based on the available off-axis calibration of the PSPC aud uxiug tie appropriate ancillary response files were ereatec aud «ata were fitted using thespec (version 11.3.1) «oectral analysis package., Response matrices based on the available off-axis calibration of the PSPC and using the appropriate ancillary response files were created and data were fitted using the (version 11.3.1) spectral analysis package. +" Spectral mioels for thermal eq1ibriuni plasma known as the Mewe-I&aastra-Liedalil or MERKAL model (Liedalil. Ox""echeld Coldstei1 1995: Mewe. Iaastra Liedahl 1995) were used."," Spectral models for thermal equilibrium plasma known as the Mewe-Kaastra-Liedahl or MEKAL model (Liedahl, Ostrecheld Goldstein 1995; Mewe, Kaastra Liedahl 1995) were used." + The subtracted) X-ray spectra were fited wih l-teiiperature (1T) and 2-temperatire (27D) plasma models. either assunrine solar plotospheric abuidieuices as given by Auders Crevess (1989) or allowing the abundance oD everv element other than II to vary. by a conunon factor relative to the solar (plotospheric} values.," The background-subtracted X-ray spectra were fitted with 1-temperature (1T) and 2-temperature (2T) plasma models, either assuming solar photospheric abundances as given by Anders Grevess (1989) or allowing the abundance of every element other than H to vary by a common factor relative to the solar (photospheric) values." + Iu eacli of the above modes the interstellar absorption was assiuniced to folow theaSOLPTIOLL eive idw Morrison McC“AMO1 (1983). and the total intervening hydrogen cohmin density Ny; was allowed ο freely.," In each of the above models the interstellar absorption was assumed to follow the absorption cross-sections given by Morrison McCammon (1983), and the total intervening hydrogen column density $N_H$ was allowed to vary freely." + The resits of varydifferent mode fits are summarized in Table 3.. , The results of different model fits are summarized in Table \ref{xdata.tab}. . +Siuele-temiperature MERAL nodels with abundances fixed to the solar Vanes eave oulacceptably high. values for. »qz. aud thus can be rejected.," Single-temperature MEKAL models with abundances fixed to the solar values gave unacceptably high values for $\chi_{\nu}^{2}$, and thus can be rejected." + However. single-tempcrature plasma models li abundauces of (1910.19ὐ11 ο solar and plasma telmpcrature o “as|!vlt were found accc»ptable.," However, single-temperature plasma models with abundances of $0.19_{-0.08}^{+0.14}$ times solar and plasma temperature of $0.84_{-0.20}^{+0.17}$ were found acceptable." +" Alatively. two-tempcrative MERAL modes with fixed solar alnudances were also found te| be acceptable: the two temperatures beingue 0.2!n2102yy πο- aud 1.1202 keV, ANhulti-temperatiure variabk* abundancee inmodels would also produce acceptable fits to the PSPC spectuui. but the siuall uuuber o| accnmulatec counts does not warrant such complex models."," Alternatively, two-temperature MEKAL models with fixed solar abundances were also found to be acceptable; the two temperatures being $0.2_{-0.1}^{+0.2}$ keV and $1.12_{-0.36}^{+0.52}$ keV. Multi-temperature variable abundance models would also produce acceptable fits to the PSPC spectrum, but the small number of accumulated counts does not warrant such complex models." + The PSPC sxDra. aud the best-fit two-temperatire plasma inodel with solar abundances are shown in Fi, The PSPC spectrum and the best-fit two-temperature plasma model with solar abundances are shown in Fig. +e. LO aloic with the significance of tje residuals i ≽⋅⋅≻↕↑↸∖↥⋅⋯↴∖↴∪↕↑∐↸∖∐⋅∖−∙," \ref{xspec.fig} + along with the significance of the residuals in terms of their $\chi^{2}$." + Based ou tje best fit 2T MERKAL no ela source x of 9.1!ÁS107 ere 7 ↓↖↖↽⋜↧↴∖↴∪↴⋝↑⋜∏↕∐∖≼↧∙, Based on the best fit 2T MEKAL model a source flux of $9.1_{-1.6}^{+0.9} \times 10^{-12}$ erg $^{-2}$ $^{-1}$ was obtained. + At a distance¢of 110 pe the Nav Iuninosiv of IID al2 is calculated to he 2.1!en«10eresἘν similar to that of known subeiauts RS CVn binewies (Drake «t al.," At a distance of 140 pc the X-ray luminosity of HD 81032 is calculated to be $2.1_{-0.4}^{+0.2} \times 10^{31} \rm {erg} \rm{s}^{-1}$, similar to that of known subgiants RS CVn binaries (Drake et al." + 1989. Sineh et al.," 1989, Singh et al." + 1995.1996: Deurpsey ot al.," 1995,1996; Dempsey et al." + 1997: Padimakar et al., 1997; Padmakar et al. + 2000: Pandey ο al., 2000; Pandey et al. + 2005)., 2005). + Tιο derived X-ray πιπιοαν is about a factor of 2 bigecr than the carlicr estimate given in sli., The derived X-ray luminosity is about a factor of 2 bigger than the earlier estimate given in 1. +" This niav be due to the non-trivial column deusitv of ↽1.1«το1029 en? ""minferred: objects. with> a |Heh colin cenusitv will typically have ahigher count rate to flux conversion factor than the standard ojo Which assunes a low column deusitv.", This may be due to the non-trivial column density of $1.4 \times 10^{20}$ $cm^{-2}$ inferred: objects with a high column density will typically have ahigher count rate to flux conversion factor than the standard one which assumes a low column density. + The values of &T4 aud, The values of $kT_{1}$ and +The currently favored model that describes the formation of structure in the Universe is the A cold dark matter (LCDALD paradigm.,The currently favored model that describes the formation of structure in the Universe is the $\Lambda$ cold dark matter (LCDM) paradigm. + In this model. the initial density. distribution of the Universe was nearly homogenous. with small Gaussian density. perturbations iniprinted curing an. inflationary epoch.," In this model, the initial density distribution of the Universe was nearly homogenous, with small Gaussian density perturbations imprinted during an inflationary epoch." + μονο Uuctuations expand linearly. until the over-dense regions undergo non-linear. gravitational collapse to form bound dark matter haloes.," These fluctuations expand linearly, until the over-dense regions undergo non-linear gravitational collapse to form bound dark matter haloes." + These haloes form in a hierarchical fashion: small haloes form first. and then larger ones assemble later via merging.," These haloes form in a hierarchical fashion: small haloes form first, and then larger ones assemble later via merging." + In the LODAL paradigm. barvons follow the dark matter.," In the LCDM paradigm, baryons follow the dark matter." + Since they can dissipate and cool. barvons condense. and eventually forem observable ealaxies in the centres of dark matter halocs.," Since they can dissipate and cool, baryons condense, and eventually form observable galaxies in the centres of dark matter haloes." + The properties of dark matter haloes in the context of the LCDAM paradigm have been studied in detail using numerical simulations over the past couple of decades with increasing resolution (e.g.Davisetal.1985:FrenkFrenk2002:Springel 2005).," The properties of dark matter haloes in the context of the LCDM paradigm have been studied in detail using numerical simulations over the past couple of decades with increasing resolution \citep[e.g.][]{Davis85, Frenk88, Efstathiou88, Katz99, Kauffmann99, Bullock01B, Frenk02, Springel05}." +. Fhis approach has been very fruitful in. providing us with a detailed. picture. of the assembly and growth. of structure in the Universe., This approach has been very fruitful in providing us with a detailed picture of the assembly and growth of structure in the Universe. + These heoretical studies provide the framework within which he role of barvons and details of galaxy formation can » probed., These theoretical studies provide the framework within which the role of baryons and details of galaxy formation can be probed. + While collisionless dark matter in the LODAL xwadiem interacts only gravitationally. barvons clissipate. jwe pressure. cool. form stars. and interact with radiation.," While collisionless dark matter in the LCDM paradigm interacts only gravitationally, baryons dissipate, have pressure, cool, form stars, and interact with radiation." + These. and other effects. introduce. complications when rving to understand the properties of dark matter haloes such as their mass. angular momentum. shape. and density xolfiles [rom observations of the barvonic component.," These, and other effects, introduce complications when trying to understand the properties of dark matter haloes such as their mass, angular momentum, shape, and density profiles from observations of the baryonic component." + There are. however two techniques that have allowed a more clirect xobe of the dark matter: gravitational lensing observations (c.g.Fischeretal.2000:Melxayct2002:Hoekstraetal.2007:Evans&Briclle 2009).. ancl measurements of ealaxy rotation curves (c.g.Rubinetal.1985:Trimble1987:Persic.Salucci.&Stel1996:Saluccietal. 2007).," There are, however two techniques that have allowed a more direct probe of the dark matter: gravitational lensing observations \citep[e.g.][]{Fischer00, McKay02, Hoekstra03, Mandelbaum06, Limousin07,Parker07,Evans09}, , and measurements of galaxy rotation curves \citep[e.g.][]{Rubin85, Trimble87, Persic96, Salucci07}." +. Due to the dillieulties and. assumptions required to translate the observed baryonic properties to dark matter halo properties. cosmological N-bods simulations oller a powerful tool to uncerstand the properties and statisties of the dark matter haloes.," Due to the difficulties and assumptions required to translate the observed baryonic properties to dark matter halo properties, cosmological N-body simulations offer a powerful tool to understand the properties and statistics of the dark matter haloes." + Even with dark. matter only numericalsimulations.," Even with dark matter only numericalsimulations," +The solar magnetic field emerges at the surface over a wide range of scales. from ubiquitous. ephemeral regions. as small as LO! Maxwells. to active. regions- as large as 107?E Maxwells. which emerge al low to midlatitudes (??)..,"The solar magnetic field emerges at the surface over a wide range of scales, from ubiquitous ephemeral regions as small as $10^{16}$ Maxwells, to active regions as large as $10^{23}$ Maxwells, which emerge at low to midlatitudes \citep[]{hagenaar2003,parnell2009}." + Observations [rom satellites aud, Observations from satellites and +Posterior odds on hypotheses can be obtained from a given dataset without ever having to consider whether the experiment could be repeated.,Posterior odds on hypotheses can be obtained from a given dataset without ever having to consider whether the experiment could be repeated. + This is the well-known advantage of Bayesian reasoning over the frequentist approach., This is the well-known advantage of Bayesian reasoning over the frequentist approach. + Yet many Kinds of experiment can be and are repeated many times: observations in astronomical surveys are an obvious example., Yet many kinds of experiment can be and are repeated many times: observations in astronomical surveys are an obvious example. + In these circumstances. the Bayesian evidence is a statistic that can be computed from a given dataset. and it is hard not to wonder what value might have been obtained had our dataset been a different realization of the experimental process.," In these circumstances, the Bayesian evidence is a statistic that can be computed from a given dataset, and it is hard not to wonder what value might have been obtained had our dataset been a different realization of the experimental process." + Clearly if we know the likelihood function. which we must do to compute the evidence. then we must be able to generate other possible realizations of the data.," Clearly if we know the likelihood function, which we must do to compute the evidence, then we must be able to generate other possible realizations of the data." + To make a decision based on the posterior odds. a threshold is set at some value of posterior odds. such as the ‘decisive’ In&=5 value advocated by Jeffreys (1961).," To make a decision based on the posterior odds, a threshold is set at some value of posterior odds, such as the `decisive' $\ln {\cal +E}=5$ value advocated by Jeffreys (1961)." + We may ask how often such a strategy might lead us to make an incorrect decision., We may ask how often such a strategy might lead us to make an incorrect decision. +" Conversely. it is useful to know if a given experimental setup is likely to yield data good enough to exceed the decision threshold and ""detect! the more complex model in cases where it is true."," Conversely, it is useful to know if a given experimental setup is likely to yield data good enough to exceed the decision threshold and `detect' the more complex model in cases where it is true." +" Suppose further that the evidence ratio turns out to be a ""noisy. statistic. in the sense that its distribution is very broad: in this case. there is little point in devoting excessive effort in computing the evidence ratio very precisely."," Suppose further that the evidence ratio turns out to be a `noisy' statistic, in the sense that its distribution is very broad: in this case, there is little point in devoting excessive effort in computing the evidence ratio very precisely." + Given that practical computations can involve difficult integrations over spaces of very high dimensionality. this is worth knowing.," Given that practical computations can involve difficult integrations over spaces of very high dimensionality, this is worth knowing." + The notion of ‘repeated trials’ needs clarification., The notion of `repeated trials' needs clarification. + In. the simplest case. the fluctuations in our data arise in the measurement process. while the object or process we are observing has fixed parameters.," In the simplest case, the fluctuations in our data arise in the measurement process, while the object or process we are observing has fixed parameters." + A distinct case arises when we make repeated measurements of objects or processes that are different on each repetition., A distinct case arises when we make repeated measurements of objects or processes that are different on each repetition. + This often happens when we are observing samples and wish to make statements about properties of whole populations., This often happens when we are observing samples and wish to make statements about properties of whole populations. + In this case. extra variance enters. often called cosmic variance.," In this case, extra variance enters, often called cosmic variance." + An elementary example is the distinction between repeated (noisy) measurements of the flux of a single galaxy. or a series of measurements where a different galaxy is observed on each occasion.," An elementary example is the distinction between repeated (noisy) measurements of the flux of a single galaxy, or a series of measurements where a different galaxy is observed on each occasion." + In the latter ease. we will have a prior distribution for the true flux of a randomly selected galaxy. and the data we obtain in a given measurement could be modelled by drawing a random number from this prior distribution. and then adding noise.," In the latter case, we will have a prior distribution for the true flux of a randomly selected galaxy, and the data we obtain in a given measurement could be modelled by drawing a random number from this prior distribution, and then adding noise." + In dealing with the evidence ratio for repeated trials. we will hus use the priorAvice.," In dealing with the evidence ratio for repeated trials, we will thus use the prior." + The standard Bayesian approach regards he data as being fixed specitic numbers. and the prior enters only when we average the likelihood function over the prior to obtain he posterior probabilities.," The standard Bayesian approach regards the data as being fixed specific numbers, and the prior enters only when we average the likelihood function over the prior to obtain the posterior probabilities." + However. when we view the Bayesian outputs as statistics. we have to treat the data as random variables. whose distribution will depend on the values of the parameters or which we have a prior.," However, when we view the Bayesian outputs as statistics, we have to treat the data as random variables, whose distribution will depend on the values of the parameters for which we have a prior." + The probability distribution of the evidence ratio involves the data. and so depends on the unknown »urameters that are the argument of the prior.," The probability distribution of the evidence ratio involves the data, and so depends on the unknown parameters that are the argument of the prior." + We can eliminate hese parameters by a further integration over the prior. in effect. marginalizing the distribution of the evidence ratio to obtain its orobability distribution independent of parameters.," We can eliminate these parameters by a further integration over the prior, in effect, marginalizing the distribution of the evidence ratio to obtain its probability distribution independent of parameters." + Suppose we have the posterior probabilities or posterior odds for our competing models., Suppose we have the posterior probabilities or posterior odds for our competing models. + These will vary with different realizations of the data., These will vary with different realizations of the data. + What do we do with these probabilities or odds?, What do we do with these probabilities or odds? + This is not a question that can be answered by probability theory but it can be illuminated by it., This is not a question that can be answered by probability theory but it can be illuminated by it. + One approach is to set a threshold in the odds. effectively taking one decision if our experiment gives posterior odds above the threshold. and another if they lie below.," One approach is to set a threshold in the odds, effectively taking one decision if our experiment gives posterior odds above the threshold, and another if they lie below." + This general idea was introduced to classical statistics by Neyman and Pearson., This general idea was introduced to classical statistics by Neyman and Pearson. + A Bayesian approach is to emphasize the posterior probabilities or odds as a complete summary of our state of knowledge after the experiment. and to resist further interpretation.," A Bayesian approach is to emphasize the posterior probabilities or odds as a complete summary of our state of knowledge after the experiment, and to resist further interpretation." + There are parallels yere with the long history of controversy in classical statistics about he Nevman-Pearson approach versus Fisher's significance testing., There are parallels here with the long history of controversy in classical statistics about the Neyman-Pearson approach versus Fisher's significance testing. +" Fisher recognized the utility of the Neyman-Pearson method in industrial acceptance testing but regarded it as too ""wooden"" © be useful in the ill-defined and creative processes of science (Fisher 1956).", Fisher recognized the utility of the Neyman-Pearson method in industrial acceptance testing but regarded it as too “wooden” to be useful in the ill-defined and creative processes of science (Fisher 1956). + His detestation of Bayesian methods aside. Fisher would perhaps have been sympathetic to the idea that posterior orobabilities should be carried forward intact through the processes of science: he took much the same view of the results of his tests of significance.," His detestation of Bayesian methods aside, Fisher would perhaps have been sympathetic to the idea that posterior probabilities should be carried forward intact through the processes of science; he took much the same view of the results of his tests of significance." + We believe that binary choice between alternatives is a relevant process in astronomy., We believe that binary choice between alternatives is a relevant process in astronomy. +" The high cost and complexity of many astronomical research projects requires a difficult decision on when to commit to construction, which is irrevocable once made."," The high cost and complexity of many astronomical research projects requires a difficult decision on when to commit to construction, which is irrevocable once made." + More generally. there is the whole issue of how a community develops a consensus.," More generally, there is the whole issue of how a community develops a consensus." + The Bayesian ideal of a set of individuals each interpreting the evidence ratio in the their own way is hardly realistic: rather. some pre-detined level of proof is needed — a threshold in evidence ratio. in short.," The Bayesian ideal of a set of individuals each interpreting the evidence ratio in the their own way is hardly realistic: rather, some pre-defined level of proof is needed – a threshold in evidence ratio, in short." + We will therefore apply a Neyman-Pearson style of analysis to the evidence ratio. despite recognizing that this is not a unique assessment of is utility.," We will therefore apply a Neyman-Pearson style of analysis to the evidence ratio, despite recognizing that this is not a unique assessment of is utility." + Given the distribution of the evidence ratio € under two competing hypotheses. we can ask how well the statistic performs.," Given the distribution of the evidence ratio ${\cal E}$ under two competing hypotheses, we can ask how well the statistic performs." + A Neyman-Pearson analysis proceeds by defining a critical threshold in the test statistic. say ὃν ," A Neyman-Pearson analysis proceeds by defining a critical threshold in the test statistic, say $ {\cal E}_c$." +"If &«ὃν, we do not see any reason to reject the simpler null hypothesis {ος and it is accepted."," If $ {\cal E}<{\cal E}_c$, we do not see any reason to reject the simpler null hypothesis $H_0$, and it is accepted." +" If €ονὃν. there is good reason to prefer the more complex hypothesis I, and ffy will be rejected."," If ${\cal E}>{\cal E}_c$, there is good reason to prefer the more complex hypothesis $H_1$ and $H_0$ will be rejected." +" A common ‘decisive’ choice for the critical threshold is ln£.=5. corresponding to odds in favour of ff, of [48:1 Jeffreys 1961: Jaynes 2003)."," A common `decisive' choice for the critical threshold is $\ln {\cal E}_c=5$, corresponding to odds in favour of $H_1$ of 148:1 (Jeffreys 1961; Jaynes 2003)." + The common restriction to two models is not critical. since we can always add the posterior probabilities for No alternative models and consider this to be a single alternative.," The common restriction to two models is not critical, since we can always add the posterior probabilities for $N$ alternative models and consider this to be a single alternative." +" This yields sensible answers. even in the case where all /N. models fit the data about as well as {ος i£ No 148. we would then decide that there was decisive evidence against {10 even though //, fitted as well as any model."," This yields sensible answers, even in the case where all $N$ models fit the data about as well as $H_0$ : if $N>148$ , we would then decide that there was decisive evidence against $H_0$, even though $H_0$ fitted as well as any model." + This simply reflects our assumption that all models are equally likely a priori., This simply reflects our assumption that all models are equally likely a priori. +" In the Neyman-Pearson approach. there are two ways in which an incorrect conclusion might be reached: The power of the test is defined as the probability that we will correctly pick //, when it is true — Le. it is unity minus the probability of a Type II error."," In the Neyman-Pearson approach, there are two ways in which an incorrect conclusion might be reached: The power of the test is defined as the probability that we will correctly pick $H_1$ when it is true – i.e. it is unity minus the probability of a Type II error." + There is the usual trade-off: if we conservatively use a high threshold. we reduce the chance of a Type I error. but we also reduce the power of the testbecausewe," There is the usual trade-off: if we conservatively use a high threshold, we reduce the chance of a Type I error, but we also reduce the power of the testbecausewe" +however. as seen in Figure 4.. the posterior probability distribution is highly non-Gaussian. leading to the separation of the point of maximum likelihood from the point of maximum probability.,"however, as seen in Figure \ref{plot:figure4}, the posterior probability distribution is highly non-Gaussian, leading to the separation of the point of maximum likelihood from the point of maximum probability." +" The marginalized most-probable parameter values represent the true ""best. model: thus. left unbroken. the degeneracies of the problem produce real errors in any lensing result."," The marginalized most-probable parameter values represent the true 'best' model; thus, left unbroken, the degeneracies of the problem produce real errors in any lensing result." + To better picture the way these degeneracies function.Figure 5 plots the posterior probability distribution in the ή plane. coloured by. respectively. each point's be. αν. 6. and τι value.," To better picture the way these degeneracies function,Figure \ref{plot:figure5} plots the posterior probability distribution in the $\eta$ $h$ plane, coloured by, respectively, each point's $b_E$, $q_p$, $\theta$, and $\beta_1$ value." +" These clearly show that the degeneraey between the slope and Hubble parameter is tightly connected to the normalisation of the potential bz. the axis ratio d, of the isopotential contours. and the sourceposition«2. but is completely independent of the orientation angle 8."," These clearly show that the degeneracy between the slope and Hubble parameter is tightly connected to the normalisation of the potential $b_E$, the axis ratio $q_p$ of the isopotential contours, and the sourceposition, but is completely independent of the orientation angle $\theta$." +" Thus. we should not speak just of a j-/ degeneracy. but rather of a strong -f-be-qg,- degeneracy!"," Thus, we should not speak just of a $\eta$ $h$ degeneracy, but rather of a strong $\eta$ $h$ $b_E$ $q_p$ ${\bf \beta}$ degeneracy!" + This demonstrates that 4d-image lens systems cannot meaningfully constrain the Hubble parameter with significance unless something can be done to at least partially break this degeneracy., This demonstrates that 4-image lens systems cannot meaningfully constrain the Hubble parameter with significance unless something can be done to at least partially break this degeneracy. + Constraints on the profile slope or normalisation seem the best hope. as it impossible to learn anything of the source position by methods other than lensing.," Constraints on the profile slope or normalisation seem the best hope, as it impossible to learn anything of the source position by methods other than lensing." + The shape of this degeneracy now makes clear the source of the error in Hubble parameter and slope returned when the slope is fixed to the wrong value. as in Figure [:: setting the slope is equivalent to drawing a line at a particular value of 7) in the scatter plots of Figure 5 and taking only the points that fall on that line.," The shape of this degeneracy now makes clear the source of the error in Hubble parameter and slope returned when the slope is fixed to the wrong value, as in Figure \ref{plot:figure1}; setting the slope is equivalent to drawing a line at a particular value of $\eta$ in the scatter plots of Figure \ref{plot:figure5} and taking only the points that fall on that line." + Ifthe line is taken at the wrong place. completely adequate models will be found that will return completely false values for the other model parameters.," If the line is taken at the wrong place, completely adequate models will be found that will return completely false values for the other model parameters." +" Figure 6 plots the marginalized mean best-titting and the maximum likelihood values for the Hubble parameter . the profile slope parameter 7. the potential normalisation bg. and the axis ratio of the isopotential ellipses q, obtained for the prolate and oblate halos as a function of orientation angle."," Figure \ref{plot:figure6} plots the marginalized mean best-fitting and the maximum likelihood values for the Hubble parameter $h$, the profile slope parameter $\eta$, the potential normalisation $b_E$, and the axis ratio of the isopotential ellipses $q_p$ obtained for the prolate and oblate halos as a function of orientation angle." + We find that the most-probable values of 7 and jj vary inversely. with / getting smaller and 7) larger with increasing visible ellipticity.," We find that the most-probable values of $h$ and $\eta$ vary inversely, with $h$ getting smaller and $\eta$ larger with increasing visible ellipticity." + The potential normalisation bg decreases significantly for the prolate halos and increases significantly for the oblate halos with increasing ellipticity: this is as expected. because in the maximum ellipticity orientation prolate halos have minimal mass hidden along the line-of-sight. and oblate halos maximum. and the converse in the circularly-symmetric orientation at O°.," The potential normalisation $b_E$ decreases significantly for the prolate halos and increases significantly for the oblate halos with increasing ellipticity; this is as expected, because in the maximum ellipticity orientation prolate halos have minimal mass hidden along the line-of-sight, and oblate halos maximum, and the converse in the circularly-symmetric orientation at $0^{\rm o}$." + This result is consistent with the behaviour found in previous analyses that weak lensing mass estimates are strongly effected by unaccounted-for triaxiality (Corless&King2007., This result is consistent with the behaviour found in previous analyses that weak lensing mass estimates are strongly effected by unaccounted-for triaxiality \citep{corl}. +" The values of the axis ratio of the isopotential contours q,, exhibit the trend expected. decreasing as the visible ellipticity increases from orientation 07 to 90°."," The values of the axis ratio of the isopotential contours $q_p$ exhibit the trend expected, decreasing as the visible ellipticity increases from orientation $0^{\rm o}$ to $90^{\rm o}$." + To better understand what is happening to the posterior probability distribution as the triaxial halo orientation is changed. in Figure we plot the 1-7 (684) confidence contours for 5j. be. qy. and ji against / for prolate and oblate halos at several orientations. again with visible ellipticity increasing with rotation angle.," To better understand what is happening to the posterior probability distribution as the triaxial halo orientation is changed, in Figure \ref{plot:figure8} we plot the $\sigma$ $\%$ ) confidence contours for $\eta$, $b_E$, $q_p$, and $\beta_1$ against $h$ for prolate and oblate halos at several orientations, again with visible ellipticity increasing with rotation angle." + For both oblate and prolate halos. the y-f contours maintain approximately the same position. but are tighter at higher visible ellipticities.," For both oblate and prolate halos, the $\eta$ $h$ contours maintain approximately the same position, but are tighter at higher visible ellipticities." + The least elliptical case alos shows an extention of its contour to lower values of jj and higher values of ., The least elliptical case alos shows an extention of its contour to lower values of $\eta$ and higher values of $h$. + The contours for the potential normalisation be-f move down to lower normalisations for the more elliptical prolate halos. and up to higher normalisations for more elliptical oblate halos. as expected given the line-of-sight masses of halos of these geometries.," The contours for the potential normalisation $b_E$ $h$ move down to lower normalisations for the more elliptical prolate halos, and up to higher normalisations for more elliptical oblate halos, as expected given the line-of-sight masses of halos of these geometries." + Further. they decrease in size as ellipticity increases. as with the #-/ contours.," Further, they decrease in size as ellipticity increases, as with the $\eta$ $h$ contours." +" For both prolate and oblate halos the contours for isopotential axis ratio q,- move down to lower values as the ellipticity increases. as expected."," For both prolate and oblate halos the contours for isopotential axis ratio $q_p$ $h$ move down to lower values as the ellipticity increases, as expected." +" The 7, -h contours behave very similarly to those for τη, maintaining similar positions in parameter space but changing size."," The $\beta_1$ $h$ contours behave very similarly to those for $h$ $\eta$ , maintaining similar positions in parameter space but changing size." + To understand the positioning and size of these contours we consider the nature of the multi-variable degeneracy., To understand the positioning and size of these contours we consider the nature of the multi-variable degeneracy. +" It lies in parameter space such that high values of the axis ratio ¢, correspond to high values of the slope parameter 7). and low values for the Hubble parameter / and source position 7."," It lies in parameter space such that high values of the axis ratio $q_p$ correspond to high values of the slope parameter $\eta$, and low values for the Hubble parameter $h$ and source position ${\bf \beta}$ ." +" Now. for halos with low amounts of visible ellipticity and thus true values of q,, near |. there is less space in parameter space for models at values of qy higher than the true value. because the posterior distribution is truncated with a hard wall of zero probability at q,,=1."," Now, for halos with low amounts of visible ellipticity and thus true values of $q_p$ near 1, there is less space in parameter space for models at values of $q_p$ higher than the true value, because the posterior distribution is truncated with a hard wall of zero probability at $q_p=1$ ." +" Thus. the contours will extend proportionally more into the regions of lower than true q,. corresponding to lower values of η and higher values of the Hubble parameter / and source position -?."," Thus, the contours will extend proportionally more into the regions of lower than true $q_p$, corresponding to lower values of $\eta$ and higher values of the Hubble parameter $h$ and source position ${\bf \beta}$." +" This trend is exactly what is seen as we move from the low-q,, halos (rotation angles near 90"") to the high-q;, halos aligned closer to the circularly symmetric (0°) position.", This trend is exactly what is seen as we move from the $q_p$ halos (rotation angles near $90^{\rm o}$ ) to the $q_p$ halos aligned closer to the circularly symmetric $0^{\rm o}$ ) position. +" In addition to their position. the high-q, halos also produce larger |o contours."," In addition to their position, the $q_p$ halos also produce larger $\sigma$ contours." + This change in contour size cannot be due to the lensing strength: in strong lensing. so long as the same number of images are resolved. the relative strength of the lens and the scale of the image separations does not change the amount of information available to constrain the lens system.," This change in contour size cannot be due to the lensing strength: in strong lensing, so long as the same number of images are resolved, the relative strength of the lens and the scale of the image separations does not change the amount of information available to constrain the lens system." + This is born out in the results. in that it is the high-g models in both oblate and prolate cases that exhibit larger contours: in the prolate case these are indeed the stronger lenses with higher projected masses. but in the oblate casethey are the weaker lenses. with very low lensing convergences.," This is born out in the results, in that it is the $q$ models in both oblate and prolate cases that exhibit larger contours; in the prolate case these are indeed the stronger lenses with higher projected masses, but in the oblate casethey are the weaker lenses, with very low lensing convergences." +" Instead. this again appears to be the natural product of the truncation of the posterior probability distribution at g,=1. which shifts and extends the lo region towards lowervalues of qp and yy and to higher values of ."," Instead, this again appears to be the natural product of the truncation of the posterior probability distribution at $q_p=1$, which shifts and extends the $\sigma$ region towards lowervalues of $q_p$ and $\eta$ and to higher values of $h$." + This effect — not an error or a problem but a true representation of the shape of the posterior probability distribution — is illustrated and explored in more detail in Appendix ??.., This effect – not an error or a problem but a true representation of the shape of the posterior probability distribution – is illustrated and explored in more detail in Appendix \ref{sec:appa}. +" Again. to understand the importance of the degree of triaxiality. now in the general ease. we carry out the same analysis as above but for prolate and oblate halos of axis ratios @=[0.5.0.6.0.7.0.8]. all oriented at SO""."," Again, to understand the importance of the degree of triaxiality, now in the general case, we carry out the same analysis as above but for prolate and oblate halos of axis ratios $a=\{0.5, 0.6, 0.7, 0.8\}$, all oriented at $80^{\rm o}$." +" Figure 8. plots the marginalized best-tit parameters fy. bg. and q, as a function of minor triaxial axis ratio « for both prolate and oblate halos."," Figure \ref{plot:figure9} plots the marginalized best-fit parameters $h$ , $\eta$, $b_E$, and $q_p$ as a function of minor triaxial axis ratio $a$ for both prolate and oblate halos." + Again. increasing the amount of triaxiality doesnos significantly change the best-fitting slope or Hubble parameter within the errors.," Again, increasing the amount of triaxiality does significantly change the best-fitting slope or Hubble parameter within the errors." + There is a weak trendtoward there being larger offsets from the true value at smaller visible ellipticities. the opposite of that seen in the fixed-slope case.," There is a weak trendtoward there being larger offsets from the true value at visible ellipticities, the opposite of that seen in the fixed-slope case." +" This trend can be understood as an extension of that seen for this general case as a function of orientation angle: again. the 10 region is shifted towards lower values of q,, and 5 andto higher values ofh for lower visible ellipticity cases: again seeAppendix ?? for further discussion."," This trend can be understood as an extension of that seen for this general case as a function of orientation angle; again, the $\sigma$ region is shifted towards lower values of $q_p$ and $\eta$ andto higher values of$h$ for lower visible ellipticity cases; again seeAppendix \ref{sec:appa} for further discussion." + These results represent those of the most general analysis. takingwide. flat priors on all parameters (0.21$ they predict a weak evolution in the $\mbh-\sigmas$ relation such that at higher redshift galaxies of a given velocity dispersion contain slightly less massive BHs." + Johanssonetal.(2009). emploved similar numerical techniques to argue that it is unlikely hat Bills are able to form significantly. before their host xulees., \citet{joha09} employed similar numerical techniques to argue that it is unlikely that BHs are able to form significantly before their host bulges. + Semi-analvtie models that reproduce many recshilt zero properties of galaxies also predict that. at a fixed σ. DII masses decrease with increasing redshift (Malbonetal.Springeletal. 2007).," Semi-analytic models that reproduce many redshift zero properties of galaxies also predict that, at a fixed $\sigmas$, BH masses decrease with increasing redshift \citep{malb07}." +. These theoretical models thus predict. evolutionary rends that go in the opposite direction to those inferred rom observations., These theoretical models thus predict evolutionary trends that go in the opposite direction to those inferred from observations. +" Finally. the models. of Hopkinset.al.(2009) predict that. at a fixed stellar velocity clispersion. DII masses at higher redshift are eitherthe same (for mpg~Q M.) or slightly more massive (for mma QM.) at ixed m, than their redshift zero counterparts. in agreement with observation."," Finally, the models of \citet{hopk09} predict that, at a fixed stellar velocity dispersion, BH masses at higher redshift are eitherthe same (for $\mbh\sim10^8\,\msun$ ) or slightly more massive (for $\mbh>10^8\,\msun$ ) at fixed $\sigmas$ than their redshift zero counterparts, in agreement with observation." + On the other hand. the relation between BIE mass and galaxy bulge mass shows a positive evolution in both models (Malbonetal.2007:Hopkinsct2009) and numerical simulations (DiMatteoetal.2008).. the magnitude of which is comparable to that observed.," On the other hand, the relation between BH mass and galaxy bulge mass shows a positive evolution in both models \citep{malb07, + hopk09} and numerical simulations \citep{dima08}, the magnitude of which is comparable to that observed." + The larger spread in the predictions for the evolution of the DpH—C. relation may reflect that it is more cillicult to prediet velocity dispersions. which depend on both mass and size. than it is to predict masses.," The larger spread in the predictions for the evolution of the $\mbh-\sigmas$ relation may reflect that it is more difficult to predict velocity dispersions, which depend on both mass and size, than it is to predict masses." + In Booth&Schave(2009.hereafter.1900) we presented: self-consistent. hyvdrodynamical simulations. of the co-evolution of the BLL and galaxy populations that reproduce the redshift zero BL scaling relations.," In \citet[][hereafter BS09]{boot09} we presented self-consistent, hydrodynamical simulations of the co-evolution of the BH and galaxy populations that reproduce the redshift zero BH scaling relations." + These same simulations also match group temperature. entropy ancl metallicity profiles. as well as the stellar masses ancl age distributions of brightest group. galaxies (MeCarthyetal.2010).," These same simulations also match group temperature, entropy and metallicity profiles, as well as the stellar masses and age distributions of brightest group galaxies \citep{mcca10}." +. In Booth&Sehave(2010) (hereafter. DSIO) we used the same simulations. as well as an analytic moclel. to demonstrate that mpg is determined by the mass of the dark matter (DM) halo. with a secondary dependence on the halo concentration. of the form that would be expected if the halo binding energy. were the fundamental property that controls the mass of the BI.," In \citet[]{boot10} (hereafter BS10) we used the same simulations, as well as an analytic model, to demonstrate that $\mbh$ is determined by the mass of the dark matter (DM) halo with a secondary dependence on the halo concentration, of the form that would be expected if the halo binding energy were the fundamental property that controls the mass of the BH." + In the present work we use the same models to investigate why and how the DII scaling relations evolve for massive galaxies., In the present work we use the same models to investigate why and how the BH scaling relations evolve for massive galaxies. + This paper is organised as follows., This paper is organised as follows. + In Sec., In Sec. + 2. we summarise the numerical methods emploved in this study and the simulation analysed., \ref{sec:method} we summarise the numerical methods employed in this study and the simulation analysed. + ln See., In Sec. + 3/— we present predictions for the evolution of the BI scaling relations and compare them to observations., \ref{sec:ev} we present predictions for the evolution of the BH scaling relations and compare them to observations. + We find that the evolution inthe mpgms relation predicted. by the simulations is in excellent. agreement with the observations. while the measured weak evolution in the mpgσ relation is in apparent disagreement. and predict that while BLL mass increases with redshift for fixed halo mass. the relations between mpg and the binding energies of both the host ealaxies and DAL haloes do not evolve.," We find that the evolution inthe $\mbh-\ms$ relation predicted by the simulations is in excellent agreement with the observations, while the measured weak evolution in the $\mbh-\sigma$ relation is in apparent disagreement, and predict that while BH mass increases with redshift for fixed halo mass, the relations between $\mbh$ and the binding energies of both the host galaxies and DM haloes do not evolve." + We demonstrate in 4 that the a analytic description in which mpg is coupled to the DM halo binding energy can reproduce the evolution of the relation between DIT ancl halo mass., We demonstrate in \ref{sec:explanation} that the a analytic description in which $\mbh$ is coupled to the DM halo binding energy can reproduce the evolution of the relation between BH and halo mass. + Furthermore. we show that the evolution in the relations between the DII and the stellar mass and binding energy can be understood in terms of the more fundamental relation with the binding energy of the dark halo and the growth of massive galaxies through dry. mergers.," Furthermore, we show that the evolution in the relations between the BH and the stellar mass and binding energy can be understood in terms of the more fundamental relation with the binding energy of the dark halo and the growth of massive galaxies through dry mergers." + Finally. we summarise our main conclusions in Sec. 5..," Finally, we summarise our main conclusions in Sec. \ref{sec:conclusions}." + We have carried out. a cosmological simulation using a significantly extended version of the parallel PNEree-Smoothecl Particle Lvclrocynamics (09Η) code (lastdescribedin.Springel2005)..," We have carried out a cosmological simulation using a significantly extended version of the parallel PMTree-Smoothed Particle Hydrodynamics (SPH) code \citep[last described in +][]{spri05b}." + Phe simulation and code are described in detail in DS509. we provide only a brief summary here.," The simulation and code are described in detail in BS09, we provide only a brief summary here." + In addition to hydrodynamic forces. we treat star formation (Schave&DallaVecchia. 2008).. supernova feedback (DallaVecchia&Schave 2008).. radiative cooling (Wiersmaetal. 2009a).. chemocdyvnamics (Wiersma and black hole accretion ancl feedback (125909. 2005)..," In addition to hydrodynamic forces, we treat star formation \citep{scha08}, , supernova feedback \citep{dall08}, , radiative cooling \citep{wier08}, , chemodynamics \citep{wier09} and black hole accretion and feedback \citep[BS09,][]{spri05}. ." + We summarise in Sec., We summarise in Sec. + 2.1 the essential features of the BLE model., \ref{sec:bhs} the essential features of the BH model. + The properties of central galaxies and DAL halocs are calculated. by first identilvine the most gravitationally, The properties of central galaxies and DM haloes are calculated by first identifying the most gravitationally +We have examined the field around aat racio and infrared wavelengths.,We have examined the field around at radio and infrared wavelengths. + We find possible nebulosity at 1.4 Gllz in the shell of near the location of the source. but otherwise no connection between (he SAR and the transient.," We find possible nebulosity at 1.4 GHz in the shell of near the location of the source, but otherwise no connection between the SNR and the transient." + The velocity required for (lo have originated at the center of and reached its current. transverse separation is only roughly 225!., The velocity required for to have originated at the center of and reached its current transverse separation is only roughly 225. +. While well within the range of velocities observed for various neutron stars. there is also no compelling reason to think that aand the SNR. are related.," While well within the range of velocities observed for various neutron stars, there is also no compelling reason to think that and the SNR are related." + Additional observations are required to determine more about the nature ofJ1745—3009., Additional observations are required to determine more about the nature of. +. As well as additional searches such as those that we report here. infrared. observations to search for a counterpart. a perioclicily search [for weaker pulsed emission. and X-rav observations to search for quiescent X-ray. emission would all be useful.," As well as additional searches such as those that we report here, infrared observations to search for a counterpart, a periodicity search for weaker pulsed emission, and X-ray observations to search for quiescent X-ray emission would all be useful." + We thank W. Cotton lor providing us with the 20 ci image from Yusel-Zadehetal. to search for possible nebulositv nearJ1745—3009., We thank W. Cotton for providing us with the 20 cm image from \cite{y-zhc04} to search for possible nebulosity near. +. This publication makes use of data products [rom the Two Micron. All Sky Survey. which is a joint project of the University of Massachusetts and the Infrared. Processing anc Analvsis Center/California Institute of Technology. funded by the National Aeronauties and Space Administration and the National Science Foundation.," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation." + The National Radio Astronomy Observatory is a facility ol the National Science Foundation operated uncer cooperative agreement by Associated Universities. Inc. iis supported by funding from (he Jeffress Memorial Trust aud Research Corporation.," The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. is supported by funding from the Jeffress Memorial Trust and Research Corporation." + Basic research in radio astronomy at the NRL is supported by the Office of Naval Research., Basic research in radio astronomy at the NRL is supported by the Office of Naval Research. +"radio source las a measted radius of 0.007 pe. an ris clectrou deusity of 1.3<10° ὃν an emission nieasuxe of 2.1«101 pe Ὁ, and an ionizing photon fiux of >2«10! s1, corresponding to an equivalent ZAMS spectral type of 05.5 or hotter (De Pree 220003.","radio source has a measured radius of 0.007 pc, an rms electron density of $1.3\times 10^6$ $^{-3}$, an emission measure of $2.4\times 10^{10}$ pc $^{-6}$, and an ionizing photon flux of $\ge 2\times 10^{49}$ $^{-1}$, corresponding to an equivalent ZAMS spectral type of O5.5 or hotter (De Pree 2000)." + WLON-B2 has a shell-like morphology with lower brightuess extensions to the NE aud SW (see Fie., W49N-B2 has a shell-like morphology with lower brightness extensions to the NE and SW (see Fig. + 2 of De Pree 22000)., 2 of De Pree 2000). +" A water maser has also beeu detected ~1"" to the uorth of the WLON-B sources.", A water maser has also been detected $\sim 1''$ to the north of the W49N-B sources. + To model the spectrum of W19N-D2. we also include a 1.1 nui observation from Wilner (2001).," To model the spectrum of W49N-B2, we also include a 1.4 mm observation from Wilner (2001)." + At this wavelength the calibration is wich more difficult., At this wavelength the calibration is much more difficult. + We have used the radio image appearing in their Figure 1l (4) to infer a lower limit of LOO andy at 1.1 nun. that appears as a poit with an upwardly directed arrow in the lower pauel of Figure 9..," We have used the radio image appearing in their Figure 1 (ii) to infer a lower limit of 400 mJy at 1.4 mm, that appears as a point with an upwardly directed arrow in the lower panel of Figure \ref{fig9}." + Although earlier work suggested a power-law slope of a5-0.9 around 7 nuu (appearing as the dotted Lue in the lower paucl of Fie. 9)).," Although earlier work suggested a power-law slope of $\alpha\approx +0.9$ around 7 mm (appearing as the dotted line in the lower panel of Fig. \ref{fig9}) )," + the lower limit of Wilneral... in conjunction with their discussion of adjacent sources. sugecstst that the spectrum is becoming optically thin around 2 wi.," the lower limit of Wilner, in conjunction with their discussion of adjacent sources, suggestst that the spectrum is becoming optically thin around 2 mm." + Although Figure 9 indicates that a satistactory match to the shape of the SED can be obtained with our model for a chumipy medium. it remains for us to determine if we can match the scale of the observed flux.," Although Figure \ref{fig9} indicates that a satisfactory match to the shape of the SED can be obtained with our model for a clumpy medium, it remains for us to determine if we can match the scale of the observed flux." + From equation (113) for the parameter Fy aud equation (15)) for the definition of the coveriug factor. one obtains We introduce a pavaincter A as so that the source fux cui be re-expressed as Using values from Table 1. for W19N-D2. aud assuuiug that (£73=5000 Ik. we lave evaluated Fy at the wavelength Ay=7 nuu. which eives FyδνςC.," From equation \ref{eq:F0}) ) for the parameter $F_0$ and equation \ref{eq:cover}) ) for the definition of the covering factor, one obtains We introduce a parameter $\Lambda$ as so that the source flux can be re-expressed as Using values from Table \ref{tab1} for W49N-B2, and assuming that $\langle T \rangle=8000$ K, we have evaluated $F_0$ at the wavelength $\lambda_0=7$ mm, which gives $F_0=1080\, {\rm mJy}\, +\times C$." +" The observed flux level at 7 mun is Fy,=550 iid.", The observed flux level at 7 mm is $F_\nu = 550$ mJy. + From Figure 9.. we find a value of logAy=10.58 at logf=logrv/my0.92.," From Figure \ref{fig9}, we find a value of $\log \Lambda_0 = +0.58$ at $\log f=\log \nu/\nu_0 = 0.92$." + Combining these umubers vields a covering factor of Cz0.15. which is quite small indicating that shadowing of clumps by other chumps is not a major concern for this source.," Combining these numbers yields a covering factor of $C\approx 0.15$, which is quite small indicating that shadowing of clumps by other clumps is not a major concern for this source." + Iu other words. foreground clips are not absorbing euission from rearward clumps.," In other words, foreground clumps are not absorbing emission from rearward clumps." + Iudeed. the shadowing effects implied by Cz15% should be considered au upper limit for the following reason.," Indeed, the shadowing effects implied by $C\approx 15\%$ should be considered an upper limit for the following reason." + Our covering factor is defined purely in terms of ecometry., Our covering factor is defined purely in terms of geometry. + If the majority of clumps are optically thin. then the “effective” covering factor may actually be less. since shadowing by thin chumps does not resultin much absorption (unless the accumulated column depth of iiultiple chuups produces a significant optical depth iu total).," If the majority of clumps are optically thin, then the “effective” covering factor may actually be less, since shadowing by thin clumps does not resultin much absorption (unless the accumulated column depth of multiple clumps produces a significant optical depth in total)." + For example. our mocel is for 5=1.1 with f»=1000 aud f4=0.1 at f=1 (appearing in the upper panel of Fig. 9)).," For example, our model is for $\gamma=1.4$ with $t_2=1000$ and $t_1=0.1$ at $f=1$ (appearing in the upper panel of Fig. \ref{fig9}) )." +" At the waveleneth of 7 wun. these upper aud lower optical depth limits become approximately 10 aud 0.001. respectively,"," At the wavelength of 7 mm, these upper and lower optical depth limits become approximately 10 and 0.001, respectively." + The mean clump optical depth is thus ouly (65.=0.2. and just of the clumps have optical depths in excess of nuity alone their diameters.," The mean clump optical depth is thus only $\langle +t \rangle \approx 0.2$, and just of the clumps have optical depths in excess of unity along their diameters." + Cousequeutly. the effective covering factor is closer to 1A«154=0.6%.," Consequently, the effective covering factor is closer to $4\% \times 15\% = 0.6\%$." + Even at1554.. the shadowing is not severe for WI9N-D2: however. this discussion illustrates how application of this model to other sources iav need to take iuto account optical effects when interpreting covering factors if found to be of order unity or larecr.," Even at, the shadowing is not severe for W49N-B2; however, this discussion illustrates how application of this model to other sources may need to take into account optical effects when interpreting covering factors if found to be of order unity or larger." +clearly suggest that the cluster candidates are not older than 100 Alvre.,clearly suggest that the cluster candidates are not older than $\sim 100$ Myr. + The spectral energy clistribution (SED) litting procedure is described in Adamoctal.(2010a)., The spectral energy distribution (SED) fitting procedure is described in \cite{A2010}. +. Phe use nmiodels are presented in Adamoetal.(2010b)., The used models are presented in \citet{A2010b}. +. Phe outpu age and mass of the clusters are shown in the mass-age diagram in Ligure 2.., The output age and mass of the clusters are shown in the mass-age diagram in Figure \ref{mas-age}. + In. blue dots. we show the 6 SSCs previously analysed.," In blue dots, we show the 6 SSCs previously analysed." + “Phe underlving black dots. represen the low mass cluster population that is present in the galaxy. detectable at the detection. limits imposed by the data.," The underlying black dots represent the low mass cluster population that is present in the galaxy, detectable at the detection limits imposed by the data." + The masses are smaller than ~5103 AJ. an the ages are vounger than 50 Myr., The masses are smaller than $\sim 5\times 10^4$ $\msun$ and the ages are younger than 50 Myr. + lt is still under debate whether an old. stellar population (older than 100. Myr) exists in SBS 0335-052E (Ostlin&Ixunth2001). or if this galaxy has recently formed. (Papacerosetal.1998)..., It is still under debate whether an old stellar population (older than 100 Myr) exists in SBS 0335-052E \citep{2001A&A...371..429O} or if this galaxy has recently formed \citep{1998A&A...338...43P}. + In previous star cluster analyses of other BOCs (1920 338. llaro 11. ESO 185. 9930). we have found a trace of some old GC's. supporting the evidence of an old undoerlving stellar population in those galaxies.," In previous star cluster analyses of other BCGs (ESO 338, Haro 11, ESO 185, 930), we have found a trace of some old GCs, supporting the evidence of an old underlying stellar population in those galaxies." + In the case of SBS 0335-052E. however. the non detection of massive GC's cannot prove/disprove either of the wo proposed scenarios.," In the case of SBS 0335-052E, however, the non detection of massive GCs cannot prove/disprove either of the two proposed scenarios." + We observe that. because of the deection limits (see inset in ligure 2)). our analysis is limited to CCs with masses higher than 5«10! AL. between 1)0 Myr and 1 yr and even more massive at older ages.," We observe that, because of the detection limits (see inset in Figure \ref{mas-age}) ), our analysis is limited to GCs with masses higher than $5\times 10^4$ $\msun$ between 100 Myr and 1 Gyr and even more massive at older ages." + Therefore. we cannot exclude that this galaxy has low-mass GC's.," Therefore, we cannot exclude that this galaxy has low-mass GCs." + Using the same method as in the case of ESO 338. we infer the mass in clusters formed. during the last LO Myr in SBS 0335.," Using the same method as in the case of ESO 338, we infer the mass in clusters formed during the last 10 Myr in SBS 0335." + We observe that the total mass contained in detected clusters younger than 10 Myr is 1.95.10° M..., We observe that the total mass contained in detected clusters younger than 10 Myr is $1.95\times 10^6$ $\msun$. +" Lhe mass contained in the 5 SSCs (one of them is much older. e.g. from La equivalent width. the age is constrained to 13 Myr is constrained. see Adamoetal. 2010b)) is roughly 73 of this total mass (1.4210"" AZ. )."," The mass contained in the 5 SSCs (one of them is much older, e.g. from $\alpha$ equivalent width, the age is constrained to $\sim13$ Myr is constrained, see \citealp{A2010b}) ) is roughly 73 of this total mass $1.42\times 10^6$ $\msun$ )." + Assuming a power Law cluster mass function and that we are complete in detecting clusters more massive than 5«10A7.. we estimate a total mass in clusters vounecr than 10 Myr of 6.4OPAL...," Assuming a power law cluster mass function and that we are complete in detecting clusters more massive than $5\times10^3 \msun$, we estimate a total mass in clusters younger than 10 Myr of $6.4\times10^6 \msun$." + The observed CER. in systems more massive than Mo5107 AL. is 0.2 A. +. while the extrapolated CLR. (Mc107 AL. 0.64 AZ. +.," The observed CFR in systems more massive than $>5\times10^3$ $\msun$ is 0.2 $\msun$ $^{-1}$, while the extrapolated CFR $>10^2$ $\msun$ $=0.64$ $\msun$ $^{-1}$." + Lhe E value of SBS 03:35 is 49 £12%. using a SER of 1.3 Ad. vr+.," The $\Gamma$ value of SBS 0335 is 49 $\pm 12 \%$, using a SFR of 1.3 $\msun$ $^{-1}$." + These values have been estimated after that a correction for Salpeter IME has been applied (sce Section 3.1.1))., These values have been estimated after that a correction for Salpeter IMF has been applied (see Section \ref{sfr_unc}) ). + The formation of a cluster appears to be correlated: with the properties of the host galaxy., The formation of a cluster appears to be correlated with the properties of the host galaxy. + A common observation is that galaxy mergers. produce more numerous anc more massive clusters than quiescent spirals (Larsen2009.andreferences therein)...sfatishes. ," A common observation is that galaxy mergers produce more numerous and more massive clusters than quiescent spirals \citep[][and references therein]{2009A&A...494..539L}. ," +"known also as size-ol-sample elfect. ναι, galaxies with a more numerous cluster population have higher chances to sample the cluster mass function. CME. at higher masses) is a possible explanation for this trend (Whitmore2000:Larsen2002.hereafterL02)."," known also as size-of-sample effect, (i.e., galaxies with a more numerous cluster population have higher chances to sample the cluster mass function, CMF, at higher masses) is a possible explanation for this trend \citep[][hereafter L02]{2000astro.ph.12546W, 2002AJ....124.1393L}." +. On the other hand. the host environment can play its role in determining the mass of the forming clusters (Giclesetal. 2006)...," On the other hand, the host environment can play its role in determining the mass of the forming clusters \citep{2006A&A...450..129G}." + Numerical simulations of different host environments suggest that the shear in rotationally supported: galaxies (Le. spirals) acts on the collapse of the giant molecular clouds (GALCs). causing fragmentation and favouring the formation of the less clustered OB associations and low mass clusters (Weidneretal.2010)...," Numerical simulations of different host environments suggest that the shear in rotationally supported galaxies (i.e., spirals) acts on the collapse of the giant molecular clouds (GMCs), causing fragmentation and favouring the formation of the less clustered OB associations and low mass clusters \citep{2010ApJ...724.1503W}." + The lack of rotation in dwarf galaxies and high external pressures in merging systems favour the collapse of massive and. gravitationally »»und. cluster., The lack of rotation in dwarf galaxies and high external pressures in merging systems favour the collapse of massive and gravitationally bound cluster. + These two scenarios were also addressed. by Dillettetal.(2002) to understand: cluster formation in dwarl galaxies., These two scenarios were also addressed by \citet{2002AJ....123.1454B} to understand cluster formation in dwarf galaxies. + Γον studied the star cluster populations of nearby cbwarf galaxies and observed that not all the systems jud bound and. luminous clusters., They studied the star cluster populations of nearby dwarf galaxies and observed that not all the systems had bound and luminous clusters. + However. some of them rosteck one or a few very massive ones.," However, some of them hosted one or a few very massive ones." + “They suggested hat. with respect to spiral galaxies which form more clusters and can. therefore. sample the eluster mass function 10mogeneously. up to high mass bins. the cluster formation in dwarf galaxies is possibly dominated. ον stochasticity ogether with Favourabe physical conditions to form single massive clusters.," They suggested that, with respect to spiral galaxies which form more clusters and can, therefore, sample the cluster mass function homogeneously up to high mass bins, the cluster formation in dwarf galaxies is possibly dominated by stochasticity together with favourable physical conditions to form single massive clusters." + Observed empirica relations between the properties of he voung star clusters and the SER in the host. support he size-ol-sample effec scenario., Observed empirical relations between the properties of the young star clusters and the SFR in the host support the size-of-sample effect scenario. + Larsen&Richtler(2000.ποσαοLROO) first noticed that the fraction of luminosity contained in the voung star clusters and the SER of the host ealaxy are correlated CE; (U)-Maupg realtion). Le.. higher SERs correspond to à more numerous cluster population (higher cluster formation cllicicney).," \citet[][hereafter LR00]{2000A&A...354..836L} first noticed that the fraction of luminosity contained in the young star clusters and the SFR of the host galaxy are correlated $_L$ $\Sigma_\mathrm{SFR}$ realtion), i.e., higher SFRs correspond to a more numerous cluster population (higher cluster formation efficiency)." + In. a follow-up work. LO2 found evidence of a positive correlation between the visual luminosity of the brightest star cluster and the SER in the host CALEB USER relation).," In a follow-up work, L02 found evidence of a positive correlation between the visual luminosity of the brightest star cluster and the SFR in the host $M_V^{\textnormal{brightest}}$ -SFR relation)." + The relation between the two quantities can be understood if higher SERs enabled the formation of more massive clusters., The relation between the two quantities can be understood if higher SFRs enabled the formation of more massive clusters. + DOS enlarged the sample of L02. including resolved. close-by. star-forming regions and [luminous and ultra-Iuminous LR galaxies (LIRGs and ULIRGs).," B08 enlarged the sample of L02, including resolved close-by star-forming regions and luminous and ultra-luminous IR galaxies (LIRGs and ULIRGs)." + Le noticed that the Antes relation holds over several orders of magnitude in SER. values. suggesting that the voungest brightest cluster is a fairly good indicator of the present SER. in the galaxy.," He noticed that the $M_V^{\textnormal{brightest}}$ -SFR relation holds over several orders of magnitude in SFR values, suggesting that the youngest brightest cluster is a fairly good indicator of the present SFR in the galaxy." + Phese observed relations clearly point towards a scenario where the cluster formation is intimately correlated with the star formation process. or in other words. the birth of a cluster is a product. of an universal star formation process which operates on many scales of cLlicicney.," These observed relations clearly point towards a scenario where the cluster formation is intimately correlated with the star formation process, or in other words, the birth of a cluster is a product of an universal star formation process which operates on many scales of efficiency." + In a recent work by GIO. it has been inferred. that the present CELE (clusters formed in the last 10. Myr). is higher for a higher current SER. in the host. the so-called L-log(Mrn) relation.," In a recent work by G10, it has been inferred that the present CFE (clusters formed in the last 10 Myr) is higher for a higher current SFR in the host, the so-called $\Gamma$ $\log(\Sigma_\mathrm{SFR})$ relation." + Silva-Villa&Larsen(2011) used a sample of 5 nearby spiral galaxies to test the CHO relation using two cdillerent. methods to estimate the CFEIs., \citet{2011arXiv1101.4021S} used a sample of 5 nearby spiral galaxies to test the G10 relation using two different methods to estimate the CFRs. + They observed. that the recovered. data points. in spite of the method used. scattered around the expected values and were impossible to reconcile with the Goddard et al.," They observed that the recovered data points, in spite of the method used, scattered around the expected values and were impossible to reconcile with the Goddard et al." + relation (see Figure 7))., relation (see Figure \ref{sfr-cfr}) ). + Despite the discrepancy between the two results. we will include the E-log(Np) relation in the tests we will perform for the BCCs.," Despite the discrepancy between the two results, we will include the $\Gamma$ $\log(\Sigma_\mathrm{SFR})$ relation in the tests we will perform for the BCGs." + A discussion. of the uncertainties allecting this relation will be presented in the next section., A discussion of the uncertainties affecting this relation will be presented in the next section. + They max. explain the disagreement between Goddard et al., They may explain the disagreement between Goddard et al. + and Silva-Villa Larsen results., and Silva-Villa Larsen results. + ‘To investigate whether BOCs follow these cluster-host relations we use the quantities listed in Table 1. and 2.., To investigate whether BCGs follow these cluster-host relations we use the quantities listed in Table \ref{table-obs} and \ref{table-obs2}. + Aefore we test the relation. and compare our data to the ones published in the literature. we cliscuss. briefly. the main source of uncertainties associated: with the derived parameters and the used methods.," Before we test the relation and compare our data to the ones published in the literature we discuss, briefly, the main source of uncertainties associated with the derived parameters and the used methods." +with periods less than one dav we find that a projected semi-major axis of more (han 0.5 light seconds will reduce the power of the signal bv more than one standard deviation in the power.,with periods less than one day we find that a projected semi-major axis of more than 0.5 light seconds will reduce the power of the signal by more than one standard deviation in the power. + We take (his to be an effective limit on the size of any orbit., We take this to be an effective limit on the size of any orbit. + For orbital periods longer than the 1.2 day observation this size limit is weakened., For orbital periods longer than the 1.2 day observation this size limit is weakened. + This absence of anv apparent binary modulation on a time scale < 1 clay is consistent with evidence lor other of the AXPs (Mereghetti 2001) for the lack of a binary companion., This absence of any apparent binary modulation on a time scale $\le$ 1 day is consistent with evidence for other of the AXPs (Mereghetti 2001) for the lack of a binary companion. + Three of the AXPs appear to be associated with relatively voung (< 20 kv) supernova remnants., Three of the AXPs appear to be associated with relatively young $<$ 20 ky) supernova remnants. + In each of these cases: (LE 22594-586: Rho Petre 1997. Parmar et al.," In each of these cases: (1E 2259+586: Rho Petre 1997, Parmar et al." + 1998): 1E 1841-045. Helfanel οἱ al.," 1998); 1E 1841-045, Helfand et al." + 1994: and J1844-0233. Vasisht et al.," 1994; and J1844-0288, Vasisht et al." + 2000) there is evidence [or extended X-ray emission., 2000) there is evidence for extended X-ray emission. + We have examined the CILANDRA data for evidence of emission bevond that which is consistent. with a point source., We have examined the CHANDRA data for evidence of emission beyond that which is consistent with a point source. + We find none., We find none. + However. a better limit on anv possible extension to the source may be derived from ROSAT URI observations (the first (wo in the Table) in which tlie source was approximately 6 are minutes from (he center of the field where the angular resolution of the IRI is better than in CILIANDRA data 10 arc minutes off-axis.," However, a better limit on any possible extension to the source may be derived from ROSAT HRI observations (the first two in the Table) in which the source was approximately 6 arc minutes from the center of the field where the angular resolution of the HRI is better than in CHANDRA data 10 arc minutes off-axis." + One-dimensional profiles though the image in the right ascension and declination directions of (he combined ILRI dataset are consistent with a point source wilh a width (σ) of 2.0 arc seconds., One-dimensional profiles though the image in the right ascension and declination directions of the combined HRI dataset are consistent with a point source with a width $\sigma$ ) of 2.0 arc seconds. + There is no evidence for eniission at a level > the counting rale at the peak of the profiles at a distance of 10 to 20 are seconds trom the source., There is no evidence for emission at a level $>$ the counting rate at the peak of the profiles at a distance of 10 to 20 arc seconds from the source. + Any extension to the source must be a distance from (he source less than the width of the point spread function of the ILRI. 10 are seconds.," Any extension to the source must be a distance from the source less than the width of the point spread function of the HRI, 10 arc seconds." + This corresponds to a limit to the size of any extended X-ray emission of 2.8 pe at the distance of the SAIC., This corresponds to a limit to the size of any extended X-ray emission of 2.8 pc at the distance of the SMC. + This limit is comparable to the X-ray extension observed for the two SNR/AXDP associations with known distances (xes 73/1E 1341-045 and CTLO9/1E 2259.12-586)., This limit is comparable to the X-ray extension observed for the two SNR/AXP associations with known distances (Kes 73/1E 1841-045 and CT109/1E 2259.1+586). + A deep CILANDRA exposure with the source centered in the field of the IRC is needed to constirain stronglv the possibilitv of a supernova remnant association for (is pulsar., A deep CHANDRA exposure with the source centered in the field of the HRC is needed to constrain strongly the possibility of a supernova remnant association for this pulsar. +their afterglow properties (Gehrels et al.,their afterglow properties (Gehrels et al. + 2008: Nysewander. Fruchter. Pe'er 2009).," 2008; Nysewander, Fruchter, Pe'er 2009)." + The concept of powering the long term X-ray light curve of GRBs by accretion onto the BH represents a departure from the standard model in which the fading corresponds to the deceleration of a baryonic jet., The concept of powering the long term X-ray light curve of GRBs by accretion onto the BH represents a departure from the standard model in which the fading corresponds to the deceleration of a baryonic jet. + In the accretion model. the jet itself would be very light. perhaps composed almost exclusively of Poynting flux. and the long term fading would not be due to variations in the Lorentz factor and beaming factor.," In the accretion model, the jet itself would be very light, perhaps composed almost exclusively of Poynting flux, and the long term fading would not be due to variations in the Lorentz factor and beaming factor." + Recent high fidelity GRMHD calculations of BH aceretion support the idea of a high Lorentz factor jet with minimal baryon loading (McKinney Narayan 2007ab)., Recent high fidelity GRMHD calculations of BH accretion support the idea of a high Lorentz factor jet with minimal baryon loading (McKinney Narayan 2007ab). + The aceretion scenario involving fall-back of the progenitor core has been examined in detail by Kumar et al. (, The accretion scenario involving fall-back of the progenitor core has been examined in detail by Kumar et al. ( +2008a. 2008b) and Lindner et al. (,"2008a, 2008b) and Lindner et al. (" +2010).,2010). + Kumar et al. (, Kumar et al. ( +2008b) argue that constraints may be placed on the density profiles and radi of the progenitor core and envelope. as well as their rotation rates relative to break-up.,"2008b) argue that constraints may be placed on the density profiles and radii of the progenitor core and envelope, as well as their rotation rates relative to break-up." + Lindner et al. (, Lindner et al. ( +2010) examined the progenitor core fall-back scenario in much greater detail with the adaptive mesh refinement FLASH code. where their calculations are done in cylindrical coordinates.,"2010) examined the progenitor core fall-back scenario in much greater detail with the adaptive mesh refinement FLASH code, where their calculations are done in cylindrical coordinates." + Starting with a Heger progenitor. they follow the fall-back evolution of the progenitor.," Starting with a Heger progenitor, they follow the fall-back evolution of the progenitor." + Their Fig., Their Fig. + 2 shows the potential for the model to obtain a steeply decaying light curve as is seen in X-rays for segment IL. where a—3 in the Zhang et al.pH (," 2 shows the potential for the model to obtain a steeply decaying light curve as is seen in X-rays for segment I, where $\alpha\simeq3$ in the Zhang et al. (" +2006) schematic.,2006) schematic. + In. their Discussion. Lindner et al.," In their Discussion, Lindner et al." + mention several caveats. such as the lack of nuclear physics in the inner disk. the neglect of the MRI. and the lack of modeling the axial relativistic jet.," mention several caveats, such as the lack of nuclear physics in the inner disk, the neglect of the MRI, and the lack of modeling the axial relativistic jet." + A more basic concern is simply the range of rate of accretion 1n comparison to that inferred from observations., A more basic concern is simply the range of rate of accretion in comparison to that inferred from observations. + Fig., Fig. + 2 of Lindner et al., 2 of Lindner et al. + shows that if progenitor core fall-back ts the correct explanation for segment I in the X-ray light curve. the rate of accretion onto the BH during this phase varies between about 0.1 and 10CAL.sὃν whereas from Fig.," shows that if progenitor core fall-back is the correct explanation for segment I in the X-ray light curve, the rate of accretion onto the BH during this phase varies between about 0.1 and $10^{-5}\msunsec$, whereas from Fig." + 2 of this work we see that. for nominal assumptions about the accretion efficiency. the rate inferred from observations on segment I for GRB 060729 varies between about 10 and 3«10CAL.vr|l lower by a factor ~10?10° than in Lindner et al. (," 2 of this work we see that, for nominal assumptions about the accretion efficiency, the rate inferred from observations on segment I for GRB 060729 varies between about 10 and $3\times 10^{-3}\msunyr$, lower by a factor $\sim10^5-10^6$ than in Lindner et al. (" +2010).,2010). + One does in fact expect for the theoretical accretion rate in this context to be an overestimate. given the potential for outflow. but the discrepancy here seems extreme.," One does in fact expect for the theoretical accretion rate in this context to be an overestimate, given the potential for outflow, but the discrepancy here seems extreme." + There are several possibilities for this discrepancy., There are several possibilities for this discrepancy. + The vertical scale shown in Fig., The vertical scale shown in Fig. + 2 of this work is already super-Eddington by between about one and eight orders of magnitude. and therefore the range in the Lindner et al.," 2 of this work is already super-Eddington by between about one and eight orders of magnitude, and therefore the range in the Lindner et al." + calculations would be correspondingly greater., calculations would be correspondingly greater. + It may be that even highly advective disks cannot accommodate that much accretion onto the BH. and that a significant fraction of the material is blown away before it can acecrete.," It may be that even highly advective disks cannot accommodate that much accretion onto the BH, and that a significant fraction of the material is blown away before it can accrete." + This would have to occur. however. in such a way that it did not interfere with the propagation of the jet.," This would have to occur, however, in such a way that it did not interfere with the propagation of the jet." + Also. for the shape of the decay light curve caleulated by Lindner et al.," Also, for the shape of the decay light curve calculated by Lindner et al." + to correspond to segment L the ratio of accreted to ejected gas would have to remain constant.," to correspond to segment I, the ratio of accreted to ejected gas would have to remain constant." + If it varied significantly. the accretion-derived luminosity would have a different decay power law.," If it varied significantly, the accretion-derived luminosity would have a different decay power law." + Another possibility is that the Lindner et al., Another possibility is that the Lindner et al. + calculations greatly over-estimate the fall-back. in which case a much greater fraction of the progenitor would be ejected on a time scale <10° s. Lindner et al.," calculations greatly over-estimate the fall-back, in which case a much greater fraction of the progenitor would be ejected on a time scale $\la10^3$ s. Lindner et al." + note that they do not find evidence for the thin disk hypothesized by CGO9 as characterizing the fate of the progenitor envelope fall-back., note that they do not find evidence for the thin disk hypothesized by CG09 as characterizing the fate of the progenitor envelope fall-back. + Given the apparent mismatch in accretion rates between their theory and the observations. and the findings of this work. their eriticism could have at least two mitigating factors: (1) In Figure 4 we see that for the period covered by the Lindner et al.," Given the apparent mismatch in accretion rates between their theory and the observations, and the findings of this work, their criticism could have at least two mitigating factors: (1) In Figure 4 we see that for the period covered by the Lindner et al." +" calculations. namely t<10° s. a significant fraction of the disk lies within (44, Le.. the more spatially extended slim disk rather than the thin disk. ("," calculations, namely $t<10^3$ s, a significant fraction of the disk lies within $r_{\rm trans}$, i.e., the more spatially extended slim disk rather than the thin disk. (" +2) Given the apparent mismatch between theory and observation for the rates of accretion. the actual densities within the volume formerly occupied by the progenitor may be much less than caleulated by Lindner et al. (,"2) Given the apparent mismatch between theory and observation for the rates of accretion, the actual densities within the volume formerly occupied by the progenitor may be much less than calculated by Lindner et al. (" +2010). which would interfere far less with an accretion disk formed from fall-back debris.,"2010), which would interfere far less with an accretion disk formed from fall-back debris." + At late times observations indicate a steepening in the rate of decay (Grupe et al., At late times observations indicate a steepening in the rate of decay (Grupe et al. + 2010). which appears to be consistent with the onset of a cooling front in the disk.," 2010), which appears to be consistent with the onset of a cooling front in the disk." + This would be an alternative to the standard jet-break interpretation discussed by Grupe et al. (, This would be an alternative to the standard jet-break interpretation discussed by Grupe et al. ( +2010).,2010). + For sGRBs. the picture is less clear. given that we only have a single well-studied example.," For sGRBs, the picture is less clear, given that we only have a single well-studied example." +" We have shown that the presence of even a very small amount of high angular momentum gas ~10.ΛΙ, can give a slight inflection to the X-ray decay. as was observed in GRB 051221A. As for the overall X-ray light curve. segments IL and ΠΠ. if only ~10.7?10ΑΙ, of gas survives either the hypernova (IGRBs) or NS-NS merger (SGRBs). then the accretion resulting from the ensuing fall-back disk should power a long-term jet."," We have shown that the presence of even a very small amount of high angular momentum gas $\sim10^{-9}\msun$ can give a slight inflection to the X-ray decay, as was observed in GRB 051221A. As for the overall X-ray light curve, segments II and III, if only $\sim 10^{-5} - 10^{-4}\msun$ of gas survives either the hypernova (lGRBs) or NS-NS merger (sGRBs), then the accretion resulting from the ensuing fall-back disk should power a long-term jet." +" Lastly. we have shown that the Dainotti relation Lj,Xful may be due to an observational bias against detecting and characterizing faint. plateaus: the relation is governed by GRBs at.=1.5 for which we only detect the upper envelope of a broad distribution."," Lastly, we have shown that the Dainotti relation $L^*_{\rm II} \simpropto {t^*}_{\rm II}^{-1}$ may be due to an observational bias against detecting and characterizing faint plateaus: the relation is governed by GRBs at $z\ga1.5$ for which we only detect the upper envelope of a broad distribution." + Nevertheless. the existence of an apparent upper limit to the total X-ray energies inferred from the X-ray fluences. and therefore the accreted masses if one assumes accretion onto the central engine as the long term powerhouse for the X-rayflux. is extremely interesting.," Nevertheless, the existence of an apparent upper limit to the total X-ray energies inferred from the X-ray fluences, and therefore the accreted masses if one assumes accretion onto the central engine as the long term powerhouse for the X-rayflux, is extremely interesting." + For nominal values of the accretion efficiency 6&4 and the beaming factor f. we find an upper limit~ LO!10541. for the accreted mass during segments II and III. (," For nominal values of the accretion efficiency $\epsilon_{\rm net}$ and the beaming factor $f$, we find an upper limit $\simeq 10^{-4} - 10^{-3} \msun$ for the accreted mass during segments II and III. (" +The— lower end of the distribution of accreted masses. which ts partially revealed for GRBs at 2<1.5. may extend down to =105. SAL...),"The lower end of the distribution of accreted masses, which is partially revealed for GRBs at $z\la1.5$, may extend down to $\simeq +10^{-8} - 10^{-7} \msun$ .)" +" This means that for à progenitor mass ~LOA... only a maximum mass fraction ~10ο! of the progenitor survives 1n the vicinity of the progenitor to be accreted as a fall-back disk (excluding the 104, that ends up in the BH during the prompt emission and subsequent segment I consisting of the steep-decay)."," This means that for a progenitor mass $\sim10\msun$, only a maximum mass fraction $\sim10^{-5} - 10^{-4}$ of the progenitor survives in the vicinity of the progenitor to be accreted as a fall-back disk (excluding the $\sim10\msun$ that ends up in the BH during the prompt emission and subsequent segment I consisting of the steep-decay)." + This has important ramifications for the energetics associated with the hypernova explosion and subsequent removal of most of the progenitor envelope., This has important ramifications for the energetics associated with the hypernova explosion and subsequent removal of most of the progenitor envelope. + We acknowledge useful conversations with Maria Dainotti. Dirk Grupe. Stephan Rosswog. and Brad Schaefer.," We acknowledge useful conversations with Maria Dainotti, Dirk Grupe, Stephan Rosswog, and Brad Schaefer." + This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester., This work made use of data supplied by the UK Science Data Centre at the University of Leicester. +The iass-shect transformation ds equivalent to an isotropic scaling of the source plaue coordinates.,The mass-sheet transformation is equivalent to an isotropic scaling of the source plane coordinates. + Ποσο. we divide (7)) bv (1.&) to obtain components.2 independe μμ," Hence, we divide \ref{eq:lenseq}) ) by $(1-\kappa)$ to obtain ^* - ^2 _1 ^* - _3 ^*)^2;." + We will now express the cocfiicicuts in the lens equation (16)) iu terms of the derivatives of the reduced shear.," We will now express the coefficients in the lens equation \ref{eq:lenseqred}) ) in terms of the derivatives of the reduced shear,." +Vau: The expression for J/(l—&) iu terms of the reduced shear and its derivatives has been derived bv IEaiser (1995): in our notation it reads κ), The expression for ${\cal F} / (1-\kappa)$ in terms of the reduced shear and its derivatives has been derived by Kaiser (1995); in our notation it reads ). + The expression for the derivative of 5 in terms of the reduced shear cau be casily obtained from differentiating the definitions=(1&Jg. as4ο τςἂν ου... =," The expression for the derivative of $\gamma$ in terms of the reduced shear can be easily obtained from differentiating the definition $\gamma=(1-\kappa)g$, =G_3-g =G_3 - -." + The derivatives Gy.1.3 of the reduced shear are those quantities we can hope to observe: to distinguish. them from F and G. one might8 call Gy.1.3 the The Jacobian determünaut detA of the mapping between the Ἱπασο8 position 0 aud the rescaled source position .J then becomes Ξ]-ο οἱ —( | is a spin-l quantity.," The derivatives $G_{1,3}$ of the reduced shear are those quantities we can hope to observe; to distinguish them from ${\cal F}$ and ${\cal +G}$ , one might call $G_{1,3}$ the The Jacobian determinant $\det\hat\A$ of the mapping between the image position $\theta$ and the rescaled source position $\hat \beta$ then becomes =1-g g^* ^* - = G_1 + is a spin-1 quantity." + Aeain. (20)) is valid onlv to linear order in 0.," Again, \ref{eq:detAhat}) ) is valid only to linear order in $\theta$." + Note that a similar equation for the determinant was obtained in Okura ct ((2007: their Al). but they consider oulv the case of g|1: this has also consequences for the relations between source aud nuage brightuess uoments. to be derived further below.," Note that a similar equation for the determinant was obtained in Okura et (2007; their A1), but they consider only the case of $|g|\ll 1$; this has also consequences for the relations between source and image brightness moments, to be derived further below." +" Flexion has a total of four commponcuts. namely the real and nunaenurv parts of Fy, and ο "," Flexion has a total of four components, namely the real and imaginary parts of ${\cal F}$ and ${\cal G}$." +A ineasureineut of flexion will tms vield. four] oy and’ σας Whigtien thes counsGueuts iue ident;," A measurement of flexion will thus yield four components, and we might ask whether these components are independent." + We recall a shular situation iu shear measurements., We recall a similar situation in shear measurements. + T1ο shear las two components: on the other laud. he shear ds chuned as second partial derivatives of the eflectiou »otential. which is a single scalar field.," The shear has two components; on the other hand, the shear is defined as second partial derivatives of the deflection potential, which is a single scalar field." + ThereOre. the two shear components cannot be mutually indevendeit if they we due to a eravitational leusimg signal.," Therefore, the two shear components cannot be mutually independent if they are due to a gravitational lensing signal." + Of coiuse. the ucasured shear is uot enarautecd to satisty f1C condition fat the two shear components can be derived from a single scalar deflection poteutial. since observational noise or mtrmsic aliguinents of galaxies may affec t1e nueasured shear field.," Of course, the measured shear is not guaranteed to satisfy the condition that the two shear components can be derived from a single scalar deflection potential, since observational noise or intrinsic alignments of galaxies may affect the measured shear field." + Therefore. one has introduced. tiC notion of andl D-110des ii shear measurements (Crittenden ct 22002).," Therefore, one has introduced the notion of E- and B-modes in shear measurements (Crittenden et 2002)." + The E-anode shear is the one that caji be written du terus of a deflection. potential. whereas the B-mode shear cannot.," The E-mode shear is the one that can be written in terms of a deflection potential, whereas the B-mode shear cannot." + Formally. the E- and B-mode decomposition can be written in terms of a complex ¢cHection potential c(0)CE)|i0P(0) ane a complex surface mass density &=RE|iw? (Schucider et 22002).," Formally, the E- and B-mode decomposition can be written in terms of a complex deflection potential $\psi(\theta)=\psi^{\rm +E}(\theta)+{\rm i}\psi^{\rm B}(\theta)$ and a complex surface mass density $\kappa=\kappa^{\rm E} + {\rm i}\kappa^{\rm B}$ (Schneider et 2002)." +" Each conrponeut of c satisfies its own Poisson equation, V2E=24E, V2,= ον, "," Each component of $\psi$ satisfies its own Poisson equation, $\nabla^2\psi^{\rm E}=2\kappa^{\rm E}$, $\nabla^2\psi^{\rm +B} =2\kappa^{\rm B}$ ." +Nadiug use of this decomposition. the shear becomes," Making use of this decomposition, the shear becomes." + The distinction between E- aud B-mode shear cau be obtained bv considering second partial derivatives of the shear components., The distinction between E- and B-mode shear can be obtained by considering second partial derivatives of the shear components. + Talking the derivative of (21)). onc obtains which can ο expressed in more compact forni as," Taking the derivative of \ref{eq:gammaEB}) ), one obtains, which can be expressed in more compact form as." + A further derivative vields for the componcuts , A further derivative yields for the components . +Towever. it is easier to consider directly the complex derivative of JF. from which we obtain," However, it is easier to consider directly the complex derivative of ${\cal F}$, from which we obtain." + Thus. if the shear field is a pure E-mode field. V2V5 is veal.," Thus, if the shear field is a pure E-mode field, $\nabla^*_{\rm +c}\nabla^*_{\rm c}\gamma$ is real." + An imaginary part of ονο is due to a D-anode field.," An imaginary part of $\nabla^*_{\rm +c}\nabla^*_{\rm c}\gamma$ is due to a B-mode field." + This then vieldls the local distinction between E- aud B-mode shear., This then yields the local distinction between E- and B-mode shear. + Since the flexionhas four compoucuts. whereasthe Ίος can be described by a single scalar field.we expect that there are three constraint relations a flexion field has to," Since the flexionhas four components, whereasthe lens can be described by a single scalar field,we expect that there are three constraint relations a flexion field has to" +"where 7, and r, are arbitrary constants.",where $T_o$ and $r_o$ are arbitrary constants. + With this solution for 7(r). one finds that In optically thick regions. the radiative flux F is Given the above temperature profile. F is equivalent to a scalar field F(r) in the radial direction (hat is given bv in optically Chick regions.," With this solution for $T(r)$, one finds that In optically thick regions, the radiative flux ${\vec F}$ is Given the above temperature profile, ${\vec F}$ is equivalent to a scalar field $F(r)$ in the radial direction that is given by in optically thick regions." +" The radiative flux in optically thick regions is calculated in ihe numerical code using The radius r, is defined to be the edge of (he optically thick region. where T(r)=Ty. and outside of which T(r)=T,. ie. the cloud is assumed to be embedded in a thermal bath at a temperature of Z;,=50 Ix. as is commonly. assumed in the Boss disk instability models."," The radiative flux in optically thick regions is calculated in the numerical code using The radius $r_o$ is defined to be the edge of the optically thick region, where $T(r_o) = T_o$, and outside of which $T(r) = T_o$, i.e., the cloud is assumed to be embedded in a thermal bath at a temperature of $T_o = 50$ K, as is commonly assumed in the Boss disk instability models." +" The envelope density (7> r;) is taken to be a [actor of 10° times smaller than in the optically thick region (r< r,). ensuring ils optical thinness."," The envelope density $r > r_o$ ) is taken to be a factor of $10^5$ times smaller than in the optically thick region $r < r_o$ ), ensuring its optical thinness." + The heating term £y=0 for r2ry. so that the radiative flux in the optically thin region must fall off with distance as rc. Le. for r>ry," The heating term $E_H = 0$ for $r > r_o$, so that the radiative flux in the optically thin region must fall off with distance as $r^2$, i.e., for $r > r_o$." + Because the numerical code uses L rather than F io calculate radiative transfer. there is no convenient expression for £F in optically thin regions that can be compared to the analvtical value above.," Because the numerical code uses $L$ rather than ${\vec F}$ to calculate radiative transfer, there is no convenient expression for ${\vec F}$ in optically thin regions that can be compared to the analytical value above." + In practice. the Boss disk instability moclels assume," In practice, the Boss disk instability models assume" +elobal SFR.,global SFR. + The revision of the SFRs of dwarf galaxies sugeested here now poses a major challenge for our theoretical understanding of star formation iu ealaxies which lad been developed with the aim of explaining the low star formation efficiencies of dwarf galaxies., The revision of the SFRs of dwarf galaxies suggested here now poses a major challenge for our theoretical understanding of star formation in galaxies which had been developed with the aim of explaining the low star formation efficiencies of dwarf galaxies. + It follows that galaxy aud cosmic evolution mniodels need a substantial revision requiring further studies., It follows that galaxy and cosmic evolution models need a substantial revision requiring further studies. +llowever. the estimated change in frequency. over the gap. caleulated from plhase-coherent solutions on each side of the gap. is negative. ie.,"However, the estimated change in frequency over the gap, calculated from phase-coherent solutions on each side of the gap, is negative, ie." + in (he opposite direction [rom a conventional elitch., in the opposite direction from a conventional glitch. + This implies that a gliteh alone cannot account for the loss in phase., This implies that a glitch alone cannot account for the loss in phase. + A second phase-coherent solution was obtained for the 1.3-vr interval from MJD with ». P. P fitted.," A second phase-coherent solution was obtained for the 1.8-yr interval from MJD 52915-53579, with $\nu$, $\dot{\nu}$, $\ddot{\nu}$ fitted." + The residuals after subtraction of the best-lit parameters are shown in the top panel of Figure 4.., The residuals after subtraction of the best-fit parameters are shown in the top panel of Figure \ref{fig:ephem2}. + As systematic trends. again interpreted as timing noise or possibly uunmnodelled glitch recovery. remained in (he residuals. three hieher-order frequency derivatives were fitted.," As systematic trends, again interpreted as timing noise or possibly unmodelled glitch recovery, remained in the residuals, three higher-order frequency derivatives were fitted." + The resulting residuals are shownin the bottom panel ol Figure 4.., The resulting residuals are shownin the bottom panel of Figure \ref{fig:ephem2}. + The measured braking index resulting from the ‘whitened? timing solution is n—2.68£0.03. in agreement with (hat measured. from the first segment. of timing data.," The measured braking index resulting from the `whitened' timing solution is $n=2.68\pm 0.03$, in agreement with that measured from the first segment of timing data." + Deterministic parameters for the second timing solution are given in Table 1.., Deterministic parameters for the second timing solution are given in Table \ref{table:ephem}. + In order to mitigate the effects of timing noise. we also performed a partially pliase coherent analvsis.," In order to mitigate the effects of timing noise, we also performed a partially phase coherent analysis." + In this wav we obtained measurements of v spanning vvr of data as well as £& and P over vvr of data., In this way we obtained measurements of $\nu$ spanning yr of data as well as $\dot{\nu}$ and $\ddot{\nu}$ over yr of data. + This method is useful to detect small glitelies. as well as to oblain more accurate measurements of » in some cases (e.g.Livingstoneοἱal.2005a).," This method is useful to detect small glitches, as well as to obtain more accurate measurements of $n$ in some cases \citep[e.g.][]{lkg05}." +. Using the overall phase-coherent ephemeris as a starting point. closely spaced observations were phase-connected to obtain a local measurement of p.," Using the overall phase-coherent ephemeris as a starting point, closely spaced observations were phase-connected to obtain a local measurement of $\nu$." + In this wav we obtained a total of 22 measurements., In this way we obtained a total of 22 measurements. + A (wo degree polynomial was fitted to these measurements to get another measurement of 7. however. in (his case. the eliteh near MJD 52210 and the possible glitch between MJD 52837-52915 seriously restricted the available time baseline and rendered this analvsis of limited value.," A two degree polynomial was fitted to these measurements to get another measurement of $n$, however, in this case, the glitch near MJD 52210 and the possible glitch between MJD 52837-52915 seriously restricted the available time baseline and rendered this analysis of limited value." + The most constraining measurement is 7=2.83+0.39. [rom 13 values of v spanning MJD 51286-52199. in agreement with our phase-colierent. value.," The most constraining measurement is $n=2.83\pm0.39$, from 13 values of $\nu$ spanning MJD 51286-52199, in agreement with our phase-coherent value." + We repeated this process. measuring eight independent values of 7. shown in the top panel of Figure 5..," We repeated this process, measuring eight independent values of $\dot{\nu}$, shown in the top panel of Figure \ref{fig:nudot}." + Note that the [ist unambiguous 7» measurement occurred before the elitch near MJD 52210 and the glitch can clearly be seen in the Figure., Note that the first unambiguous $\dot{\nu}$ measurement occurred before the glitch near MJD 52210 and the glitch can clearly be seen in the Figure. + The bottom panel ol Figure 5. shows the post-gliteh slope removed [rom the data. highlighüng the change in mat the time of the glitch. Nz/P=(9.520.3)x160.1. in agreement with the value obtained Irom the phase-coherent fit.," The bottom panel of Figure \ref{fig:nudot} shows the post-glitch slope removed from the data, highlighting the change in $\dot{\nu}$ at the time of the glitch, $\Delta{\dot{\nu}}/{\dot{\nu}}= (9.5\pm 0.3) \times 10^{-4}$, in agreement with the value obtained from the phase-coherent fit." + Note that at the σαν data gap between MJD 52837 and 52915. there is no clear Av visible in Figure 5..," Note that at the day data gap between MJD 52837 and 52915, there is no clear $\Delta{\dot{\nu}}$ visible in Figure \ref{fig:nudot}." + This indicates that if a glitch did occur during this period. it consisted of primarily a change in v.," This indicates that if a glitch did occur during this period, it consisted of primarily a change in $\nu$ ." + The only gliteh consistent with the data would have had to have occurred near MJD 52910 with magnitude Av/y«5x10 ., The only glitch consistent with the data would have had to have occurred near MJD 52910 with magnitude $\Delta{\nu}/{\nu} < 5 \times 10^{-8}$ . + A eliteh with no change in AV , A glitch with no change in $\Delta{\dot{\nu}}$ +Understanding the origin of the Cosnüc N-rav Dackerouud (CNB or NRB) aud cosmological evolution of X-ray extragalactic populations is oue of the main goals of N-rav. astrouoniv.,Understanding the origin of the Cosmic X-ray Background (CXB or XRB) and cosmological evolution of X-ray extragalactic populations is one of the main goals of X-ray astronomy. + Iu the soft N-rvav baud. the ssatellite resolved of the 0.52 keV. CNB into individual sources (Παπο 11908) aud optical identification revealed that the major population is tvpe-I AGNs (Schiunidt 11998).," In the soft X-ray band, the satellite resolved of the 0.5–2 keV CXB into individual sources (Hasinger 1998) and optical identification revealed that the major population is type-I AGNs (Schmidt 1998)." + Because of the technical difficultics. dmaecine sky surveys in the lard A-rayv baud (above 2 keV). where the bulk of the CNB cnerey arises. were not. available until the launch ofASCA.," Because of the technical difficulties, imaging sky surveys in the hard X-ray band (above 2 keV), where the bulk of the CXB energy arises, were not available until the launch of." + The scusitivity limits achieved by previous mission such as ({Piccinotti 11982) and ((IXoudo 1991) are at most ~10i (210 keV). and the sources observed by them only account for of the CNB intensity inthe 210 keV baud.," The sensitivity limits achieved by previous mission such as (Piccinotti 1982) and (Kondo 1991) are at most $\sim 10^{-11}$ (2–10 keV), and the sources observed by them only account for of the CXB intensity in the 2–10 keV band." +" In particular. there is a bie puzzle ou the CNB origin. called the ""spectral paradox”: bright ACUNS observed withπο.EXOSAT aud hhave spectra with an average photon index of P= 1.9 (e.g... Walliams 11992). which is sienificauth: softer than that of the CNB itself (D= 1.1: ee. Cendreaw 11995)."," In particular, there is a big puzzle on the CXB origin, called the “spectral paradox”: bright AGNs observed with, and have spectra with an average photon index of $\Gamma$ = $-$ 1.9 (e.g., Williams 1992), which is significantly softer than that of the CXB itself $\Gamma \simeq $ 1.4; e.g., Gendreau 1995)." +" Furthermore. the broad baud properties of sources at fluxes from —1011 to ,10.DPm ((210 keV) are somewhat puzzling according to previous studies."," Furthermore, the broad band properties of sources at fluxes from $\sim10^{-11}$ to $\sim 10^{-13}$ (2–10 keV) are somewhat puzzling according to previous studies." + The extragalactic, The extragalactic +JAw|=Jews|.,$|\Delta\omega|\lta|\epsilon\omega_1|$. + There is no general restriction on the amount of energy that can be exchanged. except that and that the energy in each oscillator. must remain positive.," There is no general restriction on the amount of energy that can be exchanged, except that and that the energy in each oscillator, must remain positive." + Phe selection rule (46)) can be explained. or at least remembered. by saving that a pair of quanta of action f=L/w in oscillators 2 and 3 combine in pairs to make a single quantum in oscillator 1.," The selection rule \ref{selection}) ) can be explained, or at least remembered, by saying that a pair of quanta of action $I=E/\omega$ in oscillators $2$ and $3$ combine in pairs to make a single quantum in oscillator $1$." + 4., 4. + In the special case that all of the energy. is initially in oscillator 1. the energies of oscillators 2 and 3 grow exponentially at growth rate 2s. where s is the growth rate of their amplitudes.," In the special case that all of the energy is initially in oscillator 1, the energies of oscillators 2 and 3 grow exponentially at growth rate $2s$, where $s$ is the growth rate of their amplitudes." + The maximum growth rate is achieved when Aw=0: Of course growth slows once a significant fraction of the total energy resides in oscillators 2 and 3., The maximum growth rate is achieved when $\Delta\omega=0$: Of course growth slows once a significant fraction of the total energy resides in oscillators 2 and 3. +" HE resonance is not exact. then the growth rate is and there is no growth at all where Aw>33,4ax-"," If resonance is not exact, then the growth rate is and there is no growth at all where $|\Delta\omega|\ge 2 s_{\rm max}$." + 5., 5. + Finally. if dissipation is present so that the free decay rate of the amplitudes of oscillators2 and 3 is η. then formula (49)) holds with suas replaced by sj1.," Finally, if dissipation is present so that the free decay rate of the amplitudes of oscillators2 and 3 is $\eta$, then formula \ref{genrate}) ) holds with $s_{\max}$ replaced by $s_{\max}-\eta$." + Finding the parametric growth rate clue to a large-scale bending mode reduces therefore to the evaluation of thecoupling parameter E given by equation (43)) in terms of the linear eigenfunetions and. eigenfrequencies Εάνων].," Finding the parametric growth rate due to a large-scale bending mode reduces therefore to the evaluation of thecoupling parameter $\Gamma$ given by equation \ref{coupling}) ) in terms of the linear eigenfunctions and eigenfrequencies $\{(\hxi_\alpha,\omega_\alpha)\}$." + In a local approximation. the background density p depends only upon z. so the Gros) dependences are separable.," In a local approximation, the background density $\bar\rho$ depends only upon $\bar z$, so the $(\bar x,\bar z)$ dependences are separable." + Lereafter we omit the overbar from quantities of the basic state except where needed for clarity., Hereafter we omit the overbar from quantities of the basic state except where needed for clarity. + Thus the horizontal dependence of the eigenfunction is expe)., Thus the horizontal dependence of the eigenfunction is $\exp(ik_\alpha x)$. + To obtain a non-zero result for the coupling (43)). we must have 1n most cases of interest. node | is a large-scale bending mode with ky«41.+. and modes 2and 3 have wavelengths ZO2xdH.so to an adequate approximation. ko=hy>Ay. and we shall write & for Ae.," To obtain a non-zero result for the coupling \ref{coupling}) ), we must have In most cases of interest, mode 1 is a large-scale bending mode with $k_1\ll H^{-1}$, and modes 2and 3 have wavelengths $\lta 2\pi H$, so to an adequate approximation, $k_2\approx -k_3\gg k_1$, and we shall write $k$ for $k_2$." +" In the limit A4,=0. assuming that 5=©. the bending mode is (cL."," In the limit $k_1=0$, assuming that $\kappa=\Omega$, the bending mode is (cf." + 83) where 5 is the vertical shear of the mode as defined by equation (18))., 3) where $S$ is the vertical shear of the mode as defined by equation \ref{vxbend}) ). +" Comparing equations (51)) and (38)). one sees that the coupling is dominated by terms involving (OE,yy. Le. by the vertical strain due to the bending mocle."," Comparing equations \ref{bend}) ) and \ref{U3}) ), one sees that the coupling is dominated by terms involving $(\pd_z\hat\xi_x)_1$, i.e. by the vertical strain due to the bending mode." + Retaiming only the leacling order ternis. where X—[dp(s) is the surface density.," Retaining only the leading order terms, where $\Sigma\equiv\int {\rm d}z\,\bar\rho(z)$ is the surface density." + Whereas the eigenfunction (51)) of the bending wave is independent of the vertical structure of the disc in the lone-wavelength limit. the eigenfunctions of the short-wavelength daughter modes 2 and 3 are not.," Whereas the eigenfunction \ref{bend}) ) of the bending wave is independent of the vertical structure of the disc in the long-wavelength limit, the eigenfunctions of the short-wavelength daughter modes 2 and 3 are not." + These are described in ?2.., These are described in \ref{LINTHEORY}. + We are now in a position to calculate the coupling (52))., We are now in a position to calculate the coupling \ref{cupapprox}) ). +" Note that modes 2 and 3 must have dillerent values of n: uncer the rellection zl.l VÉ, has the parity (..)"". whereas 0,E. has the parity (—)+ "," Note that modes 2 and 3 must have different values of $n$: under the reflection $z\to-z$, $\diver\hxi_n$ has the parity $(-)^n$, whereas $\pd_x\hat\xi_z$ has the parity $(-)^{n-1}$ ." +'Pherefore Ez0 only if neny is odd., Therefore $\Gamma\ne0$ only if $n_2-n_3$ is odd. + Εις is probably true for any vertical structure svnunetric about the mid-plane. if counts vertical nodes.," This is probably true for any vertical structure symmetric about the mid-plane, if $n$ counts vertical nodes." + For the isothermal gas. the properties of the Llerniite polynomials are such that Ez0 requires [naNo=1.," For the isothermal gas, the properties of the Hermite polynomials are such that $\Gamma\ne0$ requires $|n_3-n_2|=1$." + We must also remember to change the sign of & between the two modes. because &=heο ," We must also remember to change the sign of $k$ between the two modes, because $k\equiv +k_2\approx -k_3$ ." +Finally. it turns out that the horizontal phase of modes 3 must dilfer by 90° (a factor i in our complex notation) in order to ect the maximum coupling.," Finally, it turns out that the horizontal phase of modes 3 must differ by $90^\circ$ (a factor ${\rm i}$ in our complex notation) in order to get the maximum coupling." +" Taking &=O. we find llere zy and oy4 are implicit functions of & and n through equation. (9)) and the resonance condition ey|wyLX ο, "," Taking $\kappa=\Omega$, we find Here $\omega_n$ and $\omega_{n-1}$ are implicit functions of $k$ and $n$ through equation \ref{dispersion}) ) and the resonance condition $\omega_n+\omega_{n-1}\approx\Omega$ ." +"For comparison with results obtained in δεον, we consider the limit ]t is easy to see from (9)) that this requires 1.and then we obtain ‘Taking into account that the total energv of the harmonic oscillation (40)) is twice its mean kinetic energy. we have £j=£€7]9[2,,./2. where |giluas=[S/O] is the dimensionless semi-amplitude of the bending mode."," For comparison with results obtained in \ref{FLOQUET}, we consider the limit It is easy to see from \ref{dispersion}) ) that this requires $kH/\sqrt{3n}\to 1$ ,and then we obtain Taking into account that the total energy of the harmonic oscillation \ref{harmonic}) ) is twice its mean kinetic energy, we have $E_1=\Omega^2 |q_1|_{\max}^2/2$, where $|q_1|_{\max}=|S/\Omega|$ is the dimensionless semi-amplitude of the bending mode." + Theerowth rate (48)) reduces to In particular. for PosPx and uw»=ws 4O Saas= 3/39/32.," Thegrowth rate \ref{maxrate}) ) reduces to In particular, for $\Gamma\to\Gamma_\infty$ and $\omega_2=\omega_3=\half\Omega$ , $s_{\max}=3\sqrt{3}S/32$ ." + This is exactly half the erowth rate calculated in 8??.., This is exactly half the growth rate calculated in \ref{FLOQUET}. . + Phe explanation appears to be that each daughter mode with nl and Áz3n can participatein two parametric couplings: one with mode (n.αν&) and the other with (n|ανA).," The explanation appears to be that each daughter mode with $n\gg 1$ and $k\approx \sqrt{3n}$ can participatein two parametric couplings: one with mode $(n-1,-k)$ and the other with $(n+1,-k)$." + At sulliciently large η. both of the resonance conditions e|atip7CQ can be satisfied with nearly. equalaccuracy.," At sufficiently large $n$ , both of the resonance conditions $\omega_{n,k}+\omega_{n\pm + 1,-k}\approx\Omega$ can be satisfied with nearly equalaccuracy." + As a result. the growth rate of mode (n.k) is doubled.," As a result, the growth rate of mode $(n,k)$ is doubled." + /2307: 10” —1 Z2 NGC 1151 was observed by with ACIS-S (Carmire et al., $^{\circ}$ $10\arcsec$ $\sim$ $\gtrsim$ NGC 4151 was observed by with ACIS-S (Garmire et al. + 2000) in 1/8 sub-urav mode during March 27-29. 2008.," 2000) in 1/8 sub-array mode during March 27-29, 2008." + The nucleus was placed near the ainipoiut on the $3 chip., The nucleus was placed near the aimpoint on the S3 chip. + The data were reprocessed aud analyzed following the standard using CTAO (Version L2) aud CALDD (Version 1.2.0)., The data were reprocessed and analyzed following the standard using CIAO (Version 4.2) and CALDB (Version 4.2.0). + After removing brief times of high background couut rates. the cleaned data have total good exposure times of 116 ks and 63 ks. in ObsID 9217 and ObsID 9218 respectively.," After removing brief times of high background count rates, the cleaned data have total good exposure times of 116 ks and 63 ks, in ObsID 9217 and ObsID 9218 respectively." + The two ACTS observations of NCC 1151. were then merged to create a single eveut file., The two ACIS observations of NGC 4151 were then merged to create a single event file. + The ACTS readout streaks along P.À.— 171/35 1 were removed with CIAO toolacisreadcorr., The ACIS readout streaks along P.A.= $^{\circ}$ $^{\circ}$ were removed with CIAO tool. +. Point source detection was cone witli aud 21 sources were removed from the tages., Point source detection was done with and 24 sources were removed from the images. + We extracted the soft-baud (0.3.1 keV) image and applied adaptive smootling using CTAO toolcsimnooth. with a ΠΙΕΙ significance 30.," We extracted the soft-band (0.3–1 keV) image and applied adaptive smoothing using CIAO tool, with a minimum significance $\sigma$." + The sale smoothing kernel was applied to the exposure map. which was then divided to get the exposure corrected uae.," The same smoothing kernel was applied to the exposure map, which was then divided to get the exposure corrected image." + Figure laa shows the resulting soft N-ray nuage (32. 12 kpe ona side).," Figure \ref{fig1}a a shows the resulting soft X-ray image $3\arcmin\times 3\arcmin$, $\sim$ 12 kpc on a side)." + Note that the non-detection of X-ray cluission towards the northerunmost and southernmnost part of the nuage is artificial. because this area is out of the ACIS-S field of view (FOV) for our observation (Figure laa).," Note that the non-detection of X-ray emission towards the northernmost and southernmost part of the image is artificial, because this area is out of the ACIS-S field of view (FOV) for our observation (Figure \ref{fig1}a a)." + Figure Lob presents a composite inage of the same region in NGC 1151. consistiug of soft X-ray (0.3.1 keV). exposure corrected ACTS image (blue). with the IIT A21 cii map (red) aud a coutinuuna-subtracted Ho nage 2001)..The kpe-scale ITE distribution appears as a vine with brightest cussion im the," Figure \ref{fig1}b b presents a composite image of the same region in NGC 4151, consisting of soft X-ray (0.3–1 keV), exposure corrected ACIS image (blue), with the HI $\lambda$ 21 cm map (red) and a continuum-subtracted $\alpha$ image .The kpc-scale HI distribution appears as a ring with brightest emission in the" +modulus we derive is also consistent with other recent determinations based ou the TROB (Tikhonovetal.2005:Butler2001) if our reddening valueis used in these studies: however. our prescut determination las succeeded. in reducing the internal errors of the result by a factor ~3.,"modulus we derive is also consistent with other recent determinations based on the TRGB \citep{2005A&A...431..127T,2004AJ....127.1472B} if our reddening value is used in these studies; however, our present determination has succeeded in reducing the internal errors of the result by a factor $\sim 3$ ." +oof |A.. although the full range in ls large.,"of 4, although the full range in is large." + In the merecr sample. the median iis higher.," In the merger sample, the median is higher." + Our sample is too πα] to be certain that this difference is siguificaut: but. if verified. would sugeest the central star formation declines once the nuclei merece.," Our sample is too small to be certain that this difference is significant; but, if verified, would suggest the central star formation declines once the nuclei merge." + Iu the post mereer phase. wwould then coutiuue to increase up to roughly 8 or 9 bbefore starting to decline.," In the post merger phase, would then continue to increase up to roughly 8 or 9 before starting to decline." + By resolving the recent star formation activity iu ULIRGs over scales of 1-10. Ipc. we learned that star formation is being turued off iun ULIRGs from the outsicde inwards.," By resolving the recent star formation activity in ULIRGs over scales of 1-10 kpc, we learned that star formation is being turned off in ULIRGs from the outside inwards." + Specifically. we measure ai increase m wwith increasing radius aud argue that the only reasonable interpretation is an increasing fraction of Type A stars (relative to earlier types).," Specifically, we measure an increase in with increasing radius and argue that the only reasonable interpretation is an increasing fraction of Type A stars (relative to earlier types)." + We go oue step tuther here aud interpret the reduced star formation rate as direct evidence for eas depletion., We go one step further here and interpret the reduced star formation rate as direct evidence for gas depletion. + Above a hreshold density of approximately ~LOM.pe7. the star formation intensity enrpirieallv scales non-linearlv with the eas surface deusitv. XsggX ph where yr is he surface density of eas (22)..," Above a threshold density of approximately $\sim10~{\rm M_{\odot}~pc^{-2}}$, the star formation intensity empirically scales non-linearly with the gas surface density, $\Sigma_{SFR} \propto \mu^{1.4}$ , where $\mu$ is the surface density of gas \citep{martin01,kennicutt98}." + Tf star formation were the onary mcchanisin removing the eas. then the gas would )6 consunied more quickly in the highest deusity regions. reaSEROXnUl ie the nuce," If star formation were the primary mechanism removing the gas, then the gas would be consumed more quickly in the highest density regions, $\tau \sim \mu / SFR \propto \mu^{-0.4}$, i.e. the nuclei." + Star formation alone oxoduces a eradieut oppositely sloped compared to the one we neasured., Star formation alone produces a gradient oppositely sloped compared to the one we measured. + Our result therefore provides direct evidence that another mechanisui moves gas out of the outer disk., Our result therefore provides direct evidence that another mechanism moves gas out of the outer disk. + It is natural to ask whether mergerinduced inflows are that 1nechliiuiszin., It is natural to ask whether merger-induced inflows are that mechanism. + Suuulatious of eas-rich. galaxy ealaxv niereers predict an increase iu star formation durius the first passage and a second. strouger starburst at the time of actual mereer (277)j..," Simulations of gas-rich, galaxy – galaxy mergers predict an increase in star formation during the first passage and a second, stronger starburst at the time of actual merger \citep{mihos94,lotz08, hopkins09}." + The torques imparted on the eas during the niergeer cause the eas to flow inva. robbing the outer regions of fuel to generate stars.," The torques imparted on the gas during the merger cause the gas to flow inward, robbing the outer regions of fuel to generate stars." + The iufall is a well known result of the separation of stars froin gas in the merger remmnant: a consequence of the different collisional properties of stars and gas (2).., The infall is a well known result of the separation of stars from gas in the merger remnant; a consequence of the different collisional properties of stars and gas \citep{hopkins09}. + This separation allows the stars to impart a torque on the eas and cause iufall., This separation allows the stars to impart a torque on the gas and cause infall. + Models imply the correlation between the dynamical age of the mereer aud the age of the starburst population (7) but have vet to predict how mich of the star formation occurs in the ceutral kpc.," Models imply the correlation between the dynamical age of the merger and the age of the starburst population \citep{lotz08} + but have yet to predict how much of the star formation occurs in the central kpc." + A kev aspect of merger models should be to trace gas nueration aud the location of starformation activity throughout the merger., A key aspect of merger models should be to trace gas migration and the location of starformation activity throughout the merger. +Stellar bars are conmunuon amone spirals. and are believed. to have au important role in the evolution of their host galaxies.,"Stellar bars are common among spirals, and are believed to have an important role in the evolution of their host galaxies." + Several studies presented ideas that bars channel gas from the outer disk iuto the nuclear reeion (IIuutlev1975:Itnapenctal.1995:Tint&2005:Shethetal.Elincercen 2009).. and that they redistribute angular momentum of the barvouic and dark matter components of disk galaxies (Lyxudoeu-Sellwood2000:Athanassoula2003:Aeuerrietal. 2009).," Several studies presented ideas that bars channel gas from the outer disk into the nuclear region \citep{huntley78,knapen95,hunt99,saka99,jogee99,jogee05,sheth05,elme09}, and that they redistribute angular momentum of the baryonic and dark matter components of disk galaxies \citep{lyndenbell79,sellwood81,albada81,combes85, +weinberg85,dns00,ath2003,agu2009}." +. Bars are also thought to have a significant role in fueling of active galactic nuclei (Shlosimanetal.1989:Toal.1997). aud iu foriuug bulees or pseudo-bulees).," Bars are also thought to have a significant role in fueling of active galactic nuclei \citep{schlos89,ho97} + and in forming bulges or pseudo-bulges." +. Some simulations showed that bars can be destived by a large central iiass conceitration. (Robertseal.Athanassoulaetal. 2005).," Some simulations showed that bars can be destroyed by a large central mass concentration \citep{roberts79,norman96,snm99,ath2005}." +. Tus result iucdicates two possibilities., This result indicates two possibilities. + First. it is posside that currently barred spirals had a bar in t1C ost (I&orieudynicutt200 ..," First, it is possible that currently non-barred spirals had a bar in the past \citep{knk2004}." + Second. bars may be recurrent (Bournaud 2006).," Second, bars may be recurrent \citep{bournaud2002,berentzen2004,gad06}." +. However. there are cO1LHictiug results that JALS are dviuuaulcally robust strucures. requircing large πάν» concentrations to dissolve bars (Dehattista&Sellwood2000:Shen&Selhwood.200:Dehattistaotal. 2006).," However, there are conflicting results that bars are dynamically robust structures, requireing large mass concentrations to dissolve bars \citep{dns00,shen2004,deb+06}." +. Therefore if remaius an open question whlv some spirals have a har structure. while ohe438 do not.," Therefore it remains an open question why some spirals have a bar structure, while others do not." + Most previous studies trieL to explain the formation and evolution of bars throug1 dlufernal secular evolution oulv., Most previous studies tried to explain the formation and evolution of bars through internal secular evolution only. + To get a better understanding of bars. we need to consider not ouly iuterual but also external iuflueuce ou their evolution.," To get a better understanding of bars, we need to consider not only internal but also external influence on their evolution." + Thompson(1981) showed that the fraction of barred galaxies is siguificantlv larger in the core of the Coma cluster than iu the outer part of the, \citet{thompson81} showed that the fraction of barred galaxies is significantly larger in the core of the Coma cluster than in the outer part of the +broad-R F606WV exposure to obtain color information for anv variables identified.,broad-R F606W exposure to obtain color information for any variables identified. + The four FSIIW pictures were dithered by steps of 0.5 ΑΕpixels aligned with the CCD axes. which in the f-baud allows a Nyquist-siuupled interlace image to be constructed for the WEC CCDs (Lauer 1999a): the PCL CCD is already critically-suupled at FSIIW. Tn passing. the sharper PSF at F6OGW would require a 3<3 dither pattern to lift the aliasing.," The four F814W pictures were dithered by steps of 0.5 WFC-pixels aligned with the CCD axes, which in the $I$ -band allows a Nyquist-sampled interlace image to be constructed for the WFC CCDs (Lauer 1999a); the PC1 CCD is already critically-sampled at F814W. In passing, the sharper PSF at F606W would require a $3\times3$ dither pattern to lift the aliasing." + This schema establishes the FaliW frames as he primary search imagery. relegating the F606W to xovidiug ausilary color information and verification of he events.," This schema establishes the F814W frames as the primary search imagery, relegating the F606W to providing auxiliary color information and verification of the events." + To obtain equal quality in F606W (or another που filter) would be prohibitive: miücroleused stars are xpected to be red. requiring more than a double allocation orbits.," To obtain equal quality in F606W (or another bluer filter) would be prohibitive; microlensed stars are expected to be red, requiring more than a double allocation of orbits." + The alternative of splitting a single orbit equally )etwoeen two filters would reduce the depth iu auv single filter. and would make dithering prohibitively expensive.," The alternative of splitting a single orbit equally between two filters would reduce the depth in any single filter, and would make dithering prohibitively expensive." + While the dithering scheme that we did adopt does iuclude Hi overhead that mieht otherwise be used to collect rotons. this exposure-tine penalty is more than offset w the resolution gain returned by Nyquist sampling.," While the dithering scheme that we did adopt does include an overhead that might otherwise be used to collect photons, this exposure-time penalty is more than offset by the resolution gain returned by Nyquist sampling." +" A simpler strategy of obtaining single. or CR-split ideutical exposures, in cach filter within an orbit would reduce he seusitivitv to detecting faint poiut-sources agaiust he ALS? envelope."," A simpler strategy of obtaining single, or CR-split identical exposures, in each filter within an orbit would reduce the sensitivity to detecting faint point-sources against the M87 envelope." + The uucleus of M87 was centered iu PCL., The nucleus of M87 was centered in PC1. + The pointing aud orientation were ποια fixed over he full iuterval of the search., The pointing and orientation were held fixed over the full interval of the search. + The orientation showed no sjenificaut variations over the program. while the pointing repeated to better than a single WEC pixel: as we discuss low. this was actually less optimal than using a few PSFsavortl of pointing dither between the caily visits.," The orientation showed no significant variations over the program, while the pointing repeated to better than a single WFC pixel; as we discuss below, this was actually less optimal than using a few PSFs-worth of pointing dither between the daily visits." + The initial image reduction goal was to generate a Nyquist-saupled Fst(WV super-image for cach WEC CCD from the dither sequence for cach daily visit., The initial image reduction goal was to generate a Nyquist-sampled F814W super-image for each WFC CCD from the dither sequence for each daily visit. + This task included repair of charge traps. hot pixels. aud cosmic rav events prior to the actual reconstruction of the super mage.," This task included repair of charge traps, hot pixels, and cosmic ray events prior to the actual reconstruction of the super image." + Fortunately. the dithers were executed with sufficient accuracy that this later step could be simply doue by interlacing the four images within the dither sequence.," Fortunately, the dithers were executed with sufficient accuracy that this later step could be simply done by interlacing the four images within the dither sequence." + Each original image contributed one pixel to cach a 2«2 pixel box in the super-image: the scale of the super-dniase is twice as fine as that of the source images., Each original image contributed one pixel to each a $2\times2$ pixel box in the super-image; the scale of the super-image is twice as fine as that of the source images. + Lauer (1999a) presents an aleorithim for constructing this iuage had the dithers not been exact 0.5 pixel steps. but iu practice this method was not required.," Lauer (1999a) presents an algorithm for constructing this image had the dithers not been exact 0.5 pixel steps, but in practice this method was not required." + Since the images in cach dither set had slieltly different poiutiues. the standard method of removing cosnüc rav events (CRE) by comparing two exposures with identical positioning aud inteeration times could potentially iuisideutifv poiut sources moving with respect to the CCD pixels as cosmic rav eveuts," Since the images in each dither set had slightly different pointings, the standard method of removing cosmic ray events (CRE) by comparing two exposures with identical positioning and integration times could potentially misidentify point sources moving with respect to the CCD pixels as cosmic ray events." + For the WEC nuages in the present data set. an initial interlace image was constructed. and the intensity of each pixel was compared to the average of its neighbors.," For the WFC images in the present data set, an initial interlace image was constructed, and the intensity of each pixel was compared to the average of its neighbors." + Pixels that were discrepant at the 76 level (where 6 was estinated frou a ΑΝΕΤΟΣ noiseanodel. rather than from the deviation about the average}.end that had a value in excess of 1.6< that of the average (to avoid flageingao the peaks of poit sources centered ou one pixcl iu the sequence). were flageedao as CRE.," Pixels that were discrepant at the $7\sigma$ level (where $\sigma$ was estimated from a WFPC2 noise-model, rather than from the deviation about the average), that had a value in excess of $1.6\times$ that of the average (to avoid flagging the peaks of point sources centered on one pixel in the sequence), were flagged as CRE." + Pixels neighboring anv eiven lit in the individual exposures were considered to be part of the same eveut if they deviated from the interlaced nuage ucighboring axel average by 2.50. After the initial round of CRE identification. pixels affected by the hits were deleted frou he average neighboring pixel frame. aud additional eveuts were identified in two more rounds of CRE ideutification.," Pixels neighboring any given hit in the individual exposures were considered to be part of the same event if they deviated from the interlaced image neighboring pixel average by $2.5\sigma.$ After the initial round of CRE identification, pixels affected by the hits were deleted from the average neighboring pixel frame, and additional events were identified in two more rounds of CRE identification." + After all CRE were identified. affected pixels were replacec w the average of the remaining unaffected ucighbors im he interlace frame.," After all CRE were identified, affected pixels were replaced by the average of the remaining unaffected neighbors in the interlace frame." + Iu practice this procedure appearec ο work extremely well for removing CRE., In practice this procedure appeared to work extremely well for removing CRE. + Tn the case of the PCL data. as the dither steps were oulv slightly larecr than the PC pixel scale. detection am repair of CRE were casicr.," In the case of the PC1 data, as the dither steps were only slightly larger than the PC pixel scale, detection and repair of CRE were easier." + The nuages in a given dither set were simply compared under the assmuption that the offsets were a sinele pixel in amplitude., The images in a given dither set were simply compared under the assumption that the offsets were a single pixel in amplitude. + The average pixe values used to replace the CRE in this regard should be )tter estimates than those used in the WEC dither sets., The average pixel values used to replace the CRE in this regard should be better estimates than those used in the WFC dither sets. + After the CRE were repaired. the individual PCT images in the dither set were shifted to a precise common orien x siuc-fuuction interpolation CCastleman 1995) aud combined.," After the CRE were repaired, the individual PC1 images in the dither set were shifted to a precise common origin by sinc-function interpolation Castleman 1995) and combined." + During au initial reduction of the complete dataset. the xiehter hot pixels were often ideutiied as CRE.," During an initial reduction of the complete dataset, the brighter hot pixels were often identified as CRE." + Tine tot pixels were ideutified as deviaut pixels that appeared at a coustant CCD location over the duration of the observations., True hot pixels were identified as deviant pixels that appeared at a constant CCD location over the duration of the observations. + Unfortunately. large population of low-evel hot pixels escaped initial detection: au additional »pulatiou of hot pixels consisted of those that newly arose Within the moutlh-loug duration of the program.," Unfortunately, a large population of low-level hot pixels escaped initial detection; an additional population of hot pixels consisted of those that newly arose within the month-long duration of the program." + Most of these could be ideunti&ed by visual inspection of the interlaced super-mages., Most of these could be identified by visual inspection of the interlaced super-images. + Residual hot pixels in the iuterlaced tage for auv eiven dav made a readilyidentifiable artifact consisting of a 2« block of elevated sub-pixels., Residual hot pixels in the interlaced image for any given day made a readily-identifiable artifact consisting of a $2\times2$ block of elevated sub-pixels. + When one day's interlaced inage was blinked against those surrounding it in time. the small dav-to-day pointing variations additionally helped to isolate hot yincls from compact astronomical sources.," When one day's interlaced image was blinked against those surrounding it in time, the small day-to-day pointing variations additionally helped to isolate hot pixels from compact astronomical sources." + The program jid actually specified pointing varving by 07705 from day to day. thus the simall pointing differences were fortuitous for identifving hot pixels.," The program had actually specified pointing varying by $0\farcs05$ from day to day, thus the small pointing differences were fortuitous for identifying hot pixels." + The pointing errors were typically ess than 07005., The pointing errors were typically less than $0\farcs005$. + Random variations in the lowest-level tot pixels. however. made them difficult to distinguish roni true poiut-sources with this small amount of poiting jitter: residual hot-pixels are the most naportaut source of false positive detectious of variable sources.," Random variations in the lowest-level hot pixels, however, made them difficult to distinguish from true point-sources with this small amount of pointing jitter; residual hot-pixels are the most important source of false positive detections of variable sources." + A more optimal program design would iuclude a somewhat larger vointing dither between repeat visits to allow for complete decoherence between source aud detector structure., A more optimal program design would include a somewhat larger pointing dither between repeat visits to allow for complete decoherence between source and detector structure. + Detection of variables i MS? is discussed iu detail iu the next section. but briefly variables are ideutified bv exanunius the temporal run of residual iuteusitv values at anv pixel location after the WFC interlaced images aud PCL stacked tages have been registered to a conmunuon origin. have had the average intensity value subtracted. and were processed with au optimal filter.," Detection of variables in M87 is discussed in detail in the next section, but briefly variables are identified by examining the temporal run of residual intensity values at any pixel location after the WFC interlaced images and PC1 stacked images have been registered to a common origin, have had the average intensity value subtracted, and were processed with an optimal filter." + As noted above the pointing varied sliehtly frou day to dav., As noted above the pointing varied slightly from day to day. + Fortunately. the rich M87. elobular cluster svstem provided ample astrometric references.," Fortunately, the rich M87 globular cluster system provided ample astrometric references." + Centroids of a few dozen clusters iu each CCD field allowed precise angular, Centroids of a few dozen clusters in each CCD field allowed precise angular +In section 3. we discussed the difficulties in deducing robust 7] σ uncertainty estimates for the fluxes and polarizations of core and jet features observed in VLBI jets.,In section \ref{s:tech} we discussed the difficulties in deducing robust “1 $\sigma$ ” uncertainty estimates for the fluxes and polarizations of core and jet features observed in VLBI jets. + Lack of good a-priori uncertainty estimates led us to correlate observed fluctuations about the linear trends between our two observing bands (15 and 22 GHz). as described in§3.2.. to assess the reality of these fluctuations.," Lack of good a-priori uncertainty estimates led us to correlate observed fluctuations about the linear trends between our two observing bands (15 and 22 GHz), as described in, to assess the reality of these fluctuations." + In this appendix. we take the methods in a step further to obtain empirical estimates of the uncertainties in measuring VLBI component properties.," In this appendix, we take the methods in a step further to obtain empirical estimates of the uncertainties in measuring VLBI component properties." + Here we are interested in the un-correlated part of the fluctuations discussed in$3., Here we are interested in the un-correlated part of the fluctuations discussed in. +2... Note that these expressions are very similar to equation 2. with + replaced by (1—7). so here O is theui-correlated part of the variance of the deviations at each frequency.," Note that these expressions are very similar to equation \ref{e:corrvar} with $r$ replaced by $(1-r)$, so here $\Omega$ is the part of the variance of the deviations at each frequency." + For negative values of r. we set r=0 for the purposes of this calculation.," For negative values of $r$, we set $r=0$ for the purposes of this calculation." + The of O gives the standard deviation of the un-correlated fluctuations. and we have computed this for each quantity and frequency: ols=Oris. ete.," The square-root of $\Omega$ gives the standard deviation of the un-correlated fluctuations, and we have computed this for each quantity and frequency: $\sigma I_{15} = \sqrt{\Omega_{I\,15}}$, etc." + We used the second Monte Carlo simulation described in to place rough uncertainties on these c values., We used the second Monte Carlo simulation described in to place rough uncertainties on these $\sigma$ values. + Table 8 presents these numbers for each core and Jet feature appearing 1n our analysis., Table \ref{t:err} presents these numbers for each core and jet feature appearing in our analysis. + These un-correlated fluctuations consist of (1) real spectral changes in core and jet feature properties. and (2) any measurement. calibration.aad model-fitting errors that are not systematic between epoch or frequency.," These un-correlated fluctuations consist of (1) real spectral changes in core and jet feature properties, and (2) any measurement, calibration, model-fitting errors that are not systematic between epoch or frequency." + Because we have no way of separating out the real spectral changes. we take these estimates of the standard deviation of the un-correlated fluctuations as conservative estimates on the total (non-systematic) uncertainty in measuring VLBI flux and polarization of core and Jet features in a single epoch.," Because we have no way of separating out the real spectral changes, we take these estimates of the standard deviation of the un-correlated fluctuations as conservative estimates on the total (non-systematic) uncertainty in measuring VLBI flux and polarization of core and jet features in a single epoch." + Figures 28--30 plot these uncertainty estimates against projected radius for each quantity at both frequencies., Figures \ref{f:i_err}- \ref{f:chi_err} plot these uncertainty estimates against projected radius for each quantity at both frequencies. + For 7 at 15 GHz most features have an estimated uncertainty of less than 5% in a single epoch. with several particularly good cases of 2-—3% and a few poorer cases of ~10%.," For $I$ at 15 GHz most features have an estimated uncertainty of less than $5$ in a single epoch, with several particularly good cases of $2-3$ and a few poorer cases of $\sim 10$." +.. For / at 22 GHz. 5% or better is the case for some of the more extended core regions (where nearby jet components have been summed into the core flux). but 5—10% is more typical for jet features with a couple cases approaching 20%.," For $I$ at 22 GHz, $5$ or better is the case for some of the more extended core regions (where nearby jet components have been summed into the core flux), but $5-10$ is more typical for jet features with a couple cases approaching $20$." +. For fractional polarization. 0.5% is typical at 15 GHz. and 0.5—1.0% 1s typical at 22 GHz.," For fractional polarization, $0.5$ is typical at 15 GHz, and $0.5-1.0$ is typical at 22 GHz." + For polarization angle. uncertainties <5° are typical at both frequencies with best case values <2 and worse case values up to ~10”.," For polarization angle, uncertainties $\leq 5^\circ$ are typical at both frequencies with best case values $\leq 2^\circ$ and worse case values up to $\sim 10^\circ$ ." +ine [uxes for the Smith Cloud. we modelled the line ratio ependence with velocity in terms of two components: a tevnolds laver contribution peaking at. |S wwith a declining red wing. and a contribution from the IIVC peaking at | ((Smith D) ancl | (Smith HD).,"line fluxes for the Smith Cloud, we modelled the line ratio dependence with velocity in terms of two components: a Reynolds layer contribution peaking at $+$ with a declining red wing, and a contribution from the HVC peaking at $+$ (Smith I) and $+$ (Smith II)." +" For the Smith | field.we derive £,((la)) = (0.2411) and &,,((NIL) = 0.1410)."," For the Smith I field,we derive ) $=$ (0.24R) and ([NII]) $=$ (0.14R)." +" For the Smith. IE field. we derive ια) = (0.304. and. £,,((NII]) = (0.1710."," For the Smith II field, we derive ) $=$ (0.30R) and ([NII]) $=$ (0.17R)." + While the shot noise uncertainty is approximately10'4.. the formal errors (25. 30543) are dominated by the systematics of our model separation.," While the shot noise uncertainty is approximately, the formal errors $25-30$ ) are dominated by the systematics of our model separation." + Phe Revnolcls laver flux at both positions is 5.5O.1cem. (1.311)., The Reynolds layer flux at both positions is $\pm$ (1.8R). + In Fig. 9..," In Fig. \ref{o3}," + we show the observed spectrum for the Smith Η region in the vicinity of ((incdicated by an arrow)., we show the observed spectrum for the Smith II region in the vicinity of (indicated by an arrow). + While we have managed. only a moderately deep upper limit at ((O.12R at. 30) this provides an important constraint on photoionisation mocels.," While we have managed only a moderately deep upper limit at (0.12R at $\sigma$ ), this provides an important constraint on photoionisation models." + In this section. we argue that the {Hux from the Smith Cloud arises from photoionisation by OB stars clispersed over the Galactic disk.," In this section, we argue that the flux from the Smith Cloud arises from photoionisation by OB stars dispersed over the Galactic disk." + That the line ratio peaks close to the LSR. velocity of the ppeak is strongly suggestive of photoionisation rather than shocks., That the line ratio peaks close to the LSR velocity of the peak is strongly suggestive of photoionisation rather than shocks. + Therefore. the enhanced," Therefore, the enhanced" + Therefore. the enhanced:," Therefore, the enhanced" +Newtonian breakout. where: Therefore a significant flattening of the Inuinosityv evolution is expected at /yay.,"Newtonian breakout, where: Therefore a significant flattening of the luminosity evolution is expected at $t_{NW}$." + Frou (his point the luminosity decay is steady until recombination and/or racioactivily start plaving a role., From this point the luminosity decay is steady until recombination and/or radioactivity start playing a role. +" The initial volume of the shell is proportional to its initial width (all shells starts at £2,). d;x1H."," The initial volume of the shell is proportional to its initial width (all shells starts at $R_*$ ), $\dhat_i \propto t^{0.44}$." + The observed temperature evolves as: This slope is not verv different than (hat of the relativistic phase., The observed temperature evolves as: This slope is not very different than that of the relativistic phase. + Therefore there is no significant feature in (he temperature evolution al faye., Therefore there is no significant feature in the temperature evolution at $t_{NW}$. + Only al /a~LOἐν the temperature starts dropping rapidly until the shell gains thermal equilibrium., Only at $t_{obs} \sim 10~t_{NW}$ the temperature starts dropping rapidly until the shell gains thermal equilibrium. + We use the model developed in (he previous section to calculate the signal expected from known and hypothesized explosions., We use the model developed in the previous section to calculate the signal expected from known and hypothesized explosions. + There is a large number of explosions. such as various SNe types. in which the bulk of (he mass is moving in Newtonian velocities but (he shock accelerates a minute amount of mass (o a relativistic breakout.," There is a large number of explosions, such as various SNe types, in which the bulk of the mass is moving in Newtonian velocities but the shock accelerates a minute amount of mass to a relativistic breakout." +" Such explosions are often observed mostly in the optical. where the kinetic energy. £. (hat is carried by the bulk of the ejected mass. MM,;. can be measured."," Such explosions are often observed mostly in the optical, where the kinetic energy, $E$, that is carried by the bulk of the ejected mass, $M_{ej}$, can be measured." + Therefore we first provide the characteristic properties of the breakout and following emission ofsuch explosions as a function of E. AL; and F..," Therefore we first provide the characteristic properties of the breakout and following emission ofsuch explosions as a function of $E$, $M_{ej}$ and $R_*$." + Then we use these results to discuss the predicted signals from various explosions., Then we use these results to discuss the predicted signals from various explosions. +" Given E. .M,; and 2, the initial Lorentz [actor of the shell is determined by following the shock acceleration [rom (he Newtonian phase 049)). to the relativistic phase (5,3,xp 73): where E54=E/(10*erg)."," Given $E$, $M_{ej}$ and $R_*$ the initial Lorentz factor of the shell is determined by following the shock acceleration from the Newtonian phase $\g_s \beta_s \propto \rho^{-0.19}$ ), to the relativistic phase $\g_s \beta_s \propto \rho^{-0.23}$ ): where $\E=E/(10^{52} {\rm~erg})$." +" The numerical coefficient is taken to fit the numerical results ol Tan.Matzner&Melxee""n (2001).. which simulate the transition of the shock from Newtonian"," The numerical coefficient is taken to fit the numerical results of \cite{Tan01}, , which simulate the transition of the shock from Newtonian" +hrough the holes of the cloud.,through the holes of the cloud. + The idea of cloud clearing model was motivated by the difficulty oL the cloudy mocels by Marleyetal.(2002) to explain the observed color-iiaguitude cdiagrain. out we have W.io0wu that the color-maguituce diagram cau be accounted for by our CCA without iutroduciiο such a hypothesis as break-up of the cloud (Tsuji&Nakajima2003)..," The idea of cloud clearing model was motivated by the difficulty of the cloudy models by \citet{mar02} to explain the observed color-magnitude diagram, but we have shown that the color-magnitude diagram can be accounted for by our UCM without introducing such a hypothesis as break-up of the cloud \citep{tsu03a}." + As an alternative interpretation. we would like to call attention to the possible formation of he second couvective zoue near the surface of the late L aud early T dwarls.," As an alternative interpretation, we would like to call attention to the possible formation of the second convective zone near the surface of the late L and early T dwarfs." + This secouc convective zone is predicted by the UCMs of Teyz1200—1600 Ix and is formed by the steep temperature eracdient due to the large opacity of the dust cloud itself (Tsuji2002)., This second convective zone is predicted by the UCMs of $T_{\rm eff} \approx 1200 - 1600$ K and is formed by the steep temperature gradient due to the large opacity of the dust cloud itself \citep{tsu02}. +. The lower bouucdary of this couvective zone is [acing the region free of dust but FeH cau be abundant there., The lower boundary of this convective zone is facing the region free of dust but FeH can be abundant there. + Then these FeH molecules will be dredged up by the convection to the upper cooler region aud some FeH molecules will remain super-saturatecd until they are eventually transformed to the coudeusates., Then these FeH molecules will be dredged up by the convection to the upper cooler region and some FeH molecules will remain super-saturated until they are eventually transformed to the condensates. + Iu fact. the second convective zone Is rather thin aud some FeH molecules will survive at the upper boundary of he convective zone.," In fact, the second convective zone is rather thin and some FeH molecules will survive at the upper boundary of the convective zone." + These FeH molecules will constantly be repleuished by the convection aud cau ye observed so loug as tlie secoucd convective zone reaches the region to give observable effect., These FeH molecules will constantly be replenished by the convection and can be observed so long as the second convective zone reaches the region to give observable effect. + Such yossibility of vertical transport of FeH was also noted by Burgasseretal.(2002b). who. however. marked that the [ragility of the FeH boud (dissociation energy. of ouly eeV) will preclude 3.=cho a possibility. even if such a vertical twistug may account for the unexpectedly stroug CO =idamental bands observed in the T dwarf Cl 229B (Noll.Geballe&Marley1997:=al. 1998).," Such a possibility of vertical transport of FeH was also noted by \citet{bur02b} who, however, remarked that the fragility of the FeH bond (dissociation energy of only eV) will preclude such a possibility, even if such a vertical mixing may account for the unexpectedly strong CO fundamental bands observed in the T dwarf Gl 229B \citep{nol97,opp98}." +. Certainly. more detailed quantitaive analysis will required before we reach a defiuite Cclusion.," Certainly, more detailed quantitative analysis will required before we reach a definite conclusion." + The other prominent features are Ix I doblets at 1.1600/1.1773 and at 1.2132/1.2522. qnn. The Is I lines are rather strong in the early an muddle L dwarls. but weaken in the late L dwarls.," The other prominent features are K I doublets at 1.1690/1.1773 and at 1.2432/1.2522 $\mu$ m. The K I lines are rather strong in the early and middle L dwarfs, but weaken in the late L dwarfs." + Alter passingS the minimum at L8. hey are agal1 reinforced iu the early aud middle T dwarfs until iuasked by the strong 1.1 jun wate ‘bands it e late T dwarfs.," After passing the minimum at L8, they are again reinforced in the early and middle T dwarfs until masked by the strong 1.1 $\mu$ m water bands in the late T dwarfs." + These results are quite cousisteut with those reported by Burgassereal.(2002).., These results are quite consistent with those reported by \citet{bur02a}. + The diminishing Ix I liues towards later L dwarls can be iuterpreted as due to the elect of extinc‘ion by» dust which is located in the optically thiu photosphere in L dwarls and shows the maximin at late L dwarfs., The diminishing K I lines towards later L dwarfs can be interpreted as due to the effect of extinction by dust which is located in the optically thin photosphere in L dwarfs and shows the maximum at late L dwarfs. + For this reason. Is I lines show the ια at late L as the waer |odds αἱ 1.1 and 1.1 jun. After the cloud. is buried. below the observable photosphere. Ix lites strenethe1 again despite the uufavorable excitation at lower temperatures uutil beiug iuasked yw rapidly streugtheued water baucls.," For this reason, K I lines show the minimum at late L as the water bands at 1.1 and 1.4 $\mu$ m. After the cloud is buried below the observable photosphere, K I lines strengthen again despite the unfavorable excitation at lower temperatures until being masked by rapidly strengthened water bands." + The feature near 1.11 nin ds icentified as due to Na I doublet 1.1101/1.138 jin with loggf = —0.1856/—0.187 (Wiese.Smith&|iles1969)., The feature near 1.14 $\mu$ m is identified as due to Na I doublet 1.1404/1.138 $\mu$ m with $gf$ = $-$ $-$ 0.487 \citep{wie69}. +. However. the observed feature near 1.1L situ shows asyinmetry with the strouger absor2410 rat thestort wavelenetl side. contracictiug the expectation [rom the e[-values.," However, the observed feature near 1.14 $\mu$ m shows asymmetry with the stronger absorption at the short wavelength side, contradicting the expectation from the gf-values." +" Thus. there shoid je some other contributions such as of H2O aud CH, to the 1.11 jun feature which. however. slOWS the similar pattern as the Ix I lines."," Thus, there should be some other contributions such as of $_2$ O and $_4$ to the 1.14 $\mu$ m feature which, however, shows the similar pattern as the K I lines." + The 1.1 jun bands of water can101 je seen in the Lo να). SDSS22194-00. and tliis is unusually weak for L5. compared with the puisled results for other L5 dwarls (e.g. Geballe et al.," The 1.1 $\mu$ m bands of water cannot be seen in the L5 dwarf, SDSS2249+00, and this is unusually weak for L5, compared with the published results for other L5 dwarfs (e.g. Geballe et al." + 2002. Reicl et al.," 2002, Reid et al." + 2001b)., 2001b). + Also lx I lines just discussed above are also unusually weak for L5 in SDSS2219+00., Also K I lines just discussed above are also unusually weak for L5 in SDSS2249+00. +The distance modulus of WLM derived in (115 paper is not affected bv any significant amount by the choice of the cutoff period adopted in the PL diagrams in Figs.,The distance modulus of WLM derived in this paper is not affected by any significant amount by the choice of the cutoff period adopted in the PL diagrams in Figs. + 4 and 5., 4 and 5. + The zero points in (he WLM PL relations in both J and Ix change by less (ian 0.03 mag if we use a longer period cutoff of log P (days) = 0.7 (leaving the 14 longest-period stus in the sample). or if we use the full sample of 30 Cepheids (excluding the one stronglv. blended. Cepheid cep033).," The zero points in the WLM PL relations in both J and K change by less than 0.03 mag if we use a longer period cutoff of log P (days) = 0.7 (leaving the 14 longest-period stars in the sample), or if we use the full sample of 30 Cepheids (excluding the one strongly blended Cepheid cep038)." + Specifically. retaining the [ull Cepheid sample yields a distance modulus of 24.902 + 0.042 mag. whereas the saniple of the 14 longest-period stars vields 24.947 4 0.042 mag.," Specifically, retaining the full Cepheid sample yields a distance modulus of 24.902 $\pm$ 0.042 mag, whereas the sample of the 14 longest-period stars yields 24.947 $\pm$ 0.042 mag." + Both values agree within their statistical 1 σ errors with our adopted best distance modulus of 24.924 + 0.042 mag., Both values agree within their statistical 1 $\sigma$ errors with our adopted best distance modulus of 24.924 $\pm$ 0.042 mag. + This probably demonstrates (hat our WLM Cepheicl sample is large enough to fill the Cepheid instability strip in the IRD rather homogeneously. ancl (hat there are no overtone Cepheids among the shortest period variables in the sample. a conclusion which is supported by the asymmetric light curve shapes in V of all these variables.," This probably demonstrates that our WLM Cepheid sample is large enough to fill the Cepheid instability strip in the HRD rather homogeneously, and that there are no overtone Cepheids among the shortest period variables in the sample, a conclusion which is supported by the asymmetric light curve shapes in V of all these variables." + We estimate that the combined effect of the different sources which contribute to the svslematic uncertainty of our present mulliwaveleneth Cepheid distance result for WLM eenerate an uncertainty not exceeding + 0.06 mag. or34%.," We estimate that the combined effect of the different sources which contribute to the systematic uncertainty of our present multiwavelength Cepheid distance result for WLM generate an uncertainty not exceeding $\pm$ 0.06 mag, or." +.. These [actors include the accuracy of the photometric zero points. the effect of blending on the Cepheid photometry. (he ellect of errors in the adopted reddening ancl a possible metallicity dependence of the Cepheid PL relation.," These factors include the accuracy of the photometric zero points, the effect of blending on the Cepheid photometry, the effect of errors in the adopted reddening and a possible metallicity dependence of the Cepheid PL relation." + The typical impact of these factors on (he distance result has been discussed quite exhaustively in (he previous papers of (his series., The typical impact of these factors on the distance result has been discussed quite exhaustively in the previous papers of this series. + ere we only want (o stress (hat the zero point of the near-intrarecl photometry flor WLM reported in this paper is probably even more accurate (0.01 mag) than for the other. previously studied (target galaxies of our project. as a consequence of having data and independent photometric calibrations from 6 different photometric nights. which has been an especially fortunate circumstance.," Here we only want to stress that the zero point of the near-infrared photometry for WLM reported in this paper is probably even more accurate (0.01 mag) than for the other, previously studied target galaxies of our project, as a consequence of having data and independent photometric calibrations from 6 different photometric nights, which has been an especially fortunate circumstance." + The impact of blending of the Cepheids on the distance was found to be less than in the case ol NGC 300 (Bresolin et al., The impact of blending of the Cepheids on the distance was found to be less than in the case of NGC 300 (Bresolin et al. + 2005) which is at twice the distance of WLAL which allows us to conclude that its effect in the present case of WLM is certainly not larger than2%... or 0.04 mae. and very likely smaller than (his.," 2005) which is at twice the distance of WLM, which allows us to conclude that its effect in the present case of WLM is certainly not larger than, or 0.04 mag, and very likely smaller than this." + We adopt 0.03 mag for this source of svstematic error., We adopt 0.03 mag for this source of systematic error. + Regarding the effect of reddening. our analvsis and (he results presented in Fig.," Regarding the effect of reddening, our analysis and the results presented in Fig." + 6 and Table 4 convincinglv demonstrate that the total reddening suffered bx the WLM Cepheids has been very accurately determined in this study. and anv residual effect of reddening on our distance result is clearly less (han2%.. or 0.04 mag.," 6 and Table 4 convincingly demonstrate that the total reddening suffered by the WLM Cepheids has been very accurately determined in this study, and any residual effect of reddening on our distance result is clearly less than, or 0.04 mag." + We want to stress again that this elimination of reddening as a very serious source of systematic error in Cepheid distances {ο ealaxies based on optical photometry alone is probably the single most important advantage olfered by our combined optical-infrared. procedure to measure Cepheid distances to galaxies in our project., We want to stress again that this elimination of reddening as a very serious source of systematic error in Cepheid distances to galaxies based on optical photometry alone is probably the single most important advantage offered by our combined optical-infrared procedure to measure Cepheid distances to late-type galaxies in our project. + The influence of metallicity effects on our distance result is harder to estimate. at (he present time.," The influence of metallicity effects on our distance result is harder to estimate, at the present time." + While we have presented evidence that the effect of nelallicity differences on the slope of the PL relation is probably negligible. its effect on the," While we have presented evidence that the effect of metallicity differences on the slope of the PL relation is probably negligible, its effect on the" + ↿∖≺⊲⋜⋯⋜⊔⋅∙∖⇁↓⊳∖↓⋜⋯∠⇂⊳∖⊳∺↓≻⋜↧⊀↓⊔∃⋡∖∖⊽⋖⋅⋖≱∣⋡↥⋜↧↕↓↥∢⋅∠⇂⋜↧↓⋅∢⊾∠⇂⋯⇍⋯⇂↿⋜⊔⋅⋏∙≟∢⋅↿ sample with 10 QSO pairs.,"(Canary Islands, Spain), we obtained a reduced target sample with 10 QSO pairs." + All through this paper. each pair will be named according to the name of the background QSO.," All through this paper, each pair will be named according to the name of the background QSO." + Pwo of our pairs (1307|296 ancl 1305|298) turned up to be stars. as was seen by taking short-exposure spectra at low resolution with the William Herschel Telescope in 1993 February.," Two of our pairs (1307+296 and 1305+298) turned up to be stars, as was seen by taking short-exposure spectra at low resolution with the William Herschel Telescope in 1993 February." + The sample that we observed. consisting of three QSOs is shown in Table 1.," The sample that we observed, consisting of three QSOs is shown in Table 1." + These QSOs span a rather restricted redshift range (2=2 2.7) but cover à wider range in terms of angular separations from the foreground QSO (60B.S 12.6)., These QSOs span a rather restricted redshift range $z=2 - 2.7$ ) but cover a wider range in terms of angular separations from the foreground QSO $\theta = 3.8 - 12.6$ ). + That will allow us to test the existence of the proximity ellect. under different. circumstances (see Section 5)., That will allow us to test the existence of the proximity effect under different circumstances (see Section 5). + ALL observations were performed. at the Observatorio cel ltoque de los Muchachos in the island of La Palma (Canary Islands. Spain).," All observations were performed at the Observatorio del Roque de los Muchachos in the island of La Palma (Canary Islands, Spain)." + Data from QSO1228|077. were acquired using the Isaac Newton Telescope with the LDS spectrograph and LPCS (Image Photon Counting System) detector in 1989 February., Data from QSO1228+077 were acquired using the Isaac Newton Telescope with the IDS spectrograph and IPCS (Image Photon Counting System) detector in 1989 February. + The data from (801222|228 were taken in 1993 February. using the William Herschel Telescope with the ISLS double spectrograph and the LPCS-LE as detector in the blue arm.," The data from QSO1222+228 were taken in 1993 February, using the William Herschel Telescope with the ISIS double spectrograph and the IPCS-II as detector in the blue arm." + Finally. data from QSO1055|021 were taken in 1994 February. again using the ISIS double spectrograph and the TEI/CCD detector on the blue arm of the same telescope.," Finally, data from QSO1055+021 were taken in 1994 February, again using the ISIS double spectrograph and the TEK/CCD detector on the blue arm of the same telescope." + A reduced: version of the observing logs is listed in Table 2., A reduced version of the observing logs is listed in Table 2. + The choice of the IPCS and. ΟΣΗ to. observe QSO1228|O77 and. QSO122|228 was done because the crucial part of the spectrum. (i.e... the part. putatively influenced by the foreground QSO) falls at A<4000 where this detector has better sensitivity than any of the avallable CCDs at La Palma.," The choice of the IPCS and IPCS-II to observe QSO1228+077 and QSO1222+228 was done because the crucial part of the spectrum (i.e., the part putatively influenced by the foreground QSO) falls at $\lambda<4000$ where this detector has better sensitivity than any of the available CCDs at La Palma." + The blue gratings were chosen in order to have an approximate reciprocal resolution of about ~0.2A/pixel.," The blue gratings were chosen in order to have an approximate reciprocal resolution of about $\sim 0.2\, {\rm \AA}/{\rm pixel}$." + This produced a speetral resolution good enough to allow profile fitting of the absorption lines present in the cillerent spectra., This produced a spectral resolution good enough to allow profile fitting of the absorption lines present in the different spectra. + Although we tuned the red arm settings of the ISIS) double spectrograph (cluring the observations of Q5012221228 and QSOL055|021). in order to identify metal lines of possible heavy-cleoment absorption. svstenis with associated lines fallinge in the blue arm region.ὃν we did not find any line that either confirmed or rejected any possible svstem.," Although we tuned the red arm settings of the ISIS double spectrograph (during the observations of QSO1222+228 and QSO1055+021), in order to identify metal lines of possible heavy-element absorption systems with associated lines falling in the blue arm region, we did not find any line that either confirmed or rejected any possible system." + The data reduction was carried out. using the Starlink FIGARO package., The data reduction was carried out using the Starlink FIGARO package. + We used. standard: techniques. except that we needed. to generate and propagate through the entire process an error array for which we had to make the suitable modifications to the standard routines provided by FIGARO.," We used standard techniques, except that we needed to generate and propagate through the entire process an error array for which we had to make the suitable modifications to the standard routines provided by FIGARO." + To obtain a precise wavelength-seale. calibration are lamps were exposed before and after each integration on all of our objects.," To obtain a precise wavelength-scale, calibration arc lamps were exposed before and after each integration on all of our objects." + LLeliocentric and air-to-vacuum corrections were performed., Heliocentric and air-to-vacuum corrections were performed. + No attempt has been made to obtain a [lux callibration for any of the QSOs. which does not alfect to he parameters of the absorption lines.," No attempt has been made to obtain a flux callibration for any of the QSOs, which does not affect to the parameters of the absorption lines." + As it can be seen from Table 2. the data [rom QSO1055|021 are of a much higher quality. caused by the onger exposure time and better sky conditions during their acquisition.," As it can be seen from Table 2, the data from QSO1055+021 are of a much higher quality, caused by the longer exposure time and better sky conditions during their acquisition." + None the less. data from all three QSOs have spectral resolution and signal-to-noise ratio good enough to »erform absorption line fitting.," None the less, data from all three QSOs have spectral resolution and signal-to-noise ratio good enough to perform absorption line fitting." + Continuum [fittinge was carried out usingὃν a standard spline method., Continuum fitting was carried out using a standard spline method. + Selected regions of cach spectrum were used in an iterative way that rejected in each iteration the points that were significantly deviant. from the fitted: continuum. until the fitting procedure converged.," Selected regions of each spectrum were used in an iterative way that rejected in each iteration the points that were significantly deviant from the fitted continuum, until the fitting procedure converged." + A preliminary absorption line list καν obtained searching for sgnilicant (greater than 4o) deviations from he continuum in the normalized. spectra. following the method. presented in Young et al. (," A preliminary absorption line list was obtained searching for significant (greater than $\sigma$ ) deviations from the continuum in the normalized spectra, following the method presented in Young et al. (" +1979).,1979). + Voigt profiles were fitted. to cach Line (or. blend: of ines) in the spectra using the absorption line fitting code ALF developed by ourselves., Voigt profiles were fitted to each line (or blend of lines) in the spectra using the absorption line fitting code ALF developed by ourselves. + This program performs A? minimisation of a spectral region by introducing a Voigt wolile for cach line (that is why the error array is needed), This program performs $\chi^2$ minimisation of a spectral region by introducing a Voigt profile for each line (that is why the error array is needed). + The program finds the best-fitting column density. Doppler ispersion parameter and redshift for cach one of the lines. esumine that they correspond. to given ions ancl atomic ransitions.," The program finds the best-fitting column density, Doppler dispersion parameter and redshift for each one of the lines, assuming that they correspond to given ions and atomic transitions." + ALF also produces an estimate of the errors on lese parameters and a goocdness-oFLit given the minimum. VCο reached and the number of degrees of freedom., ALF also produces an estimate of the errors on these parameters and a goodness-of-fit given the minimum $\chi^2$ reached and the number of degrees of freedom. + A fit was considered to be good enough if it is not rejected by. more ian 99 per cent probability. according to X7 statistics.," A fit was considered to be good enough if it is not rejected by more than 99 per cent probability, according to $\chi^2$ statistics." + Η the ib over à selected region was not &ood enough. another line (with free column density. velocity dispersion parameter and redshift) was added: and the fit repeated.," If the fit over a selected region was not good enough, another line (with free column density, velocity dispersion parameter and redshift) was added and the fit repeated." + Lhe process was stopped either when the rejection probability is less than 99 per cent and the fit looked. good to the eve. or when aclelition of a new line resulted in an of the rejection probability.," The process was stopped either when the rejection probability is less than 99 per cent and the fit looked good to the eye, or when addition of a new line resulted in an of the rejection probability." + This avoids overfitting to a large extent., This avoids overfitting to a large extent. + The resulting line lists are presented in Table 3 (0801055|021). ‘Table 4 (058501222|228) anc Table 5 (8501228|077).," The resulting line lists are presented in Table 3 (QSO1055+021), Table 4 (QSO1222+228) and Table 5 (QSO1228+077)." + In Figures 1.2 and 3 we show the spectra of the 3 objects Q801055|021. Q8501222|228 and. QSO1L228|O77," In Figures 1,2 and 3 we show the spectra of the 3 objects QSO1055+021, QSO1222+228 and QSO1228+077" + (Wijnancls&vanderKlis1998). (~LlOLTz) (Alparctal.1982:1982). (ILlurtnmanetal.2008:," \citep{wij98} $\approx +401\rm\,Hz$ \citep{alp82, rad82}. \citealt{har08,har09})" +IIartinan2009)) |r|<2.5«10PHTs3 (Chosh&Lam1979)) possibly due to magneic-dipole radiatiou acting duringquiescence?.. for a surface magnetic field of the pulsar B21.5« 105C. in line with the expected field streugth of millisecond radio puNUUS.," $|\nudot|\lesssim 2.5\times10^{-14}\hzs$ \citealt{gho79}) possibly due to magnetic-dipole radiation acting during, for a surface magnetic field of the pulsar $B\simeq1.5\times10^8$ G, in line with the expected field strength of millisecond radio pulsars." + ls undergoingL an unexpectedly fas orbital evolution with the orbital period increasing on a timescale of sx qOMSY. (Tartinanetal. 2008..diSalvoetal. 2008)).," is undergoing an unexpectedly fast orbital evolution with the orbital period increasing on a timescale of $\approx70$ Myr \citealt{har08}, \citealt{dis08}) )." + The binary has an orbital period of 2.n hr (Chakrabarty&Morgau1998) and the donor star is a 0.05OLAL. brown dwart (Bildsten&Chakrabarty2001:Deloveetal.2008) suggesting that the orbita evolution should be dominated by aueularo moment loss via eravitational waves and possibly by magnetic braking (Tauris&vaudenHeuvel 2006).," The binary has an orbital period of 2.01 hr \citep{cha98} and the donor star is a $0.05-0.1\msun$ brown dwarf \citep{bil01,del08} suggesting that the orbital evolution should be dominated by angular momentum loss via gravitational waves and possibly by magnetic braking \citep{tau06}." +. The timescale ο the orbital evolution is. however. too fast to be explaince with such a scenario. and non-conservative processes wit1 large unass loss frou the system have been invoked («1Salvoctal.2008.. Durdenetal. 2009)).," The timescale of the orbital evolution is, however, too fast to be explained with such a scenario, and non-conservative processes with large mass loss from the system have been invoked \citealt{dis08}, \citealt{bur09}) )." + Tlartinanetal.(2008);IIartinanetal.(2009) sugeested mstead that interchanges of aueular nmiomeutunm between the coupanion aud the orbit can donunate the short-term orbital evolution as seen iu several binary millisecond pulsus (Arzoumanianetal.1991:Niceetal. 2000).," \citet{har08,har09} suggested instead that interchanges of angular momentum between the companion and the orbit can dominate the short-term orbital evolution as seen in several binary millisecond pulsars \citep{arz94, nic00}." +. On October 31 2011 Suvft--BAT detected a Lew outburst of citepuiarll. xpll..," On October 31 2011 -BAT detected a new outburst of \\citep{mar11,pap11}." + This is the 7th outburst observed since its discovery GutfZaudetal.1998) aud the 6th monitored withRATE., This is the 7th outburst observed since its discovery \citep{int98} and the 6th monitored with. +.. We present a coliereut pulsation analysis of he outburst and we complete the study of the spin an orbital evolution of oover a baseline of thirteen vr., We present a coherent pulsation analysis of the outburst and we complete the study of the spin and orbital evolution of over a baseline of thirteen yr. +"equal chances to detect the particle, just as we expected.","equal chances to detect the particle, just as we expected." + This simple understanding of Wheeler’s experiment may lead one to doubt whether it truly is a case of delayed choice., This simple understanding of Wheeler's experiment may lead one to doubt whether it truly is a case of delayed choice. + This is the reason why we have dealt with the (more clear-cut) quantum eraser in the main text., This is the reason why we have dealt with the (more clear-cut) quantum eraser in the main text. +" So far, the discussions in this note have been entirely independent from the specific wave function collapse mechanism."," So far, the discussions in this note have been entirely independent from the specific wave function collapse mechanism." +" We have only relied on the Born rule, independent of its underlying origin."," We have only relied on the Born rule, independent of its underlying origin." + In this appendix we assume (as an illustration) the Everettian view on the (apparent) wave function collapse., In this appendix we assume (as an illustration) the Everettian view on the (apparent) wave function collapse. +" This gives a concrete implementation of the elements we have met so far, and might provide a more intuitive understanding of the observations made above."," This gives a concrete implementation of the elements we have met so far, and might provide a more intuitive understanding of the observations made above." +" To introduce the Everettian interpretation, one usually starts with the notion of premeasurement."," To introduce the Everettian interpretation, one usually starts with the notion of premeasurement." + Say we have a particle which can be in two states: |+) and ||)., Say we have a particle which can be in two states: $|\uparrow\rangle$ and $|\downarrow\rangle$. +" Also, we have a measuring device (initially in state |I)) which can detect the state of the particle."," Also, we have a measuring device (initially in state $|I\rangle$ ) which can detect the state of the particle." +" We denote the total system (device+particle) the measurement by |UP) or |DOWN), depending on which outcome is shown in the display of the device."," We denote the total system (device+particle) the measurement by $|\textrm{UP}\rangle$ or $|\textrm{DOWN}\rangle$, depending on which outcome is shown in the display of the device." +" Since the device should do an honest job, we want the time evolution to work as follows: By linearity this necessarily means that + + rangle)) So if the particle starts out in a superposition, the measuring device has to end up in a superposition too."," Since the device should do an honest job, we want the time evolution to work as follows: By linearity this necessarily means that + + ) So if the particle starts out in a superposition, the measuring device has to end up in a superposition too." + This clearly conflicts with reality: we never see an entire measuring device in a superposition., This clearly conflicts with reality: we never see an entire measuring device in a superposition. + The explanation of Everett is that the macroscopic difference between the device states |UP) and |DOWN) implies that they can not interfere with each other anymore in the future., The explanation of Everett is that the macroscopic difference between the device states $|\textrm{UP}\rangle$ and $|\textrm{DOWN}\rangle$ implies that they can not interfere with each other anymore in the future. +" Effectively, they are ‘disconnected’ parts of the total wave function."," Effectively, they are `disconnected' parts of the total wave function." + This means that they are like separated worlds[22]., This means that they are like separated worlds. +". To an observer, it looks like the state has collapsed on one particular outcome, although in fact there are two worlds: one in which the observer sees the ‘up’ outcome, and one in which he sees the *down' outcome. ("," To an observer, it looks like the state has collapsed on one particular outcome, although in fact there are two worlds: one in which the observer sees the `up' outcome, and one in which he sees the `down' outcome. (" +"To see the role of the observer more explicitly: re-read theabove two formulae again, but now interpret |I) as the initial state of the device+observer and |UP) and |DOWN) as the final state of the particle+device+observer.)","To see the role of the observer more explicitly: re-read theabove two formulae again, but now interpret $|I\rangle$ as the initial state of the device+observer and $|\textrm{UP}\rangle$ and $|\textrm{DOWN}\rangle$ as the final state of the particle+device+observer.)" + Let us now see how we can understand the main conclusion of this paper in this framework., Let us now see how we can understand the main conclusion of this paper in this framework. +" For concreteness, consider the EPR setting again.We denote the state of observer Alice and her measuring apparatus as |Alice) and similarly for |Bob)."," For concreteness, consider the EPR setting We denote the state of observer Alice and her measuring apparatus as $|\textrm{Alice}\rangle$ and similarly for $|\textrm{Bob}\rangle$ ." +" So initially, the total"," So initially, the total" +on the S04 distance determinations. we [eel (hat the canonical BO computations offer the most palatable evolutionary scenario for studying the relation between (he Cepheid pulsation mass and (he evolutionary one.mass-loss.,"on the S04 distance determinations, we feel that the canonical B0 computations offer the most palatable evolutionary scenario for studying the relation between the Cepheid pulsation mass and the evolutionary one,." +" Fherelore. (he trend of the M,/M,can ralio with the Cepheid period disclosed in the top panel of Fig."," Therefore, the trend of the $M_p/M_{e,can}$ ratio with the Cepheid period disclosed in the top panel of Fig." + 9 should be considerecl as real. unless there are significant. faults wilh our approach or significan errors in the Cepheid adopted distance and reddening.," 9 should be considered as real, unless there are significant faults with our approach or significant errors in the Cepheid adopted distance and reddening." + In order (o remove any doubt on the reliability of the adopted procedure. we use all the pulsation models listed in Table 1 as real Cepheids. and we derive their mass from thepredicted PLC and ALCL relations.," In order to remove any doubt on the reliability of the adopted procedure, we use all the pulsation models listed in Table 1 as real Cepheids, and we derive their mass from thepredicted $PLC$ and $MCL$ relations." + We show in Fig., We show in Fig. +" ll that the ensuing ratio between the pulsation and (he evolutionary nass is Mj/M, 7120.05. which is a quite irrelevant uncertainty with respect to the results in Fig."," 11 that the ensuing ratio between the pulsation and the evolutionary mass is $M_p/M_{e,can}$ $\pm$ 0.05, which is a quite irrelevant uncertainty with respect to the results in Fig." + 9., 9. +" On the other hand. according to the derivative values listed in Table 6. the condition log.U,(VA Ale(VA) for the observed Cepheids would imply rather unrealistic corrections to the adopted distance and reddening value as given. e.g.. bv AM~ 0.5 mag or «(ο—V)~ -0.4 mag al ?=0.6."," On the other hand, according to the derivative values listed in Table 6, the condition $M_p(VK)$ $M_{e,can}(VK)$ for the observed Cepheids would imply rather unrealistic corrections to the adopted distance and reddening value as given, e.g., by $\Delta\mu_0\sim$ 0.5 mag or $\Delta +E(B-V)\sim -$ 0.4 mag at $P$ =0.6." + To further constirain the plausibility of current theoretical predictions we decided to perform a comparison wilh the dynamical mass of $ Mus., To further constrain the plausibility of current theoretical predictions we decided to perform a comparison with the dynamical mass of S Mus. + This object is the binary Cepheid with the hottest known companion and Evans et al. (, This object is the binary Cepheid with the hottest known companion and Evans et al. ( +2004) by using spectra collected with both the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer estimated a mass of M—6.0c041. This mass determination agrees quite well will the estimates of similar binary Cepheids (Dóhhim-Vitense et al.,2004) by using spectra collected with both the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer estimated a mass of $M=6.0\pm0.4 M_\odot$ .This mass determination agrees quite well with the estimates of similar binary Cepheids (Böhhm-Vitense et al. + 1997). but presents a smaller uncertainty.," 1997), but presents a smaller uncertainty." + By adopting for 5 Mus the lollowing input parameters: P=9.6599 days. V —6.115 (Fernie οἱ al.," By adopting for S Mus the following input parameters: P=9.6599 days, $V$ =6.118 (Fernie et al." + 1995). ECB—V )-0.23 (Evans οἱ al.," 1995), $B-V$ )=0.23 (Evans et al." + 2004). A —3.987 (Nimeswenger et al.," 2004), $K$ =3.987 (Kimeswenger et al." + 2004). and bv using the A-band PL relation provided by S04. we found a true distance modulus of fy=9.5520.15 mag.," 2004), and by using the $K$ -band PL relation provided by S04, we found a true distance modulus of $\mu_0=9.55\pm0.15$ mag." +" By using these data and the PW (V— A) relation (see Table 3) we find for S Mus a pulsation mass of M=5.64 0.8... while bv assuming L=Lig, and the MPL (Mg) relation (see Table 4) we find an evolutionary mass of 6.30.011..."," By using these data and the PW $V-K$ ) relation (see Table 3) we find for S Mus a pulsation mass of $M=5.6\pm0.8 M_\odot$ , while by assuming $L=L_{can}$ and the MPL $M_K$ ) relation (see Table 4) we find an evolutionary mass of $6.3\pm0.6 M_\odot$." + According to Fernie et al. (, According to Fernie et al. ( +"1995) the reddening of S Mus is ECB— V)—0.15. and in turn. the (rue distance modulus becomes ji,=9.58d0.15.","1995) the reddening of S Mus is $B-V$ )=0.15, and in turn, the true distance modulus becomes $\mu_0=9.58\pm0.15$." +" Stellar masses based on these values are only marginally different. i.e. AJ=5.8ολ, (DW). 6.3E0.6... (MPL)."," Stellar masses based on these values are only marginally different, i.e. $M=5.8\pm0.8 M_\odot$ (PW), $6.3\pm0.6 M_\odot$ (MPL)." + Note that the uncertainties affecting current mass estimates account for both the error on the distance modulus aud for the intrinsic dispersion of evolutionary. and. pulsation relation., Note that the uncertainties affecting current mass estimates account for both the error on the distance modulus and for the intrinsic dispersion of evolutionary and pulsation relation. + Pulsation and evolutionary mass agree. within the errors with the dvnamiceal mass.," Pulsation and evolutionary mass agree, within the errors with the dynamical mass." + However. no firm conclusion can be reached concerning (he mass discrepancy. due (o current empirical and theoretical uncertainties.," However, no firm conclusion can be reached concerning the mass discrepancy, due to current empirical and theoretical uncertainties." + An independent mass estimate for ο Mus was recently provided bv Petterson. Cottrell. Albrow (2004). by using high resolution spectroscopy thev found A[—6.2d 0.2...," An independent mass estimate for S Mus was recently provided by Petterson, Cottrell, Albrow (2004), by using high resolution spectroscopy they found $M=6.2\pm0.2 M_\odot$ ." + Wis noteworthy. that dynamical mass of binary Cepheids might play a crucial role in settling the discrepancy. betweenevolutionary and pulsation masses. since," It is noteworthy, that dynamical mass of binary Cepheids might play a crucial role in settling the discrepancy betweenevolutionary and pulsation masses, since" +Observations with SCUBA (ILIIolland οἱ 11999) on the 15-m James Clerk Maxwell Telescope CJCNUDE). Mauna Ixea. Llawaii. were mace using its photometry mode at 450. 850. 1350 and am during the nights of 1998 January 2931 (u,"Observations with SCUBA (Holland et 1999) on the 15-m James Clerk Maxwell Telescope (JCMT), Mauna Kea, Hawaii, were made using its photometry mode at 450, 850, 1350 and $\mu$ m during the nights of 1998 January 29--31 )." +"r) The secondary mirror was chopped in azimuth bv y at TSI and jigeled every Iss in a simple 9- pattern with 2"" offsets.", The secondary mirror was chopped in azimuth by $''$ at Hz and jiggled every s in a simple 9-point pattern with $''$ offsets. + Phe telescope was ποσοο between the signal anc reference beams every Oss in a signalreference pattern., The telescope was nodded between the signal and reference beams every s in a signal–reference–reference–signal pattern. + The pointing was checked regularly and skycips were performed every hour to measure the atmospheric opacity., The pointing was checked regularly and skydips were performed every hour to measure the atmospheric opacity. + lteducing the data. spikes were carefully rejected. then measurements in the reference beam were subtracted. from those in the signal beam.," Reducing the data, spikes were carefully rejected then measurements in the reference beam were subtracted from those in the signal beam." + The data were corrected. for atmospheric: opacity and. calibrated: against Uranus. and Mars., The data were corrected for atmospheric opacity and calibrated against Uranus and Mars. + The measured [ux densities are listed in Table 1., The measured flux densities are listed in Table 1. + The radio spectrum of CLE Cvg is shown in Table 1 and Fie., The radio spectrum of CI Cyg is shown in Table 1 and Fig. +" 1 together with earlier radio data CForbett Campbell 1989: Seaquist. Ixrogulec. ""Tavlor. 1993) and. published optical/LR measurements (Munari et 112992: Whitelock Munari 1992)."," 1 together with earlier radio data (Torbett Campbell 1989; Seaquist, Krogulec Taylor 1993) and published optical/IR measurements (Munari et 1992; Whitelock Munari 1992)." + The resulting spectral energy. distribution covers the entire radio to optical range., The resulting spectral energy distribution covers the entire radio to optical range. + The Ilt region is ‘learky dominated by photospheric emission (from an M5 UL eiant — solid line in Fig., The IR region is clearly dominated by photospheric emission (from an M5 III giant – solid line in Fig. + 1) while the em to sub-mm emission is dominated. by partially optically thick bremsstrahlung rec-free) from ionisecl gas., 1) while the cm to sub-mm emission is dominated by partially optically thick bremsstrahlung (free-free) from ionised gas. + Phe radio spectrum turns over uU mm wavelengths indicating that it has become optically jin to frec-free emission., The radio spectrum turns over at mm wavelengths indicating that it has become optically thin to free-free emission. +" ‘To estimate the turnover frequency. 44. the (partially) optically thick emewave radio data were fitted. with a power law spectrum. 5S,xον "," To estimate the turnover frequency, $\nu_{\rm t}$, the (partially) optically thick cm-wave radio data were fitted with a power law spectrum, $S_{\nu} \propto \nu^{\alpha}$." +The optically thin sub-mum data were similarly fitted. but the spectral index was arbitrary fixed at à=0.1 (appropriate for optically thin emission)., The optically thin sub-mm data were similarly fitted but the spectral index was arbitrary fixed at $\alpha = -0.1$ (appropriate for optically thin emission). +" Form. we have adopted the point at which the low-frequency extrapolation of the optically thin. frec-free emission exceeds the observed. optically thick emission.hy a factor e (7,= 1)."," For $\nu_{\rm t}$, we have adopted the point at which the low-frequency extrapolation of the optically thin free-free emission exceeds the observed optically thick emissionby a factor $e$ $\tau_{\nu}=1$ )." +" A least-squares fit to our cata vields SIDBSR—920+002(p/GlIz)£7"" mm]v and sli»—17.530.6(o/GHz)I mmy for the em and sub-nim data. respectively. and we estimate 44=7dX 50Cllz."," A least-squares fit to our data yields $S_{\nu}^{\rm thick} = +0.20\pm0.02 (\nu/\rm GHz)^{0.96(\pm0.03)}$ mJy and $S_{\nu}^{\rm +thin} = 17.5 \pm0.6 (\nu/\rm GHz)^{-0.1}$ mJy for the cm and sub-mm data, respectively, and we estimate $\nu_{\rm t} = 27 \pm 5$ GHz." +" For frec-free emission in the optically thick regime. the cHeetive radio. photosphere emitting at [requency. ν΄ and temperature Z is given approximately by the blackbocdy raclius. In the case of CL Cye. the radius at the opticalA thick-thin transition v= ™) is 52.6CE/101A)""7AU. adopting a distance of 2kkpe (Ixenvon et 11991 which should. represent the inner radius of its opticalA thick shell."," For free-free emission in the optically thick regime, the effective radio photosphere emitting at frequency $\nu$ and temperature $T$ is given approximately by the blackbody radius, In the case of CI Cyg, the radius at the optically thick-thin transition $\nu = \nu_{\rm t}$ ) is $52.6\,(T/10^4\,{\sc +k})^{-0.5}$, adopting a distance of kpc (Kenyon et 1991), which should represent the inner radius of its optically thick shell." + Phis radius is significantly larger than the size of the known binary orbit of Cl (νο for any reasonable temperature.," This radius is significantly larger than the size of the known binary orbit of CI Cyg, for any reasonable temperature." +" The emission. measure of the shell. derived from the optically thin turnover frequency. 4727 GGLIz. is around 6105(HLAthyt "" measured along the linc-of-sight through its densest region."," The emission measure of the shell, derived from the optically thin turnover frequency, $\nu_{\rm t} \sim 27$ GHz, is around $6 \times +10^{14}\,(T_{\rm e}/10^4{\sc k})^{1.35}$ $^{-6}$ measured along the line-of-sight through its densest region." + Finally. the optically thin [lux densitv is consistent with a volume emission. measure of nzV.z3 to 5107(d/2kpe)?em. for the respective range of 7.~107 to LOK found. in CL Cvg (Alikolajewska 1985: lxenvon et 11991).," Finally, the optically thin flux density is consistent with a volume emission measure of $n_{\rm e}^2\,V \approx 3$ to $5 \times 10^{58} +(d/\rm 2\,kpc)^2\,\rm cm^{-6}$ for the respective range of $T_{\rm e} +\sim 10^{4}$ to $10^{5}$ found in CI Cyg ajewska 1985; Kenyon et 1991)." + This emission measure is an order of magnitude lower than the emission. measure of 3 to 101077em.Ὁ derived [rom the optical/UV bound-free and [rec- continuum and. Balmer emission lines. adopting a reasonable range lor (D.V) (0.30.45). thus the [ree-free radio emission and the hydrogen optical/UV recombination emission [rom Cl Cve do not seem to arise from the same volume of gas.," This emission measure is an order of magnitude lower than the emission measure of $3$ to $10 \times +10^{59}\,\rm cm^{-6}$ derived from the optical/UV bound-free and free-free continuum and Balmer emission lines, adopting a reasonable range for $E(B-V)$ $\sim$ 0.3–0.45), thus the free-free radio emission and the hydrogen optical/UV recombination emission from CI Cyg do not seem to arise from the same volume of gas." + The radio emission also provides a model-indepencent lower limit to the Lyman continuum photon luminosity. Lp: (Seaquist Tavlor. 1987). which gives LyeZz5 to 2.10 pphotss+ for the appropriate range of Ti. (107 o 107). much lower than the Li.~107 ss inclicated bv studies ofthe UV continuum and emission ines observed. during quiescence (1985-94: Mikolajewska llolowacz 2000).," The radio emission also provides a model-independent lower limit to the Lyman continuum photon luminosity, $L_{\rm Ly}$: (Seaquist Taylor 1987), which gives $L_{\rm Ly} \gs 5$ to $2 \times +10^{45}$ $^{-1}$ for the appropriate range of $T_{\rm e}$ $10^4$ to $10^5$ ), much lower than the $L_{\rm Ly} \sim +10^{47}$ $^{-1}$ indicated by studies of the UV continuum and emission lines observed during quiescence (1985-94; ajewska owacz 2000)." + The current racio spectrum may be used to test. the known models for radio emission [from svmbiotic stars., The current radio spectrum may be used to test the known models for radio emission from symbiotic stars. + Above all. the very flat shape of the optically thin portion of our spectrum rules out the colliding wind model (in which he spectral index is never expected to Hatten: a~| 0.5. even for £92£4 (Ixenny. 1995).," Above all, the very flat shape of the optically thin portion of our spectrum rules out the colliding wind model (in which the spectral index is never expected to flatten: $\alpha \sim +0.5$ , even for $\nu > \nu_{\rm t}$ (Kenny 1995)." +Accelerating models show no need for the 04 term.,Accelerating models show no need for the $\delta_{1}$ term. + Assuming acceleration. the fits (Table 3)) show that reducing extinction values by about explains the data better. ancl removes an alarming correlation.," Assuming acceleration, the fits (Table \ref{table_chi2_3}) ) show that reducing extinction values by about explains the data better, and removes an alarming correlation." + On the other hand the matter-dominated model (O1;=1. O4—0) shows interesüng sensiüvilv {ο 04.," On the other hand the matter-dominated model $(\Omega_M=1$, $\Omega_\Lambda= 0)$ shows interesting sensitivity to $\delta_{1}$." +" In Fie.5 we compare the sensitivitv of different fits to parameter 2,,.", In \ref{fig:ChiSquared3Models} we compare the sensitivity of different fits to parameter $\Omega_{M}$. +" With 94=0 constrained. the effects of ὁ are rather orthogonal to those of Oi. so that the region O4,~0.3 is favored whether or not there is a significant correlation H."," With $\delta_{1}=0$ constrained, the effects of $\delta$ are rather orthogonal to those of $ \Omega_{M}$, so that the region $\Omega_{M} \sim 0.3$ is favored whether or not there is a significant correlation $R$ ." +" Yet varving 94 greatly. broadens acceptable values of Ον, while maintaining the &—0 effect of ὁ, "," Yet varying $\delta_{1}$ greatly broadens acceptable values of $\Omega_{M}$, while maintaining the $R \ra 0$ effect of $\delta$ ." +"The significance depends on ones hvpothesis: if one chooses Qa,=1a-priori. parameter ὁ is traded Dor parameter ελα,"," The significance depends on one's hypothesis: if one chooses $\Omega_{M}=1$, parameter $\delta_{1}$ is traded for parameter $\Omega_{M}$." + The overall probability of either hypothesis is only in part determined by (he p-value of the data given Che distribution: the rest depends on one's prior beliels in evolution. which we will not pursue.," The overall probability of either hypothesis is only in part determined by the $p$ -value of the data given the distribution: the rest depends on one's prior beliefs in evolution, which we will not pursue." + It is fair to sav. that the revised fils give more leeway (ο matter-dominated models on statistical grounds., It is fair to say that the revised fits give more leeway to matter-dominated models on statistical grounds. + In all cases fits are driven to sly—ον(6~—0.4)0.6.4... either simply (o improve \?/dof. ov Vo remove the correlation with residuals.," In all cases fits are driven to $A_{V} \ra A_{V}(\delta \sim -0.4) \sim 0.6 A_{V} $, either simply to improve $\chi^{2}/dof$, or to remove the correlation with residuals." + To conclude. analvsis using reported extinction coefficients is well known (o produce eood fits to acceleration of the expansion rate.," To conclude, analysis using reported extinction coefficients is well known to produce good fits to acceleration of the expansion rate." + However the extinclions show correlation with residuals with random chance probability. using (wo independent tests. the extinction correlation and 47 values. both below the level of 10..," However the extinctions show correlation with residuals with random chance probability using two independent tests, the extinction correlation and $\chi^{2}$ values, both below the level of $10^{-6}$." + The hypothesis that extinction coellicients should be corrected empirically provides substantially improved fits to Che data. while also eliminating significant correlation of residuals.," The hypothesis that extinction coefficients should be corrected empirically provides substantially improved fits to the data, while also eliminating significant correlation of residuals." + A model of linear evolution vields interesting effects of high statistical significance correlated with redshift., A model of linear evolution yields interesting effects of high statistical significance correlated with redshift. + The studies indicate either bias in host extinction assignments or evolution of the source galaxies., The studies indicate either bias in host extinction assignments or evolution of the source galaxies. + The significance ol acceleration itself cannot be resolved on the basis of these studies. but might be revised. depending on one's priors.," The significance of acceleration itself cannot be resolved on the basis of these studies, but might be revised, depending on one's priors." + We suggest that observers report uncertainties in (heir assignment of extinctionparameters. both in thefuture and for the existing data sets.," We suggest that observers report uncertainties in their assignment of extinctionparameters, both in thefuture and for the existing data sets." +1e scatter in the measured lag spectrum at low frequencies.,the scatter in the measured lag spectrum at low frequencies. + Therefore. the lag spectrum is not consistent with a single oower law and the bend down or cut-olf at. around 10 11. is real.," Therefore, the lag spectrum is not consistent with a single power law and the bend down or cut-off at around $10^{-4}$ Hz is real." + Arévaloetal.(2006) found a similar change in gaope in the lag spectrum of Ark 564. in that case however. 16 bend. was found a decade in frequeney. below the bend requency of the PDS. while in he bend in the PDS and lag spectrum appear at the same requency. within the uncertainties.," \citet{arevaloark} found a similar change in slope in the lag spectrum of Ark 564, in that case however, the bend was found a decade in frequency below the bend frequency of the PDS, while in the bend in the PDS and lag spectrum appear at the same frequency, within the uncertainties." + The length. of the time lags increases with the separation between the energies of the bands considered., The length of the time lags increases with the separation between the energies of the bands considered. + We calculated lag spectra of the 0.20.4 keV. to the 0.40.6. 0.61. 12.2 Sand 510 keV bands. finding that the higher the energy band. the more it lags the 0.20.4 keV band.," We calculated lag spectra of the 0.2–0.4 keV to the 0.4–0.6, 0.6–1, 1–2, 2--5 and 5–10 keV bands, finding that the higher the energy band, the more it lags the 0.2–0.4 keV band." + The fractional lags. r/time-scale. are approximately 0.72 for 0.4.0.6 keV. for 0.61 keV. for 1.2 keV. for 25 keV and for 510 keV. Each lag spectrum resembles the one shown in Fig. 7..," The fractional lags, $\tau$ /time-scale, are approximately 0.72 for 0.4–0.6 keV, for 0.6–1 keV, for 1–2 keV, for 2–5 keV and for 5–10 keV. Each lag spectrum resembles the one shown in Fig. \ref{lags3-10}," + having a cut-olf at high frequencies., having a cut-off at high frequencies. + These ractional lag values only represent the low-frequency part of the spectra., These fractional lag values only represent the low-frequency part of the spectra. + In Fig., In Fig. + S we plotted the lowest-Lrequency lag for cach xur as a function of the ratio between the average energy of the bands compared., \ref{lagsvsE} we plotted the lowest-frequency lag for each pair as a function of the ratio between the average energy of the bands compared. + The lags increase in an almost log-incar manner with increasing energy ratio., The lags increase in an almost log-linear manner with increasing energy ratio. + Phe best fitting og-linear model. shown by the solid line in the plot has a orm For a perfect log-linear relation. the intercept. should equal zero. i.e. lags between identical energy. bands should be V.," The best fitting log-linear model, shown by the solid line in the plot has a form For a perfect log-linear relation, the intercept should equal zero, i.e. lags between identical energy bands should be 0." + Phe intercept of the fitted relation is significantly cilferent rom this value so the behaviour of the time lags in iis not entirely consistent with (νο X-1 (Nowaketal.1999)., The intercept of the fitted relation is significantly different from this value so the behaviour of the time lags in is not entirely consistent with Cyg X-1 \citep{nowak_lags}. + otice however. that the log-inear relation in Cvg X-1 was calculated for energies above 2 keV and in wave used a baseline energy band of 0.20.4 keV. Lt 15 possible hat other spectral components in below 2 keV. in particular the soft. excess. might. be suppressing the intermediate-energy. lags.," Notice however, that the log-linear relation in Cyg X-1 was calculated for energies above 2 keV and in we used a baseline energy band of 0.2–0.4 keV. It is possible that other spectral components in below 2 keV, in particular the soft excess might be suppressing the intermediate-energy lags." + We applied. the propagating Lluctuation paradigm of Lyubarskii(L997) to attempt to reproduce the observed lag spectra.," We applied the propagating fluctuation paradigm of \citet{lyubarskii} + to attempt to reproduce the observed lag spectra." + In this scenario. the [uctuations are produced by the aceretion [low over a large range in radius. and travel towards the centre to modulate the X-ray emitting region.," In this scenario, the fluctuations are produced by the accretion flow over a large range in radius, and travel towards the centre to modulate the X-ray emitting region." + We assume that the Huctuations are produced. and propagated on the viscous time-scale of a thick accretion How and that the emitted energy spectrum hardens towards the centre. therefore producing hard. lags.," We assume that the fluctuations are produced and propagated on the viscous time-scale of a thick accretion flow and that the emitted energy spectrum hardens towards the centre, therefore producing hard lags." +Strong irregular optical variability is one of the defining characteristics of classical T-Taurt stars (CTTS.?).. together with their association with dark or bright nebulae and their strong optical emission lines.,"Strong irregular optical variability is one of the defining characteristics of classical T-Tauri stars \citep[CTTS,][]{joy45}, together with their association with dark or bright nebulae and their strong optical emission lines." + Following their discovery by ?.. CTTS were then recognized as newly formed stars that have just completed their main accretion phase and are contracting toward the main sequence (e.g.?)..," Following their discovery by \citet{joy45}, CTTS were then recognized as newly formed stars that have just completed their main accretion phase and are contracting toward the main sequence \citep[e.g.][]{wal56}." + Unlike weak line T-Tauri stars (WTTS). CTTS are still undergoing mass-aceretion: material from the inner edge of their truncated circumstellar disk is thought to be channeled along magnetic field lines toward an impact region on the stellar surface where it is shocked. producing an excess of emission with respect to the stellar photosphere. ranging from the X-ray band to the optical.," Unlike weak line T-Tauri stars (WTTS), CTTS are still undergoing mass-accretion: material from the inner edge of their truncated circumstellar disk is thought to be channeled along magnetic field lines toward an impact region on the stellar surface where it is shocked, producing an excess of emission with respect to the stellar photosphere, ranging from the X-ray band to the optical." + The large and irregular optical variability of CTTSs has generally been linked with the accretion process. but the actual mechanism involved has remained elusive. with two classes of mechanisms being generally considered. 1.ο.. 7) variability of the emission from the accretion shock(s) due to variation in mass accretion rate and/or to their rotational modulation. or ij) variable absorption due to unstable and optically thick accretion streams and/or warps in the circumstellar disk that occult part of the photosphere.," The large and irregular optical variability of CTTSs has generally been linked with the accretion process, but the actual mechanism involved has remained elusive, with two classes of mechanisms being generally considered, i.e., $i$ ) variability of the emission from the accretion shock(s) due to variation in mass accretion rate and/or to their rotational modulation, or $ii$ ) variable absorption due to unstable and optically thick accretion streams and/or warps in the circumstellar disk that occult part of the photosphere." + Recent statistical studies of CTTS observed over many years (??) suggest that in about of the cases the optical variability may be attributed to absorption. while in the remaining cases time-variable accretion is favored.," Recent statistical studies of CTTS observed over many years \citep{gra07,gra08} suggest that in about of the cases the optical variability may be attributed to absorption, while in the remaining cases time-variable accretion is favored." + However. due to the similar effects of spots and absorption on the broad-band lightcurves. the absorption scenario cannot be excluded in most cases.," However, due to the similar effects of spots and absorption on the broad-band lightcurves, the absorption scenario cannot be excluded in most cases." + A detailed study of the CTTS TTau by Bouvier and collaborators (22222) has shown that. for this near edge-on star-disk system. the large. irregular optical variability is explained well by occultation of asignificant fraction of the stellar surface by a warp in the inner disk. located at the corotation radius and thus rotating in and out of view with the same period as the stellar photosphere and evolving on similar timescales.," A detailed study of the CTTS Tau by Bouvier and collaborators \citep{bou99,bou03,men03,bou07,gro07} has shown that, for this near edge-on star-disk system, the large, irregular optical variability is explained well by occultation of a significant fraction of the stellar surface by a warp in the inner disk, located at the corotation radius and thus rotating in and out of view with the same period as the stellar photosphere and evolving on similar timescales." + The warp could be due to the misalignment of the rotation and magnetic axes and could correspond to the foot of the accretion stream., The warp could be due to the misalignment of the rotation and magnetic axes and could correspond to the foot of the accretion stream. + Until very recently the case of AA Tau could be considered peculiar. as no other similar systems had been reported.," Until very recently the case of AA Tau could be considered peculiar, as no other similar systems had been reported." + However. recent high-quality optical lighteurves of a large sample of young stars. CTTS and WTTS. in the 22264 star-forming region. obtained with the CoRoT satellite. have shown that TTau-like variability 1s rather common (?)..," However, recent high-quality optical lightcurves of a large sample of young stars, CTTS and WTTS, in the 2264 star-forming region, obtained with the CoRoT satellite, have shown that Tau-like variability is rather common \citep{ale10}." + This leads to the suggestion that time-dependent obscuration of part of the photosphere by disk warps. or else by the related accretion streams. might be an important mechanism to explain the optical variability of CTTS.," This leads to the suggestion that time-dependent obscuration of part of the photosphere by disk warps, or else by the related accretion streams, might be an important mechanism to explain the optical variability of CTTS." + CTTS are also peculiar in the X-ray band: like WTTS. they show significant coronal emission from plasma at MMK. but with average luminosities lower than those of WTTSs. at any given stellar mass or bolometric luminosity. by a factor of 3-5. and with a significantly larger scatter (??)..," CTTS are also peculiar in the X-ray band; like WTTS, they show significant coronal emission from plasma at MK, but with average luminosities lower than those of WTTSs, at any given stellar mass or bolometric luminosity, by a factor of 3-5, and with a significantly larger scatter \citep{fla03b,pre05a}." + Moreover. the X-ray emission of CTTSs may be more time variable and have a harder spectrum than the one of WTTSs (e.g.??)..," Moreover, the X-ray emission of CTTSs may be more time variable and have a harder spectrum than the one of WTTSs \citep[e.g.][]{ima01,fla06}." + These facts have so far remained unexplained., These facts have so far remained unexplained. + A variety of physical mechanisms have been suggested to explain the lower observed X-ray luminosity. such as mass-loading of coronal magnetic loops due to aceretion material (leading to cooler plasma. not visible in X-rays) and the shielding of significant fractions of the coronal plasma by dense accretion streams (?)..," A variety of physical mechanisms have been suggested to explain the lower observed X-ray luminosity, such as mass-loading of coronal magnetic loops due to accretion material (leading to cooler plasma, not visible in X-rays) and the shielding of significant fractions of the coronal plasma by dense accretion streams \citep{gre07}." + In addition to the coronal emission. a separate 2- MK X-ray spectral component related to accretion and possibly originating in the accretion shock is now believed to be common in CTTSs.," In addition to the coronal emission, a separate 2-3 MK X-ray spectral component related to accretion and possibly originating in the accretion shock is now believed to be common in CTTSs." + This soft component has only been observed to date in a dozen such stars observed at high spectral resolution with either or (e.g. ?).., This soft component has only been observed to date in a dozen such stars observed at high spectral resolution with either or \citep[e.g.][]{gue07b}. . + With the notable exception of HHya. the coronal component seems to dominate the emission for E> 500eeV. Simultaneous optical and X-ray observations can constrain the physical mechanisms responsible for the optical and X-ray variability and the location of the X-ray emitting material relative tothe photosphere.," With the notable exception of Hya, the coronal component seems to dominate the emission for $E>500$ eV. Simultaneous optical and X-ray observations can constrain the physical mechanisms responsible for the optical and X-ray variability and the location of the X-ray emitting material relative tothe photosphere." + For the case of TTau. for example. 9? searched for X-ray eclipses corresponding to two," For the case of Tau, for example, \citet{gro07} searched for X-ray eclipses corresponding to two" +"Assuming the widely used linear dark energy equation of state (Chevallier&Polarski2001;Linder 2003),, wo+(1—a)wa, we now study the dependence of the DETF FoM for (wo,wa) on the basic survey parameters: redshift accuracy, minimum redshift of the survey, and the survey area.","Assuming the widely used linear dark energy equation of state \citep{Chev01,Linder03}, , w_X(z)=w_0+(1-a)w_a, we now study the dependence of the DETF FoM for $(w_0,w_a)$ on the basic survey parameters: redshift accuracy, minimum redshift of the survey, and the survey area." +" We assume the fiducial cosmological model adopted in the Euclid Assessment Study Report (Laureijsetal. 2009):: Qn= 0.25, Qa=0.75, h=0.7, og=0.80, €)= 0.0445, wo=—0.95, Wa=0, n,=1."," We assume the fiducial cosmological model adopted in the Euclid Assessment Study Report \citep{Laureijs09}: : $\Omega_m=0.25$ , $\Omega_\Lambda=0.75$, $h=0.7$, $\sigma_8=0.80$, $\Omega_b=0.0445$ , $w_0=-0.95$, $w_a=0$, $n_s=1$." +" We assume baseline survey of Ha emission line galaxies, based on slitless aspectroscopy of the sky."," We assume a baseline survey of $\alpha$ emission line galaxies, based on slitless spectroscopy of the sky." + The empirical redshift distribution of Ha emission line galaxies derived by Geachetal.(2010) from observed Ha luminosity functions was adopted along with with the bias function derived by Orsietal.(2010) using a galaxy formation simulation.," The empirical redshift distribution of $\alpha$ emission line galaxies derived by \cite{Geach10} from observed $\alpha$ luminosity functions was adopted along with with the bias function derived by \cite{Orsi10} + using a galaxy formation simulation." + Predictions for the redshift distribution of Ha emitters are based on a simple model of the evolution of the observed Ha luminosity function since z~2 (see Geach et 2010 for full details)., Predictions for the redshift distribution of $\alpha$ emitters are based on a simple model of the evolution of the observed $\alpha$ luminosity function since $z\sim2$ (see Geach et 2010 for full details). +" Briefly, the model enforces a fixed space density over cosmic time, but allows L* to increase with (1+z)® evolution out to z=1.3 before plateauing at z>1.3."," Briefly, the model enforces a fixed space density over cosmic time, but allows $L^\star$ to increase with $(1+z)^Q$ evolution out to $z=1.3$ before plateauing at $z>1.3$." + The exponent Q is determined by fitting the evolution of observed L* derived by different workers using similarly selected Ha emitter samples over 010718 ! ccm this simple model can successfully re-produce the observed number? counts of Ho emitters over the main redshift range pertinent to future dark energy (galaxy redshift) surveys."," However, at the flux limits likely to be practical to future dark energy (galaxy redshift) surveys, galaxy counts contributed by $L<10^{-16}$ $^{-1}$ $^{-2}$ this simple model can successfully re-produce the observed number counts of $\alpha$ emitters over the main redshift range pertinent to future dark energy (galaxy redshift) surveys." + Orsi et al (2010) present predictions for the abundance and clustering of H-alpha emitters using two different versions of their galaxy formation model., Orsi et al (2010) present predictions for the abundance and clustering of H-alpha emitters using two different versions of their galaxy formation model. +" The two models contain many elements in common, but have important differences in their treatment of the formation of massive galaxies."," The two models contain many elements in common, but have important differences in their treatment of the formation of massive galaxies." +" One model invokes a superwind ejection of baryons to suppress the gas cooling rate in massive haloes, whereas the other model uses the energy released from accretion onto a central supermassive black hole."," One model invokes a superwind ejection of baryons to suppress the gas cooling rate in massive haloes, whereas the other model uses the energy released from accretion onto a central supermassive black hole." + Orsi et al show that the predicted bias of H-alpha selected galaxies does not vary significantly between these models (the upper panels of their fig., Orsi et al show that the predicted bias of H-alpha selected galaxies does not vary significantly between these models (the upper panels of their fig. + 11) and is therefore a robust prediction., 11) and is therefore a robust prediction. +" Note that we consider the redshift success rates e=0.35,0.5,0.7 in all our results, thus effective varying the redshift completeness over the entire plausible range."," Note that we consider the redshift success rates $e=0.35, 0.5, 0.7$ in all our results, thus effective varying the redshift completeness over the entire plausible range." +" The uncertainties in the redshift distribution and bias function of Ha emission line galaxies are subdominant compared to the uncertainty in the redshift success rate e, which in turn depends on the mission implementation and survey strategy."," The uncertainties in the redshift distribution and bias function of $\alpha$ emission line galaxies are subdominant compared to the uncertainty in the redshift success rate $e$, which in turn depends on the mission implementation and survey strategy." +" We present most of our results in terms of the FoM for (wo,Wa), the conventional FoM for comparing dark energy surveys proposed by the DETF (Albrechtetal."," We present most of our results in terms of the FoM for $w_0,w_a)$, the conventional FoM for comparing dark energy surveys proposed by the DETF \citep{detf}." +"2006).. Fitting formulae are provided for P(k) including growth information (denoted ""FoMp(x)j, ""). and when growth information is marginalized over (""FoM p"")."," Fitting formulae are provided for $P(k)$ including growth information (denoted $_{P(k)f_g}$ ”), and when growth information is marginalized over $_{P(k)}$ ”)." + The effect of extending the FoM definition is considered in Sec.3.7.., The effect of extending the FoM definition is considered in \ref{sec:FoM_X}. +" To include the ongoing Sloan Digital Sky Survey III (SDSS- Baryon Oscillation Spectroscopic Survey of luminous red galaxies (LRG) in our forecasts, we assume that the LRG redshifts are measured over 0.1-ray beaming explains the low observed fluxes of some nearby energetic pulsars.," We test here the first possibility, that $\gamma$ -ray beaming explains the low observed fluxes of some nearby energetic pulsars." + We also comment briefly on the possibility that objects with detected luminosities Leey May be probing an emission component different to the powerful high-altitude gap emission which apparently dominates the bulk of the LAT-detected pulsars.," We also comment briefly on the possibility that objects with detected luminosities $\ll L_{\gamma,heu}$ may be probing an emission component different to the powerful high-altitude gap emission which apparently dominates the bulk of the LAT-detected pulsars." + To find sub-luminous pulsars. we measure the DC (unpulsed) flux at thepositionsnr of nearby (7.x2 kpe). energetic (E>10?ere 1) non-recycled radio. pulsars selected from the ATNF pulsars. catalog (Manchesteretal. 2005).," To find sub-luminous pulsars, we measure the DC (unpulsed) flux at thepositions of nearby $d \le 2$ kpc), energetic $\dot{E}>10^{34}\,\mathrm{erg\,s^{-1}}$ ) non-recycled radio pulsars selected from the ATNF pulsar catalog \citep{met05}." + There are 12 such objects (Table | also includes two comparison objects)., There are 12 such objects (Table 1 also includes two comparison objects). +" Since the LAT has. detected several pulsars. especially millisecond pulsars. in the ~10Stores+ boundary of the ""death zone’ we also consider the well-studied nearby E=10°ores! pulsar PSR J1932+1059 (B1929+10). which has a low LAT flux limit."," Since the LAT has detected several pulsars, especially millisecond pulsars, in the $\sim 10^{33-34}{\rm erg\,s^{-1}}$ boundary of the `death zone' we also consider the well-studied nearby ${\dot E} = 10^{33.6}{\rm erg\, s^{-1}}$ pulsar PSR J1932+1059 (B1929+10), which has a low LAT flux limit." + Finally. for comparison we include Geminga (J0633+1746). a nearby 5-selected pulsar with an HST parallax measurement.," Finally, for comparison we include Geminga (J0633+1746), a nearby $\gamma$ -selected pulsar with an HST parallax measurement." + We should note that this distance cut-off is somewhat arbitrary: for example PSR 2958 with a CLO2 distance of kkpe is a LAT pulsed detection., We should note that this distance cut-off is somewhat arbitrary; for example PSR $-$ 2958 with a CL02 distance of kpc is a LAT pulsed detection. + To measure the unpulsed fluxes. we use 24 months of LAT data (Aug 4 2008 — Aug 4 2010) and the Po_VV11 instrument response function. a refinement to previous analyses reflecting improved understanding of the point spread function and effective area (Abdoetal.2011).," To measure the unpulsed fluxes, we use 24 months of LAT data (Aug 4 2008 – Aug 4 2010) and the V11 instrument response function, a refinement to previous analyses reflecting improved understanding of the point spread function and effective area \citep{p6v11}." +" Diffuse-Class"" events were selected from good runs with rocking angle <52°. reconstructed energies (175<Του./GeV)«2. and a reconstructed zenith angle «1007."," `Diffuse-Class' events were selected from good runs with rocking angle $<52^\circ$, reconstructed energies $-0.75 < {\rm Log} (E_\gamma/{\rm GeV}) < 2$, and a reconstructed zenith angle $<100^{\circ}$." + The list of point sources used in the background model is drawn from a preliminary version of the two-yearFermi catalog., The list of point sources used in the background model is drawn from a preliminary version of the two-year catalog. + The analysis used an updated version of the model for the diffuse background - Galactic. extragalactic. and residual cosmie rays - that is being prepared for publication by the LAT team.," The analysis used an updated version of the model for the diffuse background - Galactic, extragalactic, and residual cosmic rays - that is being prepared for publication by the LAT team." + Like the model used for the IFGL catalog (Abdoetal.2010b) it is based on fitting templates for the diffuse emission to the LAT data.," Like the model used for the 1FGL catalog \citep{1FGL} + it is based on fitting templates for the diffuse emission to the LAT data." +" For each pulsar we assume an exponentially cutoff spectrum dN/dE=Ny(EfCoV)Uoxp(E/E,)."," For each pulsar we assume an exponentially cutoff spectrum $dN/dE = +N_0\,(E/\mathrm{GeV})^{-\Gamma}\,\exp(-E/E_c)$." + For the bright LAT-detected pulsars (marked in the Table) we allow E. and Τ to vary in the fits: the results are consistent with parameters quoted in Abdoetal. (2010a)., For the bright LAT-detected pulsars (marked $^b$ in the Table) we allow $E_c$ and $\Gamma$ to vary in the fits; the results are consistent with parameters quoted in \citet{psrcat}. . +. For the other pulsars we set these parameters to values determined from an empirical fit to detected LAT pulsars (RWIO: Dl=L.10.156los4)E and {ιο=—0.15|QU.Tllog4gBree with By: the magnetic field measured at the pulsar’s light cylinder.," For the other pulsars we set these parameters to values determined from an empirical fit to detected LAT pulsars (RW10): $\Gamma=-4.1 + 0.156\log_{10}\dot{E}$ and $E_c/\mathrm{GeV}=-0.45+0.71\log_{10}B_{LC}$, with $B_{LC}$ the magnetic field measured at the pulsar's light cylinder." + We evaluate the likelihood for Ny at the knownD pulsar position using pointlike'. a binned likelihood analyst tool (Kerr2010).. and using a Bayesian approach with a uniform prior we integrate the likelihood to 07.54 to obtain a 2c upper limit on the flux.," We evaluate the likelihood for $N_0$ at the known pulsar position using `pointlike', a binned likelihood analysis tool \citep{kerr10}, and using a Bayesian approach with a uniform prior we integrate the likelihood to $97.5\%$ to obtain a $2\sigma$ upper limit on the flux." + For sources with apparent DC emission. we determine the corresponding range for the measured Ny.," For sources with apparent DC emission, we determine the corresponding range for the measured $N_0$ ." + For comparison with results in Abdo these measurements and upper limitsare then converted to LZ>0.1 GGeV fluxes using the model spectra.," For comparison with results in \citet{psrcat} + these measurements and upper limitsare then converted to $E>0.1$ GeV fluxes using the model spectra." + The uncertainties reported for the measured fluxes, The uncertainties reported for the measured fluxes +blazar spectrum (4V/dE [photons ? ! !] x E|) results in à power law index for the spectrum of the blazar LES 1101-232 of D = -0.1.,blazar spectrum $dN/dE$ [photons $^{-2}$ $^{-1}$ $^{-1}$ ] $\propto$ $E^{-\Gamma}$ ) results in a power law index for the spectrum of the blazar 1ES 1101-232 of $\Gamma$ = -0.1. + The model must be scaled down by a factor of 0.45 to the P0.45 model (lower curve in Figure 10)) to give a power law index of al least 1.5. which is considered by Aharonianetal.(2006) to be the lowest acceptable value.," The model must be scaled down by a factor of 0.45 to the P0.45 model (lower curve in Figure \ref{p1.0}) ) to give a power law index of at least 1.5, which is considered by \citet{aha06} to be the lowest acceptable value." + Alapellietal.(2006) show however that an EBL model. also based on the values al 1.25 and 2.2 pom. but with a steeper decline from 4 to 10 jin results in a power law index of D = 40.5.," \citet{map06} show however that an EBL model, also based on the \citet{elw01} values at 1.25 and 2.2 $\mu$ m, but with a steeper decline from 4 to 10 $\mu$ m results in a power law index of $\Gamma$ = +0.5." + Thev consider P= 0.6 to be the lowest acceptable index based on physical considerations and suggest then that while the DIRBE minus 2MAÀSS CIRB values al 1.25 and 2.2 jan from Wright(2001). do require a hard spectrum. and the lower limits from galaxy counts are favored. they. ancl the slightly lower values reported here ((9.15.16) kJv 1). can not be ruled out based on the current ILE.S.8. data.," They consider $\Gamma$ = 0.6 to be the lowest acceptable index based on physical considerations and suggest then that while the DIRBE minus 2MASS CIRB values at 1.25 and 2.2 $\mu$ m from \citet{elw01} do require a hard spectrum, and the lower limits from galaxy counts are favored, they, and the slightly lower values reported here ((9,15,16) kJy $^{-1}$ ), can not be ruled out based on the current H.E.S.S. data." + While the implications of -rav altenuation for CIRD measurement are still limited by the small number of observed sources. (his independent limit on the CIRB will only improve as more blazars are observed bv ILE.S.S. and eventually. VERITAS.," While the implications of $\gamma$ -ray attenuation for CIRB measurement are still limited by the small number of observed sources, this independent limit on the CIRB will only improve as more blazars are observed by H.E.S.S. and eventually, VERITAS." + There is still a substantial difference between the Fazioetal.(2004) lower limits from ealaxv counts and the intensities determined here., There is still a substantial difference between the \citet{faz04} lower limits from galaxy counts and the intensities determined here. + Progress can be made in resolving this discrepancy. with improvements in the photometry of survey data fromSpilzer.. as well as improvenienis in the zodiacal light models. aud. further data on eamima-ray attenuation.," Progress can be made in resolving this discrepancy with improvements in the photometry of survey data from, as well as improvements in the zodiacal light models and further data on gamma-ray attenuation." + llowever. the dominant source of error in directly measuring the CIRB. the model based subtraction of the zodiacal light. will not be significantly. reduced with currently available data.," However, the dominant source of error in directly measuring the CIRB, the model based subtraction of the zodiacal light, will not be significantly reduced with currently available data." + A directly measured map of the zodiacal light. whieh would have to be observed from outside the bulk of the IPD cloud. bevond about 3AU. would allow accurate removal of the zodiacal Heht from the DIRBE maps aud thus an accurate. direct measurement of the Cosmic Infrared. Background.," A directly measured map of the zodiacal light, which would have to be observed from outside the bulk of the IPD cloud, beyond about 3AU, would allow accurate removal of the zodiacal light from the DIRBE maps and thus an accurate, direct measurement of the Cosmic Infrared Background." + We have shown here that the subtraction of eatalogued stars from low resolution maps works well. (hus an instrument wilh a field of view of a few square degrees and a resolution of a few arcminutes would suffice.," We have shown here that the subtraction of catalogued stars from low resolution maps works well, thus an instrument with a field of view of a few square degrees and a resolution of a few arcminutes would suffice." + The main requirements would be sensitivitv to extremely low surface brightnesses. down to less than 1 nW 7 | lor good signal to noise. and an accurate. absolute flix calibration.," The main requirements would be sensitivity to extremely low surface brightnesses, down to less than 1 nW $^{-2}$ $^{-1}$ for good signal to noise, and an accurate, absolute flux calibration." + Such anu instrument could be a camera on a probe to one of the outer planets., Such an instrument could be a camera on a probe to one of the outer planets. + It would also be useful to have observations from different positions with respect to the IPD cloud., It would also be useful to have observations from different positions with respect to the IPD cloud. + This could be accomplished either by observing the same fields al widely different solar elongations curing a long lived mission as the eralt orbits the sun. or bv observing during the eruise from { to 3 AU as the dust density decreases.," This could be accomplished either by observing the same fields at widely different solar elongations during a long lived mission as the craft orbits the sun, or by observing during the cruise from 1 to 3 AU as the dust density decreases." + While we will continue to improve our understanding of the CIRB in the mean (nme. a space mission of (his (vpe will ultimately. be required.," While we will continue to improve our understanding of the CIRB in the mean time, a space mission of this type will ultimately be required." + The CODE datasets were developed by (he NASA Goddard Space Flight Center under the direction of the CODE Science Working Group and were provided by the NSSDC., The COBE datasets were developed by the NASA Goddard Space Flight Center under the direction of the COBE Science Working Group and were provided by the NSSDC. +"The results are reported in Table 2. together with the derived cuantities j. n,. d, aud (heir uncertainties.","The results are reported in Table \ref{para_physical_SDSS_data} together with the derived quantities $ j$ , $n_*$, $d_*$ and their uncertainties." +" Table 2. also reports M,. the number of elements \ belonging, to the sample . (he merit. functionB. 4L7 and the associated. p value that has to be understood as the maximum probability to obtain a better filling. see formula (15.2.12) in Pressetal.(1992): where GAMAIQ isa subroutine for theincomplete gamma. function."," Table \ref{para_physical_SDSS_data} also reports $M_{max}$, the number of elements $N$ belonging to the sample , the merit function $\chi^2$ and the associated $p$ –value that has to be understood as the maximum probability to obtain a better fitting, see formula (15.2.12) in \citet{press}: where GAMMQ isa subroutine for theincomplete gamma function." +" (Alaromianetal.(2006. ον.ας—Er DPc15. P1.5 (Aharonianetal.(2008):(2011))). P—1.5. (Maziu&Raue(2007))). (2000))) iu the energv band below ~LOO (ον, where the effect of absorption ou the EBL becomes ueelieible."," \cite{gould}) \cite{AhaEBL,Aha1ES0229,Orr_EBL_1ES0229}) $dN_\gamma/dE\sim E^{-\Gamma}$ $\Gamma \ge 1.5$ $\Gamma\ge 1.5$ \cite{aharonian08,bottcher08,katarzinski06,Lefa_hard1,Lefa_hard2,neronov11}) $\Gamma=1.5$ \cite{mazin}) ) in the energy band below $\sim 100$ GeV, where the effect of absorption on the EBL becomes negligible." +" However. the blazars used for the derivation of constraints ou the EBL are characterized by hard spectra, Which ales it difficult o observe their fiux below 100 Ge. Tn fact. the blazar |ES 0229|200. wicl provides the tightest coustraiuts ou the EBL (AharoΠαletal.(2007))) is not listed im the catalogue of sotTees4 detected by LAT in two-vear exyostire (Abdoοal. 20111). with ouly upper hits on the source flux derived from the LAT data (Neronov&Vovl(2010):Tavecchioetal.(2010):Tavlor (2011))) and a wea detection reported by Orretal.(2n1)."," However, the blazars used for the derivation of constraints on the EBL are characterized by hard spectra, which makes it difficult to observe their flux below 100 GeV. In fact, the blazar 1ES 0229+200, which provides the tightest constraints on the EBL \cite{Aha1ES0229}) ) is not listed in the catalogue of sources detected by LAT in two-year exposure \cite{fermi_catalog}) ), with only upper limits on the source flux derived from the LAT data \cite{NeronovEGMF,Tavecchio:2010mk,TaylorEGMF}) ) and a weak detection reported by \cite{Orr_EBL_1ES0229}." +. An additional difficulty or such constmünts is) that the spectrum of hard blazars nuüght be composed of two contributions., An additional difficulty for such constraints is that the spectrum of hard blazars might be composed of two contributions. +" Apart frou tje direct ccluission frou, the pri.Arv sOHYCOC. llb additional contribution is expected frou the ccascade initiated iu the intergalactic mediun (ICAL) bv the absorbed VIIE 7 ravs (Aharonianetal.(1991):Plaga (1995)))."," Apart from the direct emission from the primary source, an additional contribution is expected from the cascade initiated in the intergalactic medium (IGM) by the absorbed VHE $\gamma$ rays \cite{aharonian94,plaga95}) )." + The overall flux aud the spectral shape of the cascade contribution are determined by the streneth of the extragalactic magnetic field CECAIF) (Aharonianetal.(2002):Plaga(1995):Neronov&Senmükoz(2007. 2009))).," The overall flux and the spectral shape of the cascade contribution are determined by the strength of the extragalactic magnetic field (EGMF) \cite{Aharonian_cascade,plaga95,neronov07,NerSem_prediction}) )." + Uucertainty of the ECGME streneth introduces an uncertainty of the importance of the cascade coutribution aud prevents the measurement of the slope of the iutriusic sspectit of the source., Uncertainty of the EGMF strength introduces an uncertainty of the importance of the cascade contribution and prevents the measurement of the slope of the intrinsic spectrum of the source. + Iu fact. the limits ou the EBL derived up to now are based on an underlying assumption about the EGAIF streneth (the EGALIF should be strong snough to suppress the cascade coutribution up to the ~TeV αιαον baud). which is not justified a-priori.," In fact, the limits on the EBL derived up to now are based on an underlying assumption about the EGMF strength (the EGMF should be strong enough to suppress the cascade contribution up to the $\sim$ TeV energy band), which is not justified a-priori." + If the assumption on the EGAIF strength is relaxed. the ddata can be used to measure the ECAIF streneth.," If the assumption on the EGMF strength is relaxed, the data can be used to measure the EGMF strength." + Theelectron-positronpairs.created as aresult of the absorption of multi-TeV photons. up-scatter the Cosmic nücrowave backeround (CAIB) as thev cool. creating," Theelectron-positronpairs,created as aresult of the absorption of multi-TeV photons, up-scatter the Cosmic microwave background (CMB) as they cool, creating" +and the integrals are easily calculated even analytically.,and the integrals are easily calculated even analytically. + In the appendix we present an elegant wav to find the 5 s Chat maximize log£ directly. without anv iterations.," In the appendix we present an elegant way to find the $b_k$ 's that maximize $\log \likelihood$ directly, without any iterations." + In order to check the performance of and its realization we have performed several simulations. some of which are presented in Figure 2.," In order to check the performance of and its realization we have performed several simulations, some of which are presented in Figure 2." + In those simulations we generated an artificial sample of planets drawn from populations with different PDFs of the planet masses. and inclinations oriented isotropically in space.," In those simulations we generated an artificial sample of planets drawn from populations with different PDFs of the planet masses, and inclinations oriented isotropically in space." + To make the simulation similar to (he present work we chose (he size of each sample to be 50 planets., To make the simulation similar to the present work we chose the size of each sample to be 50 planets. + We assumed no selection effects., We assumed no selection effects. + We then applied ito the simulated sample. the results of which are plotted in Figure 2.," We then applied to the simulated sample, the results of which are plotted in Figure 2." + The three examples of Figure 2 clearly show the power of MAXLIMA., The three examples of Figure 2 clearly show the power of MAXLIMA. + We assume (hat the sample is constructed of planets with period. P. between Das ," We assume that the sample is constructed of planets with period, $P$, between $P_{\rm min} \leq P \leq P_{\rm max}$ ." +We further assume that the search for planets discovered. all raclial-velocity variables with amplitude A larger than ἵνμμ., We further assume that the search for planets discovered all radial-velocity variables with amplitude $K$ larger than $K_{\rm min}$. + We have to correct for planets not detected because they induce A smaller (han the threshokl., We have to correct for planets not detected because they induce $K$ smaller than the threshold. +" To do that we note that the amplitude can be written as The expression MM,xsin/is actually our y.", To do that we note that the amplitude can be written as The expression $M_p\times \sin i$is actually our $y$. +" For anv value of y and M, we can derive (he maximunm possibly detected period Prasdetect. £1ven Ain."," For any value of $y$ and $M_1$ we can derive the maximum possibly detected period — $P_{\rm max-detect}$, given $K_{\rm min}$." + This implies that if we know the period distribution and we assume that (he period is uncorrelated to the mass distribution. we can estimate for each of the given y's the fraction of planets with long periods that were not detected with the same jy.," This implies that if we know the period distribution and we assume that the period is uncorrelated to the mass distribution, we can estimate for each of the given $y$ 's the fraction of planets with long periods that were not detected with the same $y$." +" This means Chat to correct for the undetected planets with long periods we have (o consider each of the j-th detected svstems as representing some a, planets.", This means that to correct for the undetected planets with long periods we have to consider each of the j-th detected systems as representing some $\alpha_j$ planets. +" ID Psdetect 15 5maller than Dyas. then a, is larger than unity."," If $P_{\rm +max-detect}$ is smaller than $P_{\rm max}$ , then $\alpha_j$ is larger than unity." + Otherwise a; is equal to unity., Otherwise $\alpha_j$ is equal to unity. +both objects have X-ray luminosities consistent with the Eddington limit huminositv. [or spherical accretion onto a 1.4 M. neutron star (2x107 erg !). which suggests that it is conceivable that we are detecting justone low mass X-ray binary (LAINRB) svstem in each GC.,"both objects have X-ray luminosities consistent with the Eddington limit luminosity for spherical accretion onto a 1.4 $M_{\odot}$ neutron star $2\times 10^{38}$ erg $^{-1}$ ), which suggests that it is conceivable that we are detecting just low mass X-ray binary (LMXRB) system in each GC." + However. as. Angelini.Loewenstein.&Mushotzky(2001) point out. in our galaxy and in 500 GC svstems in M31 there are GC's with X-ray. luminosities exceeding 1xLO ere +.," However, as \citet{ang01} point out, in our galaxy and in 500 GC systems in M31 there are GC's with X-ray luminosities exceeding $1\times 10^{38}$ erg $^{-1}$." + Within our Galaxy all LAIXNRDB’s have luminosities between ~107? and ~7x10* ere |.," Within our Galaxy all LMXRB's have luminosities between $\sim +10^{36}$ and $\sim 7\times 10^{37}$ erg $^{-1}$." + Thus it might reasonable to assume that a population of anvthing between 2-200 LMXBRDs per GC would also produce the observed luminosity., Thus it might reasonable to assume that a population of anything between 2-200 LMXRB's per GC would also produce the observed luminosity. + such a large number of LAINRB’s in a GC indicates that the efficiency. of producing such svstenis is greatly enhanced compared to (he GC's of the Milkv Way or M31., Such a large number of LMXRB's in a GC indicates that the efficiency of producing such systems is greatly enhanced compared to the GCs of the Milky Way or M31. + The stellar ονπαΙός of (he GCs in question must therefore be different than Chat of the twpical GC in the Milky Way (or M31)., The stellar dynamics of the GCs in question must therefore be different than that of the typical GC in the Milky Way (or M31). + Ht has been shown from N-Bocly simulations. that the number of stars initially in binaries greatly enhances stellar interactions and the üghtenimg of binary orbits., It has been shown from N-Body simulations \citep{gia85} that the number of stars initially in binaries greatly enhances stellar interactions and the tightening of binary orbits. + This process eventually. after manv interactions. produces mass exchange svstems such as LAINRB’s.," This process eventually, after many interactions, produces mass exchange systems such as LMXRB's." + Large N-Bocly simulations of these svstems(> 100.000 stars) have only just begun to produce results. however. these simulations do appear to produce hundreds of LAIXRB’s.," Large N-Body simulations of these $>$ 100,000 stars) have only just begun to produce results, however, these simulations do appear to produce hundreds of LMXRB's." + The question was raised by Angelini.Loewenstein.&Mushotzkv(2001) that the denamies of the GCs in NGC 1399 would therefore have to be different to produce so many LMXRD's., The question was raised by \citet{ang01} that the dynamics of the GCs in NGC 1399 would therefore have to be different to produce so many LMXRB's. + While it is hard to imagine a scenario where the dvnamies of a GC would be so different [rom that of the Milkv. Way or M21. it should be stressed that the Fornax svstem is a cluster of galaxies that has undergone many galaxv-galaxy interactions and mergers.," While it is hard to imagine a scenario where the dynamics of a GC would be so different from that of the Milky Way or M31, it should be stressed that the Fornax system is a cluster of galaxies that has undergone many galaxy-galaxy interactions and mergers." + As well as an increase in the specilic Irequeneyv. of GCs due to the merger of populations. GC formation may also occur during the merger of giant galaxies (AshmanZepl&Ashman 1993).," As well as an increase in the specific frequency of GCs due to the merger of populations, GC formation may also occur during the merger of giant galaxies \citep{ash92,zep93}." +. If the dynamics were different for the GC's existing prior (ο mergers in Fornax the GC's must have been Udally shocked during the galaxy mergers - stripping a large Traction of the low mass stars from a GC and causing it (o undergo core collapse ancl creating manv new tight binary svstems (IxNundie&Ostriker1995:Gneclin.Lee.1999:Gnedin.Hernquist.&Ostriker 1999).," If the dynamics were different for the GCs existing prior to mergers in Fornax the GCs must have been tidally shocked during the galaxy mergers - stripping a large fraction of the low mass stars from a GC and causing it to undergo core collapse and creating many new tight binary systems \citep{kun95,gne99a,gne99b}." +. I. however. the svstems we are seeing are (he GCs createdduring the galaxy mergers. then the number of short period binaries must have been greatly enhanced from that of GCs formed prior to the mergers.," If, however, the systems we are seeing are the GCs created the galaxy mergers, then the number of short period binaries must have been greatly enhanced from that of GCs formed prior to the mergers." + It would (hen also be likely that they would be vounger (han the general GC population., It would then also be likely that they would be younger than the general GC population. + We will pursuethis «question in a future study., We will pursuethis question in a future study. +"The results of our simulations can be divided into two main findings: (1) new insights into the evolutionary behavior of twostream instabilities in multi-component plasma and (2) the change in the distribution function of the parucles, in particular the acceleration caused by the instability.","The results of our simulations can be divided into two main findings: (1) new insights into the evolutionary behavior of twostream instabilities in multi-component plasma and (2) the change in the distribution function of the particles, in particular the acceleration caused by the instability." +" Due to the huge amount of data, simulation results have been written every tenth step for the fields (electric and magnetic fields, currents) and every hundredth step for particle data."," Due to the huge amount of data, simulation results have been written every tenth step for the fields (electric and magnetic fields, currents) and every hundredth step for particle data." + In this section we analyze the evolutionary behaviour of the electric and magnetic fields and the currents in the simulations conducted., In this section we analyze the evolutionary behaviour of the electric and magnetic fields and the currents in the simulations conducted. + From previous simulations of filamentation instabiles in pair plasmas (see e.g. 2) itis well known how magnetic and electric fields evolve., From previous simulations of filamentation instabilities in pair plasmas (see e.g. \citealt{2003ApJ...596L.121S}) ) it is well known how magnetic and electric fields evolve. + We compare the behaviour of plasmas with different mass-ratios., We compare the behaviour of plasmas with different mass-ratios. +" The most significant quantity in this context is the transverse magnetic field energy averaged over the entire computational domain B-=(B;+B2), since strong magnetic fields are essential to create and maintain the flux tubes observed in kinetic. instabiliues, furthermore the point in time the instability peak occurs and also the existence of a second peak, respectively."," The most significant quantity in this context is the transverse magnetic field energy averaged over the entire computational domain $B_{\perp}^2 = (B_x^2 + B_y^2)$, since strong magnetic fields are essential to create and maintain the flux tubes observed in kinetic instabilities, furthermore the point in time the instability peak occurs and also the existence of a second peak, respectively." + In Fig., In Fig. +" | we therefore compare the Ume evolution of the transverse magnetic field energy B, computed in the lab frame as function of dillerent mass-ratos ny/n,.", \ref{B_vergleich} we therefore compare the time evolution of the transverse magnetic field energy $B_{\perp}$ computed in the lab frame as function of different mass-ratios $m_p/m_e$. +" It is evident that the maximum value of the transverse magnetic field energy reached in the different simulations are comparable, even though it has to be noted that for the non-pair plasma the maximum energy can only be found in the second peak."," It is evident that the maximum value of the transverse magnetic field energy reached in the different simulations are comparable, even though it has to be noted that for the non-pair plasma the maximum energy can only be found in the second peak." +" The development of the second peak shows a nicely observable dependence on the fundamental mass ratio: For the lower mass-ratios no two peak structure can be seen, while with increasing mass-ratio a clear distinction can be made."," The development of the second peak shows a nicely observable dependence on the fundamental mass ratio: For the lower mass-ratios no two peak structure can be seen, while with increasing mass-ratio a clear distinction can be made." +" When looking at the time until the instability fully develops. one can see that for higher mass-ratios m,/m, it takes longer to reach the peak value [or the magnetic field."," When looking at the time until the instability fully develops, one can see that for higher mass-ratios $m_p/m_e$ it takes longer to reach the peak value for the magnetic field." + lf one compares simulations with of 1 and 100 one can explain what is happening in the counterstreaming plasma: First an instability develops almost simultaneously for both mass-ratios (single peak for mass-ratio | and first peak for mass-ratio 100)., If one compares simulations with mass-ratios of 1 and 100 one can explain what is happening in the counterstreaming plasma: First an electron-positron instability develops almost simultaneously for both mass-ratios (single peak for mass-ratio 1 and first peak for mass-ratio 100). + [fa third and heavier species exists another peak will be apparent at later limes (which can be seen in Fig. 1)., If a third and heavier species exists another peak will be apparent at later times (which can be seen in Fig. \ref{B_vergleich}) ). + This behavior is not observable for medium mass-ratio simulations since both peaks overlap and can not be distinguished anymore., This behavior is not observable for medium mass-ratio simulations since both peaks overlap and can not be distinguished anymore. +" The existence of two instabiliues in the plasma has important impact on the amplitude and duration of the instability: Clearly the instability lasts longer for the high mass-ratio simulations, since in this case the heavy protons are accelerated slower compared to the lighter electrons/positrons but are able to stabilize the flux tubes for a longer period of me."," The existence of two instabilities in the plasma has important impact on the amplitude and duration of the instability: Clearly the instability lasts longer for the high mass-ratio simulations, since in this case the heavy protons are accelerated slower compared to the lighter electrons/positrons but are able to stabilize the flux tubes for a longer period of time." + Another result to note is that the maximum amplitude decreases with increasing mass-ratio., Another result to note is that the maximum amplitude decreases with increasing mass-ratio. + This effect can be attributed to the lower number of parucles constituüng each instability., This effect can be attributed to the lower number of particles constituting each instability. +"with a median redshift z,,,5,,-0.076 is compared. in Figure 3 with the results at higher-z of Norman ct al. (",with a median redshift $z_{median}=0.076$ is compared in Figure \ref{lf1} with the results at $z$ of Norman et al. ( +2004).,2004). + ‘These authors derived the first ever X-ray galaxy. luminosity function. using data from the combined CDb-North and South.," These authors derived the first ever X-ray galaxy luminosity function, using data from the combined CDF-North and South." + Their sample probing redshifts up to z&1 is split into two redshift bins with median z=0.26 anc z=0.66 respectively., Their sample probing redshifts up to $z\approx1$ is split into two redshift bins with median $z=0.26$ and $z=0.66$ respectively. + Inspection of Fig., Inspection of Fig. + 3.2 shows that their “quasi-local’ z«0.5 luminosity function is in good agreement with ours especially at the faint end., \ref{lf1} shows that their 'quasi-local' $z<0.5$ luminosity function is in good agreement with ours especially at the faint end. + At bright luminosities the CDE luminosity function is significantly higher than ours., At bright luminosities the CDF luminosity function is significantly higher than ours. + ‘This may suggest contamination of the Norman et al. (, This may suggest contamination of the Norman et al. ( +2004) sample by ACNs at bright luminosities.,2004) sample by AGNs at bright luminosities. + This is not highly unlikely. especially at luminosities brighter than 107units.. since there is no optical spectroscopy available for all he sources of Norman et al. (," This is not highly unlikely, especially at luminosities brighter than $10^{42}$, since there is no optical spectroscopy available for all the sources of Norman et al. (" +2004).,2004). +" Alternatively. we may oe Witnessing evolution of the ‘normal’ galaxy. luminosity ""unction."," Alternatively, we may be witnessing evolution of the `normal' galaxy luminosity function." + The median redshift of the 2«0.5r subsample of vorman et al., The median redshift of the $z<0.5$ subsample of Norman et al. + ds zqaian0.26 higher than our median redshift z=0.076., is $z_{median}=0.26$ higher than our median redshift $z=0.076$. +" For luminosity evolution of the form (1|s)°"" derived by Norman et al. (", For luminosity evolution of the form $(1+z)^{2.7}$ derived by Norman et al. ( +2004). a source at 2=)26 is expected to become 1.5 times more luminous relative o 2=0.076.,"2004), a source at $z=0.26$ is expected to become 1.5 times more luminous relative to $z=0.076$." + Moreover. we are excluding from our analysis systems with N-ray. to optical flux ratio log(f/f.)>»2 and therefore. our sample may. be biased. against X-ray ultra-Iuminous star-forming galaxies. especially those with LxZ107eres (sce e.g. Moran et al.," Moreover, we are excluding from our analysis systems with X-ray to optical flux ratio $\log (f_x +/f_o)>-2$ and therefore, our sample may be biased against X-ray ultra-luminous star-forming galaxies, especially those with $L_X \ga 10^{42} \rm \, erg +\, s^{-1}$ (see e.g. Moran et al." + 1999)., 1999). + Norman et al. (, Norman et al. ( +2004) use the log-norm functional Form for fitting their luminosity function.,2004) use the log-norm functional form for fitting their luminosity function. + We note that such a formi describes equally well our data: the Git vields AL1.4 relative to the Schechter best-fit. which can be considered however as only a marginal improvement as the log-norm functional form has an additional [ree parameter.," We note that such a form describes equally well our data; the fit yields $\Delta L\approx 1.4$ relative to the Schechter best-fit, which can be considered however as only a marginal improvement as the log-norm functional form has an additional free parameter." + In any case. the statistics are still limited and a detailed comparison of the Schechter and log-norm functional forms has to await till more data are accumulated.," In any case, the statistics are still limited and a detailed comparison of the Schechter and log-norm functional forms has to await till more data are accumulated." + The luminosity. function. derived. above enconipasses both late and early galaxy types., The luminosity function derived above encompasses both late and early galaxy types. + Figure 4 presents the Ó(Lx) estimates for these two classes separately., Figure \ref{lf2} presents the $\phi(L_X)$ estimates for these two classes separately. + οσο are compared with the local X-ray luminosity lunctions derived. from (i) optically selected: star-forming galaxies (Ccorgantopoulos ct al., These are compared with the local X-ray luminosity functions derived from (i) optically selected star-forming galaxies (Georgantopoulos et al. + 1999) and (ii) warm LAS galaxies (Norman et al., 1999) and (ii) warm IRAS galaxies (Norman et al. + 2004)., 2004). +" The former largely overestimates the number of emission-line svstems at low luminosities while the latter provides a better. representation of the X-ray luminosity function although it underprecicts the number of galaxies with L«L,.", The former largely overestimates the number of emission-line systems at low luminosities while the latter provides a better representation of the X-ray luminosity function although it underpredicts the number of galaxies with $L1., We find a contribution to the X-ray background of 9 and 6 per cent for emission and absorption line galaxies respectively using the p=3.3 evolution model truncated at $z=1$. + However. it is possible that the absorption line systems. associated with earlv-type galaxies. do not presen such strong evolution with cosmic time (Lilly et al.," However, it is possible that the absorption line systems, associated with early-type galaxies, do not present such strong evolution with cosmic time (Lilly et al." + 1995)., 1995). + Assuming no evolution for these systems we assess tha they contribute about 2 per cent to the ΧΙΟ., Assuming no evolution for these systems we assess that they contribute about 2 per cent to the XRB. + The fractions derived above are higher than those in the CDE-North., The fractions derived above are higher than those in the CDF-North. + For example Hornschemoeier et al. (, For example Hornschemeier et al. ( +2003) estimate that 1-2 per cent of the kkeV NRB could arise in normal galaxies.,2003) estimate that 1-2 per cent of the keV XRB could arise in normal galaxies. + Llowever. this is estimated by adding the fluxes of optically selected. galaxies in the CDE-North survey ancl therefore should be considered as a lower limit as it does not take into account the contribution of optically fainter svstenis.," However, this is estimated by adding the fluxes of optically selected galaxies in the CDF-North survey and therefore should be considered as a lower limit as it does not take into account the contribution of optically fainter systems." + The and. missions opened. a new window in the study of distant galaxies hy providing the first X-ray selected: normal galaxy sample., The and missions opened a new window in the study of distant galaxies by providing the first X-ray selected normal galaxy sample. + owing to its large field-of-view can constrain ellicientlv. the local (2X; 0.2) N-rav galaxy luminosity function., owing to its large field-of-view can constrain efficiently the local $z\la0.2$ ) X-ray galaxy luminosity function. + The deep fields. probe normal galaxies. with a median redshift of z0.3 (up to a maximum redshift of z=1) vielding information on the evolution of the galaxies at X- wavelengths., The deep fields probe normal galaxies with a median redshift of $z\approx0.3$ (up to a maximum redshift of z=1) yielding information on the evolution of the galaxies at X-ray wavelengths. + However. the peak of the star-formation activity lies at even higher redshifts which remain bevond the reach of the current X-ray. missions.," However, the peak of the star-formation activity lies at even higher redshifts which remain beyond the reach of the current X-ray missions." + “Phese distant ealaxies reside at [Iuxes fainter than 10, These distant galaxies reside at fluxes fainter than $10^{-17}$ . +particles (p*.NCr. p)) in the upstream. (downstream) region.,"particles $p^2 N(x,p)$ ) in the upstream (downstream) region." +" The curves refer to. different momenta of accelerated particles: p=O0.lp,,4,; (solid line). p=Piro. (dashed line) aud p=ρω Glash-dotted Ime)."," The curves refer to different momenta of accelerated particles: $p=0.1 p_{max}$ (solid line), $p=p_{max}$ (dashed line) and $p=2 p_{max}$ (dash-dotted line)." + The main differences with the previous case are all due to the fact that now the diffusion coellicient depends on momentum., The main differences with the previous case are all due to the fact that now the diffusion coefficient depends on momentum. +" In the upstream region. the size of the diffusion region for p«pao, scales linearly with the momentum. as clearly shown in the left panel of Fig. 3."," In the upstream region, the size of the diffusion region for $pPma» the svnehrotron losses are faster than acceleration and the spatial size of the particle distribution starts decreasing., At $p>p_{max}$ the synchrotron losses are faster than acceleration and the spatial size of the particle distribution starts decreasing. + The situation downstream is again more interesting., The situation downstream is again more interesting. + Introducing once again the (wo distances. c2.ade=toTfess(p)4oL/p and vapy?00=V/23Dyppri(p)/TMEA (constant in. momentun). one sees (hat the spatial size of the downstream region for particles of momentum p is given by riadv=usnsCp)oxL/p For all momenta such that ρω«y3(r+1)/(2r(r—1)).," Introducing once again the two distances $x_{loss}^{adv}=u_2\tau_{loss}(p)\sim 1/p$ and $x_{loss}^{diff}= \sqrt{2 D_{0,B} p\tau_{loss}(p)}$ (constant in momentum), one sees that the spatial size of the downstream region for particles of momentum $p$ is given by $x_{loss}^{adv}=u_2\tau_{loss}(p)\propto 1/p$ for all momenta such that $p/p_{max}<\sqrt{3(r+1)/(2r(r-1))}$." +" For r—4. the condition becomes p/p,,,,« 0.8."," For $r=4$, the condition becomes $p/p_{max}< 0.8$ ." + The scaling with 1/p ean again be identilied in the right panel of Fig. 3.., The scaling with $1/p$ can again be identified in the right panel of Fig. \ref{fig:space4_bohm}. +" Moving to lower and lower energies the drop in the spatial density of accelerated particles at c6>Loja, becomes increasingly sharper."," Moving to lower and lower energies the drop in the spatial density of accelerated particles at $x>L_{2,max}$ becomes increasingly sharper." + In Fig., In Fig. + 4 we plot the results for compression [actor r=7., \ref{fig:space7_bohm} we plot the results for compression factor $r=7$. + The main difference with the previous cases is the appearance of pile-ups in the spatial distribution of low energv accelerated. particles in the downstream plasma., The main difference with the previous cases is the appearance of pile-ups in the spatial distribution of low energy accelerated particles in the downstream plasma. +" This feature is due to the enerev loss of parücles al ppre, around the bump which appears right belore the cutoff (see Fig. 1)).", This feature is due to the energy loss of particles at $p\sim p_{max}$ around the bump which appears right before the cutoff (see Fig. \ref{fig:spectra}) ). + The bumps become more pronounced at lower energies while being absent al pZpiu., The bumps become more pronounced at lower energies while being absent at $p\gtrsim p_{max}$. + The bumps are not artifacts of the calculation. as can be shown rather easily at least qualitatively: if advection is (he only relevant. process. then 2=us! downstream. ancl one can write dp/dyx= —(C1l/us)p?.," The bumps are not artifacts of the calculation, as can be shown rather easily at least qualitatively: if advection is the only relevant process, then $x=u_{2}t$ downstream, and one can write $dp/dx=-(A/u_{2}) p^{2}$ ." + Conservation of the number of particles between the shock (where the particle density is ο) and the location i. where the particle density is Νορ. a). then easily leads to where p=p/(1—Xrp/ua) is the momentum (hat a particle is produced with at the shock in order (to reach the location c downstream will momentum p. as calculated [rom the rate of momentum losses.," Conservation of the number of particles between the shock (where the particle density is $N_{0}(p)$ and the location $x$, where the particle density is $N(p,x)$ , then easily leads to where $\bar p=p/(1-Axp/u_{2})$ is the momentum that a particle is produced with at the shock in order to reach the location $x$ downstream with momentum $p$, as calculated from the rate of momentum losses." + The last step in Eq., The last step in Eq. + 29. holds for (he case in which No(p)xp., \ref{eq:Npx} holds for the case in which $N_{0}(p)\propto p^{-\gamma}$. + In (his case one can easily show Chat a spike develops at values ofr such that the denominator vanishes. provided 5<2 (namely r> 4).," In this case one can easily show that a spike develops at values of $x$ such that the denominator vanishes, provided $\gamma<2$ (namely $r>4$ )." + In reality. these spikes are smoothened by the presence of a cutoffin Not) audeven more important by the fact thatat sufficiently high, In reality these spikes are smoothened by the presence of a cutoffin $N_{0}(p)$ andeven more important by the fact thatat sufficiently high +were run on SNIC computing time at HPC2N,were run on SNIC computing time at HPC2N +redshifts includes 49 stars ancl 12 quasars.,redshifts includes 49 stars and 12 quasars. + Hence. the final sample of galaxies comprises 211 objects.," Hence, the final sample of galaxies comprises 211 objects." + The majority of them (147 or 70%)) belongs to the bright-ealaxy sample., The majority of them (147 or ) belongs to the bright-galaxy sample. + On the other hand. the subsample of 36 galaxies with redshifts 1.5<<2.«5 only consists of objects from the zCOSALOS-cleep sample.," On the other hand, the subsample of 36 galaxies with redshifts $1.5 < z < 3$ only consists of objects from the zCOSMOS-deep sample." + “hese high-redshift) galaxies (quasars excluded) correspond to. of the objects identified in the deep sample., These high-redshift galaxies (quasars excluded) correspond to of the objects identified in the deep sample. + Fig., Fig. + 9 shows the redshift distribution of the full spectroscopic control sample. the COSMOS mask. the 7zZCO08MOS.fint mask. the different. ALgalaxy types defined by and Vothe quasars.," \ref{fig_tz} shows the redshift distribution of the full spectroscopic control sample, the 4-4' mask, the faint' mask, the different galaxy types defined by, and the quasars." + Alter cross-correlating (by visual inspection) the 211 spectroscopic objects with the final i-band selected catalogue in the 12 patches we end up with a final sample of 162 spectroscopic redshifts used. to calibrate the photometric redshifts., After cross-correlating (by visual inspection) the 211 spectroscopic objects with the final i-band selected catalogue in the 12 patches we end up with a final sample of 162 spectroscopic redshifts used to calibrate the photometric redshifts. + A summery of the photometric redshift. technique used o derive the distances to the galaxies can be found. in ancl(2004a)., A summary of the photometric redshift technique used to derive the distances to the galaxies can be found in and. +. Before deriving the photometric redshifts we checked: and. fine-uned the calibration of our. photometric zeropoints by means of colour-colour plots of stars., Before deriving the photometric redshifts we checked and fine-tuned the calibration of our photometric zeropoints by means of colour-colour plots of stars. + We compared. the colours of stars with the colours of stellar templates from he library of converted to the COSMOS ilier svstem., We compared the colours of stars with the colours of stellar templates from the library of converted to the COSMOS filter system. + In general. corrections to the photometric zeropoints of only a few hundredth of a magnitude: were needed to obtain an good match to the stars and. best results for the photometric redshifts (if. compared to the spectroscopic ones).," In general, corrections to the photometric zeropoints of only a few hundredth of a magnitude were needed to obtain an good match to the stars and best results for the photometric redshifts (if compared to the spectroscopic ones)." + Only in the ραπ and in the band. the correction were in the order of a few tenths of a magnitudes.," Only in the u-band and in the K-band, the correction were in the order of a few tenths of a magnitudes." + A comparison between the reduced. IKIPPNO Ix-band and our Ix-band (both convolved to the same secing of 1.379) in patch. Ole showed. that although the total magnitudes agreed very well. the fixed aperture magnitudes (especially of relatively faint sources) cilfer svstematically bv a few tenths of a magnitude.," A comparison between the reduced KPNO K-band and our K-band (both convolved to the same seeing of ) in patch 01c showed, that although the total magnitudes agreed very well, the fixed aperture magnitudes (especially of relatively faint sources) differ systematically by a few tenths of a magnitude." + Therefore. we decided. to correct the IKPNO zeropoint by matching the faint sources in the IKPNO image with those in our own field (in the fixed aperture used to derive the photometric redshifts)., Therefore we decided to correct the KPNO zeropoint by matching the faint sources in the KPNO image with those in our own field (in the fixed aperture used to derive the photometric redshifts). + Moreover when calculating the photometric redshifts. we artificially increased the magnitude errors in the Ix-band. by 0.257 (aclded in quadrature to the SExtractor errors) to reduce the relative weight of this slightly problematic band.," Moreover when calculating the photometric redshifts, we artificially increased the magnitude errors in the K-band by $0.25^m$ (added in quadrature to the SExtractor errors) to reduce the relative weight of this slightly problematic band." + Therefore. we rely mostly on the accurate photometry of the NER 11 band.," Therefore, we rely mostly on the accurate photometry of the NIR H band." +" In order to avoid contamination from close-by. objects. we derivedobject [luxes for a fixed aperture of 2.0"" (1.5 seeing) from images whieh had been convolved to the same point spread function. (PSE: 1.37))."," In order to avoid contamination from close-by objects, we derivedobject fluxes for a fixed aperture of $2.0\arcsec$ $1.5 \times$ seeing) from images which had been convolved to the same point spread function (PSF; $1.3$ )." + X redshift: probability function P(z) was then determined for each object hy matching the objects Iuxes to à set of 29 template spectra redshifted between 2=0 and z=10 and covering a wide range of ages and star-formation histories., A redshift probability function P(z) was then determined for each object by matching the object's fluxes to a set of 29 template spectra redshifted between $z=0$ and $z=10$ and covering a wide range of ages and star-formation histories. + In Fig., In Fig. + 10 (left pancl) we compare 162. high uality galaxy spectroscopic redshifts with the photometric redshifts., \ref{comp_photoz_spec} (left panel) we compare 162 high quality galaxy spectroscopic redshifts with the photometric redshifts. + Although there is à good agreement in the recdshift range between z0.2 ancl z~~1.2. it is clear from Fig. 10..," Although there is a good agreement in the redshift range between $z\sim0.2$ and $z\sim1.2$ , it is clear from Fig. \ref{comp_photoz_spec}," + ju there is a clegeneracy between high redshift (2~2.5) and low redshift (2~0.2) objects (10 catastrophic outlicrs with 0.2)., that there is a degeneracy between high redshift $z\sim2.5$ ) and low redshift $z\sim0.2$ ) objects (10 catastrophic outliers with ). + This degeneracy stems [rom 1e relatively τοῦ u-band., This degeneracy stems from the relatively red u-band. +2z ln Fig., In Fig. + 12 we show the redshift xobabilitv function as well as the SED fits to the observed ux of the spectroscopic object 000932543., \ref{photoz_sedfits} we show the redshift probability function as well as the SED fits to the observed flux of the spectroscopic object 000932543. + Although the spectroscopic redshift is ως=0.093. the best fitting shotometric redshift is ρω=2.72.," Although the spectroscopic redshift is $z_{spec}=0.093$ , the best fitting photometric redshift is $z_{phot}=2.72$." +" On the other hand. rere is also a low redshift peak around ρω=0.18 in the redshift, probability function (but with a lower probability)."," On the other hand, there is also a low redshift peak around $z_{phot}=0.18$ in the redshift probability function (but with a lower probability)." + Aloreover Fig., Moreover Fig. + 12. also shows that both. the high redshift as well as the low redshift solutions are hard to disentangle as long as no information in the UV is available (as they diller mainly in the UV).," \ref{photoz_sedfits} also shows that both, the high redshift as well as the low redshift solutions are hard to disentangle as long as no information in the UV is available (as they differ mainly in the UV)." + Therefore we decided to include in the determination of the photometric redshifts also the GALEN FUY and NUVα, Therefore we decided to include in the determination of the photometric redshifts also the GALEX FUV and NUV. +μάν As we do not want to convolve all the images to a seeing of (GALEN PSE). we decided. to isc another approach o include the UV. fluxes in our photometric redshift estimation.," As we do not want to convolve all the images to a seeing of (GALEX PSF), we decided to use another approach to include the UV fluxes in our photometric redshift estimation." +" Similar to the optical and NLR bands we used a ixecl aperture of ~1.5 PSP. Le.7.5""... As there were no obvious features in the colour-colour plots of stars inclucling he UV bands. we could not fine-tune the calibration of he zeropoints by means of colour-colour plots of stars."," Similar to the optical and NIR bands we used a fixed aperture of $\sim 1.5 \times$ PSF, i.e. As there were no obvious features in the colour-colour plots of stars including the UV bands, we could not fine-tune the calibration of the zeropoints by means of colour-colour plots of stars." + Therefore we optimised. the zeropoints by using the SED its of our galaxies with very goock photometric recdshilts (if compared with the spectroscopic ones)., Therefore we optimised the zeropoints by using the SED fits of our galaxies with very good photometric redshifts (if compared with the spectroscopic ones). + Please note that his approach can not derive accurate UV fluxes. but gives only a very rough [lux estimation in the two UV bands.," Please note that this approach can not derive accurate UV fluxes, but gives only a very rough flux estimation in the two UV bands." + evertheless. it is now possible to break the degeneracy tween the high. redshift ancl low redshift. solution.," Nevertheless, it is now possible to break the degeneracy between the high redshift and low redshift solution." + This can be best seen in Fig., This can be best seen in Fig. + 12. where we show one of the catastrophic outliers., \ref{photoz_sedfits} where we show one of the catastrophic outliers. +" Only by including the NUV and FUY luxes (right panel) we are able to obtain a photometric redshift, of z=0.08. hence very. close to the spectroscopic redshift of ον=0.093."," Only by including the NUV and FUV fluxes (right panel) we are able to obtain a photometric redshift of $z=0.08$, hence very close to the spectroscopic redshift of $z_{spec}=0.093$." + This approach crastically reduces he number of our catastrophic photometric redshift outliers (sce Fig. 10))., This approach drastically reduces the number of our catastrophic photometric redshift outliers (see Fig. \ref{comp_photoz_spec}) ). + In Fig., In Fig. + 10 (right) panel) we compare the final xhotometric and spectroscopic redshifts of the 162 ealaxics., \ref{comp_photoz_spec} (right panel) we compare the final photometric and spectroscopic redshifts of the 162 galaxies. + The agreement is very good and we have only 3 catastrophic outliers., The agreement is very good and we have only 3 catastrophic outliers. + The right panel of Fig., The right panel of Fig. + 11. shows the distribution of the redshift errors., \ref{histo_photoz} shows the distribution of the redshift errors. + It is nearly. Gaussian. and. scatters around zero with an rms error of O., It is nearly Gaussian and scatters around zero with an rms error of . +085.., Fig. + Fie. 11 (eft panel) presents the X7.distribution of the bestfitting templates and. photometric redshifts for all the objects., \ref{histo_photoz} (left panel) presents the $\chi^2$distribution of the bestfitting templates and photometric redshifts for all the objects. + The median value of the reduced. X7 is 1.5 and, The median value of the reduced $\chi^2$ is 1.5 and +and II bauds.,and H bands. + Although it is νον exciting to detect galaxies a ligher redshifts than previously kuownu. the most important ingredient to our understanding of ealaxv formation and evolution comes not from those exceptional tails of the distribution but from the overall redshift clistrihttion.," Although it is very exciting to detect galaxies at higher redshifts than previously known, the most important ingredient to our understanding of galaxy formation and evolution comes not from those exceptional tails of the distribution but from the overall redshift distribution." + shows the photometric redshift distribution. whose most remarkable feature is the drop in counts at redshifts +=2.5.," shows the photometric redshift distribution, whose most remarkable feature is the drop in counts at redshifts $z \ga 2.5$." +" A morphological breakdown of the redshift distribution shows. in fact. that spiral ealasxies disappear quickly bevoud 2=1. ixd elliptical galaxies bevond += 2.572. All the objects at higher redshifts are μα, with sizes ~1kpc."," A morphological breakdown of the redshift distribution shows, in fact, that spiral galaxies disappear quickly beyond $z=1$, and elliptical galaxies beyond $z=2.5$ \cite{driver98} All the objects at higher redshifts are small, with sizes $\sim 1\kpc$." + Recall that lieh-+redshiftOo Ooealaxies are observed at rest-UV. wavelenetC»ls. iid that the UW eiission in nearby galaxies is also οςufnued to starburstiug regions of comparable sized? It is therefore tempting to explain the sual sizes," Recall that high-redshift galaxies are observed at rest-UV wavelengths, and that the UV emission in nearby galaxies is also confined to starbursting regions of comparable \cite{meurer95} It is therefore tempting to explain the small sizes" +collisions.,collisions. +" The inelasticity is approximated by a conventional method as fv=[1—(nr,—m?)/s]/2. where s is the invariance of the square of the total four-momentim of the py (n5) system. and my is the proton mass."," The inelasticity is approximated by a conventional method as $K=[1-(m_{\rm p}^2-m^2)/s]/2$, where $s$ is the invariance of the square of the total four-momentum of the $p \gamma$ $n \gamma$ ) system, and $m_{\rm p}$ is the proton mass." + For the double-pion production. we approximate the inelasticity by replacing m. with 2.," For the double-pion production, we approximate the inelasticity by replacing $m$ with $2 m_\pi$." + Our parameter set is similar to that in DermeranclAtovan(2003): the total photon enerev in a burst £4. the number of light-eurve pulses(or spikes) N. the Lorentz factor of the shells E. and shell-collide distances from the central engine J.," Our parameter set is similar to that in \citet{der03}: : the total photon energy in a burst $E_{\rm tot}$, the number of light-curve pulses(or spikes) $N$, the Lorentz factor of the shells $\Gamma$ , and shell-collide distances from the central engine $R$." + The imunber Vv corresponds to the number of shells that emit gamma ravs., The number $N$ corresponds to the number of shells that emit gamma rays. +" The photon energy deposited into each shell is (therefore Ly,=Ly /N.", The photon energy deposited into each shell is therefore $E_{\rm sh}=E_{\rm tot}/N$ . + In the standard model. shells can collide and emit eamm ravs al distances 2 larger than 3x10(T/100)707/(lms) em from the central sources. where 9/ is the ime between shell ejection events.," In the standard model, shells can collide and emit gamma rays at distances $R$ larger than $3 \times 10^{11} (\Gamma/100)^2 \delta t/(1 {\rm ms})$ cm from the central sources, where $\delta t$ is the time between shell ejection events." + For simplification. 22 aud D are common for all Vv shells in Chis simulation.," For simplification, $R$ and $\Gamma$ are common for all $N$ shells in this simulation." + The photon number spectrum in the energy range e+de in the shell rest [rame is set ad n(e)xe| for 1 eV «ες 1 keV and ε7? for 1 keV «ες10 MeV. The break energv 1 keV corresponds to 100(D/100) keV in the observer frame., The photon number spectrum in the energy range $\epsilon+d \epsilon$ in the shell rest frame is set at $n(\epsilon) \propto \epsilon^{-1}$ for 1 eV $<\epsilon< $ 1 keV and $\epsilon^{-2.2}$ for 1 keV $<\epsilon< 10$ MeV. The break energy 1 keV corresponds to $100 (\Gamma/100)$ keV in the observer frame. + For e<1 eV. the svuchrotron sell-absorption may be crucial (Granotetal.2000).. while the pair absorption may be crucial for e>LO MeV. (e.g.. see Asano Takahara 2003. Peer Waxman 2004).," For $\epsilon<1$ eV, the synchrotron self-absorption may be crucial \citep{gra00}, while the pair absorption may be crucial for $\epsilon>10$ MeV (e.g., see Asano Takahara 2003, Pe'er Waxman 2004)." + Although the upper bound of the photon energy depends on the model parameter because of pair production. we fix the value as LO MeV (~ IGeV in the observer lame).," Although the upper bound of the photon energy depends on the model parameter because of pair production, we fix the value as 10 MeV $\sim 1$ GeV in the observer frame)." + Since higher enerev protons mainly interact with lower energy photons. the production rate of very. hieh enerev neutrinos is not sensitive to this upper bound.," Since higher energy protons mainly interact with lower energy photons, the production rate of very high energy neutrinos is not sensitive to this upper bound." + The shell width in the comoving frame is assumed to be A/T. as conventionally asstumect. although there is the possibility of thinner shells (AsanoandIwamoto 2002).," The shell width in the comoving frame is assumed to be $R/\Gamma$, as conventionally assumed, although there is the possibility of thinner shells \citep{asa02}." +. We express (he energy density of the magnetic field as fp times the photon energy density., We express the energy density of the magnetic field as $f_{\rm B}$ times the photon energy density. + In this Letter. we adopt fij=0.1.," In this Letter, we adopt $f_{\rm B}=0.1$." + We inject protons with a number spectrum proportional to 2n above 10 GeV in the shell rest frame., We inject protons with a number spectrum proportional to $\epsilon_{\rm p}^{-2}$ above 10 GeV in the shell rest frame. + The maximum proton energv is determined by the condition that (he Larmor radius is smaller Chan both the size scale of the emitting region and the energy-lIoss length., The maximum proton energy is determined by the condition that the Larmor radius is smaller than both the size scale of the emitting region and the energy-loss length. + We estimate (he enerev-loss leneth using svuchrotron. inverse Compton. ancl photomeson cooling processes.," We estimate the energy-loss length using synchrotron, inverse Compton, and photomeson cooling processes." + The total οποιον of the accelerated. protons in a shell is assumed to be (he same as £2)., The total energy of the accelerated protons in a shell is assumed to be the same as$E_{\rm sh}$ . + Our methodpursues energvloss processes of each baryvon via svnchirotron. inverse Compton. ancl photomeson cooling processes during the dvnanmical timescale 22/60 in the shell rest frame.," Our methodpursues energyloss processes of each baryon via synchrotron, inverse Compton, and photomeson cooling processes during the dynamical timescale $R/c \Gamma$ in the shell rest frame." + é-test of the [2/80 galaxies: that sample is completely free of any substructure and there the largest measured 9; was 2.25.,$\delta$ -test of the E/S0 galaxies; that sample is completely free of any substructure and there the largest measured $\delta_i$ was 2.25. + A few isolated galaxies also appear with large 9; values., A few isolated galaxies also appear with large $\delta_i$ values. + In the case of 66406 at. (oboe) = (325.69 7.227. Sy1349£35⋅ km n ) its. large heliocentric.. velocity. could. indicate that it is a background. galaxy which was mistakenly identified as a cluster member (see also Fig. 4)).," In the case of 6406 at $\ell, b, v$ ) = $325.69^{\circ}$, $-7.22^{\circ}$, $7349 \pm 35$ km $^{-1}$ ), its large heliocentric velocity could indicate that it is a background galaxy which was mistakenly identified as a cluster member (see also Fig. \ref{raddist}) )." + Close to the centre of the Norma cluster is a compact group (clubbed “Norma A‘) where we have isolated a group. of five dynamically cistinet galaxies around 66078. (including. G66OTL. 66075. 66125. 66135 and 16113352).," Close to the centre of the Norma cluster is a compact group (dubbed `Norma A') where we have isolated a group of five dynamically distinct galaxies around 6078 (including 6071, 6078, 6125, 6135 and J16113352)." + Ehis group is marked in Fig., This group is marked in Fig. + 9 bv the small solid. circle. within the RociHa region (inner dashed circle)., \ref{subgroup} by the small solid circle within the $R < \frac{1}{3} R_A$ region (inner dashed circle). +" The centre of Norma X is approximately at right ascension and declination 16""12'""007. 6104/40"" (]2000.0)."," The centre of Norma A is approximately at right ascension and declination $16^h12^m00^s$, $-61^{\circ}04'40''$ (J2000.0)." + Based on these [five ealaxies. we find à mean velocity of 4453 km (which is Ες km s.! less than the mean of the cluster. corresponding to 411 km in the cluster rest. frame).," Based on these five galaxies, we find a mean velocity of 4453 km $^{-1}$ (which is 418 km $^{-1}$ less than the mean of the cluster, corresponding to 411 km $^{-1}$ in the cluster rest frame)." + Norma A has a velocity dispersion of 312 km which is much. smaller than the velocity scale of the cluster (925 km s. 1).," Norma A has a velocity dispersion of 312 km $^{-1}$, which is much smaller than the velocity scale of the cluster (925 km $^{-1}$ )." + AO second dynamically distinct eroup of. galaxies (Norma D) is found further from the core of the cluster. centred around WIxIx55751 (other galaxies include 55718. WIxIx55779.. 55783... 55796. and 55813).," A second dynamically distinct group of galaxies (`Norma B') is found further from the core of the cluster, centred around 5751 (other galaxies include 5718, 5779, 5783, 5796 and 5813)." + Phis group is indicated by the large solid circle in Fie., This group is indicated by the large solid circle in Fig. +" 9 in the region zHa model. beinge a reference for the mocel involvinge particle pitch-angle momentum scattering. due to MIID turbulence.,"1995) to define the background model, being a reference for the model involving particle pitch-angle momentum scattering due to MHD turbulence." + Perturbations of particle trajectories due to a turbulent magnetic field. component were simulated. using small-amplitucde pitch-angle momentum scattering. enabling modelling of both small and large amplitude turbulence in à wide wave vector range.," Perturbations of particle trajectories due to a turbulent magnetic field component were simulated using small-amplitude pitch-angle momentum scattering, enabling modelling of both small and large amplitude turbulence in a wide wave vector range." + No second-order Fermi acceleration orocesses are allowed. within this approach., No second-order Fermi acceleration processes are allowed within this approach. + dn section 3 we present results of particle energy. spectrum. modelling or dilferent scattering amplitudes., In section 3 we present results of particle energy spectrum modelling for different scattering amplitudes. + Comparison of the acceleration process to the unperturbed one confirms that he turbulence can substantially increase. the acceleration cllicieney. enabling particles to form flat high-energy spectra with much increased final energies.," Comparison of the acceleration process to the unperturbed one confirms that the turbulence can substantially increase the acceleration efficiency, enabling particles to form flat high-energy spectra with much increased final energies." + Phen. in section 4. we wielly summarize these results.," Then, in section 4, we briefly summarize these results." + In the present simulations we scale the parameters of he reconnection region to those characteristic for the solar lave (e.g. Miller et al., In the present simulations we scale the parameters of the reconnection region to those characteristic for the solar flare (e.g. Miller et al. + 1997)., 1997). + However. we do not aspire to oesent a [lare acceleration model.," However, we do not aspire to present a flare acceleration model." + We provide all numerical values in SI units., We provide all numerical values in SI units. + The considered reconnection region. (Fig., The considered reconnection region (Fig. +" 1) involves. in-Ilowing plasma from the ορ) and the ""bottom! toward the eo=0 plane. and outllowing to the sides."," 1) involves in-flowing plasma from the `top' and the `bottom' toward the $x = 0$ plane, and outflowing to the sides." + ALL physical «quantities. the Low velocity. the magnetic field. ancl the," All physical quantities, the flow velocity, the magnetic field and the" +couple T; to Τι. during reionization (Ciardi&Madau2003).,couple $\mathrm{\mathrm{T_s}}$ to $\mathrm{\mathrm{T_k}}$ during reionization \citep{ciardi03}. +". As an example, in Fig."," As an example, in Fig." +" 12 we show the reionization history (ὁ Ty) assuming a high background J., in other words, assuming perfect Ts—T coupling."," \ref{fig:histcompinf} we show the reionization history $\delta \mathrm{T_b}$ ) assuming a high background $\mathrm{J_o}$, in other words, assuming perfect $\mathrm{T_s}$ $\mathrm{T_k}$ coupling." + In Fig., In Fig. +" 3 dT}, corresponding to the same redshifts as in the previous figures isshown.", \ref{fig:starbright} $\delta \mathrm{T_b}$ corresponding to the same redshifts as in the previous figures isshown. +" In this particular model ὁΤε, values are not very high (JóTu|« 10mK).", In this particular model $\delta \mathrm{T_b}$ values are not very high $|\delta \mathrm{T_b}| < 10$ mK). +" At early epochs, (top-left) at z~10, there are only a few sources and the heating of the IGM or the secondary J, is not high enough to cause substantial differential brightness temperatures."," At early epochs, (top-left) at $z\approx10$, there are only a few sources and the heating of the IGM or the secondary $\mathrm{J_o}$ is not high enough to cause substantial differential brightness temperatures." +" At later times, the ionized bubbles overlap significantly driving the brightness temperature to zero."," At later times, the ionized bubbles overlap significantly driving the brightness temperature to zero." + Thus there is only a small portion of the Universe (in volume) that has sufficient Lya coupling and neutral hydrogen density to cause large differential brightness temperatures., Thus there is only a small portion of the Universe (in volume) that has sufficient $\alpha$ coupling and neutral hydrogen density to cause large differential brightness temperatures. +" This behaviour is specific to the model assumed and will be significantly different if the parameters such as the star-formation rate, SED and escape fractions are altered."," This behaviour is specific to the model assumed and will be significantly different if the parameters such as the star-formation rate, SED and escape fractions are altered." +" In this section we will consider heating due to high energy X-ray photons emanating from power-law type sources (eg.,"," In this section we will consider heating due to high energy X-ray photons emanating from power-law type sources (eg.," + miniqsos)., miniqsos). + Because of their large mean free path (ος E?) it has been difficult to incorporate the effect of heating by power-law sources consistently in a 3-D radiative transfer simulation., Because of their large mean free path $\propto E^3$ ) it has been difficult to incorporate the effect of heating by power-law sources self-consistently in a 3-D radiative transfer simulation. + Observations reveal the energy spectrum of quasars-type sources typically follow a power-law of the form E (Vandenal.1994).," Observations reveal the energy spectrum of quasars-type sources typically follow a power-law of the form $E^{-\alpha}$ \citep{vandenberk01,vignali03,laor97,elvis94}." +". Here we assume o=1 and thus the SED of the miniqsos is given by: with the normalization constant, where Fotai is the total energy output of the miniqso within the energy range, Erange."," Here we assume $\alpha += 1$ and thus the SED of the miniqsos is given by: with the normalization constant, where $E_{total}$ is the total energy output of the miniqso within the energy range, $E_{range}$." +" Any complex, multi-slope spectral templates as in Sazonov,Ostriker,&Sunyaev(2004) can be adopted."," Any complex, multi-slope spectral templates as in \cite{sazonov04} can be adopted." +" The number of plausible SEDs that can be considered are numerous and serves as a reminder of the extent of “unexplored parameter space” even while considering the case of miniqsos alone, and argues for an extremely quick RT code likeBEARS."," The number of plausible SEDs that can be considered are numerous and serves as a reminder of the extent of “unexplored parameter space” even while considering the case of miniqsos alone, and argues for an extremely quick RT code like." +. The miniqsos are assumed to accrete at a constant fraction ε (normally 10%)) of the Eddington rate., The miniqsos are assumed to accrete at a constant fraction $\epsilon$ (normally ) of the Eddington rate. +" Therefore, the luminosity is given by: The luminosity derived from the equation above is used to normalize the relation in Eq."," Therefore, the luminosity is given by: The luminosity derived from the equation above is used to normalize the relation in Eq." + 10 according to Eq. 11.., \ref{eq:spectrum} according to Eq. \ref{eq:normalization}. + The energy range considered is between 10.4 eV and 10 keV., The energy range considered is between 10.4 $\mathrm{eV}$ and 10 $\mathrm{keV}$. + Simulations were carried out for a range of masses between 10° and 10°Mo., Simulations were carried out for a range of masses between $10^5$ and $10^9~\mathrm{M}_\odot$. +" To justify comparing the case of stars and miniqsos we argue that, although the number of photons at different energies is a function of the total luminosity and spectral index in the case of miniqsos, if we assume that all photons from the miniqso are at the hydrogen ionization threshold, then the number of ionizing photons obtained, for the mass range fixed above, is about 10°°to 1055: the same order of magnitude as the number of ionizing photons in the case of stars and it also matches the numbers being employed for simulations by various other authors like Mellemaetal.(2006) and Kuhlen&Madau(2005)."," To justify comparing the case of stars and miniqsos we argue that, although the number of photons at different energies is a function of the total luminosity and spectral index in the case of miniqsos, if we assume that all photons from the miniqso are at the hydrogen ionization threshold, then the number of ionizing photons obtained, for the mass range fixed above, is about $10^{50}~\mathrm{to}~10^{55}$ ; the same order of magnitude as the number of ionizing photons in the case of stars and it also matches the numbers being employed for simulations by various other authors like \cite{mellema06} and \cite{kuhlen05}." +. The miniqsos are embedded into an N-body output following the prescription in Thomasetal.(2009)., The miniqsos are embedded into an N-body output following the prescription in \cite{thomas09}. +". Dark-matter haloes are identified using the friends-of-friends (FoF) algorithm and masses of black holes assigned according to, where the factor 10~* reflects the Magorrian relation (Magorrianetal.1998) between the halo mass (Mnaio) and black hole mass (Manz) multiplied with the radiative efficiency assumed to be10%,, and the fraction oe gives the baryon ratio 2002)."," Dark-matter haloes are identified using the friends-of-friends (FoF) algorithm and masses of black holes assigned according to, where the factor $10^{-4}$ reflects the Magorrian relation \citep{magorrian98} between the halo mass $\mathrm{M_{halo}}$ ) and black hole mass $\mathrm{M_{BH}}$ ) multiplied with the radiative efficiency assumed to be, and the fraction $\frac{\Omega_b}{\Omega_m}$ gives the baryon ratio \citep{ferrarese02}." +". Contour plots of T,, T and and óΤι, for the case of miniqsos being the sources of reionization, at four different redshifts, are plotted in Figs. 4,,"," Contour plots of $\mathrm{T_k}$, $\mathrm{T_s}$ and and $\delta +\mathrm{T_b}$ for the case of miniqsos being the sources of reionization, at four different redshifts, are plotted in Figs. \ref{fig:qsoheat}, ," +" 5and 6,, respectively."," \ref{fig:qsospin} and \ref{fig:qsobright}, , respectively." + The high energies of the X-ray photons substantially affects the photo-ionization and thermal energy balance of the IGM., The high energies of the X-ray photons substantially affects the photo-ionization and thermal energy balance of the IGM. +" The marked difference between power-law type and stellar sources, in the extent towhich they heat the IGM, is evident in"," The marked difference between power-law type and stellar sources, in the extent towhich they heat the IGM, is evident in" +"There was very small variations due to cosmology on the re-caleulated values for the crossing time. which is given in unities of LL,. since for closer groups the impact of A is small.","There was very small variations due to cosmology on the re-calculated values for the crossing time, which is given in unities of ${\rm +H_0^{-1}}$, since for closer groups the impact of $\Lambda$ is small." + On the other hand. including or excluding galaxies from the analvsis. as we cid for WCC 15 and LCG 51. can have a considerable effect on this value.," On the other hand, including or excluding galaxies from the analysis, as we did for HCG 15 and HCG 51, can have a considerable effect on this value." +" The crossing times were calculated using the relation presented in ? lt is the mean separation in kpe between the member galaxies and De is the deprojected velocity dispersion given by where e ds the observed. recession velocity. ancl 0, is the measurement error."," The crossing times were calculated using the relation presented in \citet{hic92} + R is the mean separation in ${\rm kpc}$ between the member galaxies and $D\sigma$ is the deprojected velocity dispersion given by where $v$ is the observed recession velocity and $\sigma_v$ is the measurement error." + For ML. the total group luminosities were calculate with the member galaxies for each case and the proper distance modulus.," For $M/L$, the total group luminosities were calculated with the member galaxies for each case and the proper distance modulus." + Since NX-rav mass estimates are not available for most of groups from Llickson’s catalogue. ane for consistent comparison. we used the same mass estimators of 7. to estimate the group's masses.," Since X-ray mass estimates are not available for most of groups from Hickson's catalogue, and for consistent comparison, we used the same mass estimators of \citet{hic92} to estimate the group's masses." + The median of the four mass estimators described by?) (virial mass. projectec mass. mecian mass and mean mass) was used for each eroup.," The median of the four mass estimators described by \citet*{hei85} (virial mass, projected mass, median mass and mean mass) was used for each group." + An important. consideration should be raised here. that dynamical mass estimates using the small number of ealaxics present in a compact group can suller from severe statistical ellects and should be taken only as a guiding value.," An important consideration should be raised here, that dynamical mass estimates using the small number of galaxies present in a compact group can suffer from severe statistical effects and should be taken only as a guiding value." + These estimators only measure the mass inside the area where the galaxies are found. what corresponds only to the inner part of the detected LGL components ancl of the dark matter halo.," These estimators only measure the mass inside the area where the galaxies are found, what corresponds only to the inner part of the detected IGL components and of the dark matter halo." + Vhereforc. these estimators would not account for the mass in the outer parts of the group.," Therefore, these estimators would not account for the mass in the outer parts of the group." + We have found in the literature new recession velocity measurements for some of the galaxies. as for the case of LCG 15C. whieh diller from the originally published: values by about 30⋅kms.n. on average.," We have found in the literature new recession velocity measurements for some of the galaxies, as for the case of HCG 15C, which differ from the originally published values by about $30~{\rm km~s^{-1}}$, on average." +" ""psThis small variationEM causes an impact of up to in the estimated group parameters. like crossing times and masses. showing how sensitive they are to the small number of objects present in each group."," This small variation causes an impact of up to in the estimated group parameters, like crossing times and masses, showing how sensitive they are to the small number of objects present in each group." + For consistency we decided to use the values from ?.. unless for the case where LC 15€ is not considered a group member.," For consistency we decided to use the values from \citet{hic92}, unless for the case where HCG 15C is not considered a group member." + Using the new recession velocities would not change the cdilference between the velocity of HCX 51€ and the median velocity of this group., Using the new recession velocities would not change the difference between the velocity of HCG 51C and the median velocity of this group. + The quantities estimated here for cach group ancl its possible dillerent configurations can be seen in table 3.., The quantities estimated here for each group and its possible different configurations can be seen in table \ref{tabparam}. + The images in 2 and Roof UCC 15 were deconvolved into Ll wavelet. cocllicients (21° pixels. about the size of the image). the detected objects were reconstructed in a multiple iterations process and the group galaxies and LOL component of this group were re-composed. às is shown in figure 1..," The images in $B$ and $R$ of HCG 15 were deconvolved into 11 wavelet coefficients $2^{10}$ pixels, about the size of the image), the detected objects were reconstructed in a multiple iterations process and the group galaxies and IGL component of this group were re-composed, as is shown in figure \ref{figdifh15}." + Phe whole analysis process is made in an totally independent way for the D and £2 bands., The whole analysis process is made in an totally independent way for the $B$ and $R$ bands. + For thequintet (and sextet) configuration. the detected IGL component in this group represents 194X. (164E34 )) ofthe total light in the D band and 2104 d: (1824) in the R band. about of the light of the first-ranked. galaxy.," For thequintet (and sextet) configuration, the detected IGL component in this group represents $19\pm4$ $16\pm3$ ) of the total light in the $B$ band and $21\pm4$ $18\pm4$ ) in the $R$ band, about of the light of the first-ranked galaxy." + This component corresponds to apparent total magnitudes of D—15.00.5 and &=13.3c0.2. down to a surface xiehtness detection limit of jg.=31.3 and jj;=30.5.," This component corresponds to apparent total magnitudes of $B = 15.0\pm0.2$ and $R = 13.3\pm0.2$, down to a surface brightness detection limit of $\mu_B = 31.3$ and $\mu_R = 30.5$." + The detection limits correspond to a surface brightness of Vlσον ΝΞ0.1) in cach band. which is the detection imitof the WAV package.," The detection limits correspond to a surface brightness of $0.1\cdot \sigma_{Sky}$ $S/N = 0.1$ ) in each band, which is the detection limitof the WAV package." + The IGL presents a very irregular shape and has a very ow mean surface brightness. fe=28.4d:0.2 and 26.7cx0.2.," The IGL presents a very irregular shape and has a very low mean surface brightness, $\mu_B = 28.4\pm0.2$ and $\mu_R = 26.7\pm0.2$ ." + Its mean S/N per pixel is 1.5 in D and 3.3 in f., Its mean $S/N$ per pixel is 1.5 in $B$ and 3.3 in $R$. +" The LGL has a mean colour (D.HR),=1.6x0.2. redder. out. still consistent with the mean colour for the galaxies’ component (0f?)u=1440.2 for the quintet configuration and (BoHR),=1.5x0.2 for the sextet) anc with the old stellar population expected. [rom carly-twpe galaxies."," The IGL has a mean colour $(B-R)_0 = 1.6\pm0.2$, redder, but still consistent with the mean colour for the galaxies' component $(B-R)_0 = +1.4\pm0.2$ for the quintet configuration and $(B-R)_0 = 1.5\pm0.2$ for the sextet) and with the old stellar population expected from early-type galaxies." + The extinction corrections were made using ? extinction laws and ? extinction maps., The extinction corrections were made using \citet{rie85} extinction laws and \citet*{sch98} extinction maps. + The IGL. and galaxy components were measured in the same areas in the two different bands., The IGL and galaxy components were measured in the same areas in the two different bands. + The properties of the LGL components are sumniarized in table 4.., The properties of the IGL components are summarized in table \ref{tabres}. + The original AM/L in the D band for this group. calculated by 2... was 432 M./L..," The original $M/L$ in the $B$ band for this group, calculated by \citet{hic92}, was 432 ${\rm M_{\odot}/L_{\odot}}$." + The ML values were converted to fy=τὸkms.+Mpe while the original values were caleulated with Z4;=100kms+Alpe and Oy=LO.," The $M/L$ values were converted to $H_0 = 70~{\rm km~s^{-1}~Mpc^{-1}}$, while the original values were calculated with $H_0 = 100~{\rm km~s^{-1}~Mpc^{-1}}$ and $\Omega_M=1.0$." + Our new estimate takes these values to 614 and 424 M./L.. respectively for the quintet and. sextet cases.," Our new estimate takes these values to 614 and 424 ${\rm M_{\odot}/L_{\odot}}$, respectively for the quintet and sextet cases." + Using the light contained in the IGL component. we recalculated the AL/£ for each of the studied groups for the new total Luminosity. correcting the estimated values.," Using the light contained in the IGL component, we recalculated the $M/L$ for each of the studied groups for the new total luminosity, correcting the estimated values." + In the case of LLCG 15 the ML drops to 517 and 367 AL./L..for the two presented. cases.," In the case of HCG 15 the $M/L$ drops to 517 and 367 ${\rm M_{\odot}/L_{\odot}}$, for the two presented cases." + The AL/L values presented in this paper always refer to the 2 band., The $M/L$ values presented in this paper always refer to the $B$ band. +" The crossing times for this eroup. 0.014 1L, (2)... had no change in both configurations. quintet and sextet."," The crossing times for this group, 0.014 ${\rm H_0^{-1}}$ \citep{hic92}, had no change in both configurations, quintet and sextet." + AL and crossing time values are given in table 3.., $M/L$ and crossing time values are given in table \ref{tabparam}. + As in the case of LCG 15. the D and & images of LICC 35 were deconvolved into Ll wavelet. coellicients and the galaxies and LOL component were re-composed alter the wavelet multiple iteration process. as can be seen in figure 2.. where the analysis of the D and & bands are independent.," As in the case of HCG 15, the $B$ and $R$ images of HCG 35 were deconvolved into 11 wavelet coefficients and the galaxies and IGL component were re-composed after the wavelet multiple iteration process, as can be seen in figure \ref{figdifh35}, where the analysis of the $B$ and $R$ bands are independent." + In this group the detected. LGL component: presents an irregular shape. elongated in the same direction as the galaxy component elongation.," In this group the detected IGL component presents an irregular shape, elongated in the same direction as the galaxy component elongation." + This component represents 15E34 of the total light in the D. band and. 11+2% in the # band. of the light of the [irst-ranked.: galaxy.," This component represents $15\pm3$ of the total light in the $B$ band and $11\pm2$ in the $R$ band, of the light of the first-ranked galaxy." + The total apparent magnitudes of the LOL are 16.4+0.2 and 14.9+0.2. respectively in the D and & bands. clown to a surface brightness detection limit of yg=31.0 and flap=284.," The total apparent magnitudes of the IGL are $16.4\pm0.2$ and $14.9\pm0.2$, respectively in the $B$ and $R$ bands, down to a surface brightness detection limit of $\mu_B += 31.0$ and $\mu_R = 28.8$." + This group presents quite a faint IGL component with a mean surface brightness of fe=27.9+0.2 and 26.4d 0.2., This group presents quite a faint IGL component with a mean surface brightness of $\mu_B = 27.9\pm0.2$ and $\mu_R = 26.4\pm0.2$ . + The mean S/N per pixel of the ICGL is i D and 1.0 in. 2., The mean $S/N$ per pixel of the IGL is 1.7 in $B$ and 1.0 in $R$ . + ls mean colour is (2 and the galaxies have a mean (13Ay=lst0: , Its mean colour is $(B-R)_0 = 1.5\pm0.2$ and the galaxies have a mean $(B-R)_0 = 1.8\pm0.2$ . +In this case the LGL component is bluer than the mean colour for the galaxies. but consistent with the typical colour for old stellar population in earlyv-type galaxies. while the galaxy's component. is redder than the typical value [or earlv-tvpe galaxies.," In this case the IGL component is bluer than the mean colour for the galaxies, but consistent with the typical colour for old stellar population in early-type galaxies, while the galaxy's component is redder than the typical value for early-type galaxies." + The mean colour measured. for the galaxies’ Component is not surprising considering that. at," The mean colour measured for the galaxies' component is not surprising considering that, at" +isothermal sphere). has (he density profile Chat is proportional to the inverse radius square.,"isothermal sphere), has the density profile that is proportional to the inverse radius square." + The total mass is infinite because of the indefinite extension of the constant mass shells., The total mass is infinite because of the indefinite extension of the constant mass shells. + In practice. the tidal interaction with the neighboring systems are likely (ο define the edges ancl mass breaks of the sell-gravitating objects.," In practice, the tidal interaction with the neighboring systems are likely to define the edges and mass breaks of the self-gravitating objects." + If we truncate the SIS at a certain (24d) radius. sav r=d. and integrate for the projected mass of the lens. the 2-d mass density. function has the form MG) where (he position variable is expressed in terms of the circular coordinates as auc the mass trucation is made al /=I.," If we truncate the SIS at a certain (3-d) radius, say $r=a$, and integrate for the projected mass of the lens, the 2-d mass density function has the form (t) ); t 1 where the position variable is expressed in terms of the circular coordinates as $\xi = t a(\cos\theta + i \sin\theta)$ and the mass trucation is made at $t=1$." + In order to find the lens equation. we can use the Newton's theorem that the gravitational field of a cireularly svmimetric mass is determined by the mass inside (he circle of the radius of the probing point placed at the center. and hence we need to integrate the density function in eq. (X))," In order to find the lens equation, we can use the Newton's theorem that the gravitational field of a circularly symmetric mass is determined by the mass inside the circle of the radius of the probing point placed at the center, and hence we need to integrate the density function in eq. \ref{eqSigmaCirc}) )" + from the center to an arbitrarv / less than 1., from the center to an arbitrary $t$ less than 1. + The integration doesnt relent to a nice manageable algebraic function., The integration doesn't relent to a nice manageable algebraic function. + So we cheat a bit (maybe a lot) as is customary and ignore the arctangent [actor to obtain an easv-to-haudle densitv function X(/)x1// and truncate it at /=I., So we cheat a bit (maybe a lot) as is customary and ignore the arctangent factor to obtain an easy-to-handle density function $\Sigma(t) \propto 1/t$ and truncate it at $t=1$. + In other words. (he mass being considered is the infinite isothermal sphere cut into an infinite cvlincler that is infinitelv long along the line of sight.," In other words, the mass being considered is the infinite isothermal sphere cut into an infinite cylinder that is infinitely long along the line of sight." + Thus the (2-1) mass distribution may be best relerred (o as a cviindrically truncated isothermal lens (C'TIL)., Thus the (2-d) mass distribution may be best referred to as a cylindrically truncated isothermal lens (CTIL). + The exgravitational lens equation is exgiven bv w and 2 are variables for a source and its image in (he lens plane al the distance of the, The gravitational lens equation is given by = z - 4GD $\omega$ and $z$ are variables for a source and its image in the lens plane at the distance of the +or limiting luminosity ratio. we propose a 7-parameter fit to generally describe the full PON|Mihog-Mitin).,"or limiting luminosity ratio, we propose a 7-parameter fit to generally describe the full $P(N|M_{r,host}, M_{r,lim})$." + We use our generalized negative-binomial plus power law as defined in Equation 6.. and keep o». 7. and 7 constant.," We use our generalized negative-binomial plus power law as defined in Equation \ref{eq:fit}, and keep $\alpha_2$ , $T$, and $\tau$ constant." +" However. we parameterize (N; as a linear function. the slope of which depends on M,j,;—M,jj, and the offset of which depends on host magnitude. My..."," However, we parameterize $\langle N \rangle$ as a linear function, the slope of which depends on $M_{r,host} - M_{r,lim}$ and the offset of which depends on host magnitude, $M_{r,host}$." + Our full fit for Equation 6. then becomes a function of the parameters Nou.NobΝοΝιςσιTo. and το defined by: Midi) =ΤΙΤΛΟ D (0=pP + where P= r=]παν iN.M )j2-— μυ. ο.," Our full fit for Equation \ref{eq:fit} then becomes a function of the parameters $N_{0.a}, N_{0,b}, N_{1,a}, N_{1,b}, \alpha_{2}, T_0$, and $\tau_0$ defined by:, ) = p^r (1-p)^N + where p = r = N, ) = - ." +".. We fit this functional form to the measured ddistribution for all host halos down to M,2—18.5 and their satellites down to M,2—16 in Bolshoi stacked in bins of 0.5 mag."," We fit this functional form to the measured distribution for all host halos down to $M_r = -18.5$ and their satellites down to $M_r = +-16$ in Bolshoi stacked in bins of 0.5 mag." + We present our best fitting parameters for Equation in table 5.., We present our best fitting parameters for Equation \ref{eq:parameters} in table \ref{table:parameters}. +" As a final validation of this result. Figure 14 shows the measured PCV) distributions for a range of M,j,; and 4. along with the fits from our model in Eq. 5.."," As a final validation of this result, Figure \ref{fig:fit_verification} shows the measured $P(N)$ distributions for a range of $M_{r,host}$ and $M_{r,lim}$ , along with the fits from our model in Eq. \ref{eq:full_fit}." +" While our nominal fit can be improved using a 7 that is a power-law in M,5,—jj, with a normalization that depends on host mass. the actual fit does not significantly improve the reduced 47. so we elect to hold it constant."," While our nominal fit can be improved using a $\tau$ that is a power-law in $M_{r,host} - M_{r,lim}$ with a normalization that depends on host mass, the actual fit does not significantly improve the reduced $\chi^2$, so we elect to hold it constant." + In this work. we have examined the likelihood for simulated MW-like dark matter halos to host substructures similar to the Magellanic Clouds.," In this work, we have examined the likelihood for simulated MW-like dark matter halos to host substructures similar to the Magellanic Clouds." + We have performed this analysis using both dark matter kinematic information and an abundance-matching technique which assigns galaxy luminosities to resolved dark matter halos and allows direct comparison with observations (e.g.. LIO).," We have performed this analysis using both dark matter kinematic information and an abundance-matching technique which assigns galaxy luminosities to resolved dark matter halos and allows direct comparison with observations (e.g., L10)." + The main result of this work is that MW-like objects have a chance to host two subhalos as large or as lummous as the SMC. in basic agreement with previous simulation results (e.g.. BKΙΟ). as well as with observations.," The main result of this work is that MW-like objects have a chance to host two subhalos as large or as luminous as the SMC, in basic agreement with previous simulation results (e.g., BK10), as well as with observations." + While we have extensively compared our results for the full probability distribution for à MW-luminous galaxy to host ssatellite galaxies to the observational measurements from LIO. finding good agreement.," While we have extensively compared our results for the full probability distribution for a MW-luminous galaxy to host satellite galaxies to the observational measurements from L10, finding good agreement." + This results are also in qualitative agreement with previous results using smaller samples (Chenetal.2006:James&Ivory2010).," This results are also in qualitative agreement with previous results using smaller samples \citep{Chen06, James10}." + Our results have a number of implications., Our results have a number of implications. + First. this is a validation. of the paradigm down to the level of 10'27M... objects.," First, this is a validation of the paradigm down to the level of $10^{10}\hinv\msol$ objects." + At this level. there is no indication that either the CDM paradigm or our standard picture of galaxy formation. including the relatively tight relationship between galaxy luminosities and halo masses. breaks down.," At this level, there is no indication that either the CDM paradigm or our standard picture of galaxy formation, including the relatively tight relationship between galaxy luminosities and halo masses, breaks down." + In particular. it appears that the statistics of satellite galaxies at this mass in LCDM are in very good agreement with observations which sample a wide range of galaxy environments.," In particular, it appears that the statistics of satellite galaxies at this mass in LCDM are in very good agreement with observations which sample a wide range of galaxy environments." + One possible criticism of the model we have used for connecting galaxies to halos (SHAM) is that it may be so robust as to reproduce the observed statistics. given its assumption of the correct global luminosity function.," One possible criticism of the model we have used for connecting galaxies to halos (SHAM) is that it may be so robust as to reproduce the observed statistics, given its assumption of the correct global luminosity function." + In order to evaluate this. it is important to keep track of the exact assumptions of the approach and how these relate to the particular statistics measured.," In order to evaluate this, it is important to keep track of the exact assumptions of the approach and how these relate to the particular statistics measured." +" First and foremost. SHAM assumes that v4, of a halo or subhalo (at accretion into a larger system) is the parameter that sets the luminosity of the galaxy it hosts."," First and foremost, SHAM assumes that $\vmax$ of a halo or subhalo (at accretion into a larger system) is the parameter that sets the luminosity of the galaxy it hosts." + While this is robust to. e.g.. a temporally-variable star formation efficiency with halo mass. it would differ from model in which there was environmental dependence to the galaxy formation recipe in addition. to the inherent environmental dependence of the halo mass function.," While this is robust to, e.g., a temporally-variable star formation efficiency with halo mass, it would differ from model in which there was environmental dependence to the galaxy formation recipe in addition to the inherent environmental dependence of the halo mass function." + For example. if subhalos of a given mass evolve very differently than halos of the same mass in the field. our model would not produce good agreement.," For example, if subhalos of a given mass evolve very differently than halos of the same mass in the field, our model would not produce good agreement." +" Additionally. rf our simulated dark matter halo mass function was significantly off from reality (due to. for example. an incorrect ay or ©,,). the masses of the MCs as estimated from abundance matching would not provide a good match to the direct kinematic measurements. as we find here."," Additionally, if our simulated dark matter halo mass function was significantly off from reality (due to, for example, an incorrect $\sigma_8$ or $\Omega_m$ ), the masses of the MCs as estimated from abundance matching would not provide a good match to the direct kinematic measurements, as we find here." + Finally. this is a test of the SHAM treatment of subhalos in a mass regime lower than has been previously explored.," Finally, this is a test of the SHAM treatment of subhalos in a mass regime lower than has been previously explored." + We do see some manifestations of assembly bias with regard to the dark matter subhalo population inside MW-like galaxies: halos in higher density regions host more massive subhalos than those in lower density regions., We do see some manifestations of assembly bias with regard to the dark matter subhalo population inside MW-like galaxies: halos in higher density regions host more massive subhalos than those in lower density regions. + This effect appears to be most pronounced for relatively local measurements of density. and suggests that the MW's proximity to M31. boosts the likelihood for us to see a LMC/SMC pair by about25%.," This effect appears to be most pronounced for relatively local measurements of density, and suggests that the MW's proximity to M31 boosts the likelihood for us to see a LMC/SMC pair by about." +. The effect is strongest for densities measured on the scale of | Mpe., The effect is strongest for densities measured on the scale of 1 Mpc. + We note that such a boost seems to be present if we use either the total local mass or the total local luminosity as an environmental measure., We note that such a boost seems to be present if we use either the total local mass or the total local luminosity as an environmental measure. + This should make the effect an observable manifestation of assembly bias (though detecting it will require careful treatment of correlated structure)., This should make the effect an observable manifestation of assembly bias (though detecting it will require careful treatment of correlated structure). + It is interesting that this result is in qualitative agreement with the work of Ishiyamaetal. (2009b).. who saw a similar trend with environment butclaimed it was most sensitive at the ~5/7'Mpe scale.," It is interesting that this result is in qualitative agreement with the work of \cite{Ishiyama08}, who saw a similar trend with environment butclaimed it was most sensitive at the $\sim 5\hinv\mpc$ scale." + They notethat we are m an underdense region on these scales. and cite this as a possible ingredient for solving the missing," They notethat we are in an underdense region on these scales, and cite this as a possible ingredient for solving the missing" +extrapolation to the IRAC bands.,extrapolation to the IRAC bands. + The location. size aud pixel scale of the FILOW image is identical to the FIGQW NUDF image analvzed in Thompsonetal.(2007).," The location, size and pixel scale of the F110W image is identical to the F160W NUDF image analyzed in \citet{thm07}." +. Details of the image preparation are given in Thompsonetal.(2005)., Details of the image preparation are given in \citet{thm05}. +. The basic image production after the processing of the individual images is production of a background image which is the median of all of the individual images. subtraction of the background [rom the individual images and then combining the images with the drizzle procedure (FruchterandHook2002).," The basic image production after the processing of the individual images is production of a background image which is the median of all of the individual images, subtraction of the background from the individual images and then combining the images with the drizzle procedure \citep{fru02}." +. The fIuctaation analvsis of the F110W image is klentical to (he analvsis techniques used on the F160W image in and is not repeated in detail here., The fluctuation analysis of the F110W image is identical to the analysis techniques used on the F160W image in \citet{thm07} and is not repeated in detail here. + Source subtraction is accomplished using the SExtractor (Bertinand.Arnout1996) (SE) pixel map where each pixel that is part of a source is given a value equal to the source ID nunber ancl all other pixels have a value of zero., Source subtraction is accomplished using the SExtractor \citep{ber96} (SE) pixel map where each pixel that is part of a source is given a value equal to the source ID number and all other pixels have a value of zero. + The photometric redshifts derived in Thompsonetal.(2006) were used to identilv the redshift of each source., The photometric redshifts derived in \citet{thm06} were used to identify the redshift of each source. + Due to the much higher resolution of the NICMOS images relative to the IRAC images. even the all source subtracted image retained 93% of its pixels.," Due to the much higher resolution of the NICMOS images relative to the IRAC images, even the all source subtracted image retained $\%$ of its pixels." + This means that the objections of Nashlinskyetal.(2007a) to the Coorayetal.(2007) analysis do not apply here., This means that the objections of \citet{kas07a} to the \citet{coo07} analysis do not apply here. + All source pixels were set to zero in the subtracted image., All source pixels were set to zero in the subtracted image. + There was no altempt to replace (hem with random noise., There was no attempt to replace them with random noise. + The small area of the subtracted sources means that (his had no affect on the final fluctuation spectrum., The small area of the subtracted sources means that this had no affect on the final fluctuation spectrum. + Figure 1. shows the fluctuation power al Llyn and. 1.670n., Figure \ref{fig-fluct} shows the fluctuation power at $\micron$ and $\micron$. + To determine the redshift distribution of the L.1jam fluctuations the fInctuation analvsis was also performed on the 1.1jmi image with all sources except those in a given redshift bin removed., To determine the redshift distribution of the $\micron$ fluctuations the fluctuation analysis was also performed on the $\micron$ image with all sources except those in a given redshift bin removed. + The I.1jan fluctuation power versus redshift distribution is essentially identical to the 1.6/0 distribution shown in Figure 6 of Thompsonetal.(2007)., The $\micron$ fluctuation power versus redshift distribution is essentially identical to the $\micron$ distribution shown in Figure 6 of \citet{thm07}. +. There is a peak near z—1 and no discernible power above the background for z>4., There is a peak near z=1 and no discernible power above the background for $z>4$. + To investigate (he nature of the sources of the fluctuation power observed in the all source subtracted NICMOS and IRAC images we caleulate the expected [Inctuation power color as a [unction of redshift using galaxy Spectral Energy. Distributions (SEDs)., To investigate the nature of the sources of the fluctuation power observed in the all source subtracted NICMOS and IRAC images we calculate the expected fluctuation power color as a function of redshift using galaxy Spectral Energy Distributions (SEDs). +" At anv eiven angular scale the fluctuation power for a given wavelength band is directly proportional to the power of the galaxies (7/1,) in that band.", At any given angular scale the fluctuation power for a given wavelength band is directly proportional to the power of the galaxies $\nu I_{\nu}$ ) in that band. + The power ratios of the bands at any redshift are easily calculated [rom the numerically redshifted model SEDs., The power ratios of the bands at any redshift are easily calculated from the numerically redshifted model SEDs. + The analvsis of used 7 primary template SEDs labeled 17 going trom early to late galaxies., The analysis of \citet{thm06} used 7 primary template SEDs labeled 1–7 going from early to late galaxies. +nethocl were carried out by and(1939). who used the brightness difference between the ZAIID and the MSTO (the vertical parameter Tom now on) to estimate (he ages of sizeable samples of GGCs.,"method were carried out by and, who used the brightness difference between the ZAHB and the MSTO (the vertical parameter from now on) to estimate the ages of sizeable samples of GGCs." + This method is illustrated in (he central panel of Figure1. where the vertical parameter dependence on age is shown.," This method is illustrated in the central panel of Figure, where the vertical parameter dependence on age is shown." + Since it is well known the ZAIIB brightness level for old stellar svstems. such as GGCs. is independent of age. its level is (he same for the four plottedreference isochroues.," Since it is well known the ZAHB brightness level for old stellar systems, such as GGCs, is independent of age, its level is the same for the four plotted isochrones." + Following the same methodology as lor the horizontal method.reference isochrones were used to determine the vertical parameter as a function of age ancl [Fe/II].," Following the same methodology as for the horizontal method, isochrones were used to determine the vertical parameter as a function of age and [Fe/H]." + The results are plotted in (he central panel of Figure2., The results are plotted in the central panel of Figure. + Lines represent (he resulting vertical parameter in steps of 1 Gvr (solid lines) and 0.5 Gvr (dotted lines)., Lines represent the resulting vertical parameter in steps of 1 Gyr (solid lines) and 0.5 Gyr (dotted lines). + Again. the eurves are interpolated using a spline surface and will be used to derive relative ages based on the vertical method.," Again, the curves are interpolated using a spline surface and will be used to derive relative ages based on the vertical method." + Once the (heoretical grid is set up. the age of a GGC - or of an isochrone wilh a different Ie content and/or heavy. elements distribution - can be determined [rom its vertical parameter by comparinge it with thereference isochrone egrid.," Once the theoretical grid is set up, the age of a GGC - or of an isochrone with a different He content and/or heavy elements distribution - can be determined from its vertical parameter by comparing it with the isochrone grid." + The rMSFE method was first used to derive relative ages lor a large. homogeneous database of GGC photometry by(2009).," The rMSF method was first used to derive relative ages for a large, homogeneous database of GGC photometry by." + The method is discussed in detail in the quoted reference and only a brie! description is presented here., The method is discussed in detail in the quoted reference and only a brief description is presented here. + The CMD ocalion of (he faint MS of a GGC is independent of its age. but. hiehlv. dependent on its netallicitv.," The CMD location of the faint MS of a GGC is independent of its age, but highly dependent on its metallicity." + For this reason. MS and RGB fitting between clusters with similar metallicity is perlormed.," For this reason, MS and RGB fitting between clusters with similar metallicity is performed." + The right hand panel of Figure shows an example rMSE in which the 10. 12. and 14 Gvr isochrones have been shifted in both magnitude and color to fit the CMD ocalion of the 8 Gyr one. all isochrones having the same metallicity.," The right hand panel of Figure shows an example rMSF in which the 10, 12, and 14 Gyr isochrones have been shifted in both magnitude and color to fit the CMD location of the 8 Gyr one, all isochrones having the same metallicity." + The fit is performed ollowing the prescriptions of(2009): (hat is. in a least-squares [ashion and taking into account (vo CMD regions that have little dependence on cluster age.," The fit is performed following the prescriptions of; that is, in a least-squares fashion and taking into account two CMD regions that have little dependence on cluster age." + These regions are shaded in Figure1., These regions are shaded in Figure. + It can be seen how the rAISF method. provides gives the relative brightness of the considered isochrones’ MSTOs., It can be seen how the rMSF method provides gives the relative brightness of the considered isochrones' MSTOs. + Again. the isochrones described in Section were used (ο compute the theoretical grid.," Again, the isochrones described in Section were used to compute the theoretical grid." + The lower panel of Figure shows the model MS turn-off in the FGOGW filter ALS. as a function of [Fe/H]., The lower panel of Figure shows the model MS turn-off in the F606W filter $M_{F606W}^{\rm MSTO}$ as a function of [Fe/H]. + Lines represent MSTO magnitudes in steps of 1. Gyr (solid lines) and 0.5 Gyr (dotted lines)., Lines represent MSTO magnitudes in steps of 1 Gyr (solid lines) and 0.5 Gyr (dotted lines). + The curves are interpolated using a spline surface so (hat one can easily estimate MIU.=f(IEe/HI].age).," The curves are interpolated using a spline surface so that one can easily estimate $M_{F606W}^{\rm MSTO} = f({\rm [Fe/H], age})$." + Finally. relative ages can be estimated by," Finally, relative ages can be estimated by" +Section 3 presents three new [O III]-selected PNe and one new VMC-selected PN and their basic properties.,Section \ref{sec:results} presents three new [O III]-selected PNe and one new VMC-selected PN and their basic properties. + We conclude in Sect. 4.., We conclude in Sect. \ref{sec:end}. +" To conduct our search for new PNe we utilise the available B, V, [O III] and Ha images taken under non-photometric conditions with the Wide Field Imager (WFI) of the ESO 2.2-m telescope under program ID The data were reduced by ESO following Nonino et al. ("," To conduct our search for new PNe we utilise the publicly-available $B$ , $V$, [O III] and $\alpha$ images taken under non-photometric conditions with the Wide Field Imager (WFI) of the ESO 2.2-m telescope under program ID The data were reduced by ESO following Nonino et al. (" +"1999) and cover a large 63x arcmin? region centred near 30 Doradus (2000=05h37m5475, 032000=—69?21'55"").","1999) and cover a large $63\times63$ $^2$ region centred near 30 Doradus $\alpha_\mathrm{J2000}=05^\mathrm{h}37^\mathrm{m}54.7^\mathrm{s}$, $\delta_\mathrm{J2000}=-69^\circ21'55''$ )." +" This region is made προ of four separate sub-fields: 30Dor1, 30Dor2, 30Dor3 and 30Dor4, all sampled at 0.238”//pixel."," This region is made upo of four separate sub-fields: 30Dor1, 30Dor2, 30Dor3 and 30Dor4, all sampled at /pixel." + The world coordinate system (WCS) solution is accurate to ((rms) over the entire area., The world coordinate system (WCS) solution is accurate to (rms) over the entire area. +" Table 1 reproduces the coordinates and observation dates of the exposures taken, their total exposure times in each filter and the average measured stellar full-widths at half maximum (FWHM) as recorded at the data products webpage."," Table \ref{tab:wfi} reproduces the coordinates and observation dates of the exposures taken, their total exposure times in each filter and the average measured stellar full-widths at half maximum (FWHM) as recorded at the data products webpage." +" The central wavelengths and FWHMs of the filters were 451.1/133.5 nm (B/123), 539.6/89.4 nm (V/89) 502.4/8.0 nm (OIII/8) and 658.8/7.4 nm (Halpha/7)."," The central wavelengths and FWHMs of the filters were 451.1/133.5 nm (B/123), 539.6/89.4 nm (V/89) 502.4/8.0 nm (OIII/8) and 658.8/7.4 nm (Halpha/7)." +" Our strategy was to thoroughly search the WFI data in the form of a three-colour image of the four sub-fields made from Ha (red), [O III] (green) and B (blue) images."," Our strategy was to thoroughly search the WFI data in the form of a three-colour image of the four sub-fields made from $\alpha$ (red), [O III] (green) and $B$ (blue) images." +" In this combination bona-fide PNe typically have a telltale yellow—green hue from their strong Ha and [O III] emission, but there remains some sensitivity to Ho emitting point-sources and nebulae if there is no [O III] emission."," In this combination bona-fide PNe typically have a telltale yellow--green hue from their strong $\alpha$ and [O III] emission, but there remains some sensitivity to $\alpha$ emitting point-sources and nebulae if there is no [O III] emission." + The very large size of the four sub-fields (~8500x8500 pixels) called for a methodical approach when visualising the data to ensure no parts were left unexamined., The very large size of the four sub-fields $\sim$$8500\times8500$ pixels) called for a methodical approach when visualising the data to ensure no parts were left unexamined. + This was achieved using a custom-made plugin developed by one of us (BM) for the program (Joye Mandel 2003)., This was achieved using a custom-made plugin developed by one of us (BM) for the program (Joye Mandel 2003). + When an image is loaded the plugin divides it up into manageable sub-frames that fit within the graphical window dimensions., When an image is loaded the plugin divides it up into manageable sub-frames that fit within the graphical window dimensions. + A overlap between sub-frames ensured no parts of the images were missed when navigating from sub-frame to sub-frame., A overlap between sub-frames ensured no parts of the images were missed when navigating from sub-frame to sub-frame. + While browsing the images we made use of the many different scaling modes provided by to separately target faint emission at high contrast and point-source or compact emitters at low contrast that diminishes the high nebular background., While browsing the images we made use of the many different scaling modes provided by to separately target faint emission at high contrast and point-source or compact emitters at low contrast that diminishes the high nebular background. + The region functionality was used to overlay previously catalogued PNe and to record the position of new candidates., The region functionality was used to overlay previously catalogued PNe and to record the position of new candidates. + A total of 297 candidates were initially selected based on suspected [O III] and/or Ha emission., A total of 297 candidates were initially selected based on suspected [O III] and/or $\alpha$ emission. +" Candidates were then visualised in a web page that included the aforementioned WFI colour-composite image and a VMC colour-composite image made from K; (red), J (green) and Y (blue)."," Candidates were then visualised in a web page that included the aforementioned WFI colour-composite image and a VMC colour-composite image made from $K_s$ (red), $J$ (green) and $Y$ (blue)." + Only three promising PN candidates were found with almost all the rest turning out to be AGB stars (e.g. Miras) whose TiO bands give the false impression of Ha emission., Only three promising PN candidates were found with almost all the rest turning out to be AGB stars (e.g. Miras) whose TiO bands give the false impression of $\alpha$ emission. +" These were easily discerned as very bright sources in the VMC colour-composite images (K,S14 mag).", These were easily discerned as very bright sources in the VMC colour-composite images $K_s\la14$ mag). + We also recovered the nebula of Supernova 1987A and the [O IIIJ-bright pulsar wind nebula of PSR B0540—69.3., We also recovered the nebula of Supernova 1987A and the [O III]-bright pulsar wind nebula of PSR $-$ 69.3. + A few peculiar nebulae around luminous stars were also recovered (e.g. Henize 1956; Weis et al., A few peculiar nebulae around luminous stars were also recovered (e.g. Henize 1956; Weis et al. + 1997)., 1997). + As our focus is solely on the detection of new PNe we refrain from further discussion of these objects., As our focus is solely on the detection of new PNe we refrain from further discussion of these objects. +" In the VMC colour-composite image PNe routinely appear as resolved red sources due to nebular emission lines of Bry, He I 2.058 um and 2.112 wm, and the Hz molecular series (e.g. Hora et al."," In the VMC colour-composite image PNe routinely appear as resolved red sources due to nebular emission lines of $\gamma$, He I 2.058 $\mu$ m and 2.112 $\mu$ m, and the $_2$ molecular series (e.g. Hora et al." + 1999)., 1999). + Figure 1 shows RP1037 as a typical example of a resolved VMC PN detection., Figure \ref{fig:rp} shows RP1037 as a typical example of a resolved VMC PN detection. +" As part of an initial investigation into detecting new PNe like RP1037, we visually searched stacked VMC tiles as the VMC colour-composite in one frame and a K,—Y image in another frame."," As part of an initial investigation into detecting new PNe like RP1037, we visually searched stacked VMC tiles as the VMC colour-composite in one frame and a $K_s-Y$ image in another frame." +" The latter of which being sensitive to strong K, sources.", The latter of which being sensitive to strong $K_s$ sources. + During the search we came across an object in the 8.88 tile with an unusual pink colour quite unlike others in the whole tile., During the search we came across an object in the 8 tile with an unusual pink colour quite unlike others in the whole tile. +" As this colour is shared by some other bright PNe (e.g. SMP4, SMP6 and SMP30; see Miszalski et al."," As this colour is shared by some other bright PNe (e.g. SMP4, SMP6 and SMP30; see Miszalski et al." +" 2011), it was an excellent candidate for follow-up."," 2011), it was an excellent candidate for follow-up." + The only previous reference to the object was made by Gruendl Chu (2009) who classified it as a possible AGB star., The only previous reference to the object was made by Gruendl Chu (2009) who classified it as a possible AGB star. + Four new PNe candidates were found whose basic properties are given in Tab. 2.., Four new PNe candidates were found whose basic properties are given in Tab. \ref{tab:new}. +" These properties are their names (after the authors Miszalski, Napiwotzki Cioni), parent WFI or VMC field, PN status (Sect. 3.2)),"," These properties are their names (after the authors Miszalski, Napiwotzki Cioni), parent WFI or VMC field, PN status (Sect. \ref{sec:spec}) )," +" equatorial coordinates, Ha diameters, integrated [O III] fluxes and magnitudes (see Sect. 3.3)),"," equatorial coordinates, $\alpha$ diameters, integrated [O III] fluxes and magnitudes (see Sect. \ref{sec:fluxes}) )," +" heliocentric radial velocities (HRV, see Sect. 3.2))"," heliocentric radial velocities (HRV, see Sect. \ref{sec:spec}) )" + and morphologies., and morphologies. + Figure 2 displays their WFI and VMC images., Figure \ref{fig:new} displays their WFI and VMC images. +" Two colour compositesof Ha (red), V (green) and B (blue), and Ha (red), [O III] (green) and B (blue), were chosen to highlight the Ha and [O III] emission, respectively."," Two colour compositesof $\alpha$ (red), $V$ (green) and $B$ (blue), and $\alpha$ (red), [O III] (green) and $B$ (blue), were chosen to highlight the $\alpha$ and [O III] emission, respectively." +" The K; (red), J (green) and Y (blue) components of the VMC colour-composite are stacked images created by averaging individual images"," The $K_s$ (red), $J$ (green) and $Y$ (blue) components of the VMC colour-composite are stacked images created by averaging individual images" +The constant term 0.72+ 0.17 + places an upper bound on the intrinsic velocity dispersion for M-dwarfs in the cluster.,The constant term 0.72$\pm$ 0.17 $^{-1}$ places an upper bound on the intrinsic velocity dispersion for M-dwarfs in the cluster. + The constant C' was estimated by comparing RVs for repeated measurements made on different days with different fibre configurations., The constant $C$ was estimated by comparing RVs for repeated measurements made on different days with different fibre configurations. + This gave a value of ('c0.31 | (see equation 2) and hence our best estimate for the true velocity dispersion of the cluster is 0.66£0.17 , This gave a value of $C\simeq 0.31$ $^{-1}$ (see equation 2) and hence our best estimate for the true velocity dispersion of the cluster is $\pm$ 0.17 $^{-1}$. +"Using equation 7 gave 210 probable cluster members with a SNR 5 and a relative RV less than 2¢,. from the mean (see Fig.", Using equation 7 gave 210 probable cluster members with a $\geq$ 5 and a relative RV less than $2\sigma_e$ from the mean (see Fig. + 2)., 2). + A few fast rotating stars with a correspondingly large RV uncertainty were identitied as members even though their RVs are some distance from the mean in asolute terms., A few fast rotating stars with a correspondingly large RV uncertainty were identified as members even though their RVs are some distance from the mean in absolute terms. + There is no reason to doubt their membership since fiist rotators are rare amongst K to mid-M dwarf field stars (Del'osse et al., There is no reason to doubt their membership since fast rotators are rare amongst late-K to mid-M dwarf field stars (Delfosse et al. + 1998)., 1998). + Also shown in Fig., Also shown in Fig. + 2 is the number of stars classified as non-members., 2 is the number of stars classified as non-members. +" Nine of the non-members lie between σι. and 37, of the mean so could yet be cluster members (possibly SBI binary systems). as for a Gaussian distribution we expect ~10 further members to lie beyond 2a..."," Nine of the non-members lie between $2\sigma_e$ and $3\sigma_e$ of the mean so could yet be cluster members (possibly SB1 binary systems), as for a Gaussian distribution we expect $\sim 10$ further members to lie beyond $2 \sigma_e$." + Others may be be background or foreground stars., Others may be be background or foreground stars. + To estimate the maximum number of background stars falsely elassitied. as members. the average number of targets in δα bins centered at £10 + from the cluster mean was counted.," To estimate the maximum number of background stars falsely classified as members, the average number of targets in $\pm 2\sigma_e$ bins centered at $\pm 10$ $^{-1}$ from the cluster mean was counted." + On average these bins contained 3 non-members with periods., On average these bins contained 3 non-members with periods. + Assuming that the distribution of non members is uniform with RV this indicates that <3 of the 210 stars identified as members are likely to be non-members., Assuming that the distribution of non members is uniform with RV this indicates that $\leq 3$ of the 210 stars identified as members are likely to be non-members. + Figure 4 shows the distribution of ¢sin/ and period as a function of (Vo£)y colour for cluster members with measured periods., Figure 4 shows the distribution of of $v \sin i$ and period as a function of $(V-I)_0$ colour for cluster members with measured periods. + Colour is corrected for reddening assuming a uniform reddening of f(bV)-0.2 ¢(Terndrup et al., Colour is corrected for reddening assuming a uniform reddening of $E(B-V)=0.12$ (Terndrup et al. + 2002) and ratios of selective to total extinction A/E(D.V)=3.09 (Reike Lebofsky 1985) and ely//£7(V—[)=2.35.," 2002) and ratios of selective to total extinction $A_V/E(B-V) = +3.09$ (Reike Lebofsky 1985) and $A_I/E(V-I)=2.35$." + Spectral types are shown using the calibration from Kenyon Hartmann (19935)., Spectral types are shown using the calibration from Kenyon Hartmann (1995). + For the late-K and early-M stars. the distribution of esin/ and period are similar to those seen in other clusters at a similar age (e.g. the Pleiades. see Queloz et al.," For the late-K and early-M stars, the distribution of $v \sin i$ and period are similar to those seen in other clusters at a similar age (e.g. the Pleiades, see Queloz et al." + 1998. Terndrup et al.," 1998, Terndrup et al." + 2000)., 2000). + There is a wide range of rotation rates and periods. with significant populations of slowly rotating stars (periods of a few days and eosin? unresolved) and a tail of fast rotators with esin/ between S0 and 3.," There is a wide range of rotation rates and periods, with significant populations of slowly rotating stars (periods of a few days and $v \sin i$ unresolved) and a tail of fast rotators with $v \sin i$ between 50 and $^{-1}$." + Rotation velocities appear to increase (a decrease in period) as We move to later M-type stars., Rotation velocities appear to increase (a decrease in period) as we move to later M-type stars. + Of course. the presence of lower limits to Psin/ means an average cannot be calculated directly.," Of course, the presence of lower limits to $v \sin i$ means an average cannot be calculated directly." + Instead. Fig.," Instead, Fig." + 4 shows (on the right-hand y-axes) the fraction of rapid rotators with sins15kkmss ! or period <2 days. as a function of colour in 0.1 mag bins.," 4 shows (on the right-hand $y$ -axes) the fraction of rapid rotators with $v \sin i>15$ $^{-1}$ or period $<2$ days, as a function of colour in 0.1 mag bins." + These two criteria are approximately equivalent for stars with a radius of 0.6R.., These two criteria are approximately equivalent for stars with a radius of $R_{\odot}$. + The plots show that the fraction of rapid rotators is a sharply increasing function of colour tor decreasing mass)., The plots show that the fraction of rapid rotators is a sharply increasing function of colour (or decreasing mass). + About 90 per cent of stars of spectral type z: M4 are rapid rotators. compared to about 50 per cent at M3 and only ~20 per cent at MO-MI.," About 90 per cent of stars of spectral type $\geq$ M4 are rapid rotators, compared to about 50 per cent at M3 and only $\sim 20$ per cent at M0-M1." + This spectral type dependence appears to set in during the first few Myr of stellar evolution and develop slowly over time (Irwin et al., This spectral type dependence appears to set in during the first few Myr of stellar evolution and develop slowly over time (Irwin et al. + 2007)., 2007). + Samples of field stars. presumably with ages measured in Gyr. have almost no fast rotators earlier than type M3. but a sharp increase in the fraction of rapid rotators among cooler stars (Delfosse et a. 1998: Jenkins et al.," Samples of field stars, presumably with ages measured in Gyr, have almost no fast rotators earlier than type M3, but a sharp increase in the fraction of rapid rotators among cooler stars (Delfosse et a. 1998; Jenkins et al." + 2009: Browning et al., 2009; Browning et al. + 2010)., 2010). + West et al. (, West et al. ( +"2008) have calibrated age-magnetic activity relationships for field M-dwarfs. suggesting that while MO dwarfs have an “activity lifetime"" of GGyr. this increases to GGyr for M4 dwarfs.","2008) have calibrated age-magnetic activity relationships for field M-dwarfs, suggesting that while M0 dwarfs have an “activity lifetime” of Gyr, this increases to Gyr for M4 dwarfs." + Magnetic activity is closely related to rotation rate. so it is not surprising that the =150 MMyr old MO-MP stars in NGC 2516 rotate much faster on average than field stars (where the majority of field stars would have spun down). but have similar rotation rates to the cooler tield stars. whieh have not had time to spin down.," Magnetic activity is closely related to rotation rate, so it is not surprising that the $\simeq 150$ Myr old M0–M2 stars in NGC 2516 rotate much faster on average than field stars (where the majority of field stars would have spun down), but have similar rotation rates to the cooler field stars, which have not had time to spin down." + The usual interpretation of these phenomena (e.g. Delfosse et al. (, The usual interpretation of these phenomena (e.g. Delfosse et al. ( +1998: Jenkins et al.,1998; Jenkins et al. + 2009 ) is that spin-down timescales become much longer for cooler stars because the change from stars with radiative cores to fully convective stars changes the magnetic topology and makes angular momentum loss less efficient., 2009 ) is that spin-down timescales become much longer for cooler stars because the change from stars with radiative cores to fully convective stars changes the magnetic topology and makes angular momentum loss less efficient. + As the vast majority of targets with rotation periods have been confirmed here as cluster members. then we refer the reader to Irwin et al. (," As the vast majority of targets with rotation periods have been confirmed here as cluster members, then we refer the reader to Irwin et al. (" +2007). where the rotation period distribution is modelled in some detail in terms of angular momentum loss from a magnetized stellar wind.,"2007), where the rotation period distribution is modelled in some detail in terms of angular momentum loss from a magnetized stellar wind." + The wavelength range of our spectra (S061-8614A)) includes two of the CaT lines at rest wavelengths of and8542A., The wavelength range of our spectra ) includes two of the CaT lines at rest wavelengths of and. +. The CaT shares an upper level with the better known Ca H and K lines. which are more often used as chromospheric activity indicators.," The CaT shares an upper level with the better known Ca H and K lines, which are more often used as chromospheric activity indicators." + The CaT lines are also known to be effective indicators of chromospheric activity. with stars of similar luminosity and metallicity having different CaT line depths. owing to varying levels chromospheric emission filling the underlying absorption lines (Mallik 1994. 1997).," The CaT lines are also known to be effective indicators of chromospheric activity, with stars of similar luminosity and metallicity having different CaT line depths, owing to varying levels chromospheric emission filling the underlying absorption lines (Mallik 1994, 1997)." + Busà et al. (, Busà et al. ( +2007) show that the chromospheric component of the CaT lines is well correlated with the chromospheric Ca H and K flux.,2007) show that the chromospheric component of the CaT lines is well correlated with the chromospheric Ca H and K flux. + The method used here to measure the strength of the CaT chromospheric emission follows that described by Marsden. Carter Donati (2009).," The method used here to measure the strength of the CaT chromospheric emission follows that described by Marsden, Carter Donati (2009)." + We estimate the chromospheric component of the CaT flux by subtracting the photospherie contribution from a magnetically inactive star of similar spectral type., We estimate the chromospheric component of the CaT flux by subtracting the photospheric contribution from a magnetically inactive star of similar spectral type. + Marsden et al. (, Marsden et al. ( +2009) used this technique to measure CaT emission in FG and K stars.,"2009) used this technique to measure CaT emission in F,G and K stars." + The difficulty in using it for M dwarfs is finding suitable reference spectra at these spectral types with known low rotation and chromospheric activity., The difficulty in using it for M dwarfs is finding suitable reference spectra at these spectral types with known low rotation and chromospheric activity. + Several sources were investigated but none alone could provide a well defined set of standards spanning the range K3 to MS., Several sources were investigated but none alone could provide a well defined set of standards spanning the range K3 to M5. + For this reason results from several sources were combined to generate a semi-empirical reference spectra by scaling the measured high SNR spectrum of a magnetically inactive K3 standard by a colour-dependent scaling factor determined from lower SNR spectra of late-K and M dwarf stars., For this reason results from several sources were combined to generate a semi-empirical reference spectra by scaling the measured high SNR spectrum of a magnetically inactive K3 standard by a colour-dependent scaling factor determined from lower SNR spectra of late-K and M dwarf stars. + The first source of reference spectra was the library of high resolution spectra of Montes and Martinn (1988)., The first source of reference spectra was the library of high resolution spectra of Montes and Martínn (1988). + This yielded high SNR spectra for a K3 star (GI1OSa). an MIS star (GJL5). an M2.5 star (GJ623ab) and an M4 star (GJ748).," This yielded high SNR spectra for a K3 star (GJ105a), an M1.5 star (GJ15a), an M2.5 star (GJ623ab) and an M4 star (GJ748)." + Unfortunately only the first of these stars. GJOSa. has a Known long rotation period of 48 days. and low chromospheric activity indicated by its Ca H and K lines (Baliunas et al.," Unfortunately only the first of these stars, GJ105a, has a known long rotation period of 48 days, and low chromospheric activity indicated by its Ca H and K lines (Baliunas et al." + 1995)., 1995). + For this reason the spectra of this K3 star. braodened to match the resolution of the target spectra. was chosen as the baseline for semi-empirical reference spectra.," For this reason the spectra of this K3 star, braodened to match the resolution of the target spectra, was chosen as the baseline for semi-empirical reference spectra." + This, This +the systemic redshift of each mock QSO is set to be a value of zg=2 plus a Gaussian distributed random ,the systemic redshift of each mock QSO is set to be a value of $z_{\rm fg}=2$ plus a Gaussian distributed random error). +"In order to compare with the observational results from error).KTO08, an additional correction in the systematic error of (d2ofset)=173kms~! needs to be taken into account, i.e., the systemic redshift of each QSO host in the mock samples is set to zr+Ózogsec, where is set to 2 and the random error in óz;g4« is also σηςassumed to be Gaussian distributed (e.g., in Figures 2,, 3dd, 4,, 6, 7 below)."," In order to compare with the observational results from KT08, an additional correction in the systematic error of $\left<\delta z_{\rm offset}\right>=173\kms$ needs to be taken into account, i.e., the systemic redshift of each QSO host in the mock samples is set to $z_{\rm fg}+ \delta z_{\rm offset}$, where $z_{\rm fg}$ is set to $2$ and the random error in $\delta z_{\rm offset}$ is also assumed to be Gaussian distributed (e.g., in Figures \ref{fig:f2}, \ref{fig:f3}d d, \ref{fig:f4}, , \ref{fig:f6}, \ref{fig:f7} below)." +" For comparison, a zero error of ózogse is assumed in Figure 3aa-c below."," For comparison, a zero error of $\delta z_{\rm offset}$ is assumed in Figure \ref{fig:f3}a a-c below." +" Generally, the larger the systematic error in the systemic redshift estimates, the less the enhancement of the density in the fgQSO near zones that is required to reproduce the observed LOSPE (see Figure 2))."," Generally, the larger the systematic error in the systemic redshift estimates, the less the enhancement of the density in the fgQSO near zones that is required to reproduce the observed LOSPE (see Figure \ref{fig:f2}) )." +" Assuming that the effective density enhancement in the near zones of the fgQSOs is the same as the one required to reproduce the observations on the LOSPE byKT08?,, we generate mock samples with 500 synthetic Lya forest spectra and obtain the TPE effect from these samples."," Assuming that the effective density enhancement in the near zones of the fgQSOs is the same as the one required to reproduce the observations on the LOSPE by, we generate mock samples with 500 synthetic $\alpha$ forest spectra and obtain the TPE effect from these samples." +" Figure 3 shows the expected TPE obtained from the mock samples with different settings of the QSO age Tq, the opening angle of the torus Oo, and the error in the estimation of the fgQSO systemic redshift."," Figure \ref{fig:f3} shows the expected TPE obtained from the mock samples with different settings of the QSO age $\tauq$, the opening angle of the torus $\Theta_0$, and the error in the estimation of the fgQSO systemic redshift." +" Figure 3aa shows that for a small QSO age το, the excess of DA is significant near the fgQSOs because of the significant density enhancement in the immediate vicinity of the fgQSOs."," Figure \ref{fig:f3}a a shows that for a small QSO age $\tauq$, the excess of $DA$ is significant near the fgQSOs because of the significant density enhancement in the immediate vicinity of the fgQSOs." + This excess of DA decreases with increasing Tq because the significance of the suppression of the absorption by the UV photons from the fgQSOs increases with increasing Tq., This excess of $DA$ decreases with increasing $\tauq$ because the significance of the suppression of the absorption by the UV photons from the fgQSOs increases with increasing $\tauq$. +" In principle, the dependence of the TPE on the QSO age 7Q, as shown in Figure 3aa, suggests that the TPE can be used to constrain the QSO lifetime once the density enhancement in the fgQSO near zones is determined by the LOSPE."," In principle, the dependence of the TPE on the QSO age $\tauq$, as shown in Figure \ref{fig:f3}a a, suggests that the TPE can be used to constrain the QSO lifetime once the density enhancement in the fgQSO near zones is determined by the LOSPE." + The differences among large Tq cases shown in the panel are small because the time during which photons cross the proximity regions are smaller than or at most comparable to the QSO age in these cases., The differences among large $\tauq$ cases shown in the panel are small because the time during which photons cross the proximity regions are smaller than or at most comparable to the QSO age in these cases. +" However, none of the simulated DA (even the one with the shortest το) in Figure 3aa can match the observational results on the TPE obtained by KT08."," However, none of the simulated $DA$ (even the one with the shortest $\tauq$ ) in Figure \ref{fig:f3}a a can match the observational results on the TPE obtained by KT08." + Figure 3bb shows the dependence of the TPE on the half opening angle Θρ of the tori associated with the fgQSOs., Figure \ref{fig:f3}b b shows the dependence of the TPE on the half opening angle $\Theta_0$ of the tori associated with the fgQSOs. +" For the extreme case of Og=0? (without the PE due to the fgQSO UV radiation), the excess of the DA due to the density enhancement near fgQSOs is the most significant (red line and "," For the extreme case of $\Theta_0=0\degr $ (without the PE due to the fgQSO UV radiation), the excess of the $DA$ due to the density enhancement near fgQSOs is the most significant (red line and points)." +"With increasing Oo, the excess of DA becomes lesspoints). and less significant because the region that can be affected by the UV photons escaping out from the central engine becomes larger as shown by the color lines and points."," With increasing $\Theta_0$, the excess of $DA$ becomes less and less significant because the region that can be affected by the UV photons escaping out from the central engine becomes larger as shown by the color lines and points." +" For Og=89° (almost without obscuration to the fgQSO photons; magenta line and points), the expected excess of DA due to the density enhancement is balanced significantly by the proximity effect due to the fgQSO UV radiation."," For $\Theta_0=89\degr $ (almost without obscuration to the fgQSO photons; magenta line and points), the expected excess of $DA$ due to the density enhancement is balanced significantly by the proximity effect due to the fgQSO UV radiation." +" Figure 3cc shows the dependence of the TPE on the lifetime of fgQSOs, in which the half opening angle of the torus is fixed to Og=60°."," Figure \ref{fig:f3}c c shows the dependence of the TPE on the lifetime of fgQSOs, in which the half opening angle of the torus is fixed to $\Theta_0=60\degr $." + This value of Oo is roughly in the range determined by observations2010)., This value of $\Theta_0$ is roughly in the range determined by observations. +". In this panel, the value of the QSO age is chosen randomly over a range from 0 to the QSO Τοlifetime τι, instead of being a constant as labeled for each line inpanel (a)."," In this panel, the value of the QSO age $\tauq$ is chosen randomly over a range from 0 to the QSO lifetime $\tau_{\rm lt}$, instead of being a constant as labeled for each line inpanel (a)." +" Because of the obscuration in the transverse direction to the UV radiation from the fgQSOs, there is significant DA excess even for the case of τε=107"" yr."," Because of the obscuration in the transverse direction to the UV radiation from the fgQSOs, there is significant $DA$ excess even for the case of $\tau_{\rm lt}=10^{7.7}$ yr." +" Compared to the case without obscuration shown in Figure 3aa, the dependence of the DA excess on 7, becomes less obvious if the obscurationto the UV radiation from the fgQSOs is significant."," Compared to the case without obscuration shown in Figure \ref{fig:f3}a a, the dependence of the $DA$ excess on $\tau_{\rm lt}$ becomes less obvious if the obscurationto the UV radiation from the fgQSOs is significant." +" Note that one characteristic timescale for the luminosity evolution of a QSO is the Salpeter timescale Which is ~1077 yr if the mass-to-energy conversion Tsp,efficiency of its nuclear activity is ~0.1 and the"," Note that one characteristic timescale for the luminosity evolution of a QSO is the Salpeter timescale $\tau_{\rm sp}$ , which is $ \sim 10^{7.7}$ yr if the mass-to-energy conversion efficiency of its nuclear activity is $\sim 0.1$ and the" +non-extremal black holes. Wewillpresent corresponding tothe indices,"Introduce the rescaled variables: The latter is called the Kähhler Consider black holes with one electric charge $q_0$ and $p^A$ $A=1,2,3$ ) magnetic charges." + qn 2 Formulation ofThe Calculation We will considerV=2," In our convention $\mathcal{D}\equiv D_{ABC}p^Ap^Bp^C>0$ For $q_0>0$ one can have a non-extremal solution \cite{nonextremal} with a supersymmetric extremal limit \cite{genstabeq,r2entropy,SJR}." + Poincaré supergravity coupled to Ny Abelian NV’ =2vector multiplets. The couplings ofthe theory.," By reversing the sign of the charge $q_0$, but taking the moduli to depend on the absolute value, one can have a non-extremal solution with a non-supersymmetric extremal limit \cite{sign_reversal,nonsusy1,nonsusy2}." + are described byà prepotential. for which we assume theform: Dapce NNP NC DAN! F(N.," At the $R$ -level, i.e. without $R^2$ -terms, in addition to the sign changes, the two solutions differ also in the form of the auxiliary $T$ field." +"A) vi i (2:[Ew] whereX"". V! are the moduli.D ape. Dy areconstants.", The thermodynamic properties of the solution with the non-supersymmetric extremal limit can be obtained by an analytic continuation. +" Dape Ny. containing Tr"" couplings", This is no longer true when including higher curvature corrections. + in the Lagrangian., We will construct the $R^2$ -level solutions for both cases. +" where 7,, is an ausiliary", The extremal limits $\mu=0$ ) were discussed in \cite{allrpaper}. + field. This term may, In the following we will denote $E\equiv D_Ap^A$. +" ariseas ag,correction in thelarge volume limit!oftvpe I"," We are interested in black hole solutions of the $R^2$ curvature corrected theory, to first order in $\epsilon$ ." +LA string theory compactified on a Calabi-Yau three-lolel. or as strin," As a starting point for our ansatz, we may take the $R$ -level solution $\epsilon=0$ ), with the prepotential $F(\epsilon=0)$ replaced by $F(\epsilon)$." +gtheory compactified A3 higher 'The large Calabi-Yauvol," This, however, proves to be insufficient, and we need to introduce a further general linear $\epsilon$ -correction to the fields." +ume approximation requiresButY-3/XU) x» 1.," We look for solutions in the form: where $\mu\geq0$ isa non-extremality parameter, $(k_0,k^A)>0$ are constants with either" +"long matter era needed for structure formation and the limits set by Big Bang Nucleosynthesis (BBN), while a>2 corresponds to early universe braneworld modifications.","long matter era needed for structure formation and the limits set by Big Bang Nucleosynthesis (BBN), while $\alpha > 2$ corresponds to early universe braneworld modifications." + Using Equation it is possible to test the model with probes of the expansion history and indeed this has already been performed by ? with Baryon Acoustic Oscillations., Using Equation it is possible to test the model with probes of the expansion history and indeed this has already been performed by \citet{YamamotoBassettNichol06} with Baryon Acoustic Oscillations. +" If one wants to go beyond this and include tests of large scale structure then one needs a formalism for the growth of density perturbations analogous to Equations(7),, and therefore(9)."," If one wants to go beyond this and include tests of large scale structure then one needs a formalism for the growth of density perturbations analogous to Equations, and therefore." +. The problem in this scenario is that in order to deduce the growth of perturbations one needs an underlying covariant theory and all that exists in this modified DGP model (mDGP) is a parameterisation., The problem in this scenario is that in order to deduce the growth of perturbations one needs an underlying covariant theory and all that exists in this modified DGP model (mDGP) is a parameterisation. + ? circumvented this obstacle by taking DGP (a limit in the model) as the structure of the theory., \citet{Koyama06} circumvented this obstacle by taking DGP (a limit in the model) as the structure of the theory. +" It was subsequently found that the metric perturbations take the same form as Equations and but instead with, Figure 2 demonstrates how the growth of density pertubations alter within the mDGP model - from LCDM (a= 0) to DGP (a= 1)."," It was subsequently found that the metric perturbations take the same form as Equations and but instead with, Figure \ref{fig:alpha_growths} demonstrates how the growth of density pertubations alter within the mDGP model - from LCDM $\alpha=0$ ) to DGP $\alpha=1$ )." + As in the previous Figure it is clear that there is a suppression of growth at the more DGP end of the α spectrum., As in the previous Figure it is clear that there is a suppression of growth at the more DGP end of the $\alpha$ spectrum. +" Although a parameterisation of a general large extra dimensional model the mDGP model now has a definite Friedmann equation that governs the expansion history and, assuming the structure of any underlying theory, it has a set of metric perturbation equations and a corresponding density perturbation equation."," Although a parameterisation of a general large extra dimensional model the mDGP model now has a definite Friedmann equation that governs the expansion history and, assuming the structure of any underlying theory, it has a set of metric perturbation equations and a corresponding density perturbation equation." + We can therefore treat this as a specific model which we choose to constrain later in the paper., We can therefore treat this as a specific model which we choose to constrain later in the paper. + It is worth noting that using this as a measure of deviation from General Relativity or as a parameterisation of general modified gravity is not our aim., It is worth noting that using this as a measure of deviation from General Relativity or as a parameterisation of general modified gravity is not our aim. + This would constitute a poor choice of parameter given the severe lack of generalness and incompleteness with regards to the concept of modified gravity as a whole., This would constitute a poor choice of parameter given the severe lack of generalness and incompleteness with regards to the concept of modified gravity as a whole. + We do however touch upon the idea of parameterising modified gravity in the next section., We do however touch upon the idea of parameterising modified gravity in the next section. +" This model has, however, been extremely illustrative with regards to the extra richness that can occur in modified gravity."," This model has, however, been extremely illustrative with regards to the extra richness that can occur in modified gravity." + Not only does it have varying expansion histories but potentially a whole range of perturbation equations which alters the growth of structure and the relationship to the power spectrum., Not only does it have varying expansion histories but potentially a whole range of perturbation equations which alters the growth of structure and the relationship to the power spectrum. +" This is particularly useful when attempting to distinguish between LCDM, general dark energy and modified gravity, and insightful to the probes that will be most adept at detecting them."," This is particularly useful when attempting to distinguish between LCDM, general dark energy and modified gravity, and insightful to the probes that will be most adept at detecting them." +" Again, we discuss these issues in the following sections."," Again, we discuss these issues in the following sections." + The alteration in the growth of structure within the mDGP model demonstrated an additional observational characteristic that allows us to further constrain the model, The alteration in the growth of structure within the mDGP model demonstrated an additional observational characteristic that allows us to further constrain the model +wind problem and wind clumping. and end with concluding remarks.,"wind problem and wind clumping, and end with concluding remarks." + We briefly review those aspects of the wind driving mechanism of massive early-type stars that are relevant in the context of establishing an empirical relation between mass loss and chemical composition., We briefly review those aspects of the wind driving mechanism of massive early-type stars that are relevant in the context of establishing an empirical relation between mass loss and chemical composition. + For a more in-depth treatment of the physics of mass loss. see e.g. ? and ?..," For a more in-depth treatment of the physics of mass loss, see e.g. \cite{kudritzki00} and \cite{vink01}." + The basic mechanism driving the winds of hot massive stars is the transfer of momentum from photons to the atmospheric gas by line interactions., The basic mechanism driving the winds of hot massive stars is the transfer of momentum from photons to the atmospheric gas by line interactions. + The driving mechanism implies that the properties of the stellar wind will depend on the number of photons per second streaming through the photospheric layers (reflecting the stellar luminosity). and on the number and ability of lines being available — in particular at wavelengths around the photospheric flux maximum — to absorb or scatter these photons.," The driving mechanism implies that the properties of the stellar wind will depend on the number of photons per second streaming through the photospheric layers (reflecting the stellar luminosity), and on the number and ability of lines being available – in particular at wavelengths around the photospheric flux maximum – to absorb or scatter these photons." + The dependence of the wind driving on the number of lines present suggests that mass loss is a funetion of elemental abundance., The dependence of the wind driving on the number of lines present suggests that mass loss is a function of elemental abundance. + Whether this is indeed the case formally depends on the nature of the driving lines., Whether this is indeed the case formally depends on the nature of the driving lines. + In the hypothetical case that one would be in a regime of abundances for which all lines effectively contributing to the line force are optically thick. mass loss would be a function of elemental abundance.," In the hypothetical case that one would be in a regime of abundances for which all lines effectively contributing to the line force are optically thick, mass loss would be a function of elemental abundance." + This regime is not encountered in even the most metal rich environments known (?).., This regime is not encountered in even the most metal rich environments known \citep{vink01}. + In reality. it is found that the lines driving the wind are a mixture of optically thin and optically thick lines.," In reality, it is found that the lines driving the wind are a mixture of optically thin and optically thick lines." + Representing the distribution of line strengths by a power law. one predicts. for Galactic O stars. a ratio of the line acceleration from optically thick lines to the total line acceleratior of a~2/3 (see?).. where an even larger contribution by optically thick lines would increase this value (and vice versa).," Representing the distribution of line strengths by a power law, one predicts, for Galactic O stars, a ratio of the line acceleration from optically thick lines to the total line acceleration of $\alpha \sim 2/3$ \citep[see][]{puls00}, where an even larger contribution by optically thick lines would increase this value (and vice versa)." + This ensures a dependence of mass loss on elemental abundance., This ensures a dependence of mass loss on elemental abundance. + Which elements dominate the line force?, Which elements dominate the line force? + The answer depends on the effective temperature of the star. (Morepre-celerationregime:seealso?2)..," The answer depends on the effective temperature of the star. \citep[More precisely: on the radiation and +electron temperature in the wind acceleration regime; see +also][]{vink99,puls00}." + Although hydrogen and helium are by far the most abundant elements. their impact on the wind driving is modest.," Although hydrogen and helium are by far the most abundant elements, their impact on the wind driving is modest." + Decisive for whether or not a species is a significant contributor to the line driving is the product: abundance x tonisation fraction x number of effective lines., Decisive for whether or not a species is a significant contributor to the line driving is the product: abundance $\times$ ionisation fraction $\times$ number of effective lines. + Very roughly. the elemental abundance times the tonisation fraction of hydrogen and helium are similar to that of metals that are in the dominant stage of ionisation.," Very roughly, the elemental abundance times the ionisation fraction of hydrogen and helium are similar to that of metals that are in the dominant stage of ionisation." + It is therefore thenumber of driving lines that is decisive., It is therefore the of driving lines that is decisive. + As H and He -- due to their simple atomic structure — have only few lines that can effectively contribute to the line force. it is relatively abundant complex atoms that are the main contributors.," As H and He – due to their simple atomic structure – have only few lines that can effectively contribute to the line force, it is relatively abundant complex atoms that are the main contributors." + We estimate the relative. contributions. of the different elements by the use of a Monte Carlo method (???)— that caleulates the total momentum transfer from the radiation field to the outflowing gas particles.," We estimate the relative contributions of the different elements by the use of a Monte Carlo method \citep [] +{abbott85,dekoter97,vink99} that calculates the total momentum transfer from the radiation field to the outflowing gas particles." + Although the relative contribution to the line force is depth-dependent (see below). here we simply register the atomic number of the elements with which the photons interact somewhere in the wind. and we present the results in Tab. 1l..," Although the relative contribution to the line force is depth-dependent (see below), here we simply register the atomic number of the elements with which the photons interact somewhere in the wind, and we present the results in Tab. \ref{tab:line_force_contribution}." + For a late-O dwarf of solar composition. CNO accounts for some 15 percent: iron contributes some 25 percent.," For a late-O dwarf of solar composition, CNO accounts for some 15 percent; iron contributes some 25 percent." + Other iron-group elements (for instance Cr. Mn. Co. Ni) add a few percent.," Other iron-group elements (for instance Cr, Mn, Co, Ni) add a few percent." +" a-elements. such as Ne. Mg. Si. S. Ar. and Ca account for about 30ο, with Si being the main contributor with ~ 20%."," $\alpha$ -elements, such as Ne, Mg, Si, S, Ar, and Ca account for about 30, with Si being the main contributor with $\sim$ 20." +. We mention a decomposition of the line force in terms of iron group and α elements as their nucleosynthetie origin is different., We mention a decomposition of the line force in terms of iron group and $\alpha$ elements as their nucleosynthetic origin is different. + The former are mostly produced in thermonuclear Type Ia supernovae. the latter predominantly in core-collapse supernovae of types II and Ib/c. Beware that due to their different electronic structure specific. groups of elements have a different line-strength statistics. and dominate the line acceleration at different depths: iron group elements have a somewhat larger influence on the mass-loss rate. whereas lighterions dominate the acceleration in the outer wind. thus controlling the terminal velocity (cf. ??)».," The former are mostly produced in thermonuclear Type Ia supernovae, the latter predominantly in core-collapse supernovae of types II and Ib/c. Beware that due to their different electronic structure specific groups of elements have a different line-strength statistics, and dominate the line acceleration at different depths: iron group elements have a somewhat larger influence on the mass-loss rate, whereas lighterions dominate the acceleration in the outer wind, thus controlling the terminal velocity (cf. \citealt{vink99, puls00}) )." + These more subtle effects are not reflected in the statistics provided in Table 1.., These more subtle effects are not reflected in the statistics provided in Table \ref{tab:line_force_contribution}. + Mixing of CNO-cycled material to the surface during the supergiant phase may affect the relative abundances of these three elements., Mixing of CNO-cycled material to the surface during the supergiant phase may affect the relative abundances of these three elements. + However. in terms of their contribution to the line force not much will change when this happens. as these three elements have more or less equal numbers of effective driving lines near the photospheric flux maximum and the C+N+0 abundance remains unaffected by the CNO-cycle (?)..," However, in terms of their contribution to the line force not much will change when this happens, as these three elements have more or less equal numbers of effective driving lines near the photospheric flux maximum and the C+N+O abundance remains unaffected by the CNO-cycle \citep{vink02}." + Accounting for the fact that we are interested in the gross dependence of wind parameters on metallicity. and particularly in the. product of mass-loss rate and terminal velocity (see below). we conclude that For stars of," Accounting for the fact that we are interested in the gross dependence of wind parameters on metallicity, and particularly in the product of mass-loss rate and terminal velocity (see below), we conclude that For stars of" + 10'- 1077 LjxLU. ~6 66GM/c? 10M ," $10^{12}$ $10^{9-10}$ $L_{R} +\propto {L}_{ X}^{0.7}$ $\sim6$ $66~{\rm +GM}/{\rm c}^{2}$ $10~{\rm M}_{\odot}$ " +"olded the data by P, = 1.25826 d after subtracting out the sinusoid characterized by 2=I/f2.80282 d. Note the wo sets of 4 points obtained on Julian Dates 2440297 anc 2449312. respectively.","folded the data by $P_1$ = 1.25826 d after subtracting out the sinusoid characterized by $P_2 = 1/f_2 = 2.89282$ d. Note the two sets of 4 points obtained on Julian Dates 2449297 and 2449312, respectively." + H we had folded the data by 1/(1- fi) z JST davs. the points from these two nights would appear as nearly vertical “posts” in the folded light curve insteac of following the general run of data from other nights.," If we had folded the data by 1/(1 - $f_1$ ) $\approx$ 4.87 days, the points from these two nights would appear as nearly vertical “posts” in the folded light curve instead of following the general run of data from other nights." + A further piece of evidence that f; and not 1 - fiis the true frequeney comes from an analysis ofthe data obtainec by Guinan ane MeCook from 1993 January 30 to February 26., A further piece of evidence that $f_1$ and not 1 - $f_1$ is the true frequency comes from an analysis of the data obtained by Guinan and McCook from 1993 January 30 to February 26. + We obtain ó;=0.143+0.011 using the same epoch. which compares very well with ὧν=O.114+0.016 from ‘Table 2.," We obtain $\phi_1 = -0.143 \pm 0.011$ using the same epoch, which compares very well with $\phi_1 = -0.114 \pm 0.016$ from Table 2." + A folded. plot of the carly 1993 data is to be found in Ixrisciunas (1994) and is not reproduced here., A folded plot of the early 1993 data is to be found in Krisciunas (1994) and is not reproduced here. + A similar analysis gives G2=0419d0.026 for the early 1993 data. vs. O2=—0.481+0.018 from Table 2.," A similar analysis gives $\phi_2 = -0.419 \pm 0.026$ for the early 1993 data, vs. $\phi_2 = -0.481 \pm 0.018$ from Table 2." + These differences are not significant.> or indicate a value for the frequency fo slightly cdilferent from the one adopted (see below).," These differences are not significant, or indicate a value for the frequency $f_2$ slightly different from the one adopted (see below)." + This is strong evidence not only that fj ancl fo are true frequencies. but that the physical mechanism associated with the photometric variations can be stable over time scales of one vear or longer.," This is strong evidence not only that $f_1$ and $f_2$ are true frequencies, but that the physical mechanism associated with the photometric variations can be stable over time scales of one year or longer." + Interestingly. fo but fy shows up in the power spectrum of radial velocities (see below).," Interestingly, $f_2$ but $f_1$ shows up in the power spectrum of radial velocities (see below)." + One unresolved. issue is the variations of the amplitudes of the sinusoids., One unresolved issue is the variations of the amplitudes of the sinusoids. + We find that zl in particular varies over quite a range (see Fig., We find that $A_1$ in particular varies over quite a range (see Fig. + 5). making the precliction of future variations of the star impossible. unless it can be shown how the amplitudes vary with time.," 5), making the prediction of future variations of the star impossible, unless it can be shown how the amplitudes vary with time." + Since Guinan and MeCook obtained equivalent. B-band data. we can investigate the variations of color in 9 Aur.," Since Guinan and McCook obtained equivalent B-band data, we can investigate the variations of color in 9 Aur." + In Fie., In Fig. + 6 we show the folded plot of ACV) colors from data of the same period covered in Fig., 6 we show the folded plot of $\Delta (B-V)$ colors from data of the same period covered in Fig. + 4., 4. + Since 7;N. is in the sense 9 Aurmus BS 1561 and the least positive ACBY) corresponds to the bluest color for 9 Aur. one can clearly see that 9 Aur is bluest (Le. hottest) when it is brightest.," Since $\Delta$ ” is in the sense 9 Aur BS 1561 and the least positive $\Delta (B-V)$ corresponds to the bluest color for 9 Aur, one can clearly see that 9 Aur is bluest (i.e. hottest) when it is brightest." +" This is the case for both the f, ancl f» sinusoids. since the phases ©; derived from the 2BV colors match the phases derived from the V-band photometry (compare Tables 2 and 3)."," This is the case for both the $f_1$ and $f_2$ sinusoids, since the phases $\phi_i$ derived from the $B-V$ colors match the phases derived from the V-band photometry (compare Tables 2 and 3)." + We note that the mean. B-V amplitudes of the 1993/4 season about about one-third of the V-band amplitudes., We note that the mean B-V amplitudes of the 1993/4 season about about one-third of the V-band amplitudes. +ou AZ. is the possiblity of an age spread among the stars rear the main-sequence turcXf.,on $M_c$ is the possiblity of an age spread among the stars near the main-sequence turnoff. + For cxaunple. it is possible hat the lower lnass stars formed first. by a sufficient narein that some stars sliehtlv below top of the inain-sequence are evolving on to the red eiut branch at the sale fine as more Wassive stars.," For example, it is possible that the lower mass stars formed first, by a sufficient margin that some stars slightly below top of the main-sequence are evolving on to the red giant branch at the same time as more massive stars." + The most massive stars lve main-sequenuce Lifetimes about 5 Myr. so the total age Spreac js af most a few Myr.," The most massive stars have main-sequence lifetimes about 5 Myr, so the total age spread is at most a few Myr." +" Such a spread in age would nen hat stars evolving on to the red eiut branch could lave masses SSΟΛ. ess than the measure turnoff mass which would imply M,SAL...rom", Such a spread in age would mean that stars evolving on to the red giant branch could have masses $\ltsim 0.3 \msun$ less than the measured turnoff mass which would imply $M_c \gtsim 7.3 \msun$. +eMoeasunug such an age spreads requires accurate plitrv for stars just |olov he turnoff. and we will be acquiring this daring Cycle 7," Measuring such an age spreads requires accurate photometry for stars just below the turnoff, and we will be acquiring this during Cycle 7." + Another source of uncertaiutv is the yossibility that the object is a member of a masstrausfer binary. but this is uulikelv. ane would require it now be a fiel white cdwart ιοτο star binary.," Another source of uncertainty is the possibility that the object is a member of a mass–transfer binary, but this is unlikely and would require it now be a tight white dwarf – neutron star binary." + Because voune white dwarfs are bright aud verv blue. detecting candidates even in eround DAser data is nof diffienlt.," Because young white dwarfs are bright and very blue, detecting candidates even in ground based data is not difficult." + They would be exjrected to be preset iu any star forming region coutainius sigeuificaut numbers of stars with uasses near AL., They would be expected to be present in any star forming region containing significant numbers of stars with masses near $M_c$. + For example. a recen CMD of an association in the Simall MageHanic Cloud containing stars with ages 10.60 My. cout:dus three stars whose colors and magnitudes are consistewt with those of voung white dwarts ).," For example, a recent CMD of an association in the Small Magellanic Cloud containing stars with ages $10-60$ Myr contains three stars whose colors and magnitudes are consistent with those of young white dwarfs )." +" Future IIST observations )f NCC I818 and other vouug LAIC clusters. to determine t16 cooling sequence. ages ad masses of the white dw]xopulatiou iu these clusters. should allow us to determiine AL more precisely. aud possibly for a range of metalicitics,"," Future HST observations of NGC 1818 and other young LMC clusters, to determine the cooling sequence, ages and masses of the white dwarf population in these clusters, should allow us to determine $M_c$ more precisely, and possibly for a range of metallicities." + We have ideutifiecd a caucdilate luminous white dwarf in the voung star cluster NGC tals in the LAIC., We have identified a candidate luminous white dwarf in the young star cluster NGC 1818 in the LMC. + The objectud is ~3hran aresee from the cluster center on (T2000. 0.675)., The object is $\sim 35 $ arcsec from the cluster center (about $4.5 r_c$ and $0.6 r_h$ ). + It has coordinates 5:PLAS. INL66:20:s im," It has coordinates 5:04:13.8, $-$ 66:26:33.4 (J2000)." + Iu the IIST passbauds it has Vus and (C535;—V333)=H.," In the HST passbands it has $V_{555}=18.43$, and $(U_{336}-V_{555})=-1.67$." + Iu the Joliusou-C'ousius system this corresponds to hese.ΊδιΕν (VI)025 and (CFVy)=132.," In the Johnson-Cousins system this corresponds to $V=18.44$ , $(V-I)=-0.25$ and $(U-V)=-1.32$." + values are corrected for reddening assuming £(DVW)=0.05., These values are corrected for reddening assuming $E(B-V)=0.05$. + Posissou crrors are £0.03 for V aud £0.01 for the colors., Posisson errors are $\pm 0.03$ for $V$ and $\pm 0.04$ for the colors. + These do not include wucertaitics in the transformation to the Joliuson-Cousin system., These do not include uncertainties in the transformation to the Johnson-Cousin system. + The temperature is probably <20.000 Ix but is poorly coustraimed by the (VW) color.," The temperature is probably $\gtsim 20,000$ K but is poorly constrained by the $(U-V)$ color." + With the adopted distance modulus of 18.5.the object has absolute magnitude AA;=0.06.," With the adopted distance modulus of 18.5, the object has absolute magnitude $M_V=-0.06$." + If this object is indeed a white dwarf. then its mass ds probably 1.1L3AL. 1990)).," If this object is indeed a white dwarf, then its mass is probably $ 1.1-1.3 \msun$ )." + The composition of white dwarfs formed from high ass progenitors is expected to he OxveenNeouMagnesium. but may be Carbon/Oxveeu.," The composition of white dwarfs formed from high mass progenitors is expected to be Oxygen--Neon--Magnesium, but may be Carbon/Oxygen." + A spectroscopic determination of its composition ids a priority., A spectroscopic determination of its composition is a priority. +" If spectroscopic followup observations confi the identity of the candidate star as a huninous voung white dwarf. we have strouely constrained the critical mass at which stars stop evolving to type II supernovae to M,21.6M..."," If spectroscopic followup observations confirm the identity of the candidate star as a luminous young white dwarf, we have strongly constrained the critical mass at which stars stop evolving to type II supernovae to $M_c \gtsim 7.6 \msun$." + A preliminary spectrum of the white dwarf candidate was obtained at the AAT 5 March 1998., A preliminary spectrum of the white dwarf candidate was obtained at the AAT 5 March 1998. + The spectrm rules out the possibility that the object is a quasar., The spectrum rules out the possibility that the object is a quasar. + The velocity is indistiuguishable from that of two other cluster members so it is also very unlikely to be a foreerouncd )bject., The velocity is indistinguishable from that of two other cluster members so it is also very unlikely to be a foreground object. + Detailed modelling of the spectrum is currently iu progress., Detailed modelling of the spectrum is currently in progress. + This research was supported in part by à PPARC rolling eraut., This research was supported in part by a PPARC rolling grant. + SS ackuowledecs the support of the Evropeau Union through a Marie Cure Individual Fellowship., SS acknowledges the support of the European Union through a Marie Curie Individual Fellowship. + MBD eratcfully ackuoxledges the support of the Roval Society through a URE., MBD gratefully acknowledges the support of the Royal Society through a URF. + Fuudiug for JID was provided by a erant from the Cambridge Comunomwealth Trust. aud frou Trinity College.," Funding for JH was provided by a grant from the Cambridge Commonwealth Trust, and from Trinity College." + We would like to thanx Brian Doyle. Matt Burleigh. Heleu Johustonaud Rav Stathakis for obtaiuiug a spectrum of the caudidate white dwarf.," We would like to thank Brian Boyle, Matt Burleigh, Helen Johnstonand Ray Stathakis for obtaining a spectrum of the candidate white dwarf." +The discovery of GRBO90423 at redshift z~8.2 (Salvaterra et al.,The discovery of GRB090423 at redshift $z\sim 8.2$ (Salvaterra et al. + 2009: Tanyir et al., 2009; Tanvir et al. + 2009) has shown that Ganuma-Rav 3ursts (CBs) can directly probe the very distant Universe., 2009) has shown that Gamma-Ray Bursts (GRBs) can directly probe the very distant Universe. +" GltDs are so bright that they can ""illuminate. for a shor time. regions of distant galaxies otherwise unobservable."," GRBs are so bright that they can `illuminate', for a short time, regions of distant galaxies otherwise unobservable." + The optical alterglow of one of the most distant. objects ever observed. (GRBOSO904 at redshift 2=6.3. WKawai e al.," The optical afterglow of one of the most distant objects ever observed (GRB050904 at redshift $z=6.3$, Kawai et al." + 2006) was observed. with a 25 em telescope (Bocer e al., 2006) was observed with a 25 cm telescope (Böeer et al. + 2006) and could have been detected up too.~10 with the Swift BAT (Cusumano et al., 2006) and could have been detected up to $z\sim 10$ with the Swift BAT (Cusumano et al. + 2007)., 2007). + The optica afterglow of GRBOSOSLOB could have been observed. with the naked eve (Racusin et al., The optical afterglow of GRB080319B could have been observed with the naked eye (Racusin et al. + 2008) and GRBOSOSZISB coulc also have been detected by ονολ up to z10.7 ane up to z32 at the nominal EXIST sensitivity. (Bloom et al., 2008) and GRB080319B could also have been detected by Swift-BAT up to $z\sim 10.7$ and up to $z\sim 32$ at the nominal EXIST sensitivity (Bloom et al. + 2009)., 2009). + Phe use of CRBs as llashlights allows us to cover a large number of astrophysical topies. from chemica evolution and reionization of the Universe to cust formation and composition.," The use of GRBs as flashlights allows us to cover a large number of astrophysical topics, from chemical evolution and reionization of the Universe to dust formation and composition." + Several studies indicate that (long duration) CRBs are associated with the death. of massive stars (e.g. Bloom Woosley 2006) and their explosion sites are concentrated in the very brightest. regions of their host. galaxies more than the core-collapse supernovae. (Fruchter et al., Several studies indicate that (long duration) GRBs are associated with the death of massive stars (e.g. Bloom Woosley 2006) and their explosion sites are concentrated in the very brightest regions of their host galaxies more than the core-collapse supernovae (Fruchter et al. + 2006: Svensson et al., 2006; Svensson et al. + 2010)., 2010). + The high level of Xray absorption often observed suggests that GRBs occur in the densest part of their host galaxy (Campana ct al., The high level of X–ray absorption often observed suggests that GRBs occur in the densest part of their host galaxy (Campana et al. + 2009)., 2009). + Εις implies that the GRB light in distant galaxies shines through a gas medium that is very different from. the typical interstellar medium. (LSAT) observed with traclitional tools. such. as quasar stuclics.," This implies that the GRB light in distant galaxies shines through a gas medium that is very different from the typical interstellar medium (ISM) observed with traditional tools, such as quasar studies." + The 18M in distant galaxies is usually probed by using wieght higher-redshift quasi-stcllar objects (quasars) which are used to illuminate the intervening objects., The ISM in distant galaxies is usually probed by using bright higher-redshift quasi-stellar objects (quasars) which are used to illuminate the intervening objects. + The optical absorption lines superposed on the quasar spectra were used o explore the chemical enrichment in the Universe (Wolfe. CGawiser Prochaska 2005).," The optical absorption lines superposed on the quasar spectra were used to explore the chemical enrichment in the Universe (Wolfe, Gawiser Prochaska 2005)." + Hlowever. the investigation of the high redshift. ISAT backlit: by (bright). quasars. is jased since. for geometrical reasons. quasars probe mainlv (intervening) galaxy halos. rather than galaxy bulges or disks. and for observational reasons since quasars are usually," However, the investigation of the high redshift ISM backlit by (bright) quasars is biased since, for geometrical reasons, quasars probe mainly (intervening) galaxy halos, rather than galaxy bulges or disks, and for observational reasons since quasars are usually" +hhas a huninosity of approximately huninosity. which is consistent with an iradiatiou model.,"has a luminosity of approximately luminosity, which is consistent with an irradiation model." + Our results therefore demonstrate that X-πανEUW irradiation bas a measurable effect even iu quescent DITNRTs. aud that optical observations cau be used to perform an indirect study of Nav (1... dancer disk) variability. at least forCre.," Our results therefore demonstrate that X-ray/EUV irradiation has a measurable effect even in quiescent BHXRTs, and that optical observations can be used to perform an indirect study of X-ray (i.e., inner disk) variability, at least for." +. RIIis supported 0.01-by NASA vous IInbble Fellowship erant zIIIIE-0115A awarded derby STScI. which is operatedby AURA. for NASA. contract NAS Chandra observatious were supported by NASA evant GO3-I0LLX. The WIIT is operated on La Palma w the ING in the Spanish Observatorio del Roque de los Miichachos of the Iustituto de issica de Canarias.," RIH is supported by NASA through Hubble Fellowship grant HF-01150.01-A awarded by STScI, which is operated by AURA, for NASA, under contract NAS Chandra observations were supported by NASA grant GO3-4044X. The WHT is operated on La Palma by the ING in the Spanish Observatorio del Roque de los Muchachos of the Instituto de sica de Canarias." + The Gemini Observatory is operated » AURA. under a cooperative agreement with the NSF on behalf of the Gemini partnership: NSF (United States). PPARC (United Kingdom). NRC (Canada). ieCONIuWeyM PUMAWile 2(7 AMstr:Hο”la).," The Gemini Observatory is operated by AURA, under a cooperative agreement with the NSF on behalf of the Gemini partnership: NSF (United States), PPARC (United Kingdom), NRC (Canada), CONICYT (Chile), ARC (Australia), CNPq (Brazil) and CONICET (Argentina)." + NP MN1121 i the NASAAG ADS; Abstract↴⋅↔⋡∖ Service., This work has also made use of the NASA ADS Abstract Service. +The self absorption limit rules out also the region in the parameter space that corresponds to external shocks.,The self absorption limit rules out also the region in the parameter space that corresponds to external shocks. + This solution requires a very low seed frequency which would have implied a very small self-absorption limit., This solution requires a very low seed frequency which would have implied a very small self-absorption limit. +" For a typical GRB, IC has to amplify the total energy of a low energy seed photon flux by a factor of z1000 to produce the observed prompt gamma-ray flux."," For a typical GRB, IC has to amplify the total energy of a low energy seed photon flux by a factor of $\approx 1000$ to produce the observed prompt gamma-ray flux." +" The same relativistic electrons will, however, continue and upscatter the gamma-ray flux to very high energies in the TeV range."," The same relativistic electrons will, however, continue and upscatter the gamma-ray flux to very high energies in the TeV range." +" In many cases this second generation IC will be in the Klein-Nishina regime (that is the photon's energy will be larger than the electrons rest mass, in the electron's rest frame)."," In many cases this second generation IC will be in the Klein-Nishina regime (that is the photon's energy will be larger than the electrons rest mass, in the electron's rest frame)." +" This will suppress somewhat the efficiency of conversion of gamma-rays to very high energy gamma-rays, however it won't stop it altogether."," This will suppress somewhat the efficiency of conversion of gamma-rays to very high energy gamma-rays, however it won't stop it altogether." + Our analysis focused on the case that the low energy seed photons are produced within the moving region that includes the IC scattering relativistic electrons., Our analysis focused on the case that the low energy seed photons are produced within the moving region that includes the IC scattering relativistic electrons. +" Such will be the case, for example, in Synchrotron self-Compton."," Such will be the case, for example, in Synchrotron self-Compton." +" Related considerations, that will be published elsewhere, apply when the seed photons are external and constrain IC processes in this case as well."," Related considerations, that will be published elsewhere, apply when the seed photons are external and constrain IC processes in this case as well." + The analysis is also limited to the important implicit assumption that the emitting, The analysis is also limited to the important implicit assumption that the emitting + , +population undergoes a major change m its morphological mix (?) and star formation properties (?)..,population undergoes a major change in its morphological mix \citep{Desai+07} and star formation properties \citep{Poggianti+06}. + We might then be witnessing two effects of the same underlying physical phenomenon., We might then be witnessing two effects of the same underlying physical phenomenon. + The transformation of ELGs into nELGs may be at least partly responsible for another evolutionary trend we observe in our clusters. that of the nELG number density profile.," The transformation of ELGs into nELGs may be at least partly responsible for another evolutionary trend we observe in our clusters, that of the nELG number density profile." + This profile becomes less concentrated with time. an evolution in the opposite sense to that observed for the mass density profile.," This profile becomes less concentrated with time, an evolution in the opposite sense to that observed for the mass density profile." + The (projected) NFW models fitted to the number density profile of low- and high-z nELGs have best-fit concentrations ¢=2.4-0.229 and e=7.5719πο c.l:, The (projected) NFW models fitted to the number density profile of low- and $z$ nELGs have best-fit concentrations $c=2.4_{-0.2}^{+0.6}$ and $c=7.5_{-0.9}^{+1.6}$ c.l.; + see also Figure 1))., see also Figure \ref{f:nprofs}) ). + On the other hand. no significant evolution is found for the number density profile of nELGs and ELGs together.," On the other hand, no significant evolution is found for the number density profile of nELGs and ELGs together." + This profile is dominated by nELGs at low-z. but not at high-z.," This profile is dominated by nELGs at $z$, but not at $z$." + If high-z ELGs transform into nELGs with time. the ΠΕΙΟΕΕ number density profile would not change. but the nELG number density profile would flatten. since ELGs are less spatially concentrated than nELGs.," If $z$ ELGs transform into nELGs with time, the nELG+ELG number density profile would not change, but the nELG number density profile would flatten, since ELGs are less spatially concentrated than nELGs." + Also the ELG number density profile flattens with time., Also the ELG number density profile flattens with time. + This might be related to the cluster environment growing more hostile with time. and making more difficult for infalling field galaxies to conserve their gas as they approach and cross the cluster centers.," This might be related to the cluster environment growing more hostile with time, and making more difficult for infalling field galaxies to conserve their gas as they approach and cross the cluster centers." + The results we have obtained in the present study are based on the still rather limited. amount of available data for high-z cluster galaxies., The results we have obtained in the present study are based on the still rather limited amount of available data for $z$ cluster galaxies. + Moreover. our high-z and low-z cluster samples span quite a substantial range in masses.," Moreover, our $z$ and $z$ cluster samples span quite a substantial range in masses." + It will then be important to tighten the current constraints on the orbital evolution of cluster galaxies using future. larger spectroscopic data-sets for high-z clusters. and also to re-assess such an evolution às a function of cluster mass.," It will then be important to tighten the current constraints on the orbital evolution of cluster galaxies using future, larger spectroscopic data-sets for $z$ clusters, and also to re-assess such an evolution as a function of cluster mass." + From these future analyses we will obtain a more thorough understanding of the hierarchical assembly history and evolution of galaxy clusters., From these future analyses we will obtain a more thorough understanding of the hierarchical assembly history and evolution of galaxy clusters. +surveys and finally to constrain the composite ealaxy contribution to the X-ray background.,surveys and finally to constrain the 'composite' galaxy contribution to the X-ray background. + LRASOOB17-2142 was observed with Clanaka. Inoue Holt 1994) between the 11 ancl 12th of December 1995.," IRAS00317-2142 was observed with (Tanaka, Inoue Holt 1994) between the 11 and 12th of December 1995." +" 1 have used the “Rev2"" processed data from the HIASATKC database at the Goddard. Space Flight Center.", I have used the “Rev2” processed data from the HEASARC database at the Goddard Space Flight Center. + For the selection criteria applied on Itev2 data. see the Data ABC guide (Yaqoob 1997).," For the selection criteria applied on Rev2 data, see the Data ABC guide (Yaqoob 1997)." + Data reduction was performed using ΕΕΟΟ v4.2., Data reduction was performed using FTOOLS v4.2. + Phe net exposure time is about 40 ksec and 37 ksec for the CLS and the SIS detectors respectively., The net exposure time is about 40 ksec and 37 ksec for the GIS and the SIS detectors respectively. + The two GIS and the two SIS detectors on-board ASCA have an energy range roughly between 0.8-10 keV and 0.5-10 keV respectively., The two GIS and the two SIS detectors on-board ASCA have an energy range roughly between 0.8-10 keV and 0.5-10 keV respectively. + The energy resolution of the SIS CCD detectors is 2 per cent at 6 keV. while of the GIS detectors is S per cent at the same energy., The energy resolution of the SIS CCD detectors is 2 per cent at 6 keV while of the GIS detectors is 8 per cent at the same energy. + For more details on the detectors see Tanaka et al. (, For more details on the detectors see Tanaka et al. ( +1994).,1994). + A circular. extraction cell for the source of 2 arcminute radius has been used., A circular extraction cell for the source of 2 arcminute radius has been used. + Background counts were estimated from source-[ree regions on the same images., Background counts were estimated from source-free regions on the same images. + The observed flux in the 2-H0keV. banc is fotomycSe10D while the one in the 1-2 keV band is fjομως=2.510Peres7s the Iluxes are estimated. using the best-fit power law mode below (L= 1.8)., The observed flux in the 2-10keV band is $f_{2-10keV}\simeq 8\times10^{-13}$ while the one in the 1-2 keV band is $f_{1-2keV}=2.5\times10^{-13}$; the fluxes are estimated using the best-fit power law model below $\Gamma=1.8$ ). + observed LtASO0317-2142 on two occasions., observed IRAS00317-2142 on two occasions. + 1 was first. detected: during the RASS (exposure time 340 s)., It was first detected during the RASS (exposure time 340 s). + Lis RASS [lux is 274046101° (0.1-2 keV). (Moran e al.," Its RASS flux is $2.7\pm0.46\times 10^{-12}$ (0.1-2 keV), (Moran et al." + 1996)., 1996). + It was also observed by PSPC as a targe during a pointed observation between the 22 ane 283rcl of June 1992 (exposure time 9.3 ksec)., It was also observed by PSPC as a target during a pointed observation between the 22 and 23rd of June 1992 (exposure time 9.3 ksec). + Phe derived [ux was 2.£0.05.10D in the 0.1-2 band. in excellen agreement with the LASS Lux.," The derived flux was $2.7\pm0.05 \times 10^{-12}$ in the 0.1-2 band, in excellent agreement with the RASS flux." + In the 1-2 keV band theLux is 7310“ores a [actor of three above that of in the same band., In the 1-2 keV band the flux is $ 7.3\times 10^{-13}$ a factor of three above that of in the same band. + “Phere is no evidence for extension in the pointed PSPC image (ce Pildis. Dregman Evrarcl 1995) suggesting that the bulk of the X-ray emission originates in IRASOO317-2142 rather than being dilluse emission from hot intergalactic gas in the galaxy. &roup.," There is no evidence for extension in the pointed PSPC image (eg Pildis, Bregman Evrard 1995) suggesting that the bulk of the X-ray emission originates in IRAS00317-2142 rather than being diffuse emission from hot intergalactic gas in the galaxy group." + Hore. E re-analvse the cata in order to make comparisons with the spectral fits and to perform joint fits with the data.," Here, I re-analyse the data in order to make comparisons with the spectral fits and to perform joint fits with the data." + Throughout this paper E adopt Ες=50kms!Mpe.! and go=0., Throughout this paper I adopt $ \rm H_\circ=50 km s^{-1} Mpc^{-1}$ and $q_o=0$. + For the spectral fitting Louse ASPLEC v.10., For the spectral fitting I use XSPEC v.10. + I bin the data so that there are at least 20 counts per bin (source and background)., I bin the data so that there are at least 20 counts per bin (source and background). + Quoted. errors to the best-fitting spectral parameters are 90 per cent confidence regions for one parameter of interest., Quoted errors to the best-fitting spectral parameters are 90 per cent confidence regions for one parameter of interest. + ] first fit à single power-law to the data., I first fit a single power-law to the data. + These are consistent witha zero hydrogen column density. Ny.," These are consistent with a zero hydrogen column density, $N_H$." +" Hence. hereafter. L have fixed the column to the Galactic column density (Ng~1.5107"" em.7)."," Hence, hereafter, I have fixed the column to the Galactic column density $N_H\sim 1.5\times 10^{20}$ $\rm cm^{-2}$ )." + Lhe results of the spectral fits are given in Table 1., The results of the spectral fits are given in Table 1. + Entries with no associated error bars were fixed to this value during the fit., Entries with no associated error bars were fixed to this value during the fit. + The power- slope PosLs. is consistent with the canonical spectral index of AGN (eg Nandra Pounds 1994).," The power-law slope $\Gamma \approx 1.8$, is consistent with the canonical spectral index of AGN (eg Nandra Pounds 1994)." + Although this simple model provides an acceptable fit. V7=1182/114 degrees of freedom. (dof). E have also added a. CGiaussian ine component to the fit (the energv. and the line width ixecd at GA keV and. 0.01. keV respectively) as this is a common feature in ACN spectra.," Although this simple model provides an acceptable fit, $\chi^2=118.2/114$ degrees of freedom (dof), I have also added a Gaussian line component to the fit (the energy and the line width fixed at 6.4 keV and 0.01 keV respectively) as this is a common feature in AGN spectra." + The additional component mareinally improves the fit (Ay?=24 for one additional xwanmeter): this is statistically significant at only the 90 per cent confidence level., The additional component marginally improves the fit $\Delta\chi^2=2.4$ for one additional parameter); this is statistically significant at only the 90 per cent confidence level. + The 90 per cent upper limit for the equivalent width is 0.9 keV. In Fig., The 90 per cent upper limit for the equivalent width is 0.9 keV. In Fig. + 1 the spectrum ogether with the best Gt power-law model are given: the data residuals from the model are also plotted., 1 the spectrum together with the best fit power-law model are given; the data residuals from the model are also plotted. + The data mve been rebinned in the plot for clarity., The data have been rebinned in the plot for clarity. + A Havmond-Smith (RS) thermal mocel results in a worse fit (\7=128.0/113)., A Raymond-Smith (RS) thermal model results in a worse fit $\chi^2=128.0/113$ ). + The temperature. derived. (kP=5.8S keV) is reminiscent of nearby normal galaxies., The temperature derived (kT=5.8 keV) is reminiscent of nearby normal galaxies. + Next. | fit an ionisecl warm absorber model (eg Brandt. Fabian Pounds 1996) in addition to the Galactic column density.," Next, I fit an ionised warm absorber model (eg Brandt, Fabian Pounds 1996) in addition to the Galactic column density." + Indeed: warm absorbers are etected in more than 50 per cent of Sevfert 1s (Branelt et al., Indeed warm absorbers are detected in more than 50 per cent of Seyfert 1s (Brandt et al. + 1999)., 1999). + The temperature of the absorber is fixed. at T—10lx (Brandt ct al., The temperature of the absorber is fixed at $T=10^{5} \rm K$ (Brandt et al. + 1999)., 1999). +" ""Phe best fit warm? column density is Ny~1077 while the ionisation parameter is practically unconstrained.", The best fit 'warm' column density is $N_H\sim 10^{22}$ while the ionisation parameter is practically unconstrained. + However. N47z2.4 for two accditional parameters and thus the warm. absorber model oes not represent a statistically significant improvement.," However, $\Delta\chi^2\approx 2.4 $ for two additional parameters and thus the warm absorber model does not represent a statistically significant improvement." + L also attempt to fit à more complicated. model with both a power-law and a RS component., I also attempt to fit a more complicated model with both a power-law and a RS component. + This is because the optical spectrum strongly suggests the presence of a strong star-[orming component., This is because the optical spectrum strongly suggests the presence of a strong star-forming component. + The spectral fit above vields 4?= 115.3/112: the inclusion of the additional RS component is not statistically significant ( lo)., The spectral fit above yields $\chi^2=115.3/112$ ; the inclusion of the additional RS component is not statistically significant $<1\sigma$ ). + E derive a spectral index of P=LT(da., I derive a spectral index of $\Gamma=1.7^{+0.10}_{-0.10}$. + The RS component has a temperature of KE 0.2 keV lower but consistent with those of the star-orming regions in nearby galaxies (og Read Ponman 1997)., The RS component has a temperature of $\sim$ 0.2 keV lower but consistent with those of the star-forming regions in nearby galaxies (eg Read Ponman 1997). + The abundance remains practically unconstrained and thus it was fixed to the solar value (Z= 1)., The abundance remains practically unconstrained and thus it was fixed to the solar value $Z=1$ ). + The uminositv of the RS component is 5«104 eres|! or about 25 per cent of the total luminosity in the 0.5-2 keV band., The luminosity of the RS component is $\sim 5\times 10^{41}$ $\rm erg ~s^{-1}$ or about 25 per cent of the total luminosity in the 0.5-2 keV band. + Finally. a power-law ancl RS naioclel is fit where he obscuring column densities are different in the two components.," Finally, a power-law and RS model is fit where the obscuring column densities are different in the two components." + For example in many Seyfert-2. the power-aw component is heavily obscurecl while the star-forming component is outside the obscuring screen and is relatively unobscured.," For example in many Seyfert-2, the power-law component is heavily obscured while the star-forming component is outside the obscuring screen and is relatively unobscured." + However. both best fit columns are close to the Galactic disfavouring the above scenario.," However, both best fit columns are close to the Galactic disfavouring the above scenario." + Due to the low energy coverage of the PSPC (0.1-2 keV) and its high effective area. it is quite instructive to fit the," Due to the low energy coverage of the PSPC (0.1-2 keV) and its high effective area, it is quite instructive to fit the" +interstellar polarization. (he principle component. P. changes sign with wavelength from blue to red.,"interstellar polarization, the principle component, $P_d$, changes sign with wavelength from blue to red." + In the pre-maximum spectra (see the first (wo panels of Figure 9)., In the pre-maximum spectra (see the first two panels of Figure 9). + A flip of the polarization vector can occur if the location of an energy source changes will respect (o the photosphere., A flip of the polarization vector can occur if the location of an energy source changes with respect to the photosphere. +" As discussed for SN 1993J (Tranοἱal.1997:Hoflich.1995a).. if the ""Ni source is well below the photosphere. the flux is radial. but the flux acquires a taigential component if the energv source is close to the photosphere."," As discussed for SN 1993J \citep{Tran:1997, Hoeflich:93Jpol}, if the $^{56}$ Ni source is well below the photosphere, the flux is radial, but the flux acquires a tangential component if the energy source is close to the photosphere." +" This ""skin effect"" can cause a flip in the polarization anele."," This “skin effect"" can cause a flip in the polarization angle." +" In. 2001el. the flip of 2, with wavelength may be the result of such a ""skin elfect in combination with the Irequency-dependent opacity."," In 2001el, the flip of $P_d$ with wavelength may be the result of such a “skin effect"" in combination with the frequency-dependent opacity." + In the blue. the photosphere is formed at much Iarger radii (bv a factor of 2) compared to the red.," In the blue, the photosphere is formed at much larger radii (by a factor of 2) compared to the red." + II an excitation blob is buried in the blue but revealed in the red. the polarized flux will be determined by the radial ancl tangentüial Πας. respectively. with an associated difference in (he orientation of the polarization.," If an excitation blob is buried in the blue but revealed in the red, the polarized flux will be determined by the radial and tangential flux, respectively, with an associated difference in the orientation of the polarization." +" In SN Ia. (his flip of the sign of the polarization along the dominant axis might be due lo a single large ""Ni clump revealed at the photosphere in the red IHóflich.(1995a)."," In SN Ia, this flip of the sign of the polarization along the dominant axis might be due to a single large $^{56}$ Ni clump revealed at the photosphere in the red \citet{Hoeflich:93Jpol}." +. Such a single dominant blob would have to fall off the dominant geometric axis to produce the sien flip., Such a single dominant blob would have to fall off the dominant geometric axis to produce the sign flip. + Alternatively. there could be a distribution of à nunber of small blobs that are on average concentrated along the preferred axis.," Alternatively, there could be a distribution of a number of small blobs that are on average concentrated along the preferred axis." + In Chis case the sign flip could occur when a number of these clumps are exposed. first in the red. by the receding photosphere.," In this case the sign flip could occur when a number of these clumps are exposed, first in the red, by the receding photosphere." + If this were (he case. both the dominant polarization axis and the dispersion around it might be attributed (o a common origin.," If this were the case, both the dominant polarization axis and the dispersion around it might be attributed to a common origin." + About 1 to 2 weeks after maximum light. the photosphere has receded well into the PONT nich region and. consequently. the effects of anisotropic excitation and ionization will vanish as the 7-rav deposition becomes smooth (Llóflichetal.2002).," About 1 to 2 weeks after maximum light, the photosphere has receded well into the $^{56}$ Ni rich region and, consequently, the effects of anisotropic excitation and ionization will vanish as the $\gamma$ -ray deposition becomes smooth \citep{Hoeflich99byIR}." +. The polarization is then expected to become small. consistent with the observations (see the last panel in Figure 9).," The polarization is then expected to become small, consistent with the observations (see the last panel in Figure 9)." + The most dramatic aspect of the polarization of SN 2001el is the feature at 800nm., The most dramatic aspect of the polarization of SN 2001el is the feature at 800nm. + This behavior of the Ca II IR. triplet max. provide a kev (ο understanding the departure from axial symmetry., This behavior of the Ca II IR triplet may provide a key to understanding the departure from axial symmetry. + Among the possibilities to explain the strong high-velocity Ca H IR. triplet in absorption at 22.000 aare a spherical shell. dense clumps. some of which fall along the line of sieht. or a torus that intersects the line of sight to the photosphere of the supernova.," Among the possibilities to explain the strong high-velocity Ca II IR triplet in absorption at 22,000 are a spherical shell, dense clumps, some of which fall along the line of sight, or a torus that intersects the line of sight to the photosphere of the supernova." + As noted in 83. the sharp edee to the photospheric component of the Ca II UR triplet. implies that the clensity of Ca drops olf bevond the photosphere before the high-velocity component is encountered.," As noted in 3, the sharp edge to the photospheric component of the Ca II IR triplet, implies that the density of Ca drops off beyond the photosphere before the high-velocity component is encountered." + The hieh-velocity component is thus a distinct geometrical component. not simply a monotonic," The high-velocity component is thus a distinct geometrical component, not simply a monotonic" +stars are.,stars are. +" As can be seen, the isochrone fitting technique is suitable for BD +34 2473, HD 153580 (both F stars) and for BD —01 469A (K subgiant)."," As can be seen, the isochrone fitting technique is suitable for BD $+$ 34 2473, HD 153580 (both F stars) and for BD $-$ 01 469A (K subgiant)." + The rest of stars are too close to the ZAMS and hence the use of isochrones does not provide accurate values for their ages., The rest of stars are too close to the ZAMS and hence the use of isochrones does not provide accurate values for their ages. +" When the isochrone fitting is appropriate, we have performed an interpolation in the grid of"," When the isochrone fitting is appropriate, we have performed an interpolation in the grid of" +prior to SExtractor object detection and the background subtraction algorithm used by SExtractor was switched off.,prior to SExtractor object detection and the background subtraction algorithm used by SExtractor was switched off. + Convolving the data with a Gaussian filter of full width half maximum (FWHM) close to the seeing is known to optimise detections and reduce noise levels during the source extraction., Convolving the data with a Gaussian filter of full width half maximum (FWHM) close to the seeing is known to optimise detections and reduce noise levels during the source extraction. +" Hence. a Gaussian filter described by a 3.-3 matrix with an FWHM of 1.56.1 pixels (= 0.5""— 2"") depending on the seeing. was utilised which had proved. after initial tests. the most effective at faint source extraction."," Hence, a Gaussian filter described by a $3\times3$ matrix with an FWHM of $1.5-6.1$ pixels (= $0.5^{\prime\prime}-2^{\prime\prime}$ ) depending on the seeing, was utilised which had proved, after initial tests, the most effective at faint source extraction." + Objects meeting the extraction criteria of having 8 connected pixels with flux —0.4c above the local background level were analysed.," Objects meeting the extraction criteria of having 8 connected pixels with flux $ > +0.4 \sigma$ above the local background level were analysed." + This corresponded to a minimum of71.30 per object detection (2).. however in practise only 75e detections are included in the final catalogues.," This corresponded to a minimum of $> 1.3 \sigma$ per object detection \cite{booth}, however in practise only $> 5 \sigma$ detections are included in the final catalogues." + Within SExtraetor. the intensity profile of each source was automatically examined in order to ascertain whether it was a single source or a merged object. where the latter initiates the de-blending procedure within SExtractor.," Within SExtractor, the intensity profile of each source was automatically examined in order to ascertain whether it was a single source or a merged object, where the latter initiates the de-blending procedure within SExtractor." + Simulations suggest that photometric errors for objects de-blended by SExtractor are <0.2 magnitudes and in most cases are «0.1 magnitudes., Simulations suggest that photometric errors for objects de-blended by SExtractor are $< 0.2$ magnitudes and in most cases are $< 0.1$ magnitudes. + Astrometrie errors due to de-blending are typically <0.4 pixels (0.17) (2)., Astrometric errors due to de-blending are typically $< 0.4$ pixels $0.1^{\prime\prime}$ ) \cite{sex}. + On occasion. the comparatively low detection threshold usec resulted in spurious detections in the wings of both bright and extended objects where the local background noise level was relatively high.," On occasion, the comparatively low detection threshold used resulted in spurious detections in the wings of both bright and extended objects where the local background noise level was relatively high." + Hence the “cleaning” procedure was implemented within SExtractor whereby the contribution to the background from bright/extended objects is estimated by fitting them with appropriate Gaussian profiles., Hence the 'cleaning' procedure was implemented within SExtractor whereby the contribution to the background from bright/extended objects is estimated by fitting them with appropriate Gaussian profiles. + Local object intensities remaining above the detection threshold when the adjusted local background was subtracted were accepted into the tinal catalogue., Local object intensities remaining above the detection threshold when the adjusted local background was subtracted were accepted into the final catalogue. + These spurious detections typically accounted for 1020% of al detections and those few which remained after cleaning were deal with during the image masking process detailed in section 4.4., These spurious detections typically accounted for $10-20\%$ of all detections and those few which remained after cleaning were dealt with during the image masking process detailed in section \ref{sec:holes}. + SExtractor was used to calculate aperture and isophota corrected magnitudes for every source., SExtractor was used to calculate aperture and isophotal corrected magnitudes for every source. + Aperture magnitudes were obtained by integrating the flux within a fixed aperture and subtracting the contribution from the sky background. its value estimated within an annulus outside the aperture.," Aperture magnitudes were obtained by integrating the flux within a fixed aperture and subtracting the contribution from the sky background, its value estimated within an annulus outside the aperture." + For the ODTS. an aperture size of diameter 10 pixels (3.337) was used for all bands.," For the ODTS, an aperture size of diameter $10$ pixels $3.33^{\prime\prime}$ ) was used for all bands." + Isophotal corrected. magnitudes were also computed whereby the flux within a specified isophote. set at 2.5. the local background level. was integrated.," Isophotal corrected magnitudes were also computed whereby the flux within a specified isophote, set at $2.5 \times$ the local background level, was integrated." + To retrieve flux existing outside the limiting isophote. a Gaussian profile was then fit to the intensity distribution of the object and an estimation of the omitted flux made and subtracted.," To retrieve flux existing outside the limiting isophote, a Gaussian profile was then fit to the intensity distribution of the object and an estimation of the omitted flux made and subtracted." + All extracted magnitudes have an associated rms error calculated within SExtraetor., All extracted magnitudes have an associated rms error calculated within SExtractor. + This random error increases with faintness. but remains small to the limiting depths of the ODTS compared with the various calibration uncertainties (see section 6.3)).," This random error increases with faintness, but remains small to the limiting depths of the ODTS compared with the various calibration uncertainties (see section \ref{sec:errors}) )." + Aperture magnitudes. although consistent. will tend to underestimate the actual magnitude of an extended object due to he flux lost outside the aperture.," Aperture magnitudes, although consistent, will tend to underestimate the actual magnitude of an extended object due to the flux lost outside the aperture." + Simulations suggest that this is negligible for seeing-limited objects fainter than 4~18.5 in he ODTS data (2).., Simulations suggest that this is negligible for seeing-limited objects fainter than $R \sim 18.5$ in the ODTS data \cite{olding}. +" Isophotal corrected magnitudes work well or the brighter more extended objects but become unstable at the ""unt end as they involve assumptions about the shapes of objects which become highly uncertain at faint magnitudes.", Isophotal corrected magnitudes work well for the brighter more extended objects but become unstable at the faint end as they involve assumptions about the shapes of objects which become highly uncertain at faint magnitudes. + In general he isophotal corrected. magnitudes were found to be less than the aperture magnitudes. ascertained by comparing the spread of the ODTS stellar data around the main sequence and the scatter in the difference in magnitudes for common objects found in the overlap regions.," In general the isophotal corrected magnitudes were found to be less than the aperture magnitudes, ascertained by comparing the spread of the ODTS stellar data around the main sequence and the scatter in the difference in magnitudes for common objects found in the overlap regions." + Ultimately catalogues containing both aperture and isophotal corrected source magnitudes for each frame at each pointing in every band were archived. but aperture magnitudes were used in the final calibrations performed in section 6.. as they give much more consistent colours.," Ultimately catalogues containing both aperture and isophotal corrected source magnitudes for each frame at each pointing in every band were archived, but aperture magnitudes were used in the final calibrations performed in section \ref{sec:photocalib}, as they give much more consistent colours." + Archiving both magnitudes allows the user to choose the magnitude regime most appropriate for their work., Archiving both magnitudes allows the user to choose the magnitude regime most appropriate for their work. + During the source extraction. SExtractor classities each object as a star or galaxy reflected in the value of theindex parameter.," During the source extraction, SExtractor classifies each object as a star or galaxy reflected in the value of the parameter." + A trained neural network was employed to determine the stellarity index for each object dependent on the seeing. peak intensity and a measurement of the isophotal area (see 2? for details).," A trained neural network was employed to determine the stellarity index for each object dependent on the seeing, peak intensity and a measurement of the isophotal area (see \scite{sex} for details)." + The seeing for each pointing was obtained by taking the median FWHM of all bright. unsaturated objects in the image. identified from their profiles as stars.," The seeing for each pointing was obtained by taking the median FWHM of all bright, unsaturated objects in the image, identified from their profiles as stars." + The stellarity index has a value between O and |. where 0 represents a galaxy. | a star and intermediate values. by design. give an indication of the uncertainty of the classification.," The stellarity index has a value between 0 and 1, where 0 represents a galaxy, 1 a star and intermediate values, by design, give an indication of the uncertainty of the classification." +" ? claim an algorithm success rate of z054 o 4? z: 22 when the seeing is zz0.9"". however the seeing varies quite dramatically across the ODTS fields."," \scite{sex} claim an algorithm success rate of $\approx 95 \%$ to $R$ $\approx$ 22 when the seeing is $\approx 0.9^{\prime\prime}$, however the seeing varies quite dramatically across the ODTS fields." + Figure 6 depicts the behaviour of the stellarity index as a function of magnitude for each band in the Andromeda field., Figure \ref{fig:star} depicts the behaviour of the stellarity index as a function of magnitude for each band in the Andromeda field. + As expected. at faint magnitudes he stellarity index tends towards 0.5 as the distinction between stars and galaxies becomes less pronounced due to object profiles becoming seeing dominated.," As expected, at faint magnitudes the stellarity index tends towards 0.5 as the distinction between stars and galaxies becomes less pronounced due to object profiles becoming seeing dominated." + At very bright magnitudes. the index ends to drop due to saturation effects.," At very bright magnitudes, the index tends to drop due to saturation effects." + From figure 6.. it is apparent hat the classifier begins to break down at magnitudes of /5722.5. U2. H721.5 and 7.721.5.," From figure \ref{fig:star}, it is apparent that the classifier begins to break down at magnitudes of $B > 22.5 $, $V > 22$, $R +> 21.5 $ and $I > 21.5 $." + However. it should be noted that he depths to which the classifier is successful is a strong function of seeing and therefore varies between pointings.," However, it should be noted that the depths to which the classifier is successful is a strong function of seeing and therefore varies between pointings." + All objects with a stellarity index 7 0.9 were considered to be stars., All objects with a stellarity index $ > $ 0.9 were considered to be stars. + False detections caused by the presence of asteroid and satellite trails. excessive vignetting. low-level fringing. diffraction spikes. and halos around bright stars had to be removed from. or flagged in. the final catalogues.," False detections caused by the presence of asteroid and satellite trails, excessive vignetting, low-level fringing, diffraction spikes, and halos around bright stars had to be removed from, or flagged in, the final catalogues." + For each image a mask was created manually which identified all the contaminated image areas., For each image a mask was created manually which identified all the contaminated image areas. + The method employed consisted of drawing either rectangular or circular shaped holes around the spurious structures in the data, The method employed consisted of drawing either rectangular or circular shaped holes around the spurious structures in the data +where -L2.3$ Gyr, roughly the longest $t_{\rm MS}$ of CO+CO DD, there are no more new-born CO+CO DDs." + ONeMge+X DDs show a reduction in v and c. except for the ONeMg--He DDs which make a residual contribution ov as the dise continue to evolve.," ONeMg+X DDs show a reduction in $\nu$ and $\zeta$, except for the ONeMg+He DDs which make a residual contribution to $\nu$ as the disc continue to evolve." + Again. some oscillations are seen in the birth and merger rates in the instantaneous SF model.," Again, some oscillations are seen in the birth and merger rates in the instantaneous SF model." + These are due to statistical noise from the contribution functions oroduced by the Monte Carlo simulations. and numerical noise Tom the quadrature of refequérthirale..," These are due to statistical noise from the contribution functions produced by the Monte Carlo simulations, and numerical noise from the quadrature of \\ref{eq_birthrate}." + A big difference for » and ¢ in the other three models can also be seen from the tigures., A big difference for $\nu$ and $\zeta$ in the other three models can also be seen from the figures. + Enhanced SF causes the present and ¢ of CO+CO and ONeMg+X DDs to be slightly higher than constant SF. while the quasi-exponential SF can produce a higher wand ¢ of CO+CO and ONeMg+X DDs than enhanced SF when has4 Gyr.," Enhanced SF causes the present $\nu$ and $\zeta$ of CO+CO and ONeMg+X DDs to be slightly higher than constant SF, while the quasi-exponential SF can produce a higher $\nu$ and $\zeta$ of CO+CO and ONeMg+X DDs than enhanced SF when $t_{\rm disc}<4$ Gyr." + When fice74 Gyr. we find v and ¢ of CO+CO and ONeMe+X DDs decrease dramatically in the quasi-exponential SF model. while the values of 7 and ¢ in the constant SF model remain almost constant and higher than the v and ¢ in the quasi-exponential SF model. up to faice=10 Gyr.," When $t_{\rm disc}>4$ Gyr, we find $\nu$ and $\zeta$ of CO+CO and ONeMg+X DDs decrease dramatically in the quasi-exponential SF model, while the values of $\nu$ and $\zeta$ in the constant SF model remain almost constant and higher than the $\nu$ and $\zeta$ in the quasi-exponential SF model, up to $t_{\rm disc}=10$ Gyr." + The significant decreases and increases of the values of 7 and ¢ of CO+CO and ONeMg+X DDs in the enhanced SF model are the response of these variables to sudden changes in the SF rate., The significant decreases and increases of the values of $\nu$ and $\zeta$ of CO+CO and ONeMg+X DDs in the enhanced SF model are the response of these variables to sudden changes in the SF rate. + The present values of 7 and ¢ are similar because we adopt a similar value of the average SF rate at the present age of the thin dise in these three models., The present values of $\nu$ and $\zeta$ are similar because we adopt a similar value of the average SF rate at the present age of the thin disc in these three models. + The present number and the total merger number of different types of DDs are shown in Figs., The present number and the total merger number of different types of DDs are shown in Figs. + 12. to 15.., \ref{fig_hehenum} to \ref{fig_othernum}. . + A similar evolutionary, A similar evolutionary +Peacock(1951) developed: the calculating. method. to obtain a power-law index which was originally used by All(1978)..,\citet{b17} developed the calculating method to obtain a power-law index which was originally used by \citet{b4}. +. Peacock's approximation can be applied to a relativistic shock., Peacock's approximation can be applied to a relativistic shock. + He considered. Ny particles crossing from. the upstream to the downstream with an initial energy. Lo., He considered $N_0$ particles crossing from the upstream to the downstream with an initial energy $E_0$. + We use a return. probability Peas) that a particle will eventually return to the upstream., We use a return probability $P_R(\mu_0)$ that a particle will eventually return to the upstream. + The particles energy. is increased by a energv-gain factor Cyto.p). where fry and qi are the initial pitch angle and the last. pitch angle for one step.," The particle's energy is increased by a energy-gain factor $G(\mu_0,\mu)$, where $\mu_0$ and $\mu$ are the initial pitch angle and the last pitch angle for one step." + After eveles. number of particles that remains in the upstream (CN) is expressed as where lere. (Pp) is the return. probability averaged: over fo with the weight of the lux crossing the shock with various values of gig.," After cycles, number of particles that remains in the upstream $(N)$ is expressed as where Here, $\langle P_R \rangle$ is the return probability averaged over $\mu_0$ with the weight of the flux crossing the shock with various values of $\mu_0$." + As particles cross and. re-cross the garock. the distribution of energies is hroaclened.," As particles cross and re-cross the shock, the distribution of energies is broadened." + Peacock's Upproximation assumes the numbers of cveles are. large enough to use the central limit theorem., Peacock's approximation assumes the numbers of cycles are large enough to use the central limit theorem. + Lt is also necessary that the energv-gain. of each step is fully uncorrelated., It is also necessary that the energy-gain of each step is fully uncorrelated. + Lt particles cross the shock front many times. the distribution of energies can be expressed by a Gaussian by a central limit theorem.," If particles cross the shock front many times, the distribution of energies can be expressed by a Gaussian by a central limit theorem." + In such a situation. we can approximate particle's enerey is amplified at the same rate per one evcle and the elect of the variance is neglected.," In such a situation, we can approximate particle's energy is amplified at the same rate per one cycle and the effect of the variance is neglected." + We can calculate the power-law index only using the averaged energv-gain factor., We can calculate the power-law index only using the averaged energy-gain factor. + After eveles. the particle energy is given by where Cis the energv-gain factor ancl expressed as Cpu)=(4h).," After cycles, the particle energy is given by where $G$ is the energy-gain factor and expressed as $G(\mu_{out},\mu)=\left(\frac{1-V_r\mu_{out}}{1-V_r\mu}\right)$." +" Phe averaged In€ is defined as: Llere. V,=“#—“Loa indicates the relative velocity of the upstream Ες with tsrespect to the downstream uid."," The averaged $\ln G$ is defined as: Here, $V_r=\frac{u_u-u_d}{1-u_uu_d}$ indicates the relative velocity of the upstream fluid with respect to the downstream fluid." + From Ίσα., From Eq. + (18) and (20). the integrated energy spectrum is written as Thus the dillerential energy spectrum is obtained as where ext; we explain derivation of a power-law spectrum given » Vietri(2003).," $(18)$ and $(20)$, the integrated energy spectrum is written as Thus the differential energy spectrum is obtained as where Next, we explain derivation of a power-law spectrum given by \citet{b20}." +.. He derived: the relativistically covariant equation for the distribution function ofparticles accelerated ab à shock. which is applicable to a relativistic shock.," He derived the relativistically covariant equation for the distribution function of particles accelerated at a shock, which is applicable to a relativistic shock." + His ormulation gives the exact power-law index and does. not assume uncorre[ation among various energv-gains., His formulation gives the exact power-law index and does not assume uncorrelation among various energy-gains. +" Blasi&Vietri(2005). solved the transport equation providing the roundary condition for the Lux whieh crosses the shock ront to the downstream (6,4) (upstream (O..)) by using xwticles which crosses the shock front to the upstream (6,5) (downstream: (6,,)). and they derived. 2, and. P."," \citet{b6} solved the transport equation providing the boundary condition for the flux which crosses the shock front to the downstream $\phi_{ud}$ ) (upstream $\phi_{du}$ )) by using particles which crosses the shock front to the upstream $\phi_{du}$ ) (downstream $\phi_{ud}$ )), and they derived $P_u$ and $P_d$." +" In this »iper. we use Z2, and 2, which are caleulated in section 2.2."," In this paper, we use $P_u$ and $P_d$ which are calculated in section 2.2." + The power-law index is given by this boundary condition: Ες equation can be integrated over the whole range of ye and divided by the whole [lux entering into theupstream. which gives The left term is the inverse of the averaged return probability. from. the downstream.," The power-law index is given by this boundary condition: This equation can be integrated over the whole range of $\mu$ and divided by the whole flux entering into theupstream, which gives The left term is the inverse of the averaged return probability from the downstream." + The right. term. is the average of the (s3) power of the energv-gain factor. Cr., The right term is the average of the $(s-3)$ power of the energy-gain factor $G$ . + Eq., Eq. + (26) can be rewritten as, $(26)$ can be rewritten as +"the properties that are observed, as can be seen in the significantly different trends obtained in figures 3 and 4 where we have selected a different set of galaxies to compare to observations.","the properties that are observed, as can be seen in the significantly different trends obtained in figures \ref{fig:Balogh} and \ref{fig:ver} where we have selected a different set of galaxies to compare to observations." +" We compare our Shocks model (red solid lines), with the Font (green solid lines) and Bower (blue solid lines) models."," We compare our Shocks model (red solid lines), with the Font (green solid lines) and Bower (blue solid lines) models." +" It should be noted that there are other parameter differences between these models: the Shocks model has had a parameter associated with AGN feedback adjusted from its Bower model value to match the local galaxy 5;- and K-band luminosity functions, while the Font model has a different value of the metal yield to match the zero point colors of the red and blue sequences."," It should be noted that there are other parameter differences between these models: the Shocks model has had a parameter associated with AGN feedback adjusted from its Bower model value to match the local galaxy $b_J$ - and $K$ -band luminosity functions, while the Font model has a different value of the metal yield to match the zero point colors of the red and blue sequences." +" Thus, the difference between the Bower model and the Shocks and Font models is due both to their differing treatments of RPS, and to their different physical parameters."," Thus, the difference between the Bower model and the Shocks and Font models is due both to their differing treatments of RPS, and to their different physical parameters." +" To assess the relative contributions of each of these components, we also consider the Shocks, Font and Bower models without RPS, thus isolating the effects of the parameter changes green and blue dotted "," To assess the relative contributions of each of these components, we also consider the Shocks, Font and Bower models without RPS, thus isolating the effects of the parameter changes (red, green and blue dotted lines)." +"We also show the position (red,of the average accretion shock lines).radius of these clusters as a black dashed vertical line, and the properties of the central galaxies as crosses."," We also show the position of the average accretion shock radius of these clusters as a black dashed vertical line, and the properties of the central galaxies as crosses." +" When these values are very different from those of the satellite galaxies, we leave them out of the plot as the satellite galaxy trends are more interesting for the purposes of this work."," When these values are very different from those of the satellite galaxies, we leave them out of the plot as the satellite galaxy trends are more interesting for the purposes of this work." +" In the top panel of Figure 1,, we see that in all of the models there is a peak in galactic stellar mass in the centers of clusters; as the central galaxy has been excluded, this shows an increase in stellar mass of the innermost satellites in all models."," In the top panel of Figure \ref{fig:mass}, we see that in all of the models there is a peak in galactic stellar mass in the centers of clusters; as the central galaxy has been excluded, this shows an increase in stellar mass of the innermost satellites in all models." +" This is reasonable, as we expect more massive satellite galaxies to sink deeper into the potential well of the cluster."," This is reasonable, as we expect more massive satellite galaxies to sink deeper into the potential well of the cluster." +" Further, other than a slight rise in stellar mass towards the center of clusters in the Font and Shocks models, the average stellar mass of galaxies remains more or less constant with radius, with the Shocks model having the lowest average level of stellar mass, the Bower model slightly more, and the Font model having the most stellar mass of all."," Further, other than a slight rise in stellar mass towards the center of clusters in the Font and Shocks models, the average stellar mass of galaxies remains more or less constant with radius, with the Shocks model having the lowest average level of stellar mass, the Bower model slightly more, and the Font model having the most stellar mass of all." + The flatness of these curves indicates that most of the stars of satellite galaxies were formed before they merged with the cluster., The flatness of these curves indicates that most of the stars of satellite galaxies were formed before they merged with the cluster. +" Note that the central galaxies in all of the models have more than an order of magnitude more stellar mass than the satellite galaxies, as would be expected since they are at the center of the potential well of the cluster and are not subject to RPS."," Note that the central galaxies in all of the models have more than an order of magnitude more stellar mass than the satellite galaxies, as would be expected since they are at the center of the potential well of the cluster and are not subject to RPS." +" The distribution of cold gas mass, in the middle panel of Figure 1,, shows a different trend."," The distribution of cold gas mass, in the middle panel of Figure \ref{fig:mass}, shows a different trend." +" The Bower model, with its more extreme removal of gas in clusters, shows the least cold gas in satellite galaxies, with a very distinct drop in gas mass at around 1.5 times the virial radius."," The Bower model, with its more extreme removal of gas in clusters, shows the least cold gas in satellite galaxies, with a very distinct drop in gas mass at around $1.5$ times the virial radius." +" This drop in cold gas mass is quite steep, with its slope determined by the timescale of satellite orbits as compared to the timescale on which cold gas is made into stars in the satellite galaxies."," This drop in cold gas mass is quite steep, with its slope determined by the timescale of satellite orbits as compared to the timescale on which cold gas is made into stars in the satellite galaxies." +" Interestingly, the Shocks model shows a very similar trend with slightly more gas mass inside the radius of the accretion shock, as would be expected."," Interestingly, the Shocks model shows a very similar trend with slightly more gas mass inside the radius of the accretion shock, as would be expected." +" That the Bower model also shows a drop at around this radius, which happens to be the average accretion shock radius, is interesting, and points to the ‘preprocessing’ of satellite galaxies, in which satellite galaxies experience weaker environmental effects as members of smaller groups of galaxies before merging with the cluster."," That the Bower model also shows a drop at around this radius, which happens to be the average accretion shock radius, is interesting, and points to the `preprocessing' of satellite galaxies, in which satellite galaxies experience weaker environmental effects as members of smaller groups of galaxies before merging with the cluster." +" The Bower model is likely to exhibit stronger group effects than the Shocks and Font models, since its RPS efficiency is always very high, while the RPS of the Shocks and Font models depend on the density of the halo intracluster medium (ICM)."," The Bower model is likely to exhibit stronger group effects than the Shocks and Font models, since its RPS efficiency is always very high, while the RPS of the Shocks and Font models depend on the density of the halo intracluster medium (ICM)." +" Thus, we see that these two very different models of environmental effects give a similar qualitative prediction for the radial dependence of satellite gas mass, indicating that if such a trend in gas mass is observed, we cannot distinguish between a model whose RPS starts at the accretion radius and a much stronger RPS model which starts at the virial radius."," Thus, we see that these two very different models of environmental effects give a similar qualitative prediction for the radial dependence of satellite gas mass, indicating that if such a trend in gas mass is observed, we cannot distinguish between a model whose RPS starts at the accretion radius and a much stronger RPS model which starts at the virial radius." +" The Font model predicts a higher level of gas mass at all radii, as is reasonable due to its less harsh RPS implementation, while as expected the models without ram pressure exhibit significantly higher gas mass at all radii than the other models, since it is RPS that is mainly responsible for the sharp drop in gas mass with decreasing cluster-centric radius."," The Font model predicts a higher level of gas mass at all radii, as is reasonable due to its less harsh RPS implementation, while as expected the models without ram pressure exhibit significantly higher gas mass at all radii than the other models, since it is RPS that is mainly responsible for the sharp drop in gas mass with decreasing cluster-centric radius." +" It is reasonable that there is a slight drop-off in gas mass towards the center of the cluster even in these models, since in these models the accretion of new gas from the intergalactic medium (IGM) onto the hot gaseous halo of the satellites is suppressed though none of their halo gas is removed."," It is reasonable that there is a slight drop-off in gas mass towards the center of the cluster even in these models, since in these models the accretion of new gas from the intergalactic medium (IGM) onto the hot gaseous halo of the satellites is suppressed though none of their halo gas is removed." +" We see that the central galaxies have higher gas mass than satellites, as they are not affected by RPS and also gain gas through mergers."," We see that the central galaxies have higher gas mass than satellites, as they are not affected by RPS and also gain gas through mergers." +" The higher level of gas mass in central galaxies in the models without RPS is likely due to merging satellites, which have not had gas removed by RPS and therefore give more gas mass to the central galaxy."," The higher level of gas mass in central galaxies in the models without RPS is likely due to merging satellites, which have not had gas removed by RPS and therefore give more gas mass to the central galaxy." +:The nearby starburst galaxy NGC253τααν. has been extensively: mapped in. COD» emission. bv various authors (727)..,"The nearby starburst galaxy NGC253 has been extensively mapped in $^{12}$ CO emission by various authors \citep{Bayet:04,Bradford:n253cr,Gusten:06}." +" 7. compute line intensities for various CO (ransitions corrected lo a 15"" beam.", \citet{Bradford:n253cr} compute line intensities for various CO transitions corrected to a 15” beam. + We use these values from their Table 3 (Column 6) to derive line intensity a −⊳few of the↽ CO− lines ancl∙ find−− observed line− intensity ratios− of⊳⋖⊲∩⊇↓⊐ πιratios ~for 8.0andCOW Gy., We use these values from their Table 3 (Column 6) to derive line intensity ratios for a few of the CO lines and find observed line intensity ratios of $\frac{CO(2-1)}{CO(1-0)} \sim 8.0$ and $\frac{CO(7-6)}{CO(4-3)} \sim 3.3$. + In⋅BOO.NGC253 was cited as⋅ an example⋅ of a galaxy wilh a high cosmic-ray“oon e» 3.3. ionisation rate due to the presence of a starburst nucleus.," In B09, NGC253 was cited as an example of a galaxy with a high cosmic-ray ionisation rate due to the presence of a starburst nucleus." + The cosmic rav ionisation rate for {his galaxy is thought to be 800 times greater than in the Galaxy (?).., The cosmic ray ionisation rate for this galaxy is thought to be $\sim$ 800 times greater than in the Galaxy \citep{Bradford:n253cr}. +" The theoretical line intensity ratios derived [rom our model with a cosmic-ray ionisation rate of (=LO| ⋟∖⇁↓≼⇂≼↲⋟∖⊽≺∢↕⋅↕∣↽≻≼↲≼⊔∐≝∣≩≡↽⊰⋅≊↽⊰≀⋯↲− −⋅⋅⋅ roCO(D~8.3 ancl cOCOW6]ου. αἱ cl,~8.", The theoretical line intensity ratios derived from our model with a cosmic-ray ionisation rate of $\zeta = 10^{-14}$ $^{-1}$ described in $\S$ \ref{sec:cr} are $\frac{CO(2-1)}{CO(1-0)} \sim 8.3$ and $\frac{CO(7-6)}{CO(4-3)} \sim 4.1$ at $A_v \sim 8$. + ↴−Taking the ratio−⊳ of intensities [rom Table 301? we find COR~9.3 lor a bein size of 23° (??). in both cases and woCOUT6)~4.5 for− a beam size↴ of⋅ 21.9° (?) in both cases.," Taking the ratio of intensities from Table 3 of \citet{Bayet:04} we find $\frac{CO(2-1)}{CO(1-0)} \sim 9.3$ for a beam size of 23” \citep{Mauersberger:96, Harrison:99} in both cases and $\frac{CO(7-6)}{CO(4-3)} \sim 4.5$ for a beam size of 21.9” \citep{Guesten:93} in both cases." + The ratio of fluxes eiven in Table 1 of ? gives COWCOU6)3)~2., The ratio of fluxes given in Table 1 of \citet{Gusten:06} gives $\frac{CO(7-6)}{CO(4-3)} \sim 2$. + Given that we have not attempted to accurately moclel the physical conditions of this particular galaxy. (he agreement between (he observed and theoretical results is remarkably good.," Given that we have not attempted to accurately model the physical conditions of this particular galaxy, the agreement between the observed and theoretical results is remarkably good." + Note that these ratios are the ratios of the line intensities. /. rather (han the velocity integrated temperature plotted in the figures as only ihe intensities in Table 3 of ? are all corrected to the same beam size.," Note that these ratios are the ratios of the line intensities, $I$, rather than the velocity integrated temperature plotted in the figures as only the intensities in Table 3 of \citet{Bradford:n253cr} are all corrected to the same beam size." + We note that the ratios of our velocity integrated. temperatures agree with those in 72. (o the same level as (he intensity ratios., We note that the ratios of our velocity integrated temperatures agree with those in \citet{Bayet:04} to the same level as the intensity ratios. + Our predicted line intensities and ratios also agree with the theoretical work of ?. (Tables 2. 3 and 4) who have looked at the effect of high cosmic-ray ionisation rates and FUV radiation fields on the CO lines The gravitationally lensed QSO. Cloverleal (L114132-117) at a redshilt of ~ 2.5. was cited as an example of a higli-redshift source in BOO.," Our predicted line intensities and ratios also agree with the theoretical work of \citet{Meijerink:cr} (Tables 2, 3 and 4) who have looked at the effect of high cosmic-ray ionisation rates and FUV radiation fields on the $^{12}$ CO lines The gravitationally lensed QSO, Cloverleaf (H1413+117) at a redshift of $\sim$ 2.5, was cited as an example of a high-redshift source in B09." + ? report CO observations for (his source and lind (he CO(4-3) line to be the strongest line in terms of the brightness temperature., \citet{Barvainis:97} report CO observations for this source and find the CO(4-3) line to be the strongest line in terms of the brightness temperature. + These authors compute brightness temperature ratios ol COUCOLS2)=⋅(.33-E0.16. -COL=0.73+0.16⋅ and cOCOW6)=(.68⋅20.13 relative⋅ to the brightest⋅ line.," These authors compute brightness temperature ratios of $\frac{CO(3-2)}{CO(4-3)} = 0.83 \pm 0.16$, $\frac{CO(5-4)}{CO(4-3)} = 0.73 \pm 0.16$ and $\frac{CO(7-6)}{CO(4-3)} = 0.68 \pm 0.13$ relative to the brightest line." + ⋅↴There is⋅ therefore.⋅⋅ a definite⋅ drop in the ratios relative to the brightest line when going from the low-J to the high-J transitions in this source.," There is therefore, a definite drop in the ratios relative to the brightest line when going from the low-J to the high-J transitions in this source." +" Figure 13. shows that for Model ID at both A,~3 and A,~8 as well as Model HI at sl.~3. the CO(5-4) line is the strongest line."," Figure \ref{fig:IMF1} shows that for Model II at both $A_v \sim 3$ and $A_v \sim 8$ as well as Model III at $A_v \sim 3$, the CO(5-4) line is the strongest line." +" For Model III at sl,~&. the CO(3-2) line is marginally brighter than the CO(4-3) line and is now the strongest line."," For Model III at $A_v \sim 8$, the CO(3-2) line is marginally brighter than the CO(4-3) line and is now the strongest line." + We compute ratios relative to the brightest line for both our hieh redshift models IL and ILI., We compute ratios relative to the brightest line for both our high redshift models II and III. + For Model IH which shows little evidence for having a high-mass biased IME. the ratios go from," For Model II which shows little evidence for having a high-mass biased IMF, the ratios go from" +üinpossible to detect srectoscopicallv.,impossible to detect spectroscopically. + CO would be extremely difficult o detect on Eris or Sedua. and. to date. no mealinetul upper limits have been placed.," CO would be extremely difficult to detect on Eris or Sedna, and, to date, no meaningful upper limits have been placed." + The next major 'e0οςime in the moclel is occupied only by Makemase., The next major regime in the model is occupied only by Makemake. + Masemake has just the right size and eniperature to be able to retain its CH. but to be on tle edge of not being able to retain No and CO.," Makemake has just the right size and temperature to be able to retain its $_4$, but to be on the edge of not being able to retain $_2$ and CO." + Tle uusual surface of Makemake appears well expainecl by ils model., The unusual surface of Makemake appears well explained by this model. +" With a low abuud:ce of No «dL the surface. CH, becomes the major coustitleu ald anneals into large slabs. giving ri setot le [9]=© optical path leneths which saturate the infrared spectrum."," With a low abundance of $_2$ on the surface, $_4$ becomes the major constituent and anneals into large slabs, giving rise to the long optical path lengths which saturate the infrared spectrum." +" The tlird regime ir (ie model is the transition where CH, cau only barely be retainecl aud other volaties ale DOUeNISeut.", The third regime in the model is the transition where $_4$ can only barely be retained and other volatiles are nonexistent. + Quaoar aud potentially 2007 ORLO are both in this regime., Quaoar and potentially 2007 OR10 are both in this regime. + These objects are both sulficienty depleted even in methane that their water ice substrate is visible in regions not covered by 11οhane., These objects are both sufficiently depleted even in methane that their water ice substrate is visible in regions not covered by methane. + The object 2001 V.e12. though likely small has a perihelion of I7. AU and thus stays cold enough to potentlally retain at least CH.," The object 2004 VN112, though likely small, has a perihelion of 47 AU and thus stays cold enough to potentially retain at least $_4$." + This object is too faint for iufrared spectroscopy. so we lave no clirect lndicatio rolis surface composition. audi ts albedo. aud thus. size is unknown.," This object is too faint for infrared spectroscopy, so we have no direct indication of its surface composition, and its albedo, and thus, size is unknown." + IS optical colors are 'elatively neutral. however. suggestiug tlat it is uot domiuated by CH irradiation »roducts (see belyw).," Its optical colors are relatively neutral, however, suggesting that it is not dominated by $_4$ irradiation products (see below)." + Εuthe ‘physical study of his object is clearly warrautect., Further physical study of this object is clearly warranted. + The final regime wihin tliis model is the regio= in which most of the Ixuiper belt resides. where enmperatures are too high atcl masses are too low. so that even with slow Jeans escape. the three nalu volatiles nust be depleed over solar system ime scales.," The final regime within this model is the region in which most of the Kuiper belt resides, where temperatures are too high and masses are too low, so that even with slow Jeans escape, the three main volatiles must be depleted over solar system time scales." + To date. this model has been [awess lor deermiuiug whicl objects do aud do not retain volatiles in the Ixuiyer belt (with the imporaut exceptiou of Haunea. which is discussed below).," To date, this model has been flawless for determining which objects do and do not retain volatiles in the Kuiper belt (with the important exception of Haumea, which is discussed below)." + It is interesting — axl even unexpected — that sucl a simple model would work so well., It is interesting – and even unexpected – that such a simple model would work so well. + The atmospheres of Pluto aud Triton. lor exatmple. do not couorl totie ΠΡΟ. ol surlace temperaure livclrostatic equilibriUUM ald Jeaus escape.," The well-studied atmospheres of Pluto and Triton, for example, do not conform to the simple assumptions of surface temperature hydrostatic equilibrium and Jeans escape." + Perhaps. however. the power oL the inodel is that as νοaliles begin to jecome depleted. th191. faster inechanisijs suche as iwdrodyuamic escaye. tlie auospliere evenwally becomes tenuois enough tal Jeans escape is the only remiaini1g nec‘hanisi unctiouing.," Perhaps, however, the power of the model is that as volatiles begin to become depleted through faster mechanisms such as hydrodynamic escape, the atmosphere eventually becomes tenuous enough that Jeans escape is the only remaining mechanism functioning." + Jeans escaye is then so slow compa'ed to othe© Processes hat it eventtally «onmiuates the toal amouit of time that it tases for volaile loss., Jeans escape is then so slow compared to other processes that it eventually dominates the total amount of time that it takes for volatile loss. + While Isuiper belt volaties Lave mostly been stlied from iufrared spectκcopy. stelar occultations »ovide anoljer alteruative Or study of volatile compositions.," While Kuiper belt volatiles have mostly been studied from infrared spectroscopy, stellar occultations provide another alternative for study of volatile compositions." + 9ich occultaions should be able to srovide iusigus into No» abudances on Eris. Makerrake ancl Sedua aid oceualions shoild provide he best ineans of looking for volatiles arotud sia| distant objects such as 2001 VN112.," Such occultations should be able to provide insights into $_2$ abundances on Eris, Makemake and Sedna and occultations should provide the best means of looking for volatiles around small distant objects such as 2004 VN112." + All bare surfaces in the solar system are subject to irradiation by solar wind. UV photons. aud cosinic rays. all of which are capable of inducing chemical changes in tle surfaces.," All bare surfaces in the solar system are subject to irradiation by solar wind, UV photons, and cosmic rays, all of which are capable of inducing chemical changes in the surfaces." + The surface colors, The surface colors +lack objects to spectral (vpes between G5 ancl 195. compromising an analysis for the onset ol activity in those regions.,"lack objects to spectral types between G5 and K5, compromising an analysis for the onset of activity in those regions." + Thus. from our data alone we cannot definitely rule out activity evolution between 6 and MMyr.," Thus, from our data alone we cannot definitely rule out activity evolution between 6 and Myr." + When comparing our data will vounger objects. however. we see evidence for activity evolution on this timescale. in the sense that the transition to enission occurs al somewhat earlier spectral (vpes in T Taur stars.," When comparing our data with younger objects, however, we see evidence for activity evolution on this timescale, in the sense that the transition to emission occurs at somewhat earlier spectral types in T Tauri stars." + Taken together. the analvsis in (his section indicates that chromospheric activity. steadilv declines as the stus evolve from the T Tauri phase to the main sequence.," Taken together, the analysis in this section indicates that chromospheric activity steadily declines as the stars evolve from the T Tauri phase to the main sequence." + since we have more (han one epoch for most of our targets. we are able lo probe variability. in the [la emission.," Since we have more than one epoch for most of our targets, we are able to probe variability in the $\alpha$ emission." + Because both photospheric Ila absorption and bolometric Iuninosity are not expected to change significantly namore (han a few percent) for these objects. variability in Wa EW basically traces changes in the level of chromospheric emission.," Because both photospheric $\alpha$ absorption and bolometric luminosity are not expected to change significantly more than a few percent) for these objects, variability in $\alpha$ EW basically traces changes in the level of chromospheric emission." + For a lew objects in (he voungest regions. weak levels of episodic accretion cannot be excluded and might contribute somewhat to the variability (seeJavawardhanaetal.2006)..," For a few objects in the youngest regions, weak levels of episodic accretion cannot be excluded and might contribute somewhat to the variability \citep[see][]{2006ApJ...648.1206J}." + The primary estimate of variability is the stancarcl deviations in our EW time series., The primary estimate of variability is the standard deviations in our EW time series. + In Fie., In Fig. + 4 (left panel) we plot the absolute values of La EW σ sspectral tvpe., \ref{f5} (left panel) we plot the absolute values of $\alpha$ EW $\sigma$ spectral type. + The dashed line marks the measurement uncertainty., The dashed line marks the measurement uncertainty. + As can be seen [rom (his plot. many objects with late spectral tvpes show significantly higher Wa variations (han expected [rom the formal error. indicating variability in activitv.," As can be seen from this plot, many objects with late spectral types show significantly higher $\alpha$ variations than expected from the formal error, indicating variability in activity." + Interestingly. (he onset of measurable variability occurs ad early IX spectral (vpes. where Ha changes Irom absorption to emission.," Interestingly, the onset of measurable variability occurs at early K spectral types, where $\alpha$ changes from absorption to emission." + This confirms (hat (he variations can indeed be attributed to chromospheric activity stars without measurable activity and thus only photospheric Ho do not show variabilitv., This confirms that the variations can indeed be attributed to chromospheric activity – stars without measurable activity and thus only photospheric $\alpha$ do not show variability. + The plot shows no significant difference between the four groups. indicating that the level of variability does not strongly change between 6 and MMvi.," The plot shows no significant difference between the four groups, indicating that the level of variability does not strongly change between 6 and Myr." + llo emission originates from active regions in (he chromosphere. which are typically not uniformly distributed.," $\alpha$ emission originates from active regions in the chromosphere, which are typically not uniformly distributed." + Thus. one main cause of the Ho. variations is rotational modulation.," Thus, one main cause of the $\alpha$ variations is rotational modulation." + Additionally. the light eurves can be affected. by flare activity and overall changes in the activity level. ddue to an activity cvele.," Additionally, the light curves can be affected by flare activity and overall changes in the activity level, due to an activity cycle." + Our time sampling makes it difficult to distinguish between these three scenarios., Our time sampling makes it difficult to distinguish between these three scenarios. + In most cases. we have only one spectrum per night per target: the longest time baseline is eight months.," In most cases, we have only one spectrum per night per target; the longest time baseline is eight months." + Rotational changes occur on timescales of the rotation periods. which are (vpically a few davs for our targets.," Rotational changes occur on timescales of the rotation periods, which are typically a few days for our targets." + These changes are periodic. but with our sparse sampling we are not able (to recover the periods.," These changes are periodic, but with our sparse sampling we are not able to recover the periods." + General activily level changes are a long-term phenomenon. and thus might introduce a gradual trend in our time series.," General activity level changes are a long-term phenomenon, and thus might introduce a gradual trend in our time series." + Isolated. [lare events would be detectable. but only if they are clearly stronger than," Isolated flare events would be detectable, but only if they are clearly stronger than" +Sun than 1862 Apollo.,Sun than 1862 Apollo. + For example. a sub-km NEA with a<1 AU can have /yogp several limes shorter than 1362 Apollo.," For example, a sub-km NEA with $a<1$ AU can have $t_{\rm YORP}$ several times shorter than 1862 Apollo." + We therefore speculate that the YORDP ellect can contribute to the observed excess of Q-tvpe NEAs in these low-a orbits., We therefore speculate that the YORP effect can contribute to the observed excess of Q-type NEAs in these $a$ orbits. + A detailed analvsis of this problem goes bevond the scope of (his paper., A detailed analysis of this problem goes beyond the scope of this paper. + The main results obtained in this work can be summarized as Iollows: 1) The NJWIOD5 model (822) is consistent with the current spectroscopic observations of NEAs., The main results obtained in this work can be summarized as follows: 1) The NJWI05 model 2) is consistent with the current spectroscopic observations of NEAs. + The effect of planetary encounters can therefore explain the tenceney towards seeing the fresh OC-like material among NEAs., The effect of planetary encounters can therefore explain the tendency towards seeing the fresh OC-like material among NEAs. + The fraction of Q-tvpe asteroids in the main bell should be small because the processes that affect MDAs (e.g.. collisions) lack the efficiency of planetary encounters.," The fraction of Q-type asteroids in the main belt should be small because the processes that affect MBAs (e.g., collisions) lack the efficiency of planetary encounters." + 2) From modeling the spectral properties of NEAs we found that the SW timescale is longer (han ~0.1 My. and shorter (han 10 My., 2) From modeling the spectral properties of NEAs we found that the SW timescale is longer than $\sim$ 0.1 My and shorter than $\sim$ 10 My. + It is most plausible (hat {ως1 My and rows5 Ry., It is most plausible that $t_{\rm sw}\sim1$ My and $r^* \sim 5$ $R_{\rm pl}$. +" This result is in a broad agreement with /,, estimated from studies of asteroid families and our current understanding of the effects of tidal gravity.", This result is in a broad agreement with $t_{\rm sw}$ estimated from studies of asteroid families and our current understanding of the effects of tidal gravity. + 3) We found that /.xq. expected if the solar wind sputtering controls /.... provides a. better fit to the orbital distribution of Q-tvpe NEAs than models with fixed .," 3) We found that $t_{\rm sw} \propto q^2$, expected if the solar wind sputtering controls $t_{\rm sw}$, provides a better fit to the orbital distribution of Q-type NEAs than models with fixed $t_{\rm sw}$." + layxq. however. our simple model fails to explain the excess of Q-tvpe NEAs with low-a orbits.," If $t_{\rm sw} \propto q^2$, however, our simple model fails to explain the excess of Q-type NEAs with $a$ orbits." + We speculate that this population could be susceptible to the YORP effect., We speculate that this population could be susceptible to the YORP effect. + 4) Tidal encounters of NEAs with Venus and Earth are important. but those with Mars (and Mercury) are rare.," 4) Tidal encounters of NEAs with Venus and Earth are important, but those with Mars (and Mercury) are rare." + This is mainly due (ο the fact that Mars is a much smaller planet than Venus and Earth and has a relatively large orbit., This is mainly due to the fact that Mars is a much smaller planet than Venus and Earth and has a relatively large orbit. + From the statistics of Mars encounters we estimate that a small fraction of ΧΙΑς could be Qs (S 1960)., From the statistics of Mars encounters we estimate that a small fraction of MCAs could be Qs $\lesssim1$ ). + This fraction should be above the main belt average., This fraction should be above the main belt average. + A laree observational sample will be needed to test this prediction., A large observational sample will be needed to test this prediction. + 5) The effects of the Earth's magnetosphere can be more important (han tidal gravity for distant. Earth encounters., 5) The effects of the Earth's magnetosphere can be more important than tidal gravity for distant Earth encounters. + These distant encounter effects are not required. however. to explain the observed fraction of Q-tvpe NEAs. if a.~1 Aly.," These distant encounter effects are not required, however, to explain the observed fraction of Q-type NEAs, if $t_{\rm sw}\sim1$ My." + This work was funded by the NASA Planetary Geology and Geophysics program., This work was funded by the NASA Planetary Geology and Geophysics program. + The work of DV was also partially supported by the Czech Grant. Ageneyv (grant. 205/08/0064) and the Research Program AISAIOO21620860 of the Czech Ministry of Education., The work of DV was also partially supported by the Czech Grant Agency (grant 205/08/0064) and the Research Program MSM0021620860 of the Czech Ministry of Education. + We thank Bruce Lapke and Robert Jedicke for their very. helpful referee reports., We thank Bruce Hapke and Robert Jedicke for their very helpful referee reports. +"the initial radius Ro (e.g.Arnett1996),, as the radiative flux FοT*/(kespoRo)οςRo’.","the initial radius $R_0$ \citep[e.g.][]{arnett96}, as the radiative flux $F\propto T^4/(\kappa_{es} \rho_0 R_0) \propto R_0^{-1}$." +" The lower initial photospheric velocity, longer plateau and higher initial temperature are a consequence of the smaller PdV work done by bigger expanding envelopes."," The lower initial photospheric velocity, longer plateau and higher initial temperature are a consequence of the smaller $PdV$ work done by bigger expanding envelopes." +" Less internal energy is initially converted into kinetic energy, the expansion is slower and more energy remains available for heating up the envelope."," Less internal energy is initially converted into kinetic energy, the expansion is slower and more energy remains available for heating up the envelope." + Figure 21 shows the effects of varying the total energy (with ratio between thermal and kinetic energy equal to 1; see Sect. , Figure \ref{fig:energy3} shows the effects of varying the total energy (with ratio between thermal and kinetic energy equal to 1; see Sect. \ref{sec:simul:models}) ). +"Increasing it causes a higher luminosity in the bolometric3.2)). light curve during the diffusive and recombination phases, a shorter plateau, a higher photospheric velocity up to ~60—70 days and a faster decline at longer times."," Increasing it causes a higher luminosity in the bolometric light curve during the diffusive and recombination phases, a shorter plateau, a higher photospheric velocity up to $\sim 60-70$ days and a faster decline at longer times." +" The early behavior can be easily understood as a consequence of the larger internal energy dumped in the ejecta, that increases their initial velocity and accelerates all the evolutionary stages."," The early behavior can be easily understood as a consequence of the larger internal energy dumped in the ejecta, that increases their initial velocity and accelerates all the evolutionary stages." +" As for the effects of varying (see Figure 22)), increasing it makes the plateau phase longer and causes a slower decline of the bolometric light curve towards the radioactive tail."," As for the effects of varying (see Figure \ref{fig:ni}) ), increasing it makes the plateau phase longer and causes a slower decline of the bolometric light curve towards the radioactive tail." +" Furthermore, as My; increases, also the decline of the photospheric velocity is slower, while the bolometric luminosity becomes higher during the radioactive tail."," Furthermore, as $M_{Ni}$ increases, also the decline of the photospheric velocity is slower, while the bolometric luminosity becomes higher during the radioactive tail." +" All these effects are related to the increased heating provided by the larger amount of concentrated in the innermost part of the envelope, that increases the internal energy and luminosity especially at late phases and slows down the motion of the RW (e.g.Arnett1996;Hamuy2003b;Nadyozhin 2003)."," All these effects are related to the increased heating provided by the larger amount of concentrated in the innermost part of the envelope, that increases the internal energy and luminosity especially at late phases and slows down the motion of the RW \citep[e.g.][]{arnett96,hamuy03b,Nadyozhin03}." +". We developed (a general-relativistic, radiation hydrodynamics, Lagrangian code tailored to the radiation-hydrodynamical modelling of CC-SNe, whose"," We developed a general-relativistic, radiation hydrodynamics, Lagrangian code tailored to the radiation-hydrodynamical modelling of CC-SNe, whose" +the accretor were treated as rigid spheres.,the accretor were treated as rigid spheres. + The results presented therefore do not account for orbital evolution due to tidal torques or for the radial response of the donor star to mass loss., The results presented therefore do not account for orbital evolution due to tidal torques or for the radial response of the donor star to mass loss. + Our caleulatious nevertheless clearly illustrate that mass overflow leading to direct Hupact accretion or sclfaceretion can both enhance or counteract the effects of tides im eccentric effective Roche lobe overflowing binaries., Our calculations nevertheless clearly illustrate that mass overflow leading to direct impact accretion or self-accretion can both enhance or counteract the effects of tides in eccentric effective Roche lobe overflowing binaries. + A similar conclusion was reached by 77. for binaries in which mass trausfer leads to the formation of an accretion disk.," A similar conclusion was reached by \citet{2007ApJ...667.1170S, +2009ApJ...702.1387S} for binaries in which mass transfer leads to the formation of an accretion disk." + As one of the uext steps iu our investigation. we will inuiplemieut more realistic stellar iiodoels in our ballistic particle trajectory code aud examine the effects of tides aud stellar evolutiou on nass transfer in eccentric binaries.," As one of the next steps in our investigation, we will implement more realistic stellar models in our ballistic particle trajectory code and examine the effects of tides and stellar evolution on mass transfer in eccentric binaries." + While not discussed in detail here. we also find that direct inaipact accretion does not necessarily deposit all of the accreted matters augular momenta into the spin of the accretor.," While not discussed in detail here, we also find that direct impact accretion does not necessarily deposit all of the accreted matter's angular momentum into the spin of the accretor." + Instead. some of this augular momentum. which originated from both spin aud orbital augular momentiun of the donor star. is deposited into the accretor's spin while the remaining part is returned to the orbit.," Instead, some of this angular momentum, which originated from both spin and orbital angular momentum of the donor star, is deposited into the accretor's spin while the remaining part is returned to the orbit." +" This is in stark coutrast to conunuonly adopted assuniptious in stability studies of mass transfer in ultra-conrpact binaries (ee.οδν, "," This is in stark contrast to commonly adopted assumptions in stability studies of mass transfer in ultra-compact binaries \citep[e.g.,][]{1988ApJ...332..193V, +2004MNRAS.350..113M}." +The possibility of avoiding strong orbital augular momentum loss during direct iupact accretion is particularly relevant iu predicting expected eravitational wave detection rates from παν”transferring double white dwarfs CCVu stars} by the Laser Interferometer Space Auteuna (LISA)., The possibility of avoiding strong orbital angular momentum loss during direct impact accretion is particularly relevant in predicting expected gravitational wave detection rates from mass-transferring double white dwarfs CVn stars) by the Laser Interferometer Space Antenna (LISA). + We thank Christopher Delove for numerous uscti discussions. Francesca Valsecchi for the use of her C Huplementation of Steffens (?)) iuterpolatiou algoritlin used to caleulate the time derivatives of the orbita elements. aud Christopher Tout for a muuber of uscti sugeestious.," We thank Christopher Deloye for numerous useful discussions, Francesca Valsecchi for the use of her C implementation of Steffen's \citeyear{1990A&A...239..443S}) ) interpolation algorithm used to calculate the time derivatives of the orbital elements, and Christopher Tout for a number of useful suggestions." + This work is partially supported by a NASA Graduate Fellowship CNNGOIGDPOLIII/SI) to J.S.. ane a NSF CAREER Award (AST-0119558). a Packare Followship in Science aud Eugineering. aud a NASA ATP Award (NACG5-13236) to Vs.," This work is partially supported by a NASA Graduate Fellowship (NNG04GP04H/S1) to J.S., and a NSF CAREER Award (AST-0449558), a Packard Fellowship in Science and Engineering, and a NASA ATP Award (NAG5-13236) to V.K." +and no single-star evolution path is known that could form these objects (Kawka Vennes 2009).,and no single-star evolution path is known that could form these objects (Kawka Vennes 2009). + In Fig. 6..," In Fig. \ref{fig:wd}," + we reported the masses and radit of several white dwarfs from the literature for comparison purposes with KOI 7Àb., we reported the masses and radii of several white dwarfs from the literature for comparison purposes with KOI 74b. + We included a sample of white dwarfs in envelope eclipsing binaries (PCEEB) (Parsons 22010. and references therein).," We included a sample of white dwarfs in post-common-envelope eclipsing binaries (PCEEB) (Parsons 2010, and references therein)." + The masses and radit of these degenerate stars can be directly derived with velocimetry and photometry. similarly to ΚΟΙ 74b.," The masses and radii of these degenerate stars can be directly derived with velocimetry and photometry, similarly to KOI 74b." + Few of these eclipsing systems are known., Few of these eclipsing systems are known. + Most of them are paired with an M dwarf that is less massive than the white dwarf itself., Most of them are paired with an M dwarf that is less massive than the white dwarf itself. + As can be seen in Fig. 6..," As can be seen in Fig. \ref{fig:wd}," + KOI 74b is both larger and less massive. 1.e.. less dense. than any other PCEEB white dwarf known so far.," KOI 74b is both larger and less massive, i.e., less dense, than any other PCEEB white dwarf known so far." + This might point to a difference in internal composition or to a different evolutionary path since the primary star KOI 74 is much more massive than the white dwarf companion., This might point to a difference in internal composition or to a different evolutionary path since the primary star KOI 74 is much more massive than the white dwarf companion. + This agrees with the discussion of van Kerkwijk ((2010) about the unlikely common-envelope evolution of the KOI 74 system., This agrees with the discussion of van Kerkwijk (2010) about the unlikely common-envelope evolution of the KOI 74 system. + In fact. KOI 74b seems more similar to extremely low-mass (ELM) white dwarfs.," In fact, KOI 74b seems more similar to extremely low-mass (ELM) white dwarfs." + These objects were initially. detected as companions to pulsars. such as (van Kerkwijk. Bergeron Kulkarni 1996). (Bassa 22006). (Edmonds 22001). or (Kulkarni van Kerkwijk 2010).," These objects were initially detected as companions to pulsars, such as (van Kerkwijk, Bergeron Kulkarni 1996), (Bassa 2006), (Edmonds 2001), or (Kulkarni van Kerkwijk 2010)." + Some ELM white dwarfs identified in deep surveys are known as binaries solely οἱ the basis of radial velocity variations. since their companions remain unseen (see for instance the case ofJ123410.37-022802.9:: Liebert 22004). (," Some ELM white dwarfs identified in deep surveys are known as binaries solely on the basis of radial velocity variations, since their companions remain unseen (see for instance the case of; Liebert 2004). (" +The radii of these objects are usually determined from mass-radius relations.),The radii of these objects are usually determined from mass-radius relations.) + Recently. the system (Kawka Vennes 2009: Kawka. Vennes Vaccaro 2010) has been identified as the first ELM-white dwarf eclipsing binary (Steinfadt 22010). allowing a direct estimation of an ELM radius.," Recently, the system (Kawka Vennes 2009; Kawka, Vennes Vaccaro 2010) has been identified as the first ELM-white dwarf eclipsing binary (Steinfadt 2010), allowing a direct estimation of an ELM radius." + On the other hand. the KOI 74 system again distinguishes itself from these systems. owing to the mass of the primary Al star.," On the other hand, the KOI 74 system again distinguishes itself from these systems, owing to the mass of the primary A1 star." + Van Kerkwijk ((2010) note that the KOI 74 system. and maybe KOI 81. could be downscale versions of the Regulus binary system. consisting ina BB7V star (« Leo A) and a recently identified ~0.3 wwhite dwarf (a Leo Ab) on a 40-day orbit (Gies 22008).," Van Kerkwijk (2010) note that the KOI 74 system, and maybe KOI 81, could be downscale versions of the Regulus binary system, consisting in a B7V star $\alpha$ Leo A) and a recently identified $\sim0.3$ white dwarf $\alpha$ Leo Ab) on a 40-day orbit (Gies 2008)." + Besides. Di Stefano (submitted) proposes that the primary stars KOI 74 and KOI 81 could be classified as blue stragglers: In fact. we found that the blue straggler system F190 in the M67 open cluster (Milone 1991; Milone Latham 1992) is aclose analog to the KOI 74 system. with component masses of 0.2 and 2.] aand with a period of 4.18 days. (," Besides, Di Stefano (submitted) proposes that the primary stars KOI 74 and KOI 81 could be classified as blue stragglers: In fact, we found that the blue straggler system F190 in the M67 open cluster (Milone 1991; Milone Latham 1992) is a close analog to the KOI 74 system, with component masses of 0.2 and 2.1 and with a period of 4.18 days. (" +This system is. however. centric.?) To our knowledge. systems composed of an extremely mass white dwarf or a low-mass white dwarf and an early-type main-sequence star are excessively rare.,"This system is, however, ) To our knowledge, systems composed of an extremely low-mass white dwarf or a low-mass white dwarf and an early-type main-sequence star are excessively rare." + Meanwhile. the rarity of these systems may not be intrinsic but could result from the following bias: in imaging surveys such as the Sloan Digital Sky Survey. the detected white dwarf-main sequence star binaries usually include a late type (M or K) dwarf. because such a cool star does not outshine the white dwarf.," Meanwhile, the rarity of these systems may not be intrinsic but could result from the following bias: in imaging surveys such as the Sloan Digital Sky Survey, the detected white dwarf-main sequence star binaries usually include a late type (M or K) dwarf, because such a cool star does not outshine the white dwarf." + Nevertheless. the white dwarf mass distribution inferred for these binary systems peaks at 0.5M... close to the average mass of single white dwarfs (Rebassa-Mansergas 22010).," Nevertheless, the white dwarf mass distribution inferred for these binary systems peaks at 0.5, close to the average mass of single white dwarfs (Rebassa-Mansergas 2010)." + Owing to its rarity. a system like KOI 74 will be an invaluable target for testing atmospheric models commonly used to derive radii and masses for white dwarfs (e.g.. Serenellt 22001. 2002) and binary evolution scenarios.," Owing to its rarity, a system like KOI 74 will be an invaluable target for testing atmospheric models commonly used to derive radii and masses for white dwarfs (e.g., Serenelli 2001, 2002) and binary evolution scenarios." + We have obtained radial velocity measurements of KOI 74. a massive and early main-sequence star transited by a hot compact object.," We have obtained radial velocity measurements of KOI 74, a massive and early main-sequence star transited by a hot compact object." + The measurements indicate that the companion Is a oobject. most probably a low-mass white dwarf.," The measurements indicate that the companion is a object, most probably a low-mass white dwarf." + We emphasize that this transiting low-mass white dwarf. whose mass. radius. and temperature have been directly measured through radial velocimetry and photometry. will be a precious template object for binary evolution theories.," We emphasize that this transiting low-mass white dwarf, whose mass, radius, and temperature have been directly measured through radial velocimetry and photometry, will be a precious template object for binary evolution theories." +The ideal shear maps ; without noise can then be estimated from (he convergence map Dv,The ideal shear maps $\gamma_i$ without noise can then be estimated from the convergence map $\kappa$. +" noting that 2,+7%=1. an estimator of the mass distribution & can easily be derived by inversion The deformation induced by weak gravitational lensing on a single galaxy is very weak compared to its intrinsic ellipticity."," By noting that $\hat{P_1}^2+\hat{P_2}^2=1$, an estimator of the mass distribution $\kappa$ can easily be derived by inversion The deformation induced by weak gravitational lensing on a single galaxy is very weak compared to its intrinsic ellipticity." + The lensing signal therefore must be extracted [rom the ealaxy image ellipticitv by assuming the intrinsic ellipticity is randomly. oriented in the absence of gravitational lensing., The lensing signal therefore must be extracted from the galaxy image ellipticity by assuming the intrinsic ellipticity is randomly oriented in the absence of gravitational lensing. + The observed shear σε is then obtained by averaging over a [mite nunber of galaxies and. therefore. is noisy.," The observed shear $\gamma_{i,n}$ is then obtained by averaging over a finite number of galaxies and, therefore, is noisy." +" The relationship between (he observed data 71,4.52s, binned in pixels of area vt and the (rue convergence map & are eiven bv: where Nj and NZ are white Gaussian noise with zero mean and standard deviation c,~σ/ VES where V,=n, is the average number of galaxies in a pixel (5, is the average number of galaxies per area unit and A is the pixel area in the same unit)."," The relationship between the observed data $\gamma_{1, n},\gamma_{2, n}$ binned in pixels of area $A$ and the true convergence map $\kappa$ are given by: where $N_1^{\gamma}$ and $N_2^{\gamma}$ are white Gaussian noise with zero mean and standard deviation $\sigma_n \simeq \sigma^{\gamma}_{\epsilon}/\sqrt{N_g}$ , where $N_g = n_g A$ is the average number of galaxies in a pixel $n_g$ is the average number of galaxies per area unit and A is the pixel area in the same unit)." + The rms shear dispersion per galaxy 0; arises both from measurement errors and the intrinsic shape dispersion of galaxies., The rms shear dispersion per galaxy $\sigma^{\gamma}_{\epsilon}$ arises both from measurement errors and the intrinsic shape dispersion of galaxies. + In this analysis. we will assume o;0.3 as is approximately found for eround-based aud space-based weak lensing surveys (Brainerdeal. 1996).," In this analysis, we will assume $\sigma^{\gamma}_{\epsilon} \simeq 0.3$ as is approximately found for ground-based and space-based weak lensing surveys \citep{astro:brainerd96}." +".. Typical values for the galaxy surface density [or weak lensing are 7,~10 gal/arcmin? for ground-based surveys and n,~50 gal/arcmin? for relatively deep space-based survevs.", Typical values for the galaxy surface density for weak lensing are $n_g \sim 10$ $^2$ for ground-based surveys and $n_g \sim 50$ $^2$ for relatively deep space-based surveys. + In presence of noise. the estimator of the convergence & 1s: As for shear. the flexion estimation can be caleulated with shapelets (Goldbergetal.Baconetal.2006:Massey.2007) or by clirectly measuring the higher-orcler moments of the galaxy image (Okuraetal.2007).," In presence of noise, the estimator of the convergence $\kappa$ is: As for shear, the flexion estimation can be calculated with shapelets \citep{flexion:goldberg05,flexion:bacon06,flexion:massey07} or by directly measuring the higher-order moments of the galaxy image \citep{flexion:okura07}." +. Flexion has two components. F and G.," Flexion has two components, $\mathcal{F}$ and $\mathcal{G}$." + A (hirc-order inversion can be performed (o recover the convergence field &(9) [rom theflexion field F or G.It has been shown by Okuraetal.(2007). that measurements of the second, A third-order inversion can be performed to recover the convergence field $\kappa(\theta)$ from theflexion field $\mathcal{F}$ or $\mathcal{G}$.It has been shown by \cite{flexion:okura07} that measurements of the second + ↾↿↓⋖⋅↾∣↓∣≻⋖⋅∣⋅∖∖∖⋰∐∣↿↥↕↾↿↓⋖⋅−∖⋖⋅∣⋅↕⋖⋅∖∣≻∣⋯↥∪↾↿↓⋖⋅↕∣⋅∙∖⇁⋡⋯⊔⊔∣∥⋅∣⋅⋖⋅∖⋖⋅↾↿↓∣≻↥⋯∥⊾⋖⋅∖ ↥∪∐∖∖⊽⊾↔≼⊾↥⋜⋯∠⇂↼∐≟⋅↱⊐⊤⋯⋅⋖⋅∖⊓∣≻∖↥⋜⋯↥⊲↓⋜↧↥∶ These resemblances. and the clilficullics with alternative models. seem sullicient to accept both BW Sel and JL457 as new menibers of the GW Lib class.,"members with time-series photometry, and the resemblances to BW Scl and J1457 are substantial: These resemblances, and the difficulties with alternative models, seem sufficient to accept both BW Scl and J1457 as new members of the GW Lib class." +m this Letter woe investigate lhiouxIQCTICOTLS aud stoacilv drwen ducoupressible maguetoliydiνταλαο (MIID) turbulence.,In this Letter we investigate homogeneous and steadily driven incompressible magnetohydrodynamic (MHD) turbulence. + Ta practical applications. such as fusio devices. solar wind. and interstellar medi. ↑↿∐⋅↴⋝∏↕↸∖∐↸⊳↸∖↕↴∖↴≼⊔⋅↕↖↽↸∖∐⋝⋅↖⊽↖↽⋜∐⋅↕∪∏↴∖↴↕⋜∐⋅∶↴⊾⊾↸∖≓↴∖↴↸⊳⋜↧↕↸∖↕∐↴∖↴↑⋜∏⋝↕∐↑↕↸∖↴∖↴∙ aud urbulent cucrey istjen spread over a broad range of spatial scales duc +) nonlinear interactions πι] πια dissipative scaes are reached where the energv ]s renoved from the SVSein.," In practical applications, such as fusion devices, solar wind, and interstellar medium, turbulence is driven by various large-scale instabilities, and turbulent energy is then spread over a broad range of spatial scales due to nonlinear interactions until small dissipative scales are reached where the energy is removed from the system." +" In the interval of scales between the injection aud dissipation regions turbulence properties are though: to )o universal (ο,οι,Frisch1995:Diskuup 2003).."," In the interval of scales between the injection and dissipation regions turbulence properties are thought to be universal \citep[e.g.,][]{frisch,biskamp}." +" The MIID equations describing the evolution of lnaegnetic aid velocity fluctuations b(x.t£) aud v(x.t) iu the xeseuce of a guide ficld Bo cau be represeuted in the so-called Elsüssser variables z—vXb: where V,=Bo/VIzp is the Alfvéun velocity. p is the tid density. P is the pressure that is determined frou he incompressillity condition. V«z=0. f represents a large-scale forejug. and we omit the ternis represcuting sanall viscosity aid resistivitv."," The MHD equations describing the evolution of magnetic and velocity fluctuations ${\bf b}(\bf x,t)$ and ${\bf v}(\bf x,t)$ in the presence of a guide field ${\bf B_0}$ can be represented in the so-called Elsässser variables ${\bf z}^{\pm}={\bf v}\pm {\bf b}$: where ${\bf V}_{A}={\bf B}_{0}/\sqrt{4\pi \rho}$ is the Alfvénn velocity, $\rho$ is the fluid density, $P$ is the pressure that is determined from the incompressibility condition, $\nabla \cdot {\bf + z}^{\pm}=0$, ${\bf f}$ represents a large-scale forcing, and we omit the terms representing small viscosity and resistivity." +" The linear term on the left- side of equatious (13). (Voy:Va"". is responsible or advection of the 2! aud io save packets. with the Alfvénn velocity along the guide field."," The linear term on the left-hand side of equations \ref{mhd1}) ), $({\bf V}_A\cdot \nabla){\bf z}^{\pm}$, is responsible for advection of the $z^+$ and $z^-$ wave packets, with the Alfvénn velocity along the guide field." +" The nonlinear ern. (ft.WV)"". describes the interaction of turbulent flnetuations. au Lit is responsible for the energy trauster among different spatial scales."," The nonlinear term, $({\bf z}^{\mp}\cdot \nabla){\bf z}^{\pm}$, describes the interaction of turbulent fluctuations, and it is responsible for the energy transfer among different spatial scales." + The nonlinear termi is considered sual if where fy) ane Ay απο typical field-parallel aud field-perpeudieular wavenunnbers of the fluctuations’| Spectruni. aud by (κ By) is the typical maecuitude of fluctuations at tje A~L/h.," The nonlinear term is considered small if where $k_{\|}$ and $k_{\perp}$ are typical field-parallel and field-perpendicular wavenumbers of the fluctuations' spectrum, and $b_{\lambda}$ $\ll B_0$ ) is the typical magnitude of fluctuations at the scale $\lambda\sim 1/k_{\perp}$." +" This reeiue is referred to as ""weak turπω.", This regime is referred to as “weak turbulence.” + The regime when the noulinear term iu not formally: πια will be caled “strong turbulence.”, The regime when the nonlinear term in not formally small will be called “strong turbulence.” + One cau argue that in strong turbulence the following critical balance condition should be maintained at all scales (Ctoldreicli&Sridhar 1995):: ↕∐↸↧↸∖↸∖↸↧∙⋔∐∐↓∶↰≔∏↓↸∖↸↾↕↕⋮∪⋯⋟↾↸∖⊔↴∖⊔↸⋟↾↕ ∙ ∙∙∙ ue of nonlinear luteraction. Ty~LAAby). the flucuations become correlated alone the guide feld up to a distauce Hi Vary.," One can argue that in strong turbulence the following critical balance condition should be maintained at all scales \citep{goldreich}: Indeed, during the characteristic time of nonlinear interaction, $\tau_N\sim 1/(k_{\perp} b_{\lambda})$, the fluctuations become correlated along the guide field up to a distance $l_\|\sim V_A\tau_N$ ." + This causality condition eusPOS the critical balance (3))., This causality condition ensures the critical balance \ref{crit}) ). + Depending on the wav turbuleuce is excited. it satisfies either coucition (2)) or (3)) 1La certain range of scales.," Depending on the way turbulence is excited, it satisfies either condition \ref{weak-turb}) ) or \ref{crit}) ) in a certain range of scales." + Recent numerical simiatious and analytic modcling Sugeest that in the case of strong turbulence (3)). the field-perpeudiculaur eueres- spectrin is L(A)xaa? (Maron&Coldreich20Hd:Müller:Crappiun.2005:Boldvrev2005.2006:Aasonotal.2006. 2007).," Recent numerical simulations and analytic modeling suggest that in the case of strong turbulence \ref{crit}) ), the field-perpendicular energy spectrum is $E(k_{\perp})\propto k_{\perp}^{-3/2}$ \citep{maron,muller,boldyrev,boldyrev2,mason,mason2}." +. Ilowewver. gcopwesical aud astrophysical observations often exhibit somewhat sceper spectra (6.9...Goldsteiuetal.1995:Bale.al2 305)..," However, geophysical and astrophysical observations often exhibit somewhat steeper spectra \citep[e.g.,][]{goldstein,bale}." + This raises the question of ο what extent such systems can be described iu the ralework. of MIID τιοιonce., This raises the question of to what extent such systems can be described in the framework of MHD turbulence. + Iu hne present work we conduct direct nunerical siuulations of reduced ΑΠΟ equations. driven by a oree with varviug Mosoectral width.," In the present work we conduct direct numerical simulations of reduced MHD equations, driven by a force with varying $k_{\|}$ spectral width." + This provides a unifius nunuerical sotΠιο allowing one to address he reguues of weak αιid strong turbulence in the sune framework., This provides a unifying numerical setting allowing one to address the regimes of weak and strong turbulence in the same framework. + We observe that when the critical valance (3)) is satisfied. he spectrum of strong MIID urbuleuce is close to. 32.," We observe that when the critical balance \ref{crit}) ) is satisfied, the spectrum of strong MHD turbulence is close to $-3/2$." + When the critical balance condition (3)) Is evel osightly broken. the spectrum stecpeus.," When the critical balance condition \ref{crit}) ) is even slightly broken, the spectrum steepens." + As the weak tur»ilence coudition (2)) becomes etter satistied. the specral exponent approaches 32 in accord with the theory of weak urbulence (Ne& 2000).," As the weak turbulence condition \ref{weak-turb}) ) becomes better satisfied, the spectral exponent approaches $-2$ in accord with the theory of weak turbulence \citep{ng96,galtier}." +..The observed sensitivity of the spectruu to the forcing details may explain conflicting results of nunerical aud astrophysical observations. where the spectral properties of forcing are either not well controlled or not well kuown.," .The observed sensitivity of the spectrum to the forcing details may explain conflicting results of numerical and astrophysical observations, where the spectral properties of forcing are either not well controlled or not well known." + According to the standard derivation, According to the standard derivation +non adaptive rav tracing.,non adaptive ray tracing. + As a new illustrative example we integrate the radial jump condition of an ionization front in three dimensions., As a new illustrative example we integrate the radial jump condition of an ionization front in three dimensions. + Consider the simple case of a constant Luminosity point source embedded in a static medium of neutral hydrogen., Consider the simple case of a constant luminosity point source embedded in a static medium of neutral hydrogen. + The jump condition along a rav at the location of the ionization front caused by the source reads Llere. n. denotes the number density of hydrogen nuclei. o(D). the (in general) temperature dependent recombination rate cocllicient. 2. the location of the ionization front and Np 1ο ionizing photon number flux of the source.," The jump condition along a ray at the location of the ionization front caused by the source reads Here, $n$, denotes the number density of hydrogen nuclei, $\alpha(T)$, the (in general) temperature dependent recombination rate coefficient, $R$, the location of the ionization front and $N_P$ the ionizing photon number flux of the source." +" IP we assume the ionized material to have a constant temperature and define⋅ a,=allo”LaeW) one can integrate. this. equat.ron with first order differencing to find the passing time. /,CR)."," If we assume the ionized material to have a constant temperature and define $\alpha_4=\alpha(10^4\K)$ one can integrate this equation with first order differencing to find the passing time, $t_p(R)$." + ‘The ray tracing gives one a list of AR; rav segments fron which one finds ἐν via The integral of the recombinations from. the source o the ionization front is evaluated on the [ly," The ray tracing gives one a list of $\triangle +R_i$ ray segments from which one finds $t_p$ via The integral of the recombinations from the source to the ionization front is evaluated on the fly." + ία this echnique one finds the entire evolution of the ionization ront in one radial integration., Via this technique one finds the entire evolution of the ionization front in one radial integration. + The passing time through a cell is taken to be the maximunr passing time evaluated rom all rays passing the cell., The passing time through a cell is taken to be the maximum passing time evaluated from all rays passing the cell. + The classical jump condition eives in the limit of small /? à speed of the ionization front dItídl exceeding the speed of light., The classical jump condition gives in the limit of small $R$ a speed of the ionization front $dR/dt$ exceeding the speed of light. +" Vo avoid. unphysicallv ast expansion times we therefore limit the maximum £A, o be the light crossing time Ονο. where. e. denotes the speed of light."," To avoid unphysically fast expansion times we therefore limit the maximum $\triangle +t_p$ to be the light crossing time $\triangle R/c$, where, $c$, denotes the speed of light." + Phe computation is carried out on a uniform Cartesian grid containing 128” cells with the source at one of he corners of the grid., The computation is carried out on a uniform Cartesian grid containing $^3$ cells with the source at one of the corners of the grid. + We start with /=2 giving 192 base ravs., We start with $l=2$ giving 192 base rays. + ‘To evaluate all arrival times 1.43.107 nrays were used., To evaluate all arrival times $1.4\tento{5}$ rays were used. + We used a homogeneous initial neutral hydrogen density of lem with a cubic obstacle of 10 times larger density aic a source with. a photonluminosityM of ⋅⇁Mp=I01Lsc., We used a homogeneous initial neutral hydrogen density of $1\cm^{-3}$ with a cubic obstacle of 10 times larger density and a source with a photon–luminosity of $N_P=10^{47}\s^{-1}$. + Contours in Figure 3 indicate the ionization [ron location at different times., Contours in Figure \ref{con} indicate the ionization front location at different times. + A two dimensional slice of the three dimensional volume through the position of the source is shown., A two dimensional slice of the three dimensional volume through the position of the source is shown. + The perfect shadowing is evident., The perfect shadowing is evident. + Compared. to nonadaptive rav tracing this new method is about 20 times faster in this test problem., Compared to non–adaptive ray tracing this new method is about 20 times faster in this test problem. + Using the tree for the integration led in our implementation to a further speed.up of a factor of two., Using the tree for the integration led in our implementation to a further speed–up of a factor of two. + Note. however. that larger speed:ups will be achieved in situations with large ονπαο range. where one can stop ravs that enter optically thick regions.," Note, however, that larger speed–ups will be achieved in situations with large dynamic range, where one can stop rays that enter optically thick regions." + ln summary we have presented a novel approach to simulate the effects. of radiative transfer. around. multiple point sources., In summary we have presented a novel approach to simulate the effects of radiative transfer around multiple point sources. + The use of adaptive ravs with a an inherent tree structure allows significant προσups in comparison to uniform ray tracing., The use of adaptive rays with a an inherent tree structure allows significant speed–ups in comparison to uniform ray tracing. + Although we have developed. it with applications to astrophysical hydrodynamics in. mind it is equally well suited for studying static situations ancl maw find application also for volume rendering in computer eraphics., Although we have developed it with applications to astrophysical hydrodynamics in mind it is equally well suited for studying static situations and may find application also for volume rendering in computer graphics. + The method. may also be. used. for extended emitting sources which are then modeled by a collection of point sources., The method may also be used for extended emitting sources which are then modeled by a collection of point sources. + lt seems clear that generalization of this method may be exploited. to speed. up Monte. Carlo radiative transfer techniques (e.g. Ciardi et al 2001 and references therein)., It seems clear that generalization of this method may be exploited to speed up Monte Carlo radiative transfer techniques (e.g. Ciardi et al 2001 and references therein). + lere one would start with fewer luminous photon packages at the source and split up the the packages to ensure similar number of packages to transverse the numerical eric on which the opacity is defined., Here one would start with fewer luminous photon packages at the source and split up the the packages to ensure similar number of packages to transverse the numerical grid on which the opacity is defined. + This should speec up the calculations significantly since again cells close to the source need not to be accessed more often than any other grid cells., This should speed up the calculations significantly since again cells close to the source need not to be accessed more often than any other grid cells. + The adaptive rav tracing scheme suggested. in this Letter. allows fast multiple integrations in the case of non-moving sources using a quadtree.," The adaptive ray tracing scheme suggested in this Letter, allows fast multiple integrations in the case of non-moving sources using a quad–tree." + Also. for a variety of woblems one may not always have to trace all ravs [rom he source to all other erid cells Cor particles).," Also, for a variety of problems one may not always have to trace all rays from the source to all other grid cells (or particles)." + For example. in the case of a thin ionization front penetrating into a high density medium the opacity changes only significantIy at the ront.," For example, in the case of a thin ionization front penetrating into a high density medium the opacity changes only significantly at the front." + Ravs need not to be traced far ahead of the front where most of their photons have been consumed., Rays need not to be traced far ahead of the front where most of their photons have been consumed. + Ravs close to the source may also not needed to be traced if heir (already low) opacity does not change significantly., Rays close to the source may also not needed to be traced if their (already low) opacity does not change significantly. + Dased on this one can formulate a scheme in which ravs carry their own opacity time step., Based on this one can formulate a scheme in which rays carry their own opacity time step. + As one integrates the, As one integrates the +to constrain values. of halo parameters such as Moog. or c for the NEW. profile (sce for example Brainerd οἱ al.,to constrain values of halo parameters such as $M_{200}$ or $c$ for the NFW profile (see for example Brainerd et al. + 1996: Lockstra et al., 1996; Hoekstra et al. + 2004. hereafter LEYG04 in this section: WWleinheinrich et al.," 2004, hereafter HYG04 in this section; Kleinheinrich et al." + 2005) have used measurements of shear exclusively., 2005) have used measurements of shear exclusively. + Recently Goldberg Bacon (2005) have shown that in many lensing scenarios the signal-to-noise ratio will be larger for the flexion aan for the shear at small (but still easily measurable) angular separations between source and lens., Recently Goldberg Bacon (2005) have shown that in many lensing scenarios the signal-to-noise ratio will be larger for the flexion than for the shear at small (but still easily measurable) angular separations between source and lens. + H is therefore =vorthwhile considering whether combining measurements of shear and flexion. might improve constraints for the halo parameters such as e or Moog derived. [rom measurements of shear alone., It is therefore worthwhile considering whether combining measurements of shear and flexion might improve constraints for the halo parameters such as $c$ or $M_{200}$ derived from measurements of shear alone. + In order to do this we construct a simplified bu illustrative mocel., In order to do this we construct a simplified but illustrative model. + We can generate mock data for a sample of lens and source galaxies such as might be available using current or forthcoming galaxy imaging surveys., We can generate mock data for a sample of lens and source galaxies such as might be available using current or forthcoming galaxy imaging surveys. + We mode lens halos as NEW. profiles. and (as in LYCOL) we assume we can scale cach lensing measurement in the sample to a fiducial mass Afooy or corresponding rest-frame B-hanc luminosity Lg using an observationally motivated. scaling relation between the two. such as that. proposed by Cuzil Seljak (2002).," We model lens halos as NFW profiles, and (as in HYG04) we assume we can scale each lensing measurement in the sample to a fiducial mass $M_{200}$ or corresponding rest-frame B-band luminosity $L_B$ using an observationally motivated scaling relation between the two, such as that proposed by Guzil Seljak (2002)." + In order to estimate the confidence limits we might reasonably expect from weak lensing measurements. we must consider the ellect of cllipticity ancl [Lexion of unlensed galaxies.," In order to estimate the confidence limits we might reasonably expect from weak lensing measurements, we must consider the effect of ellipticity and flexion of unlensed galaxies." +" We use values ol 5;,;=0.2 and Fi,=0.04 for the intrinsic shear ancl flexion in this model (c.f.", We use values of $\gamma_{int} = 0.2$ and $\flex_{int} = 0.04$ for the intrinsic shear and flexion in this model (c.f. + the intrinsic Lexion measured by Goldberg Bacon 2005)., the intrinsic flexion measured by Goldberg Bacon 2005). + ltedshift errors must also be considered: we assume for this simulation that we have access to photometric redshifts for each galaxy. with an uncertainty of As on cach individual redshift measurement (with values assigned below for broacl-band and mecdium-band. photometric redshift surveys).," Redshift errors must also be considered; we assume for this simulation that we have access to photometric redshifts for each galaxy, with an uncertainty of $\Delta +z$ on each individual redshift measurement (with values assigned below for broad-band and medium-band photometric redshift surveys)." +" We note (e.g. Wright. Brainerch 2000) that the streneth of the shear signal due to an NEW halo varies as ""NpwXDUDL/Di. whereas we found in Section 4.4. that the strength. of the Uexion varies as FpxpwXD?Di,D.."," We note (e.g. Wright Brainerd 2000) that the strength of the shear signal due to an NFW halo varies as $\gamma_{\rm NFW} \propto +D_lD_{ls}/D_s$, whereas we found in Section \ref{nfwsect} that the strength of the flexion varies as $\flex_{\rm NFW} \propto D^2_l +D_{ls}/D_s$." +" We thus model the error on measurements of the shear and Hexion due to redshift uncertainties by calculating errors on DiDi,/D, and D7Dj,/D, by numerical integration of terms such as where P(zj|z) and [ος2.) are the probability of measuring a redshift 2; or 24/ for a lens or source galaxy respectively. given that its true redshift is cy or ος."," We thus model the error on measurements of the shear and flexion due to redshift uncertainties by calculating errors on $D_l +D_{ls}/D_s$ and $D_l^2D_{ls}/D_s$ by numerical integration of terms such as where $P(z_l'|z_l)$ and $P(z_s'|z_s)$ are the probability of measuring a redshift $z_l'$ or $z_s'$ for a lens or source galaxy respectively, given that its true redshift is $z_l$ or $z_s$." + We moce these probability distributions as Gaussians with standi deviation zz. and assume a standard ACDAL cosmology (as in Section 4.4)).," We model these probability distributions as Gaussians with standard deviation $\Delta +z$, and assume a standard $\Lambda$ CDM cosmology (as in Section \ref{nfwsect}) )." + We therefore estimate the fractional error in a single measurement of shear and Iexion cue to redshif uncertainties (given an underlying z; and ος)., We therefore estimate the fractional error in a single measurement of shear and flexion due to redshift uncertainties (given an underlying $z_l$ and $z_s$ ). + While the size of these fractional errors depends upon each specific lens anc source redshift. for the purpose of this example we set them equal to the median lens and source redshifts for each mock sample we consider.," While the size of these fractional errors depends upon each specific lens and source redshift, for the purpose of this example we set them equal to the median lens and source redshifts for each mock sample we consider." + Note that while. i£. we had no redshit information. there would. be a Large scatter in the signa caused by not knowing the geometry of the lensing. this is drastically recluced with accurate photometric redshifts anc is assumed to be subdominant here.," Note that while, if we had no redshift information, there would be a large scatter in the signal caused by not knowing the geometry of the lensing, this is drastically reduced with accurate photometric redshifts and is assumed to be subdominant here." + For the fiducial virial halo mass we choose Afouy= (corresponding to a vest-Lrame L-boux," For the fiducial virial halo mass we choose $M_{200} = 1\times 10^{12} +h^{-1}M_{\odot}$ (corresponding to a rest-frame L-band" + For the fiducial virial halo mass we choose Afouy= (corresponding to a vest-Lrame L-bouxc," For the fiducial virial halo mass we choose $M_{200} = 1\times 10^{12} +h^{-1}M_{\odot}$ (corresponding to a rest-frame L-band" +As au illustration. a system Af; = 1 M. and AM» = 0.5 M. at ¢=68 degree would produce the observed A».,"As an illustration, a system $M_1$ = 1 $_{\odot}$ and $M_2$ = 0.5 $_{\odot}$ at $i = 68$ degree would produce the observed $K_2$." + Note that Lipkinetal.(2001) do not detect eclipses despite inteusive coverage., Note that \citet{lipkin04} do not detect eclipses despite intensive coverage. + Our spectrum appears similar to that published by Munuarietal.(1997)., Our spectrum appears similar to that published by \citet{munari97}. +.. We clearly detect au M-dwarf secondary., We clearly detect an M-dwarf secondary. + The gross period (Table 6)) is based on emission-liue velocities., The gross period (Table \ref{tab:parameters}) ) is based on emission-line velocities. + lt is uuambiguous. but the fine period is aliased ou a scale of one cycle per IY d due to uncertain cycle count between observing ruis: the allowed precise periods satisfy where the clenominator is au integer.," It is unambiguous, but the fine period is aliased on a scale of one cycle per 47 d due to uncertain cycle count between observing runs; the allowed precise periods satisfy where the denominator is an integer." + The cross-correlation tecliuuique was sensitive enough to measure M-dwarf velocities [or some of our spectra. but these were uot extensive or accurate enough to shed light ou the period: however. they did confirm that the Νανα light. is from the binary companion aud uot [rom an iuterloper.," The cross-correlation technique was sensitive enough to measure M-dwarf velocities for some of our spectra, but these were not extensive or accurate enough to shed light on the period; however, they did confirm that the M-dwarf light is from the binary companion and not from an interloper." + Combining our spectra into a siugle-trailed ereyscale representation confirmed tlie preseuce of secondary features: in particular. the Cal A 6122 absorption line appeared faintly. with a velocity semiamplitucde of ~170 km s...," Combining our spectra into a single-trailed greyscale representation confirmed the presence of secondary features; in particular, the CaI $\lambda$ 6122 absorption line appeared faintly, with a velocity semiamplitude of $\sim 170$ km $^{-1}$." + V31II Ori is at /=1957.05.06—0°.72. for which Schlegel.Finkbeiner.&Davis(1998) eive E(B—V)=1.138M to the edge of the Galaxy.," V344 Ori is at $l = 195^{\circ}.05, b = -0^{\circ}.72$, for which \citet{schlegel98} give $E(B-V) = 1.13$ to the edge of the Galaxy." + However. its spectrum shows neither diffuse interstellar bands nor interstellar NaD absorption. which would be expected if the reddening were this large.," However, its spectrum shows neither diffuse interstellar bands nor interstellar NaD absorption, which would be expected if the reddening were this large." + Standardized CBV observations taken 2008 Jau. 16.0 UT give V215.76. B—V=0.60. U—B——1.01. aud V—/=1.72.," Standardized $UBVI$ observations taken 2008 Jan. 16.0 UT give $V = 18.76$, $B-V = 0.60$ , $U-B = -1.01$, and $V - I = 1.72$." + At minimem light. dwarf novae typically have 8—V+0.1 aud U—B—(.5 (see. e.g.. Vogt 1983)): the very blue Ü—B suggests near-zero redcdeniug. while the redder E—V suggests E(B—V)—0.5.," At minimum light, dwarf novae typically have $B - V \sim +0.1$ and $U - B \sim -0.8$ (see, e.g., \citealt{vogt83}) ); the very blue $U-B$ suggests near-zero reddening, while the redder $B-V$ suggests $E(B-V) \sim 0.5$." + The poorly-coustrained reddening coutributes substantially to the distauce uncertainty (Table 7))., The poorly-constrained reddening contributes substantially to the distance uncertainty (Table \ref{tab:inferences}) ). + Jiangetal.(2000) obtained a spectrum of this ROSAT all-sky survey source that showed the broad emission lines ofa CV., \citet{jiangvzsex} obtained a spectrum of this ROSAT all-sky survey source that showed the broad emission lines of a CV. + Mennickentetal.(2002) obtainecl more exteusive spectrophotometry from which they ceduced a spectral type of M2 for the secondary., \citet{mennickent02} obtained more extensive spectrophotometry from which they deduced a spectral type of M2 for the secondary. + They also loud a radial-velocity periodieity that corroborated au early version of the period reported here., They also found a radial-velocity periodicity that corroborated an early version of the period reported here. + Nearly all our observations are from 2001 March. but we also have two velocities from 2000 April.," Nearly all our observations are from 2001 March, but we also have two velocities from 2000 April." + The period measured in 2001 March is not precise enough to extrapolate the cycle count to the previous year. but the extra data do coustrain the precise periodto a group of aliases which can be expressed as," The period measured in 2001 March is not precise enough to extrapolate the cycle count to the previous year, but the extra data do constrain the precise periodto a group of aliases which can be expressed as" +constrain any of these values without assumptions similar to those mentioned above.,constrain any of these values without assumptions similar to those mentioned above. + The results for determining the spin of the central black holes of the AGN in this sample suggest that the spin derived is very much dependent upon which interpretation of the KK line region is followed., The results for determining the spin of the central black holes of the AGN in this sample suggest that the spin derived is very much dependent upon which interpretation of the K line region is followed. +" Modelling the soft excess through an independent model such ascompTT tends to yield low to intermediate spin constraints for the objects in this sample, the exceptions being Ark 120 and MCG-02-14-009 in which only an upper limit could be placed."," Modelling the soft excess through an independent model such as tends to yield low to intermediate spin constraints for the objects in this sample, the exceptions being Ark 120 and MCG-02-14-009 in which only an upper limit could be placed." + The employment of this interpretation also yields low to intermediate emissivity indicies for the accretion discs (i.e. q~ 2)., The employment of this interpretation also yields low to intermediate emissivity indicies for the accretion discs (i.e. $q\sim2$ ). +" Modelling the 0.5-100.0kkeV spectrum with a blurred reflection component and no other modelling of the soft excess (i.e. Model E) gives particularly high values of both emissivity index and spin parameter, typically q24 and a=0.9, but these fits are statistically ruled out here."," Modelling the keV spectrum with a blurred reflection component and no other modelling of the soft excess (i.e. Model E) gives particularly high values of both emissivity index and spin parameter, typically $q\gtrsim4$ and $a\gtrsim0.9$, but these fits are statistically ruled out here." +" This is, however, only in objects featuring a soft excess."," This is, however, only in objects featuring a soft excess." +" In MCG-02-14-009, which has no obvious excess"," In MCG-02-14-009, which has no obvious excess" +The photomeson production takes place for photon energies above ει£145 MeV (measured in the rest-frame of the proton).,The photomeson production takes place for photon energies above $\epsilon_{\rm{th}} \approx 145$ MeV (measured in the rest-frame of the proton). +" Near the threshold, a single pion is produced per interaction; at higher energies, the production of multiple pions dominates."," Near the threshold, a single pion is produced per interaction; at higher energies, the production of multiple pions dominates." +" In our model, the relevant photons come from the corona and, to a lesser extent, from the accretion disk."," In our model, the relevant photons come from the corona and, to a lesser extent, from the accretion disk." +" The cooling rate due to photopion production for a proton of energy E, in an isotropic photon field of density nn(e) is E by (?) where ε’ is the photon energy in the rest-frame of the proton and Kp, is the inelasticity of the interaction."," The cooling rate due to photopion production for a proton of energy $E_{p}$ in an isotropic photon field of density $n_{\rm{ph}}(\epsilon)$ is given by \citep{stecker} + where $\epsilon'$ is the photon energy in the rest-frame of the proton and $K_{p\gamma}$ is the inelasticity of the interaction." +" ? introduced a simplified approach to treat the cross-section and the inelasticity, which can be written as and At energies below the threshold for photomeson production, the main channel of proton-photon interaction is the direct production of electrons or positrons."," \citet{atoyan} introduced a simplified approach to treat the cross-section and the inelasticity, which can be written as and At energies below the threshold for photomeson production, the main channel of proton-photon interaction is the direct production of electrons or positrons." +" The cooling rate is also given by Eq. (13)),"," The cooling rate is also given by Eq. \ref{eq:pgamma}) )," + and the corresponding cross-section and inelasticity., and the corresponding cross-section and inelasticity. + The cross-section for this channel -also known as the Bethe-Heitler cross-section- increases with the energy of the photon., The cross-section for this channel -also known as the Bethe-Heitler cross-section- increases with the energy of the photon. + Both the cross-section and inelasticity approximations in the limits of low and high energies can be found in ? (see Appendix A)., Both the cross-section and inelasticity approximations in the limits of low and high energies can be found in \citet{begelman} (see Appendix A). +" The mean lifetime of charged pions in their rest-frame is τη=2.6x107? s, and then they decay into muons and neutrinos; the mean lifetime of muons is —2.2x1079 s. They decay yielding neutrinos/anti-neutrinos and electrons/positrons."," The mean lifetime of charged pions in their rest-frame is $\tau_{\pi}=2.6\times10^{-8}$ s, and then they decay into muons and neutrinos; the mean lifetime of muons is $\tau_{\mu}=2.2\times 10^{-6}$ s. They decay yielding neutrinos/anti-neutrinos and electrons/positrons." +" In the observer frame, the decay rate is We consider two types of corona."," In the observer rest-frame, the decay rate is We consider two types of corona." +" One is an ADAF-like corona, where matter is advected to the black hole."," One is an ADAF-like corona, where matter is advected to the black hole." + This model was discussed in detail for Cygnus X-1 by ? and ?.., This model was discussed in detail for Cygnus X-1 by \citet{dove} and \citet{esin02}. +" In this case, particles fall onto the compact object at a mean radial velocity v=0.16, the free-fall velocity (?).."," In this case, particles fall onto the compact object at a mean radial velocity $v = 0.1c$, the free-fall velocity \citep{begelman}." +" Therefore, the convection rate is The other model considered here is a static corona (e.g., supported by magnetic fields, see ?)) where the relativistic particles can be removed by diffusion."," Therefore, the convection rate is The other model considered here is a static corona (e.g., supported by magnetic fields, see \citealt{beloborodov}) ) where the relativistic particles can be removed by diffusion." +" In the Bohm regime, the diffusion coefficient is D(E)=rgc/3, where rg=E/(eB) is the giroradius of the particle."," In the Bohm regime, the diffusion coefficient is $D(E)=r_{\rm{g}}c/3$, where $r_{\rm{g}}=E/(eB)$ is the giroradius of the particle." + The diffusion rate is 'The maximum energy that a relativistic particle can attain depends on the acceleration mechanism and the different processes of energy loss., The diffusion rate is The maximum energy that a relativistic particle can attain depends on the acceleration mechanism and the different processes of energy loss. +" The acceleration rate tj.E-dE|/dt for a particle of energy E in a magnetic field B, in a region where diffusive shock acceleration takes place, is given by where 7<1 is a parameter that characterizes the efficiency of the acceleration."," The acceleration rate $t^{-1}_{\rm{acc}}=E^{-1}dE/dt$ for a particle of energy $E$ in a magnetic field $B$, in a region where diffusive shock acceleration takes place, is given by where $\eta\leq1$ is a parameter that characterizes the efficiency of the acceleration." +" We fix η=1072, which describes the efficient acceleration by shocks with v,~0.16 in the Bohm regime."," We fix $\eta=10^{-2}$, which describes the efficient acceleration by shocks with $v_{\rm s}\sim 0.1c$ in the Bohm regime." +" Figure 2 shows the cooling rates for different energy-loss processes, together 13with the acceleration and escape rates, for each type of particle considered."," Figure \ref{fig:perdidas} shows the cooling rates for different energy-loss processes, together with the acceleration and escape rates, for each type of particle considered." +" Under the physical conditions previously described, the main channel of energy loss for electrons is synchrotron radiation."," Under the physical conditions previously described, the main channel of energy loss for electrons is synchrotron radiation." + Only for low-energy electrons IC losses are significant., Only for low-energy electrons IC losses are significant. +" For protons, both pp and py interactions are relevant."," For protons, both $pp$ and $p \gamma$ interactions are relevant." +" While diffusion has almost no effect on particle distributions, advection plays a decisive role in the behavior of protons: in the model with advection, most protons fall onto the black hole before radiating their energy."," While diffusion has almost no effect on particle distributions, advection plays a decisive role in the behavior of protons: in the model with advection, most protons fall onto the black hole before radiating their energy." + Itis possible to estimate the maximum energy achieved by the electrons equating whereas for protons wheremn a is ‘the timescale during which the relativistic particles escape from the system., It is possible to estimate the maximum energy achieved by the electrons equating whereas for protons where $t_{\rm{esc}}$ is the timescale during which the relativistic particles escape from the system. + This timescale is given by Eq. (15)), This timescale is given by Eq. \ref{eq:conv}) ) +" for models with convection, and by Eq. (16))"," for models with convection, and by Eq. \ref{eq:diff}) )" + for models with diffusion., for models with diffusion. +" The maximum energies obtained by electrons and protons are EX.&7.9x10? eV and EG.=~8.0x10! eV, respectively."," The maximum energies obtained by electrons and protons are $E_{\rm{max}}^{(e)}\approx 7.9\times 10^9$ eV and $E_{\rm{max}}^{(p)}\approx 8.0\times 10^{14}$ eV, respectively." +" These values are compatible with the Hillas criterion, given the size of the corona."," These values are compatible with the Hillas criterion, given the size of the corona." +" For pions, the main channel of energy loss is the my interaction, but an important fraction of these pions decay before cooling (those of lower energies)."," For pions, the main channel of energy loss is the $\pi \gamma$ interaction, but an important fraction of these pions decay before cooling (those of lower energies)." + Muons with energies above 10!? eV cool mostly by synchrotron radiation in models with a static corona., Muons with energies above $\sim 10^{13}$ eV cool mostly by synchrotron radiation in models with a static corona. +" The most energetic muons fall into the black hole, in all models with dominant convection."," The most energetic muons fall into the black hole, in all models with dominant convection." + The steady state particle distributions N(E) can be derived from the solution to the transport equation (?) where dB is the injection function.," The steady state particle distributions $N(E)$ can be derived from the solution to the transport equation \citep{ginzburg} + where $Q(E)$ is the injection function." +" The= corresponding— solution is where The injection= function for non-thermal protons and electrons is a powerlaw of the energy of the particles Q(E)= QogE-*e-P/Pw«, as a consequence of the diffusive particle acceleration by shock waves."," The corresponding solution is where The injection function for non-thermal protons and electrons is a powerlaw of the energy of the particles $Q(E)=Q_{0} E^{-\alpha}e^{-E/E_{\rm{max}}}$ , as a consequence of the diffusive particle acceleration by shock waves." + Following, Following +" x, ce Urn] Art Ax, (E).", = x + ) ] t + . + This last step uses the same diffusive step as in the predictor cycle but corrects the advective step using the predicted position X (see Eqn. 23))., This last step uses the same diffusive step as in the predictor cycle but corrects the advective step using the predicted position $\bar{x}$ (see Eqn. \ref{pstep}) ). + This is a reasonable approach as (on average) Avg2Ax.adc, This is a reasonable approach as (on average) $\Delta x_{\rm diff} \gg \Delta x_{\rm adv}$. + Tt was already noted by Marcowith Kirk (1999) that a careful treatment of the advective step (including drift) is more important for the accuracy of the scheme than the treatment of the diffusive step., It was already noted by Marcowith Kirk (1999) that a careful treatment of the advective step (including drift) is more important for the accuracy of the scheme than the treatment of the diffusive step. + This scheme and the tests presented below bear that out., This scheme and the tests presented below bear that out. + A few remarks about the implementation of this scheme are in order., A few remarks about the implementation of this scheme are in order. + First of all. this scheme is computationally about 6 times more expensive than the Cauchy-Euler scheme.," First of all, this scheme is computationally about 6 times more expensive than the Cauchy-Euler scheme." + An order-of-magnitude increase of the computational etfort is typical when switching from an explicit. first-order scheme to a second-order accurate predictor-corrector scheme or the closely related Runge-Kutta type schemes.," An order-of-magnitude increase of the computational effort is typical when switching from an explicit, first-order scheme to a second-order accurate predictor-corrector scheme or the closely related Runge-Kutta type schemes." +" Secondly: for the term that corrects for diffusivity gradients to be ettective one should employ an often-used numerical approximation for the Wiener process that replaces the normal distribution for £ by a two-point disribution of values. choosing £,=+1. where the two yossible signs are drawn randomly with equal probability P,=οLl."," Secondly: for the term that corrects for diffusivity gradients to be effective one should employ an often-used numerical approximation for the Wiener process that replaces the normal distribution for $\xi_{t}$ by a two-point distribution of values, choosing $\xi_{t} = \pm 1$, where the two possible signs are drawn randomly with equal probability ${\cal P}_{+} = {\cal P}_{-} = \half$." + In that numerical approximation for the Wiener process the second term in the expression (25)) vanishes identically. and much of the scheme's improved accuracy with respect to the Cauchy-Euler scheme is lost.," In that numerical approximation for the Wiener process the second term in the expression \ref{barDiff}) ) vanishes identically, and much of the scheme's improved accuracy with respect to the Cauchy-Euler scheme is lost." +" In that respect one might expect that a symmetric three-value scheme for &,. for example tin the notation [value probability] Ius |r. peine works better."," In that respect one might expect that a symmetric three-value scheme for $\xi_{t}$ , for example (in the notation $[value \: | \: probability]$ ) | ], ], | ], works better." + We have tested the KPPC scheme as described here. comparing its performance to the performance of the simpler Cauchy-Euler scheme.," We have tested the KPPC scheme as described here, comparing its performance to the performance of the simpler Cauchy-Euler scheme." +" For this test we use scaled (dimensionless) variables where the fluid velocity V. is measured in units of the shock speed and position x along the shock normal is in units of the shock thickness L, For clarity we keep £L, in the equations even though £L,=| in the numerical implementation.", For this test we use scaled (dimensionless) variables where the fluid velocity $V$ is measured in units of the shock speed and position $x$ along the shock normal is in units of the shock thickness $L_{\rm s}$ For clarity we keep $L_{\rm s}$ in the equations even though $L_{\rm s} = 1$ in the numerical implementation. + The velocity VGo is in the direction of positive x. given by Vix) unici m," The velocity $V(x)$ is in the direction of positive $x$ , given by V(x) = - ( )." + The velocity decreases with increasing ας from V{-co)= to νο)=V»ας.," The velocity decreases with increasing $x$, from $V(-\infty) \equiv V_{1} = 1$ to $V(+ \infty) \equiv V_{2} = 1/r$." + This means that we work in the rest frame of the shock and measure the flow velocity in units of the shock velocity with respect of the upstream medium., This means that we work in the rest frame of the shock and measure the flow velocity in units of the shock velocity with respect of the upstream medium. + Here r>| is the compression ratio of the shock transition in the sense that (for this one-dimensional steady flow) the conservation of mass implies py=constant. with the mass density.," Here $r > 1$ is the compression ratio of the shock transition in the sense that (for this one-dimensional steady flow) the conservation of mass implies $\rho V = {\rm constant}$, with $\rho$ the mass density." + The density contrast between the far upstream and far downstream state follows as This velocity profile models the shock as a stationary and smooth transition. with a width (velocity gradient scale) ἐς.," The density contrast between the far upstream and far downstream state follows as = = r. This velocity profile models the shock as a stationary and smooth transition, with a width (velocity gradient scale) $L_{\rm s}$ ." + To model a varying diffusion coetflicient we adopt a diffusion coethcient that varies with position .v as Dt) ο., To model a varying diffusion coefficient we adopt a diffusion coefficient that varies with position $x$ as D(x) = - ( ) ]. +" Here D, is a constant dimensionless ditfusivity that is related to the physical diffusivity δν. far ahead of the shock by D,=Duy,/LV, with V, the shock velocity.", Here $D_{1}$ is a constant dimensionless diffusivity that is related to the physical diffusivity $D_{\rm phys}$ far ahead of the shock by $D_{1} = D_{\rm phys}/L_{s} V_{s}$ with $V_{s}$ the shock velocity. + The ditfusivity decreases if one moves from upstream Cx<0) to downstream Cv>0) across the shock. with a ratio of asymptotic values equal to————— the kind of behavior one expects in astrophysical applications.," The diffusivity decreases if one moves from upstream $x < 0$ ) to downstream $x > 0$ ) across the shock, with a ratio of asymptotic values equal to = 1 , the kind of behavior one expects in astrophysical applications." + The seale length for the variation of the diffusion coetficient in these units is of order Ly., The scale length for the variation of the diffusion coefficient in these units is of order $L_{\rm d}$. + For future use we define the quantity c, For future use we define the quantity =. + This is essentially thenumber of the shock based on the cosmic ray ditfusivity., This is essentially the of the shock based on the cosmic ray diffusivity. + In terms of this quantity one has , In terms of this quantity one has | |. +A sharp shockin the present context corresponds to 5«I., A sharp shockin the present context corresponds to $\varepsilon \ll 1$. +" The main test of the algorithm lies in its ability © reproduce the spectrum predicted by the analytical theory of DSA at a steady shock with e« ση and L,=Ly."," The main test of the algorithm lies in its ability to reproduce the spectrum predicted by the analytical theory of DSA at a steady shock with $\varepsilon \ll 1$, $\sigma \simeq r$ and $L_{\rm s} \simeq L_{\rm d}$." + In the limit of a infinitely thin shock with &=0 tin physical terms: a shock thickness that is much smaller than the scattering mean free path of the accelerating cosmic rays) and in the absence of radiation losses the predicted shape of the spectrum is a power law in momentum. with an index g that depends only on the compression ratio r (e.g. Axford. Leer Skadron. 1977. Bell. 1978: Blandford Ostriker. 1978).," In the limit of a infinitely thin shock with $\varepsilon =0$ (in physical terms: a shock thickness that is much smaller than the scattering mean free path of the accelerating cosmic rays) and in the absence of radiation losses the predicted shape of the spectrum is a power law in momentum, with an index $q$ that depends only on the compression ratio $r$ (e.g. Axford, Leer Skadron, 1977, Bell, 1978; Blandford Ostriker, 1978)." + In present notation. using the momenum p rather than v=Intp/nmc Nix p-2dNpsp ο esism:—.," In present notation, using the momentum $p$ rather than $y = \ln(p/mc)$: N(x, p) = , = 0) =." + In our tests of the algorithm we have assumed a diffusion coethcient that is independent of particle momentum. so this power-law behavior is valid uniformly across the grid. with only the concentration of test particles varying with position x.," In our tests of the algorithm we have assumed a diffusion coefficient that is independent of particle momentum, so this power-law behavior is valid uniformly across the grid, with only the concentration of test particles varying with position $x$." + Since we assume a finite shock thickness. a situation. typical of shocks obtained through numerical simulation. we need an expression for the slope g for finite e.," Since we assume a finite shock thickness, a situation typical of shocks obtained through numerical simulation, we need an expression for the slope $q$ for finite $\varepsilon$ ." + We use a perturbation analysis adapted from Drury (1983) and the closely related method of Schneider Kirk(1987)., We use a perturbation analysis adapted from Drury (1983) and the closely related method of Schneider Kirk(1987). + The analysis presented below isvalid when there is a small parameter &. in this case the ratio ofthe shock thickness and the cosmic ray diffusion length:," The analysis presented below isvalid when there is a small parameter $\varepsilon$ , in this case the ratio ofthe shock thickness and the cosmic ray diffusion length: 1 ." +Galaxy (90? = 35$ at $\=3 \Rg$. + For this temperature the average energy amplification per scattering is 124-40.41607zz1.9x101. consistent with the seed photons with energies LotHy (11jn>A2.9 pm).," For this temperature the average energy amplification per scattering is $1 + +4\Theta_e + 16 \Theta_e^2 \approx 1.9 \times 10^4$, consistent with the seed photons with energies $2.5 \times 10^{13} < \nu < 10^{14} \Hz$ $11 +{\rm \mum} > \lambda > 2.9 {\rm \mum}$ )." + This means that many of the seed photons are produced in current sheets. ancl so some uncertainty attaches to the Compton scattered πας.," This means that many of the seed photons are produced in current sheets, and so some uncertainty attaches to the Compton scattered flux." + We know observational thal pproduces frequent flares with fluxes larger than those produced by our quiescent-source moclel. so there is a source of seed photons in (his energy band. albeit a f[Inctuating one.," We know observationally that produces frequent flares with fluxes larger than those produced by our quiescent-source model, so there is a source of seed photons in this energy band, albeit a fluctuating one." +" A small fraction of photons are emitted [rom the funnel wall at large radii /c) where the gas temperature is O,~10%."," A small fraction of photons are emitted from the funnel wall at large radii $15-40 \Rg$ ) where the gas temperature is $\Theta_e \sim +10^3$." + This is also likely an artifact of the inability of aand similar codes to track the internal energy of a fhud when the internal energy is much smaller than the other energy density scales., This is also likely an artifact of the inability of and similar codes to track the internal energy of a fluid when the internal energy is much smaller than the other energy density scales. + Nevertheless. this raises (he interesting cuestion ol what the electron distribution functionshould be in the funnel.," Nevertheless, this raises the interesting question of what the electron distribution function be in the funnel." + High energy electrons might be naturally generated within (his tenuous plasma bv steepening of MIID. waves excited by turbulence near the equatorial plane., High energy electrons might be naturally generated within this tenuous plasma by steepening of MHD waves excited by turbulence near the equatorial plane. + In Figure 4.. we present averaged spectra for models wilh different spins (referred to as A. D. €. D. E and F: see Tables 1.. 2.. and 3)). inclination angles 7=85deg.45deg and 5deg in (he upper. middle and bottom panels. respectively ancl temperature ratio 77/7.=1.3. and 10 from left to right.," In Figure \ref{fig:3}, we present averaged spectra for models with different spins (referred to as A, B, C, D, E and F; see Tables \ref{tab:1}, \ref{tab:2}, and \ref{tab:3}) ), inclination angles $i=85\deg, 45\deg$ and $5\deg$ in the upper, middle and bottom panels, respectively and temperature ratio $\Trat = 1, 3,$ and $10$ from left to right." + All SEDs are averaged over time and runs as described in 3.., All SEDs are averaged over time and runs as described in \ref{sec:3}. + The tables indicate whether the model is consistent with observations., The tables indicate whether the model is consistent with observations. + The model can fail in one of four ways: db can produce the wrong submillimeter spectral slope o: it can overproduce the quiescent NUR flux: it can overproduce the quiescent X-ray flux: ancl it can be too large al 230GIIz to be consistent with the VLBI data., The model can fail in one of four ways: it can produce the wrong submillimeter spectral slope $\alpha$ ; it can overproduce the quiescent NIR flux; it can overproduce the quiescent X-ray flux; and it can be too large at $230\GHz$ to be consistent with the VLBI data. + The last constraint we will discuss separately in (he next section., The last constraint we will discuss separately in the next section. +It may be useful to recall that M is adjusted in each,It may be useful to recall that $\munit$ is adjusted in each +harmonics.,harmonics. + Only terms satisfying the following two conditions contribute to the sum in Eq. (8)):, Only terms satisfying the following two conditions contribute to the sum in Eq. \ref{eq:multipoles}) ): + and. The coefficients are given by the relation. (c.f..," and, The coefficients are given by the relation, (c.f.," + Messiah 1962 and the Appendix)., Messiah 1962 and the Appendix). + As 1n Paper L the scattering factors can be expressed as and so that. upon substitution in the integrals contained in Eq. (1)).," As in Paper I, the scattering factors can be expressed as and so that, upon substitution in the integrals contained in Eq. \ref{eq:stokes}) )," +" together with the other expressions above. and using the properties of spherical harmonies. £F, and Z can be rewritten as: and where Thus. the scattered flux and the Stokes parameters can be expressed as sums of increasing order of multipole contribution."," together with the other expressions above, and using the properties of spherical harmonics, $F_{\rm sc}$ and $Z^*$ can be rewritten as: and where Thus, the scattered flux and the Stokes parameters can be expressed as sums of increasing order of multipole contribution." +" This helps to separate the effects of anisotropy in the flux F and in the density distribution ή, and to study how they can lead to the production of polarization."," This helps to separate the effects of anisotropy in the flux $F$ and in the density distribution $n$, and to study how they can lead to the production of polarization." +" If the functions are smooth. the summations will converge rapidly. so the first few terms (/ and /""€ 2) should provide reasonable approximations for the behavior of the polarization."," If the functions are smooth, the summations will converge rapidly, so the first few terms $l$ and $l' \le 2$ ) should provide reasonable approximations for the behavior of the polarization." +frou «1lU0vr for à 8M star to co3x10* vr for a lMg (ee eg. 21).,"from $<$ $\,$ yr for a $\,$ star to $\sim\,$ $\times$ $^4$ yr for a $\,$ (see e.g. \citealt{villaver02}) )." + Ny(m) stauds for the number of stars of the mass rm currently present in the GC population., $N_{*}(m)$ stands for the number of stars of the mass $m$ currently present in the GC population. + 7 present the Ik-baud luminosity function (LE) resulting from deep observations of the several IIST/NICMOS fields in the GC region., \citet{figer04} present the K-band luminosity function (LF) resulting from deep observations of the several HST/NICMOS fields in the GC region. + To estimate the stellar counts at the faint cud of the LF. we fit a powcr aw to the uumber counts in the range Ezzl16.5 19.5. where the data are reasonably complete.," To estimate the stellar counts at the faint end of the LF, we fit a power law to the number counts in the range $\approx$ 16.5–19.5, where the data are reasonably complete." + We also attempt to correct for the conipleteuness using the data from ?.., We also attempt to correct for the completeness using the data from \citet{figer99}. + By fittine the LF in his ranee5 we avoid the red clamp population. but also the xopulatiou of massive bright stars that domunate the LE in the central parsec.," By fitting the LF in this range we avoid the red clump population, but also the population of massive bright stars that dominate the LF in the central parsec." + For scaling. we use the observed (completeness corrected) nuniber counts in the ceutral )nrsec. at I&— 17 (?).. while accounting for the different uaeuitude bin sizes in ? aud ?..," For scaling, we use the observed (completeness corrected) number counts in the central parsec, at $\,$ $\,$ 17 \citep{schoedel07}, while accounting for the different magnitude bin sizes in \citet{schoedel07} and \citet{figer04}." + This results in probability of ~ 1095 to find oue PNe within this region., This results in probability of $\sim$ $\%$ to find one PNe within this region. + We observe wo sources m a nmch smaller volume. which makes it less ikelv that they are both of the same short-liviug type.," We observe two sources in a much smaller volume, which makes it less likely that they are both of the same short-living type." + This speaks in favor of N3 actually being a dust feature., This speaks in favor of X3 actually being a dust feature. + The aliguinenut of the two features is still not explained., The alignment of the two features is still not explained. + Iu case of an isotropic Wind arising frou the mass-Iosiug stars. one would expect a iore random distribution of such sources around the center.," In case of an isotropic wind arising from the mass-losing stars, one would expect a more random distribution of such sources around the center." + Curiously. the two sources are arranged in the exact direction in which the miui- is projected onto the sky.," Curiously, the two sources are arranged in the exact direction in which the mini-cavity is projected onto the sky." + Tf we do not think of this arrangement as a chance coufieuration. this might indicate that (2) all three features (X3. NT ancl tle wini-cavity) are produced by the same event. and (4) there is a preferential direction in which the mass is expelled at the GC.," If we do not think of this arrangement as a chance configuration, this might indicate that $(i)$ all three features (X3, X7 and the mini-cavity) are produced by the same event, and $(ii)$ there is a preferential direction in which the mass is expelled at the GC." + The vosstbility of a collimated outflow was already discussed by ?.., The possibility of a collimated outflow was already discussed by \citet{muzic07}. + This outflow could also account or narrow dust fibbuueuts of the Northern Ax ofthe iuiui-PAoral. as well as the ITa-brieght lobes of the circiun-unuclear aisc (CND).," This outflow could also account for narrow dust filaments of the Northern Arm of the mini-spiral, as well as the $_2$ -bright lobes of the circum-nuclear disc (CND)." + As the authors argue. the outflow could be inked to the plane of the mass-losiue stars iu he way iat the matter provided by stars and not accreted onto À* is expelled perpendicular to the plane.," As the authors argue, the outflow could be linked to the plane of the mass-losing stars in the way that the matter provided by stars and not accreted onto $\,$ A* is expelled perpendicular to the plane." + Waving an pene auele of about 30°. this outflow could account for 1ο nini-cavitv. N3 and N7 at the same time.," Having an opening angle of about $^{\circ}$ , this outflow could account for the mini-cavity, X3 and X7 at the same time." + In this case N3 and X7 should be located not too far away from the lane containing A*. which is already suggested by the Yeh inchnation (12290?) of the two bow shocks to the line of sight resulting from our modeclue.," In this case X3 and X7 should be located not too far away from the plane containing $\,$ A*, which is already suggested by the high inclination $\approx$ $^{\circ}$ ) of the two bow shocks to the line of sight resulting from our modeling." + We have preseuted L-baud observations of the two cometarv-xhaped sources in the vicinity of À*. namic’ N3 and XT.," We have presented L'-band observations of the two cometary-shaped sources in the vicinity of $\,$ A*, named X3 and X7." + The svuuuetrv axes of the two sources are aligned within 5° iu the plane of the sky anc the tips of their bow-shocks point towards A*.," The symmetry axes of the two sources are aligned within $^{\circ}$ in the plane of the sky and the tips of their bow-shocks point towards $\,$ A*." + Our nieasurenients show that the proper motion vectors of both features ave pointing in directions more than 15? away from the line that connects them with À*.," Our measurements show that the proper motion vectors of both features are pointing in directions more than $^{\circ}$ away from the line that connects them with $\,$ A*." + Proper motion velocities are high. of the order of several 1001s.," Proper motion velocities are high, of the order of several $\,$ $\,$ $^{-1}$." + This uisalicuiment of the bow-shock sviunietry axes and their proper motion vectors. togetler with high proper motions. sugeest that the bow-shocks must be produced by an interaction with some external strong wind. possibly comune from A*. or stars in its vicinity.," This misalignment of the bow-shock symmetry axes and their proper motion vectors, together with high proper motions, suggest that the bow-shocks must be produced by an interaction with some external strong wind, possibly coming from $\,$ A*, or stars in its vicinity." + We have developed a bow-shock model iu order to fit the observed morphology and constrain the source of the external wind., We have developed a bow-shock model in order to fit the observed morphology and constrain the source of the external wind. + The stellar types of the wo stars are not known., The stellar types of the two stars are not known. + Moreover. oue of the features is likely not a star. but just a dust structure.," Moreover, one of the features is likely not a star, but just a dust structure." + It might © located at the edge of the müuicavitv. aud shaped * the same wind that produces the X7 bow-shock.," It might be located at the edge of the mini-cavity, and shaped by the same wind that produces the X7 bow-shock." + We discuss the nature of the exterual wiud aud show that wither one of the features can arise via interaction with an external wind originating from a sinele. mass-losine star.," We discuss the nature of the external wind and show that neither one of the features can arise via interaction with an external wind originating from a single, mass-losing star." + Tustead. the observed properties of the bow-shocks xovide evidence for interaction with a fast and strong wind produced probably by au eusenible of miass-losine sources.," Instead, the observed properties of the bow-shocks provide evidence for interaction with a fast and strong wind produced probably by an ensemble of mass-losing sources." + Alternatively. a possible source of the wind could ο A*.," Alternatively, a possible source of the wind could be $\,$ A*." + Shock velocities that can result from such a colmbined outflow over a distance assumed for the two catures X3 and X7. match the velocities. required ) xoduce the bow shocks of stis in the late evolution stages of CSPNe or [WC|-stirs.," Shock velocities that can result from such a combined outflow over a distance assumed for the two features X3 and X7, match the velocities required to produce the bow shocks of stars in the late evolution stages of CSPNe or [WC]-stars." + Short lifetimes of such stars can explain the lack of other simular cometary sources in the central parsec., Short lifetimes of such stars can explain the lack of other similar cometary sources in the central parsec. + We diseuss our results in the light of the partially-collmmated outflow already proposed in? and argue that such au outflow. arising perpendicular to the CAS. can account for N3 aud XT. as well as for the nuini-," We discuss our results in the light of the partially-collimated outflow already proposed in \citet{muzic07} and argue that such an outflow, arising perpendicular to the CWS, can account for X3 and X7, as well as for the mini-cavity." + The collective wind from the CWS has a scale of ~ LO aresee., The collective wind from the CWS has a scale of $\sim$ 10 arcsec. + On scales of about an arcsecond or less theoretical studies predict a radius-depeudent accretion flow (e.g.?7)..," On scales of about an arcsecond or less theoretical studies predict a radius-dependent accretion flow \citep[e.g.][]{narayan98, yuan03}." + Within this region the flow of a major portion of the material originally bound for accretion onto A* isinverted aud the material is expelled again towards larger radi.," Within this region the flow of a major portion of the material originally bound for accretion onto $\,$ A* isinverted and the material is expelled again towards larger radii." + The presence of a strong outbound wind at projected distances frou A* of only 0.87 (X7) with a mass load of LOT? ," The presence of a strong outbound wind at projected distances from $\,$ A* of only 0.8"" (X7) with a mass load of $^{-3}$ " +We provide hieh temperature line lists for NIL; using a similar approach to (hat of (2003): in addition we derive empirical lower state energies lor many of the lines.,We provide high temperature line lists for $_{3}$ using a similar approach to that of \citet{nassar03}; in addition we derive empirical lower state energies for many of the lines. + The line lists can be used directly to model the SEDs of brown cwarls leading to a better understanding of the T-/Y-dwarf boundary. and perhaps allow the first identification of NIL; in an exoplanet atmosphere., The line lists can be used directly to model the SEDs of brown dwarfs leading to a better understanding of the T-/Y-dwarf boundary and perhaps allow the first identification of $_{3}$ in an exoplanet atmosphere. +The inner regions of the Milky Way have been mapped thoroughly at all wavelengths.,The inner regions of the Milky Way have been mapped thoroughly at all wavelengths. + Yet. it is not known if there are still some distant globular clusters awaiting to be discovered. hidden beyond the bulge. due to the high density of stellar sources and the large and inhomogeneous interstellar extinction.," Yet, it is not known if there are still some distant globular clusters awaiting to be discovered, hidden beyond the bulge, due to the high density of stellar sources and the large and inhomogeneous interstellar extinction." + Near-IR surveys have an advantage for searching these regions., Near-IR surveys have an advantage for searching these regions. + Indeed. the 2MASS discovered two new globular clusters (?)..," Indeed, the 2MASS discovered two new globular clusters \citep{Hurt}." + But the limiting magnitude of 2MASS (ΚςΞ14.3. for10c-detections: may prevent the discovery of fainter objects. especially if they are located in highly reddened regions.," But the limiting magnitude of 2MASS \citep[$K_{\rm S}$ $=14.3, for $\sigma$ may prevent the discovery of fainter objects, especially if they are located in highly reddened regions." + The asymmetry of the spatial distribution of known globular clusters around the Galactic center indicates that previous observations may have overlooked some additional globular clusters., The asymmetry of the spatial distribution of known globular clusters around the Galactic center indicates that previous observations may have overlooked some additional globular clusters. + ? recently estimated that there may be about 10 clusters missing towards the inner Milky Way., \cite{Ivanov2005} recently estimated that there may be about 10 clusters missing towards the inner Milky Way. + The recent discoveries (last 10 years) include both faint dow mass) halo clusters as well as reddened globular clusters projected toward the bulge. e.g. 2MASS GCOI and 2MASS GCO2 by ? also ?).. ESO 280 SCO06 by ?.. GLIMPSE COL by Kobulnicky et al. (," The recent discoveries (last 10 years) include both faint (low mass) halo clusters as well as reddened globular clusters projected toward the bulge, e.g. 2MASS GC01 and 2MASS GC02 by \cite{Hurt} \citep[see also][]{Ivanov2000}, ESO 280 SC06 by \cite{Ortolani2000}, GLIMPSE C01 by Kobulnicky et al. (" +2005: but see also Ivanov et al.,2005; but see also Ivanov et al. + 2005: Davies et al., 2005; Davies et al. + 2010). GLIMPSE C02 by ?.. AL-3 by ?.. FSR 1735 by ?.. Koposov I and Koposov 2 by ?.. FSR 1767 by ?.. Whiting 1 (?) and Pfleiderer 2 by ?..," 2010), GLIMPSE C02 by \cite{Kurtev}, AL-3 by \cite{Ortolani2006}, FSR 1735 by \cite{Froebrich}, Koposov 1 and Koposov 2 by \cite{koposov07}, FSR 1767 by \cite{Bonatto}, Whiting 1 \citep[][]{carraro05} and Pfleiderer 2 by \cite{Ortolani2009}." + The VISTA Variables in the Via Lactea (VVV) Public Survey has started mapping the inner disk and bulge of our Galaxy with VISTA 4m telescope (Visible and Infrared Survey Telescope for Astronomy) in the near-IR (??)..," The VISTA Variables in the Via Lactea (VVV) Public Survey has started mapping the inner disk and bulge of our Galaxy with VISTA 4m telescope (Visible and Infrared Survey Telescope for Astronomy) in the near-IR \citep{Minniti,Saito}." + One of the main scientific goals of the VVV Survey is to study the bulge globular clusters and to search for new clusters., One of the main scientific goals of the VVV Survey is to study the bulge globular clusters and to search for new clusters. + Here we present VVV CLOOI. the first globular cluster candidate discovered by the VVV Survey.," Here we present VVV CL001, the first globular cluster candidate discovered by the VVV Survey." + The VVV Survey data are acquired with the VISTA 4m telescope at ESO Paranal Observatory (?).., The VVV Survey data are acquired with the VISTA 4m telescope at ESO Paranal Observatory \citep[][]{Emerson}. + The VVV field b351 was observed in the ΗΚς bands under subaresee seeing conditions (0.8 aresec in As)., The VVV field b351 was observed in the $JHK_{\rm S}$ bands under subarcsec seeing conditions $0.8$ arcsec in $K_{\rm S}$ ). + The YZ- band observations are still pending., The YZ- band observations are still pending. + Each one of the VVV fields (tiles) covers 1.636deg? in total (1.475? in / by 1.109° in 5)., Each one of the VVV fields (tiles) covers $1.636\deg^{2}$ in total $1.475^\circ$ in $l$ by $1.109^\circ$ in $b$ ). +" The bulge field b351 observed here is centered at &=17:5005.42. ó= -23:43:106.7.[24.9877. b=1.838"","," The bulge field b351 observed here is centered at $\alpha=17:50:05.42$, $\delta=-23:43:16.7$, $l=4.987^\circ$, $b=1.838^\circ$." + We use here the images processed by CASU. VIRCAM pipeline v1.0 (e.g.2).., We use here the images processed by CASU VIRCAM pipeline v1.0 \citep[e.g.][]{irwin04}. + The photometry was obtained with DoPhot (2)., The photometry was obtained with DoPhot \citep{Schechter}. + Also. the photometry is uniformly calibrated against the 2MASS catalog (2)..," Also, the photometry is uniformly calibrated against the 2MASS catalog \citep{Skrutskie06}." + The limiting magnitude of the single epoch VVV images is Ks=18.1 in the bulge fields (for details on the observing strategy. see Minniti et al.," The limiting magnitude of the single epoch VVV images is $Ks=18.1$ in the bulge fields (for details on the observing strategy, see Minniti et al." + 2010)., 2010). + The distance probed along the line of sight depends on the reddening of the fields., The distance probed along the line of sight depends on the reddening of the fields. + For example. in zero reddening disk fields we would see horizontal branch red clump beyond 50 kpe.," For example, in zero reddening disk fields we would see horizontal branch red clump beyond 50 kpc." + Therefore we can search for distant galactie globular clusters and measure their physical parameters., Therefore we can search for distant galactic globular clusters and measure their physical parameters. + Visual inspection. of the images of the field b351 led to the serendipitous discovery of a star cluster candidate that we name VVV 01001., Visual inspection of the images of the field b351 led to the serendipitous discovery of a star cluster candidate that we name VVV CL001. + This object is located in the vicinity of the known globular cluster UKS 1 (Figure 1))., This object is located in the vicinity of the known globular cluster UKS 1 (Figure \ref{fig1}) ). + Based on near infrared stellar density maps (see Figure 2)) we conclude that this is not a statistical fluctuation of the background. and that the cluster VVV CLOOI is centered at e=17:54 42.5.," Based on near infrared stellar density maps (see Figure \ref{density}) ) we conclude that this is not a statistical fluctuation of the background, and that the cluster VVV CL001 is centered at $\alpha=17:54:42.5$ ," +error circle of the EGRET source. 31561. 2033|4188.,error circle of the EGRET source 3EG J2033+4188. + llowever. no connection between the EGIT source and the TeV signal has vet been confirmed.," However, no connection between the EGRET source and the TeV signal has yet been confirmed." + Lt has been shown that GeV photons can be produced in the pulsar magnetosphere in outer gap mocdels (Cheng et al., It has been shown that GeV photons can be produced in the pulsar magnetosphere in outer gap models (Cheng et al. + 1986: Zhang Cheng 1997)., 1986; Zhang Cheng 1997). + A revised outer gap model (Zhang ct al., A revised outer gap model (Zhang et al. + 2004) takes into account the elfect of the inclination angle a between the magnetic axis and the rotational axis. which can determine the gap size of the outer gap.," 2004) takes into account the effect of the inclination angle $\alpha$ between the magnetic axis and the rotational axis, which can determine the gap size of the outer gap." + This allows some pulsars with appropriate combinations of a.P? and D. to maintain the outer gap for at least ~Q vears.," This allows some pulsars with appropriate combinations of $\alpha, P$ and $B$, to maintain the outer gap for at least $\sim~10^6$ years." + Their advanced ages allow these pulsars enough time to move up to high Galactic latitudes as weak ~-ray sources., Their advanced ages allow these pulsars enough time to move up to high Galactic latitudes as weak $\gamma$ -ray sources. + This leads Cheng et al. (, This leads Cheng et al. ( +2004a) to propose that mature + - pulsars with ages 10° vears can contribute to he unidentified ECGIU. sources.,2004a) to propose that mature $\gamma$ -ray pulsars with ages $\sim 10^5-10^6$ years can contribute to the unidentified EGRET sources. + These mature pulsars also remain active in producing relativistic wind. particles. and orm compact wind nebulae.," These mature pulsars also remain active in producing relativistic wind particles, and form compact wind nebulae." + In addition. Γον) photons can »e created in the nebulae through the LCS process.," In addition, TeV photons can be created in the nebulae through the ICS process." + In this paper. we study the possible connection between TeV > -ray sources and the Unidentilied EGRET sources.," In this paper, we study the possible connection between TeV $\gamma$ -ray sources and the Unidentified EGRET sources." + We do not snow if the Unidentified EGRET sources are pulsars: even if they are pulsars we still do not. know their. properties. i.c. period. magnetic field. inclination. angle. distance etc.," We do not know if the Unidentified EGRET sources are pulsars; even if they are pulsars we still do not know their properties, i.e. period, magnetic field, inclination angle, distance etc." + Without these parameters we cannot calculate their οταν operties., Without these parameters we cannot calculate their $\gamma$ -ray properties. + Fherefore. we apply a statistical approach using Monte Carlo simulation to study the Unidentified Cammma-rav EGRET Sources.," Therefore, we apply a statistical approach using Monte Carlo simulation to study the Unidentified Gamma-ray EGRET Sources." + First we will simulate the galactic »ulsar population ancl use the outer gap mocdel to calculate he MeV-GeV photon power from these simulated: pulsars., First we will simulate the galactic pulsar population and use the outer gap model to calculate the MeV-GeV photon power from these simulated pulsars. + We have ignored. the contribution from the polar gap for simplicity., We have ignored the contribution from the polar gap for simplicity. + We can determine which simulated. pulsars can »j detected by EGRET in 5-ravs: we call them οταν loud pulsars., We can determine which simulated pulsars can be detected by EGRET in $\gamma$ -rays; we call them $\gamma$ -ray loud pulsars. + “Phe next step is to caleulate the 5-ray emission from he pulsar wind based on the simulated. pulsar paranieters., The next step is to calculate the $\gamma$ -ray emission from the pulsar wind based on the simulated pulsar parameters. + We should point out that the distribution of 5-rav. loud »ulsars is model dependent., We should point out that the distribution of $\gamma$ -ray loud pulsars is model dependent. + Subsequently we study the TeV 5-ravs emitted from the pulsar wind when they interact with heir ambient interstellar medium., Subsequently we study the TeV $\gamma$ -rays emitted from the pulsar wind when they interact with their ambient interstellar medium. + We argue that. strong EGRET sources may be potential TeV source. candidates or current and future TeV telescopes., We argue that strong EGRET sources may be potential TeV source candidates for current and future TeV telescopes. + In €2. theories of radiation of mature pulsars from both inside and outside the light evlinder will be briclly reviewed.," In 2, theories of radiation of mature pulsars from both inside and outside the light cylinder will be briefly reviewed." + A detailed discussions of the LCS processes of relativistic electrons on the background and svochrotron photons using a one-zone wind nebula model (Chevalier 2000; Cheng. Taam Wang 2004b) will be presented in 3.," A detailed discussions of the ICS processes of relativistic electrons on the background and synchrotron photons using a one-zone wind nebula model (Chevalier 2000; Cheng, Taam Wang 2004b) will be presented in 3." + In d. the properties of the identified: TeV pulsar wind: nebulae sources are reviewed and compared with our models.," In 4, the properties of the identified TeV pulsar wind nebulae sources are reviewed and compared with our models." + In 5. we describe the Monte Carlo simulations. similar to those carried in Cheng et al. (," In 5, we describe the Monte Carlo simulations, similar to those carried in Cheng et al. (" +20042). for deriving the distribution of 5-rav pulsars in the Galaxy and Could. Belt which can be detected. by EGBRIT.,"2004a), for deriving the distribution of $\gamma$ -ray pulsars in the Galaxy and Gould Belt which can be detected by EGRET." + We then calculate the expected GeV and TeV Uuxes from these 5-ray. pulsars generated bv the Monte Carlo simulations., We then calculate the expected GeV and TeV fluxes from these $\gamma$ -ray pulsars generated by the Monte Carlo simulations. + Phe TeV tus distribution of the unidentified EGRET source candidates. which could possibly be detected by the present and future egrouncd-based TeV telescopes. will be presented in 6.," The TeV flux distribution of the unidentified EGRET source candidates, which could possibly be detected by the present and future ground-based TeV telescopes, will be presented in 6." + Finally. we present our summary and discussions in T.," Finally, we present our summary and discussions in 7." +" In this section. we will review the emission. properties. of mature pulsars whose ages are [rom 10”10"" vears."," In this section, we will review the emission properties of mature pulsars whose ages are from $\sim 10^5-10^6$ years." + The high energy radiation of mature pulsars can come both from the pulsar magnetosphere inside light evlinder. and from the pulsar wind nebula outside light evlinder.," The high energy radiation of mature pulsars can come both from the pulsar magnetosphere inside light cylinder, and from the pulsar wind nebula outside light cylinder." + We present the 5-ray. emission. properties of pulsars using he outer gap mocels originally proposed bv. Cheng et al. (, We present the $\gamma$ -ray emission properties of pulsars using the outer gap models originally proposed by Cheng et al. ( +1986a.b).,"1986a,b)." + Based on the model. Zhang Cheng (1997) jwe developed a self-consistent mechanism to describe the ugh energy radiation from spin-powered pulsars.," Based on the model, Zhang Cheng (1997) have developed a self-consistent mechanism to describe the high energy radiation from spin-powered pulsars." + In their model. relativistic charged. particles from a thick. outer magnetospheric accelerator. (outer. gap) raciate through he svnchro-curvature radiation mechanism (Cheng Zhang 1996) rather than the svnchrotron. and. curvature mechanisms in general. producing non-thermal photons from he primary e pairs along the curved magnetic field. [ines in the outer gap.," In their model, relativistic charged particles from a thick outer magnetospheric accelerator (outer gap) radiate through the synchro-curvature radiation mechanism (Cheng Zhang 1996) rather than the synchrotron and curvature mechanisms in general, producing non-thermal photons from the primary $e^\pm$ pairs along the curved magnetic field lines in the outer gap." +" The characteristic emission. energv of high energy οποίος emitted from the outer gap is given by (Zhang Cheng 1997) rmEjpoye where P is the rotation period. D,» is the dipolar magnetic licld in units of LOY GG. Re=cP/2x is the light evlinder radius. r ds the distance to the neutron star. ancl f. ds the fractional size of the outer gap."," The characteristic emission energy of high energy photons emitted from the outer gap is given by (Zhang Cheng 1997) 10^7, where $P$ is the rotation period, $B_{12}$ is the dipolar magnetic field in units of $10^{12}$ G, $R_L=cP/2\pi$ is the light cylinder radius, $r$ is the distance to the neutron star, and $f$ is the fractional size of the outer gap." + The >-ray spectrum crops exponentially bevond the energy. ος.," The $\gamma$ -ray spectrum drops exponentially beyond the energy $E_{\gamma,c}$." + The factor f. defined as the the ratio between the mean vertical separation of the outer gap boundaries in the plane of the rotation axis and the magnetic axis to the light cylinder radius. is limited by the pair production between the soft thermal X-rays from the neutron star surface and the high energy. 5-ray. photons emitted. from the outer gap region. and can be approximated as ο5.5/7Mug," The factor $f$, defined as the the ratio between the mean vertical separation of the outer gap boundaries in the plane of the rotation axis and the magnetic axis to the light cylinder radius, is limited by the pair production between the soft thermal X-rays from the neutron star surface and the high energy $\gamma$ -ray photons emitted from the outer gap region, and can be approximated as $f\simeq 5.5 P^{26/21}B_{12}^{-4/7}$." + The size of f in turn determines the total 5-rav. luminosity of the pulsar. which is given bv (Zhang Cheng 1997) f! Lac where Loup=3.8o1071D.P1cres is. the pulsar spin. down power.," The size of $f$ in turn determines the total $\gamma$ -ray luminosity of the pulsar, which is given by (Zhang Cheng 1997) f^3 , where $L_{\rm sd}= 3.8\times 10^{31}B_{12}^2P^{-4}\ {\rm +erg\ s^{-1}}$ is the pulsar spin down power." +" Llowever. the estimation of gap size f by Zhang Cheng (1997) does not include the ellect. of inclination angle and their model can produce very. few. pulsars with age ~LO”10"" ves."," However, the estimation of gap size $f$ by Zhang Cheng (1997) does not include the effect of inclination angle and their model can produce very few pulsars with age $\sim 10^5-10^6$ yrs." + Zhang et al. (, Zhang et al. ( +2004) have studied the properties of the outer gapby including the οσοι of the inclination angle.,2004) have studied the properties of the outer gapby including the effect of the inclination angle. + Also. instead oftaking half of the," Also, instead oftaking half of the" +due to immense numerical challenges. one will have to wait until global 3-D radiative simulations are performed over a large enough range of parameter space before a clear answer will emerge.,"due to immense numerical challenges, one will have to wait until global 3-D radiative simulations are performed over a large enough range of parameter space before a clear answer will emerge." + In this paper we investigate the time-dependent evolution of magnetized accretion clises hy means. of semi-analvtic techniques ancl discuss their relation to observations., In this paper we investigate the time-dependent evolution of magnetized accretion discs by means of semi-analytic techniques and discuss their relation to observations. + ln particular. we suggest. plausible scalines for the fraction of power dissipated in the corona and. the viscosity law. and we perform a local viscous disc stability analysis. later checked with time-dependent dise models.," In particular, we suggest plausible scalings for the fraction of power dissipated in the corona and the viscosity law, and we perform a local viscous disc stability analysis, later checked with time-dependent disc models." + We find that the observed stability. properties of galactie black hole disces are most likely explained by a modified: viscosity law rather than by an extra coronal or jet cooling., We find that the observed stability properties of galactic black hole discs are most likely explained by a modified viscosity law rather than by an extra coronal or jet cooling. + The nature and extent of the posited limit evele instabilities at high acerction rates depend critically on the poorly understood: prescription for the viscous torques: it is well known that assuming viscous stresses scale proportionally to the eas pressure results in accretion clises which are stable throughout. even at the highest accretion rates (Lightman and Eardley 1974: Stella and. Rosner. 1984).," The nature and extent of the posited limit cycle instabilities at high accretion rates depend critically on the poorly understood prescription for the viscous torques: it is well known that assuming viscous stresses scale proportionally to the gas pressure results in accretion discs which are stable throughout, even at the highest accretion rates (Lightman and Eardley 1974; Stella and Rosner, 1984)." +" In fact. our ignorance of the physical mechanisms giving rise to the disc viscosity. ancl in particular of its exact scaling. has Led many authors to consider the outcome of radiation pressure dominated dises obeying a more general prescription for the viscous stresses /,4, (Laan& POOR): with ay constant. where is the sum of gas plus radiation pressure (for hydrogen rich material). 2 is the mid-plane disc temperature ancl my is the proton mass."," In fact, our ignorance of the physical mechanisms giving rise to the disc viscosity, and in particular of its exact scaling, has led many authors to consider the outcome of radiation pressure dominated discs obeying a more general prescription for the viscous stresses $t_{r\phi}$ \cite{tl84,szu90,hmk91,wm03}: with $\alpha_0$ constant, where is the sum of gas plus radiation pressure (for hydrogen rich material), $T$ is the mid-plane disc temperature and $m_p$ is the proton mass." + Within this approach. the parameter. fi can take any value between 0 (stresses proportional to total pressure) and 2 (stresses proportional to gas pressure only).," Within this approach, the parameter $\mu$ can take any value between 0 (stresses proportional to total pressure) and 2 (stresses proportional to gas pressure only)." + Numerical studies of the last decade have shed new light on the nature of viscosity in accretion dises. by elucidating the crucial role of ALLLD turbulence for their enhanced transport properties.," Numerical studies of the last decade have shed new light on the nature of viscosity in accretion discs, by elucidating the crucial role of MHD turbulence for their enhanced transport properties." + Since magneto-rotational instability (ALR: see Balbus Hawley 1998. and reference therein) is the primary driver of the angular momentum transfer in the disces. the turbulent magnetic stresses scale with magnetic pressure. and therefore fooxPane. where Pas=[Bais|-Siz is the magnetic pressure inside the clisc.," Since magneto-rotational instability (MRI; see Balbus Hawley 1998, and reference therein) is the primary driver of the angular momentum transfer in the discs, the turbulent magnetic stresses scale with magnetic pressure, and therefore $t_{r \phi} +\propto P_{\rm mag}$, where $P_{\rm mag} = |B_{\rm disc}|^2/8\pi$ is the magnetic pressure inside the disc." + One of the main open issues in the physics of black hole accretion disces is the relationship between the disc AM:I-driven turbulent viscosity and the generation of the hot coronae that are usually postulated in order to explain the observed. X-ray emission (Liang Price 1977: Caleev. ltosner Vaiana 1979: Blackman Field 2000: Ixuncic Bieknell 2004).," One of the main open issues in the physics of black hole accretion discs is the relationship between the disc MRI-driven turbulent viscosity and the generation of the hot coronae that are usually postulated in order to explain the observed X-ray emission (Liang Price 1977; Galeev, Rosner Vaiana 1979; Blackman Field 2000; Kuncic Bicknell 2004)." + Phenomenological models usually assume that at cach radius. a fraction. f of the internally gencratec power is transferred. vertically outside the disc. ancl powers amagnetically dominated corona (Llaardt Maraschi 1991: Svensson Zelziarski 1994).," Phenomenological models usually assume that at each radius, a fraction $f$ of the internally generated power is transferred vertically outside the disc, and powers a magnetically dominated corona (Haardt Maraschi 1991; Svensson Zdziarski 1994)." + As customary (see e.g. Svensson Zdziarski 1994: Alerloni 2003). we assume that in \IRI-turbulent dises such a fraction f of the binding energy is transported from large to small depths by some form. of collective mean electromagnetic action (Poynting flux).," As customary (see e.g. Svensson Zdziarski 1994; Merloni 2003), we assume that in MRI-turbulent discs such a fraction $f$ of the binding energy is transported from large to small depths by some form of collective mean electromagnetic action (Poynting flux)." + One should. always keep in mind. however. that this is by no means the only wav in which energv can be removed. non-raciatively from the optically thick dise (for an alternative. see eg. Tageer Pellat 1999).," One should always keep in mind, however, that this is by no means the only way in which energy can be removed non-radiatively from the optically thick disc (for an alternative, see e.g. Tagger Pellat 1999)." + We can now estimate the vertical Povnting lux. £i. in the simplest way. assuming that £I:2epus. where rp is the upward drift velocity of a magnetic Εαν tube within the disc.," We can now estimate the vertical Poynting flux, $F_{\rm P}$, in the simplest way, assuming that $F_{\rm P}\simeq v_{\rm D} P_{\rm mag}$, where $v_{\rm D}$ is the upward drift velocity of a magnetic flux tube within the disc." + In. Alerloni (2003) it was argued. that rp should in general be of the order of the Alfvénn speed ey., In Merloni (2003) it was argued that $v_{\rm D}$ should in general be of the order of the Alfvénn speed $v_{\rm A}$. + This translates into the following expression for the fraction of power dissipated in the corona. uniquely relating this quantity to the magnetic dise viscosity parameter uo (Alerloni2003:Lirose.Ixrolik&Stone20060): where 3=1/(1|£). is the ratio of gas to total pressure. £—DPaaf/Daso ds the ratio of the radiation to the gas pressure.," This translates into the following expression for the fraction of power dissipated in the corona, uniquely relating this quantity to the magnetic disc viscosity parameter $\alpha_0$ \cite{mer03,hks06}: where $\beta = 1/(1+\xi)$, is the ratio of gas to total pressure, $\xi = +\pr/\pg$ is the ratio of the radiation to the gas pressure." + Note that in this approach f is an implicit function of radius. through the radial dependence of the pressures.," Note that in this approach $f$ is an implicit function of radius, through the radial dependence of the pressures." + Recent progress in numerical studies of the disc-corona coupling has been made by simulating a gas-pressure dominated. local pateh of an accretion disc (with vertical eravity included) in which heating by dissipation of the AUID turbulence is balanced. by radiative cooling (Llirose. IWwrolik Stone 2006: κου also Miller Stone 2000).," Recent progress in numerical studies of the disc-corona coupling has been made by simulating a gas-pressure dominated local patch of an accretion disc (with vertical gravity included) in which heating by dissipation of the MHD turbulence is balanced by radiative cooling (Hirose, Krolik Stone 2006; see also Miller Stone 2000)." + In broad. accordance with eq. (3)).," In broad accordance with eq. \ref{eq_f}) )," + it was found. that. the fraction of power released outside the dise main body was less than about for a measured. stress parameter. of ay720.02., it was found that the fraction of power released outside the disc main body was less than about for a measured stress parameter of $\alpha_0 \approx 0.02$. + However. due to the inereased magnetic pressure support in the upper disc lavers. most of the Povnting Lux emerging from the disc main bods is clissipateclbelow the photosphere. and therefore cannot be directly associated with the observed hot. optically thin X-ray emitting plasma.," However, due to the increased magnetic pressure support in the upper disc layers, most of the Poynting flux emerging from the disc main body is dissipated the photosphere, and therefore cannot be directly associated with the observed hot, optically thin X-ray emitting plasma." + Obviously. global radiative simulations are needed to assess the role of long-wavelength Parker instability modes. and the scaling with the radiation pressure predicted by eq. (3))," Obviously, global radiative simulations are needed to assess the role of long-wavelength Parker instability modes, and the scaling with the radiation pressure predicted by eq. \ref{eq_f}) )" + for the generation of genuinely hot coronae from disc magentic fielcls., for the generation of genuinely hot coronae from disc magentic fields. + Let us consider now the general case of the viscosity prescription (1). with O0«µ2.," Let us consider now the general case of the viscosity prescription \ref{eq:defmu}) ), with $0<\mu<2$." + We can calculate analytically the value of the dise parameters at which the instability sets in by studying the stability. properties of the stationary solution., We can calculate analytically the value of the disc parameters at which the instability sets in by studying the stability properties of the stationary solution. + In the one (vertical) zone limit. the equation for hyclrostatic equilibrium in the vertical direction is while the angular momentum conservation. equation reacls:," In the one (vertical) zone limit, the equation for hydrostatic equilibrium in the vertical direction is while the angular momentum conservation equation reads:" +is ~4.6x104° erg cm~? s-! deg-?.,is $\sim$ $\times$ $^{46}$ erg $^{-2}$ $^{-1}$ $^{-2}$. +" For comparison, the total emission from all the X-ray detected AGN in the CDF-S is 1.63x104"" erg cm-? s! deg-?."," For comparison, the total emission from all the X-ray detected AGN in the CDF-S is $\times$ $^{47}$ erg $^{-2}$ $^{-1}$ $^{-2}$." +" Hence, this extra AGN activity can account for ~22% of the total SMBH accretion."," Hence, this extra AGN activity can account for $\sim$ of the total SMBH accretion." +" Adding this to the obscured SMBH growth in X-ray detected AGN etal.2008),, we confirm that most SMBH growth, (Luo~70%,, is significantly obscured and missed by even the deepest X-ray surveys (Treisteretal.2004,2010)."," Adding this to the obscured SMBH growth in X-ray detected AGN \citep{luo08}, we confirm that most SMBH growth, $\sim$, is significantly obscured and missed by even the deepest X-ray surveys \citep{treister04,treister10}." +". Performing a similar study on the 28 sources with fn 21000 and R-K 74.5 that we previously excluded, we fo4/find a very hard X-ray spectrum, harder than that of the Lrg»10!!Lc sources."," Performing a similar study on the 28 sources with $f_{24}$ $f_R$$>$ 1000 and $R$ $K$$>$ 4.5 that we previously excluded, we find a very hard X-ray spectrum, harder than that of the $L_{IR}$$>$ $^{11}$$L_\odot$ sources." +" This spectrum is consistent with a population of luminous AGN with intrinsic rest-frame 2-10 keV luminosity ~2x10* erg s! and negligible contribution from the host galaxy, except at E<2 keV where the thermal component is ~30% of the total emission."," This spectrum is consistent with a population of luminous AGN with intrinsic rest-frame 2-10 keV luminosity $\sim$ $\times$ $^{43}$ erg $^{-1}$ and negligible contribution from the host galaxy, except at $<$ 2 keV where the thermal component is $\sim$ of the total emission." +" This result justifies our choice of removing these sources from our study (otherwise they would dominate the stacked signal), while at the same time it confirms the AGN nature of the vast majority of these sources, in contrast to the suggestion that the extra IR emission could be due to star-formation processes (Donleyetal.2008;PopeGeorgakakis"," This result justifies our choice of removing these sources from our study (otherwise they would dominate the stacked signal), while at the same time it confirms the AGN nature of the vast majority of these sources, in contrast to the suggestion that the extra IR emission could be due to star-formation processes \citep{donley08, pope08,georgakakis10}." +" A similar result for these high-luminosity sources was 2010)..found by Fiore (2010):: In a sample of 99 mid-IR excess sources in the COSMOS field he found a strong stacked signal at E~6 keV, which he interpreted as due to the Fe Ka line, a clear signature of AGN emission and high obscuration (see discussion below)."," A similar result for these high-luminosity sources was found by \citet{fiore10}: : In a sample of 99 mid-IR excess sources in the COSMOS field he found a strong stacked signal at $\sim$ 6 keV, which he interpreted as due to the Fe $\alpha$ line, a clear signature of AGN emission and high obscuration (see discussion below)." +" By design, none of the sources in our sample are individually detected in X-rays, nor do they satisfy the selection criteria of Fioreetal.(2008)."," By design, none of the sources in our sample are individually detected in X-rays, nor do they satisfy the selection criteria of \citet{fiore08}." +". However, it is interesting to investigate if they present other AGN signatures."," However, it is interesting to investigate if they present other AGN signatures." +" For example, 237 out of the 1545 sources with Lrg»5x10!9L5 in our sample (15%)) are found inside the AGN IRAC color-color region defined by Sternetal.(2005)."," For example, 237 out of the 1545 sources with $L_{IR}$$>$ $\times$ $^{10}$$L_\odot$ in our sample ) are found inside the AGN IRAC color-color region defined by \citet{stern05}." +". For comparison, in the sample of 2342 sources with 5x10? — in which from the stacked hard X-ray signal we L5»Lr;g»10!'0L5determined a negligible AGN fraction — there are 327 galaxies (1496)) in the Sternetal.(2005) region."," For comparison, in the sample of 2342 sources with $\times$ $^{10}$$L_\odot$$>$$L_{IR}$$>$ $^{10}$$L_\odot$ — in which from the stacked hard X-ray signal we determined a negligible AGN fraction — there are 327 galaxies ) in the \citet{stern05} region." +" This suggests that the IRAC color-color diagram cannot be used to identify heavily-obscured low-luminosity AGN, because the near-IR. emission in these sources is dominated by the host galaxy (Cardamoneetal.2008)."," This suggests that the IRAC color-color diagram cannot be used to identify heavily-obscured low-luminosity AGN, because the near-IR emission in these sources is dominated by the host galaxy \citep{cardamone08}." +". At longer wavelengths, 83 of the 1545 sources with Lrg»5x10!9L. were detected in the deep VLA observations of the CDF-S (Kellermannetal.2008)."," At longer wavelengths, 83 of the 1545 sources with $L_{IR}$$>$ $\times$ $^{10}$$L_\odot$ were detected in the deep VLA observations of the CDF-S \citep{kellermann08}." +". In contrast, only 33 sources in the Lo» 5x1019L;5»10!9 sample were detected in these observations."," In contrast, only 33 sources in the $\times$ $^{10}$$L_\odot$$>$$L_{IR}$$>$ $^{10}$$L_\odot$ sample were detected in these observations." +" Using the Loqo4 ratio between 1.4 GHz and 24 ym flux densities Appletonetal. we find that in the Lrg»5x10!9(e.g., sample, only 14 2004)),sources have q24«-0.23 and can be consideredLc “radio-loud” (Ibaretal. and in the L5 sample only 10 2008),,sources have q94«-0.23."," Using the $q_{24}$ ratio between 1.4 GHz and 24 $\mu$ m flux densities (e.g., \citealp{appleton04}) ), we find that in the $L_{IR}$$>$ $\times$ $^{10}$$L_\odot$ sample, only 14 sources have $q_{24}$$<$ -0.23 and can be considered “radio-loud” \citep{ibar08}, and in the $\times$ $^{10}$$L_\odot$$>$$L_{IR}$$>$ $^{10}$$L_\odot$ sample only 10 sources have $q_{24}$$<$ -0.23." +" Hence, we 5x10!9Lrg»10!9concludeL that the fraction of bona fide radio-loud sources is negligible and that in most cases the radio emission is produced by star-formation processes."," Hence, we conclude that the fraction of bona fide radio-loud sources is negligible and that in most cases the radio emission is produced by star-formation processes." +" In order to investigate the fraction of heavily-obscured AGN as a function of other galaxy parameters, we performed X-ray stacking of samples sorted by stellar mass."," In order to investigate the fraction of heavily-obscured AGN as a function of other galaxy parameters, we performed X-ray stacking of samples sorted by stellar mass." +" Stellar masses were taken from Cardamoneetal.(2010a),, who performed spectral fitting to the extensive optical and near-IR. spectro-photometry using FAST (Krieketal. and the stellar templates of Maraston(2005) assuming2009) the Kroupa(2001) initial mass function and solar metallicity."," Stellar masses were taken from \citet{cardamone10}, who performed spectral fitting to the extensive optical and near-IR spectro-photometry using FAST \citep{kriek09} and the stellar templates of \citet{maraston05} assuming the \citet{kroupa01} initial mass function and solar metallicity." +" We further restricted our sample to sources with z«1.2, for which photometric redshifts and stellar masses are very well determined (Az/(14-2)—0.007)."," We further restricted our sample to sources with $z$$<$ 1.2, for which photometric redshifts and stellar masses are very well determined $\Delta$ $z$ )=0.007)." +" We then divided the sample into three mass bins: M»10 Mo, 10H-M (Μο) 1019 and 10!°>M 105."," We then divided the sample into three mass bins: $>$ $^{11}$ $_\odot$, $^{11}$$>$ M $_\odot$ $>$ $^{10}$ and $^{10}$$>$ M $_\odot$ $>$ $^{9}$." + The resulting stacked X-ray spectra are shown in (Μ9)Fig. 3.., The resulting stacked X-ray spectra are shown in Fig. \ref{obs_spec_mass}. +" For sources with M>10!4Mo, there is a significant excess at 6-7 keV, above a spectrum that otherwise declines with increasingenergy."," For sources with $>$ $^{11}$ $_\odot$, there is a significant excess at 6-7 keV, above a spectrum that otherwise declines with increasingenergy." +" This might be due to the presence of the Fe Ka line, a clear indicator of AGN activity."," This might be due to the presence of the Fe $\alpha$ line, a clear indicator of AGN activity." + Contrary to the case of stacking as a function of IR luminosity ," Contrary to the case of stacking as a function of IR luminosity (Fig. \ref{simul_spec}) )," +"here we do not find evidence for an absorbed power-law(Fig. 2)),—the 6-7 keV feature is simply too sharply peaked.", here we do not find evidence for an absorbed power-law —the 6-7 keV feature is simply too sharply peaked. +" Possibly the restriction to z<1.2 for the mass-binned stacking, where photometric redshifts are most accurate, reveals an emission line that is broadened by less accurate photometric redshifts in the full sample."," Possibly the restriction to $z$$<$ 1.2 for the mass-binned stacking, where photometric redshifts are most accurate, reveals an emission line that is broadened by less accurate photometric redshifts in the full sample." +" That is, the feature in the Lr; g-binned stack that we interpreted as a heavily absorbed power law may instead be an Fe Ka line broadened artificially by bad photometric redshifts."," That is, the feature in the $L_{IR}$ -binned stack that we interpreted as a heavily absorbed power law may instead be an Fe $\alpha$ line broadened artificially by bad photometric redshifts." +" In the 1011 2M (M)»10!? sample wefound significant hardening of the X-ray spectrum (Fig. 3)),"," In the $^{11}$$>$ M $_\odot$ $>$ $^{10}$ sample wefound a significant hardening of the X-ray spectrum (Fig. \ref{obs_spec_mass}) )," + asuggesting the presence of a significant fraction of AGN., suggesting the presence of a significant fraction of AGN. +" In contrast, only a soft spectrum, consistent with star-formation emission, can be seen for sources with 10!°>M (Μο) 105."," In contrast, only a soft spectrum, consistent with star-formation emission, can be seen for sources with $^{10}$$>$ M $_\odot$ $>$ $^{9}$ ." +" Taken together, these results indicate that AGN are predominantly present in the most massive galaxies, in agreement with the conclusions of Cardamoneetal.(2010b) and others."," Taken together, these results indicate that AGN are predominantly present in the most massive galaxies, in agreement with the conclusions of \citet{cardamone10b} and others." + This will be elaborated in a paper currently in preparation., This will be elaborated in a paper currently in preparation. +stronger meridional flows and thus forming more intense polar spots.,stronger meridional flows and thus forming more intense polar spots. + Such a mechanism might well explain the bimodal spot distribution seen in Fig., Such a mechanism might well explain the bimodal spot distribution seen in Fig. + LO with the lower peak in the distribution representing the Latitude at. which he Hux tubes emerge and the polar spot those spots that jwe been driven to the poles by the meridional Low., \ref{Fig_frac_spot_lat} with the lower peak in the distribution representing the latitude at which the flux tubes emerge and the polar spot those spots that have been driven to the poles by the meridional flow. + Such a mechanism may also explain the non-uniform polar spots seen on a number of stars. if the polar spot is being formed » a number of smaller spot features.," Such a mechanism may also explain the non-uniform polar spots seen on a number of stars, if the polar spot is being formed by a number of smaller spot features." + This is still just speculative. but Weber.Strassmeier&Washucttl(2005) jwe shown tentative evidence for large poleward meridional lows on earlv-Ix. giants.," This is still just speculative, but \citet*{WeberM:2005} have shown tentative evidence for large poleward meridional flows on early-K giants." + maps of the large-scale. magnetic topology on LID 30-20-10 from three epochs (Fig. 3..," The maps of the large-scale magnetic topology on HD 141943 from three epochs (Fig. \ref{Fig_allmap2007}," + Fig., Fig. + 4 and Fig. 5)), \ref{Fig_allmap2009} and Fig. \ref{Fig_allmap2010}) ) + show that the racial field on LID 141948 had a mixed polarity at all [atitudes for all epochs., show that the radial field on HD 141943 had a mixed polarity at all latitudes for all epochs. + Phe azimuthal field appears to be dominated by a ring of positive field around the pole at all epochs. although the intensity of the polar ring is reduced in 2009.," The azimuthal field appears to be dominated by a ring of positive field around the pole at all epochs, although the intensity of the polar ring is reduced in 2009." + This is shown in the results from Table 4.. which show that the toroidal field is preclominately axisvmmetric (10 75 per cent) while the poloidal field is predominatelvy non-axisvmmetric (10 SO per cent). with the ratio not appearing to change significantly between the three epochs.," This is shown in the results from Table \ref{Tab_magcomp}, which show that the toroidal field is predominately axisymmetric $\sim$ 70 – 75 per cent) while the poloidal field is predominately non-axisymmetric $\sim$ 70 – 80 per cent), with the ratio not appearing to change significantly between the three epochs." + Vhe other obvious feature of the azimuthal Ποια is the increase in the amount of negative field on the stellar surface, The other obvious feature of the azimuthal field is the increase in the amount of negative field on the stellar surface + , +also with high confidence: low-accretion objects are more X-ray. active tha simular high-accretio[un objects.,also with high confidence: low-accretion objects are more X-ray active that similar high-accretion objects. + In order to check that the depeucence of activity ou accretion is not due to differeut mea[un ages/bolometric luminosities in he two subsets. we repeated this analysis in several mass.and age slices. similar o those of Figure 10..," In order to check that the dependence of activity on accretion is not due to different mean ages/bolometric luminosities in the two subsets, we repeated this analysis in several mass age slices, similar to those of Figure \ref{fig:LXvsM4}." + When we did this. we invariably confirmed that the stars are less X-ray acive than the low-:vweretion Ones.," When we did this, we invariably confirmed that the high-accretion stars are less X-ray active than the low-accretion ones." + For any 1lass and age biu where the two subsaliples are well rep'esented. we obtai1 highly siguilicant resuls (e.g..oe) in the bin with M/M.=0.25—0.50 and. Log(Age)6.0—6.9. uull-hypothliesis tests οἱve better than coulicdence tha the two accretio1 categories cliffer).," For any mass and age bin where the two subsamples are well represented, we obtain highly significant results (e.g., in the bin with $M/M_{\odot}=0.25-0.50$ and $Log(Age)=6.0-6.5$, null-hypothesis tests give better than confidence that the two accretion categories differ)." + Diflereuces in X-ray activivy level aside. treuds of mean activity with mass seem to hold preferentially for low accretion stars.," Differences in X-ray activity level aside, trends of mean activity with mass seem to hold preferentially for low accretion stars." + The scatter in X-ray activity levels in auy given lass range also appears lower for low-aceretion stars than for the whole sample (cf., The scatter in X-ray activity levels in any given mass range also appears lower for low-accretion stars than for the whole sample (cf. + Figures | and 11))., Figures \ref{fig:LXvsMb} and \ref{fig:LXvsM_CWa}) ). + A relationship of activity with mass isof apparent lor high-accretion stars. which also evidence larger spreads in their activity levels.," A relationship of activity with mass is apparent for high-accretion stars, which also evidence larger spreads in their activity levels." +"line widths on the emission measure maps on Fig. 11,,","line widths on the emission measure maps on Fig. \ref{fig:sizemaps}," + showing they are comparable., showing they are comparable. + The solid line in Fig., The solid line in Fig. +" 10 shows the expected distribution of emission measure for a simple isobaric cooling flow, cooling at the rate of 1OMoyr~! without any heating."," \ref{fig:norms} shows the expected distribution of emission measure for a simple isobaric cooling flow, cooling at the rate of $10 \Msunpyr$ without any heating." + It can be seen that the observed emission measure of gas decreases more steeply with temperature than predicted by a simple cooling flow., It can be seen that the observed emission measure of gas decreases more steeply with temperature than predicted by a simple cooling flow. + We have investigated how well the observed spectrum can be modelled by a simple cooling flow., We have investigated how well the observed spectrum can be modelled by a simple cooling flow. + Our first model was based on a component plus a cooling flow component., Our first model was based on a component plus a cooling flow component. + We used the new feature in version 12 to base the cooling flow model spectrum on a thermal model rather than a one., We used the new feature in version 12 to base the cooling flow model spectrum on a thermal model rather than a one. +" We note, however, that this form of the model is not internally self consistent, as the quantity of gas at each temperature is computed by assuming the luminosities of the model."," We note, however, that this form of the model is not internally self consistent, as the quantity of gas at each temperature is computed by assuming the luminosities of the model." +" We made our own consistent version of the model, but this had no effect on the predicted spectrum, so we show results from the model here."," We made our own consistent version of the model, but this had no effect on the predicted spectrum, so we show results from the model here." + We tried two forms of the model: a full cooling flow where the lower temperature of the cooling flow was constrained to be the minimum possible (0.0808 keV) and the second reduced model where it was allowed to be a free parameter., We tried two forms of the model: a full cooling flow where the lower temperature of the cooling flow was constrained to be the minimum possible (0.0808 keV) and the second reduced model where it was allowed to be a free parameter. +" In this model we allowed the N, O and Fe metallicites to vary between the and components, but fixed the other metallicities to have the same values in the two components."," In this model we allowed the N, O and Fe metallicites to vary between the and components, but fixed the other metallicities to have the same values in the two components." + The best fitting parameters for the two models are shown in Table 2.., The best fitting parameters for the two models are shown in Table \ref{tab:fitresults}. +" The full cooling flow model gives a mass deposition rate of 7.4+0.5MoΥΓ1, whereas the reduced model obtained a rate of 8.70.5Mayr! cooling to 0.54+0.01keV."," The full cooling flow model gives a mass deposition rate of $7.4 \pm 0.5 \Msunpyr$, whereas the reduced model obtained a rate of $8.7 \pm 0.5 \Msunpyr$ cooling to $0.54 \pm 0.01 +\keV$." +" The metallicities of the cooling flow component were lower for the model where the gas cools to the minimum value, presumably to decrease the strength of the emission lines."," The metallicities of the cooling flow component were lower for the model where the gas cools to the minimum value, presumably to decrease the strength of the emission lines." +" The reduced cooling flow model gives a substantially better quality of fit to the spectrum than the full model (y?=6381 versus 6494), but is poorer than the five component multitemperature model (x?= 6362)."," The reduced cooling flow model gives a substantially better quality of fit to the spectrum than the full model $\chi^2=6381$ versus 6494), but is poorer than the five component multitemperature model $\chi^2=6362$ )." +" A simple cooling flow is unlikely to be a good model to the complex distribution of gas in the core of the Centaurus cluster, even in the presence of cooling gas."," A simple cooling flow is unlikely to be a good model to the complex distribution of gas in the core of the Centaurus cluster, even in the presence of cooling gas." + We have therefore used a model where the cooling flow is split into different temperature ranges and we allow the mass deposition rate to vary in each range., We have therefore used a model where the cooling flow is split into different temperature ranges and we allow the mass deposition rate to vary in each range. + We use fixed ranges in temperature to obtain a stable fit., We use fixed ranges in temperature to obtain a stable fit. +" The model examined here has steps in temperature from 3.2 to 2.4, 2.4 to 1.6, 1.6 to 0.8, 0.8 to 0.4 and 0.4 to 0.0808 keV. The metallicities are assumed to be the same in each component, except for the N metallicity in the three coolest components, which is allowed to vary separately from the hotter components."," The model examined here has steps in temperature from 3.2 to 2.4, 2.4 to 1.6, 1.6 to 0.8, 0.8 to 0.4 and 0.4 to 0.0808 keV. The metallicities are assumed to be the same in each component, except for the N metallicity in the three coolest components, which is allowed to vary separately from the hotter components." + We show in Fig., We show in Fig. + 12 the mass deposition rate in the absence of heating for each of the cooling flow components., \ref{fig:mdott} the mass deposition rate in the absence of heating for each of the cooling flow components. + We measure mass deposition rates down to 0.4 keV and an upper limit of 0.8Mcyr! below that temperature., We measure mass deposition rates down to 0.4 keV and an upper limit of $0.8\Msunpyr$ below that temperature. + The results are consistent with the multitemperature model results., The results are consistent with the multitemperature model results. + There is systematically less gas detected at lower temperature than expected from a simple cooling flow (as in Fig. 10))., There is systematically less gas detected at lower temperature than expected from a simple cooling flow (as in Fig. \ref{fig:norms}) ). +" Instead of direct spectral fitting to the whole of the spectrum, the strength of the emission lines can be used to gauge the amount of cooling taking place through the temperature range they are sensitive to."," Instead of direct spectral fitting to the whole of the spectrum, the strength of the emission lines can be used to gauge the amount of cooling taking place through the temperature range they are sensitive to." + The amount of flux in a line can be compared to that expected from a cooling flow model., The amount of flux in a line can be compared to that expected from a cooling flow model. +" As there are several possible lines which can be examined, this allows independent determinations of the mass deposition rate, but does not use the full spectral information available when spectral fitting."," As there are several possible lines which can be examined, this allows independent determinations of the mass deposition rate, but does not use the full spectral information available when spectral fitting." +"Both the near and far distances of each one of the four clouds have been computed, using the rotation curve of","Both the near and far distances of each one of the four clouds have been computed, using the rotation curve of" +no correlation between the initial angular momentum of the core and the number of objects that later form.,no correlation between the initial angular momentum of the core and the number of objects that later form. + The 3 cores with the lowest initial angular momentum (runs A013. A012 and AO28)form 10. 4 and | objects. and the 3 cores with the highest initial angular momentum (runs A019. AOI4 and A016) form cores with 8. 3 and 3 objects.," The 3 cores with the lowest initial angular momentum (runs A013, A012 and A028)form 10, 4 and 1 objects, and the 3 cores with the highest initial angular momentum (runs A019, A014 and A016) form cores with 8, 3 and 3 objects." + The amount of angular momentum varies by a factor of 4.3 between these two extremes., The amount of angular momentum varies by a factor of 4.3 between these two extremes. + The differences between runs AOI3 and A028 are solely due to the different infall histories caused by the turbulent velocity field., The differences between runs A013 and A028 are solely due to the different infall histories caused by the turbulent velocity field. + If more than two objects form in a core. the resulting N-body system is generally unstable (e.g. Valtonnen Mikkola 1991).," If more than two objects form in a core, the resulting ${\cal N}$ -body system is generally unstable (e.g. Valtonnen Mikkola 1991)." + The dynamics of unstable multiple systems are chaotic. and usually result in the ejection of low-mass members and the hardening of binaries (Anosova 1986: Sterzik Durisen 1998).," The dynamics of unstable multiple systems are chaotic, and usually result in the ejection of low-mass members and the hardening of binaries (Anosova 1986; Sterzik Durisen 1998)." + In our simulations. this dynamical phase usually ends about 0.10 to 0.12 Myr after the start of the simulation. leaving an expanding halo of ejected objects and a central system containing between 2 and 4 stars.," In our simulations, this dynamical phase usually ends about 0.10 to 0.12 Myr after the start of the simulation, leaving an expanding halo of ejected objects and a central system containing between 2 and 4 stars." + Simulations that produce more than two objects show a high level of dynamical instability. and no systems remain with more than 4 objects bound in the central region after 0.3Myr.," Simulations that produce more than two objects show a high level of dynamical instability, and no systems remain with more than 4 objects bound in the central region after $0.3\,{\rm Myr}\,$." + The timescale for dynamical evolution and. ejection matches that given by Anosova (1986) who argues that systems decay on a timescale of order one hundred crossing times. 1.9. where R is the scale-length of the system (here ~ 200au) and M is the total mass (here ~ 2M. so we obtain yay Myrs. which ts à good fit to the decay timescales we observe in the simulations.," The timescale for dynamical evolution and ejection matches that given by Anosova (1986) who argues that systems decay on a timescale of order one hundred crossing times, i.e. where $R$ is the scale-length of the system (here $\sim 200\,{\rm au}$ ) and $M$ is the total mass (here $\sim 2 M_\odot$ ), so we obtain $t_{\rm decay} \sim 0.03\,{\rm Myrs}\,$ , which is a good fit to the decay timescales we observe in the simulations." + Figure 7. shows the relationship between the velocities of the objects formed (relative to the centre of mass of the core) and their masses., Figure \ref{fig:massvel} shows the relationship between the velocities of the objects formed (relative to the centre of mass of the core) and their masses. + The initial escape velocity from a core is ~O.d4kms! and this is marked by the horizontal dashed-line on Fig. 7)).," The initial escape velocity from a core is $\sim 0.44\,{\rm km}\,{\rm s}^{-1}$ and this is marked by the horizontal dashed-line on Fig. \ref{fig:massvel}) )." + There is a slight anti-correlation between ejection velocity and mass., There is a slight anti-correlation between ejection velocity and mass. + Brown dwarves have a higher mean ejection velocity (. 2.9kms7!) than stars (~ 2.0kms7!). but this correlation is not statistically very significant.," Brown dwarves have a higher mean ejection velocity $\sim 2.9\,{\rm km}\,{\rm s}^{-1}$ ) than stars $\sim 2.0\,{\rm km}\,{\rm s}^{-1}$ ), but this correlation is not statistically very significant." + Dynamical interactions and ejections have been proposed by Reipurth Clarke (2001) (see also Bate et al., Dynamical interactions and ejections have been proposed by Reipurth Clarke (2001) (see also Bate et al. + 2002a. Delgardo-Donate et al.," 2002a, Delgardo-Donate et al." + 2003) as a mechanism for the production of brown dwarves: stellar embryos are ejected from cores before they can accrete enough material to become hydrogen-burning stars., 2003) as a mechanism for the production of brown dwarves: stellar embryos are ejected from cores before they can accrete enough material to become hydrogen-burning stars. + This appears to be the formation mechanism for all but one of the brown dwarfs formed in these simulations., This appears to be the formation mechanism for all but one of the brown dwarfs formed in these simulations. + Dynamical interactions eject 36 low-mass objects from our cores. and of these I4 have not acereted enough material to pass the hydrogen-burning limit at 0.0844...," Dynamical interactions eject 36 low-mass objects from our cores, and of these 14 have not accreted enough material to pass the hydrogen-burning limit at $0.08 M_{\odot}$." + Only one brown dwarf is still bound in a core at 0.3Myr: that one is in à binary with à 0.29M. star.," Only one brown dwarf is still bound in a core at $0.3\,{\rm Myr}\,$; that one is in a binary with a $0.29 M_{\odot}$ star." + Figure 8 shows the mass function of objects from all of the low-turbulence simulations at 0.3Myr.," Figure \ref{fig:imf} shows the mass function of objects from all of the low-turbulence simulations at $0.3\,{\rm Myr}\,$." + The filled portion of the histogram shows objects that are in multiple systems. while the open part shows single objects. and the hashed region shows the three low-mass stars which form late in Run A013: the final status of these three stars is unclear as the system is highly unstable when the simulation ends.," The filled portion of the histogram shows objects that are in multiple systems, while the open part shows single objects, and the hashed region shows the three low-mass stars which form late in Run A013; the final status of these three stars is unclear as the system is highly unstable when the simulation ends." + The probability of ejection scales as ~M? (Anosova 1986) and ejected objects very seldom belong to multiple systems., The probability of ejection scales as $\sim M^{-1/3}$ (Anosova 1986) and ejected objects very seldom belong to multiple systems. + Consequently all but one of the brown dwarfs and most of the low-mass stars are single and have been ejected (see also Fig. 7))., Consequently all but one of the brown dwarfs and most of the low-mass stars are single and have been ejected (see also Fig. \ref{fig:massvel}) ). + The proportion of single stars decreases with increasing mass. because the longer a star remains in à core. the larger its nass grows. and the less likely it is to be ejected.," The proportion of single stars decreases with increasing mass, because the longer a star remains in a core, the larger its mass grows, and the less likely it is to be ejected." + The low-mass tail in the mass function below ~05Η. arises because secondary objects have difficulty. growing beyond that mass before they are ejected., The low-mass tail in the mass function below $\sim 0.5 M_{\odot}$ arises because secondary objects have difficulty growing beyond that mass before they are ejected. + For example. the mean ejection timescale of ~0.03Myr multiplied by the mea initial accretion rate of ~107M.yr! gives a typical mass at ejection of ~0.3M...," For example, the mean ejection timescale of $\sim 0.03\,{\rm Myr}$ multiplied by the mean initial accretion rate of $\sim 10^{-5} M_{\odot}\,{\rm yr}^{-1}$ gives a typical mass at ejection of $\sim 0.3 M_{\odot}$." + Stars with final masses greater than this are likely to be part of a central multiple system. as only 1 the dense central region. where accretion is on-going. can th[27 mass grow beyond ~0.5M...," Stars with final masses greater than this are likely to be part of a central multiple system, as only in the dense central region, where accretion is on-going, can the mass grow beyond $\sim 0.5 M_{\odot}$ ." + This is shown in Fig., This is shown in Fig. + 8. by th[27 high proportion of stars having M>0.5M. which are still 1 multiple systems at 0.3Myr.," \ref{fig:imf} by the high proportion of stars having $M > 0.5 M_{\odot}$ which are still in multiple systems at $0.3\,{\rm Myr}\,$." + The mass function shown in Fig., The mass function shown in Fig. + 8. should not be taken às a full initial mass function (IMF)., \ref{fig:imf} should not be taken as a full initial mass function (IMF). + It represents the statistical output from only one nass of core. with only one level of turbulence.," It represents the statistical output from only one mass of core, with only one level of turbulence." + Figure 8 is apparently deficient in low-mass objects and brown dwarfs compared with the observed IMF (e.g. Kroupa 2002)., Figure \ref{fig:imf} is apparently deficient in low-mass objects and brown dwarfs compared with the observed IMF (e.g. Kroupa 2002). + Lower mass cores may well produce the smaller objects needed to populate this region. as their gas reservoir Is smaller (e.g. Delgardo-Donate et al.," Lower mass cores may well produce the smaller objects needed to populate this region, as their gas reservoir is smaller (e.g. Delgardo-Donate et al." + 2003: Sterzik Duriset 2003)., 2003; Sterzik Durisen 2003). + Alternatively. more turbulent cores may eject objects more rapidly. and hence with lower masses (e.g. Bate et al.," Alternatively, more turbulent cores may eject objects more rapidly, and hence with lower masses (e.g. Bate et al." + 2002a.b; 2003).," 2002a,b; 2003)." + The true IMF is presumably a convolutior of the object production from a distribution of cores masses. turbulence levels. and so on.," The true IMF is presumably a convolution of the object production from a distribution of cores masses, turbulence levels, and so on." + For example. Delgardo-Donate et al. (," For example, Delgardo-Donate et al. (" +2003) convolve the distribution of objects producec by one mass of core and one of level of turbulence with a core mass function. to produce an IMF.,"2003) convolve the distribution of objects produced by one mass of core and one of level of turbulence with a core mass function, to produce an IMF." + What is clear from these simulations ts that the relationship between a core mass spectrum and a stellar IMF is non-trivial and that core mass spectra that do not resemble the stellar IMF (e.g. some of the core mass spectra from Klessen 2001) may still produce à reasonable stellar IMF., What is clear from these simulations is that the relationship between a core mass spectrum and a stellar IMF is non-trivial and that core mass spectra that do not resemble the stellar IMF (e.g. some of the core mass spectra from Klessen 2001) may still produce a reasonable stellar IMF. + Four simulations. produce only single stars., Four simulations produce only single stars. + The turbulent velocity. fields 1n these simulations are such that an extended overdense region does not form., The turbulent velocity fields in these simulations are such that an extended overdense region does not form. + The core collapses in a monolithic fashion similar to the zero-turbulence case (see Section 4.1)., The core collapses in a monolithic fashion similar to the zero-turbulence case (see Section 4.1). + The only difference isthat the accretion rate Is, The only difference isthat the accretion rate is +elemental abundances can be measured up to redshift z£zb.,elemental abundances can be measured up to redshift $z\approx5$. + The chemical abundances of DLA systems give us complementary observational constraints on the formation and evolution of galaxies., The chemical abundances of DLA systems give us complementary observational constraints on the formation and evolution of galaxies. + Abundance measurements in DLA systems relevant for the present work are listed in Table 1 and plotted in Fig., Abundance measurements in DLA systems relevant for the present work are listed in Table \ref{Tab:DLA} and plotted in Fig. + 3 (green squares)., \ref{Fig:obsabund} (green squares). + In comparing DLA abundances with model predictions care must be taken for dust depletion effects., In comparing DLA abundances with model predictions care must be taken for dust depletion effects. +" Luckily, these effects are expected to be negligible for most of the elements used in the present investigation, such as C, N, O and S: in fact these elements show little values of depletion, if any, in nearby interstellar clouds (Jenkins2009) and are expected to be even less depleted in DLA systems."," Luckily, these effects are expected to be negligible for most of the elements used in the present investigation, such as C, N, O and S: in fact these elements show little values of depletion, if any, in nearby interstellar clouds \citep{Jenkins09} and are expected to be even less depleted in DLA systems." +" On the other hand, we expect some depletion effects for Fe and, to a lesser extent, for Si."," On the other hand, we expect some depletion effects for Fe and, to a lesser extent, for Si." + Estimates of Fe depletion in DLAs based on the comparison with Zn measurements (Vladilo2004) are available only for a few systems of Table 1..," Estimates of Fe depletion in DLAs based on the comparison with Zn measurements \citep{Vladilo04} + are available only for a few systems of Table \ref{Tab:DLA}." + These results indicate that Fe tend to be underestimated when the level of metallicity is relatively high., These results indicate that Fe tend to be underestimated when the level of metallicity is relatively high. +" This explain the few cases with largest deviations from BCD measurements and from the modelpredictions shown in Figs. 3,, 5,, 8,, 10,, 11,, 13,,"," This explain the few cases with largest deviations from BCD measurements and from the modelpredictions shown in Figs. \ref{Fig:obsabund}, \ref{Fig:nowdOFeH}, \ref{Fig:wdZmuY}, \ref{Fig:mwdZmuY1}, , \ref{Fig:mwdZmuY2}, \ref{Fig:bestabund}," + and 17.., and \ref{Fig:DLAabund}. +" The determination of primordial helium abundance, Y,, is important for the study of cosmology and the evolution of galaxies, because an accurate initial Y is required to test Big Bang nucleosynthesis and build chemical evolution models."," The determination of primordial helium abundance, $Y_p$, is important for the study of cosmology and the evolution of galaxies, because an accurate initial $Y$ is required to test Big Bang nucleosynthesis and build chemical evolution models." +" One way of estimating Y, is by extrapolating the observed helium-metallicity (Y— Z) relation to Z—0 by assuming the slope AY /AZ to be constant.", One way of estimating $Y_p$ is by extrapolating the observed helium-metallicity $Y-Z$ ) relation to $Z=0$ by assuming the slope $\bigtriangleup Y$ $\bigtriangleup Z$ to be constant. +" More recently, it has been common practice to use AY /AO since the oxygen abundance is easier to determine and can represent the metals."," More recently, it has been common practice to use $\bigtriangleup +Y$ $\bigtriangleup O$ since the oxygen abundance is easier to determine and can represent the metals." +" To obtain an accurate Y, value, a reliable determination of AY/ AO for oxygen-poor objects is needed (e.g., Izotovetal.1999;A.Peimbert2003; 2007)). Izotov&Thuan(20"," To obtain an accurate $Y_p$ value, a reliable determination of $\bigtriangleup +Y$ $\bigtriangleup O$ for oxygen-poor objects is needed (e.g., \citealt{Izotov99b, Peimbert03, Luridiana03, Izotov04a, +Peimbert07}) )." +"04a) derived the primordial helium Y,=0.2429+0.0009 and the slope AY /AO=4.3+0.7 from observations of 82 regions."," \cite{Izotov04a} derived the primordial helium $Y_p=0.2429\pm0.0009$ and the slope $\bigtriangleup +Y$ $\bigtriangleup O=4.3\pm0.7$ from observations of 82 regions." +" For a restricted sample (7 regions), they obtained Y,=0.2421+0.0021 and AY /AO=5.7+1.8."," For a restricted sample (7 regions), they obtained $Y_p=0.2421\pm0.0021$ and $\bigtriangleup +Y$ $\bigtriangleup O=5.7\pm1.8$." +" Later, Izotovetal.(2006) derived Y,=0.2463+0.0030 from the emission of the whole region of the extremely metal-deficient blue compact dwarf galaxy SBS 0335— 052E. M.Peimbert(2007) has adopted AY/AO=3.3X:0.7 from theoretical and observational results, and derived Y,—0.2474+ 0.0029."," Later, \cite{Izotov06} derived $Y_p=0.2463\pm0.0030$ from the emission of the whole region of the extremely metal-deficient blue compact dwarf galaxy SBS $0335-052$ E. \cite{Peimbert07} has adopted $\bigtriangleup +Y$ $\bigtriangleup O=3.3\pm0.7$ from theoretical and observational results, and derived $Y_p=0.2474\pm0.0029$ ." +" These values are in excellent agreement with the value derived by Spergeletal.(2007) from the WMAP results, Y,=0.2482+0.0004."," These values are in excellent agreement with the value derived by \cite{Spergel07} from the WMAP results, $Y_p=0.2482\pm0.0004$." + In Fig., In Fig. + 4 we replot the helium-oxygen abundance relation of Izotov&Thuan(2004a) by using their data in Table 5., \ref{Fig:obsYZ} we replot the helium-oxygen abundance relation of \cite{Izotov04a} by using their data in Table 5. + The linear regression is the one derived from the whole sample Y=0.2429+43(Ο/Η)., The linear regression is the one derived from the whole sample $Y=0.2429+43*(O/H)$. +" In this work, we used an updated version of the chemical evolution model developed by Bradamanteetal.(1998) to study the formation and evolution of late-type dwarf galaxies, dIrrs and BCDs."," In this work, we used an updated version of the chemical evolution model developed by \cite{Bradamante98} to study the formation and evolution of late-type dwarf galaxies, dIrrs and BCDs." +" 'The general picture is the following: our model is one-zone and assumes the galaxy built up by continuous infall of primordial gas (X=0.7571,Y,0.2429,Z 0)."," The general picture is the following: our model is one-zone and assumes the galaxy built up by continuous infall of primordial gas $X=0.7571,~Y_p=0.2429,~Z=0$ )." + Stars form and then contaminate the interstellar medium (ISM) with their newly produced elements which mix with the ISM instantaneously and completely., Stars form and then contaminate the interstellar medium (ISM) with their newly produced elements which mix with the ISM instantaneously and completely. +" Stellar lifetimes are taken into account in detail, ie. the instantaneous recycling approximation (IRA) is relaxed."," Stellar lifetimes are taken into account in detail, i.e. the instantaneous recycling approximation (IRA) is relaxed." +" The energy released by supernovae (SNe) and stellar winds is partially deposited in the ISM, and galactic winds develop when the thermal energy of the gas exceeds its binding energy."," The energy released by supernovae (SNe) and stellar winds is partially deposited in the ISM, and galactic winds develop when the thermal energy of the gas exceeds its binding energy." +" Thewind expels metals from the galaxy, hence it has a significant influence on the chemical enrichment of the galaxy."," Thewind expels metals from the galaxy, hence it has a significant influence on the chemical enrichment of the galaxy." +" The time evolution of the fractional mass of the element i in the gas, G;, is described by the equations: where G;(t)=M,(t)X;(t)/Mz(tg) is the gas mass in the form of an element 7 normalized tothe total baryonic"," The time evolution of the fractional mass of the element $i$ in the gas, $G_i$ , is described by the equations: where $G_i(t)=M_g(t)X_i(t)/M_L(t_G)$ is the gas mass in the form of an element $i$ normalized tothe total baryonic" +Livio and Truran (1994) cautioned observers about identifying ONeMg WD progenitors in CN ejecta that show Ne emission lines in their optical spectra.,Livio and Truran (1994) cautioned observers about identifying ONeMg WD progenitors in CN ejecta that show Ne emission lines in their optical spectra. + They showed that moderate Ne abundances (with respect to solar) can be explained either by abundance uncertainties or dredged-up material from the underlying CO WD. or with the breakout of the CNO cyele under special conditions.," They showed that moderate Ne abundances (with respect to solar) can be explained either by abundance uncertainties or dredged-up material from the underlying CO WD, or with the breakout of the CNO cycle under special conditions." +" The authors identified a group of “true ONeMg WDs"" in those novae that showed extreme enrichment of Ne and heavier elements.", The authors identified a group of “true ONeMg WDs” in those novae that showed extreme enrichment of Ne and heavier elements. + Table 2 lists the novae used by Livio and Truran (1994) for their analysis. às well as a number of CNe whose WD and abundances have been determined via photo-ionization modeling of UV and optical observations. simultaneously. by Schwarz and collaborators.," Table 2 lists the novae used by Livio and Truran (1994) for their analysis, as well as a number of CNe whose WD and abundances have been determined via photo-ionization modeling of UV and optical observations, simultaneously, by Schwarz and collaborators." + The table reports the [Ne/O] abundances for each nova as well as the SSco 111 relative abundance derived in this paper., The table reports the [Ne/O] abundances for each nova as well as the Sco 11 relative abundance derived in this paper. + From Table 2 it is evident that the CNe hosting a CO WD are characterized by [Ne/O] abundances <0. while those possessing an ONeMg WD have [Ne/O]>0.," From Table 2 it is evident that the CNe hosting a CO WD are characterized by [Ne/O] abundances $\leq$ 0, while those possessing an ONeMg WD have $>$ 0." + This is also shown in Fig.3. which plots the distribution of CNe as a function of their [Ne/O] abundance.," This is also shown in Fig.3, which plots the distribution of CNe as a function of their [Ne/O] abundance." + The shaded histogram of Fig.3 corresponds to the “fiducial sample” of ONeMg CN white dwarfs: while the black areas correspond to two CNe that are considered as dubious by Livio and Truran (1994) on the basis of the high measured Ne abundances but relatively low values of the total heavy elements enrichment., The shaded histogram of Fig.3 corresponds to the “fiducial sample” of ONeMg CN white dwarfs; while the black areas correspond to two CNe that are considered as dubious by Livio and Truran (1994) on the basis of the high measured Ne abundances but relatively low values of the total heavy elements enrichment. + It should be noted that there were initially three dubious cases identified by Livio and Truran (1994). but IUE observations of Nova NN.I (Starrfield et 11992. Vanlandingham et al.," It should be noted that there were initially three dubious cases identified by Livio and Truran (1994), but IUE observations of Nova N.1 (Starrfield et 1992, Vanlandingham et al." +" 1999) confirmed it to be an ONeMg nova similar to CCrA. The value of [Ne/O]>1 determined in this paper for SSco places the binary among the ""true Ne novae"". hosting an ONeMg WD."," 1999) confirmed it to be an ONeMg nova similar to CrA. The value of $>$ 1 determined in this paper for Sco places the binary among the “true Ne novae”, hosting an ONeMg WD." + It should also be noted that SSco was observed by IUE during the 1979 outburst and on that occasion Williams et al. (, It should also be noted that Sco was observed by IUE during the 1979 outburst and on that occasion Williams et al. ( +1981) reported absorption lines and P-Cyg profiles fromCiv. and in their early epoch data.,"1981) reported absorption lines and P-Cyg profiles from, and in their early epoch data." + All ONeMg novae - contrary to the CO novae- show a P-Cyg profile phase in their UV spectra after the iron curtain phase and before the transition to the nebular spectrum (Shore 2008)., All ONeMg novae - contrary to the CO novae- show a P-Cyg profile phase in their UV spectra after the iron curtain phase and before the transition to the nebular spectrum (Shore 2008). + The UV lines displayed at this stage are 1400. 155 0. 1860. and 2800 and show a saturated absorption trough with very high terminal velocity (Shore 2008).," The UV lines displayed at this stage are 1400, 155 0, 1860, and 2800 and show a saturated absorption trough with very high terminal velocity (Shore 2008)." + The IUE spectra of SSco taken +4 and +6 days after the maximum clearly show P-Cyg profiles with broad absorption troughs that are very similar to the IUE spectra of the ONeMg novae discussed by Shore (2008)., The IUE spectra of Sco taken +4 and +6 days after the maximum clearly show P-Cyg profiles with broad absorption troughs that are very similar to the IUE spectra of the ONeMg novae discussed by Shore (2008). + Hence. SSco should be regarded as a recurrent nova hosting a massive ONeMg WD (Μην~1.37-1.55 Mo. Hachisu et 22000 and Thoroughgood et 22001).," Hence, Sco should be regarded as a recurrent nova hosting a massive ONeMg WD $_{WD}\sim$ 1.37-1.55 $\odot$, Hachisu et 2000 and Thoroughgood et 2001)." + The WD will undergo core collapse and will not explode as a IIa. unless the current models about accreting ONeMe WDs are significantly in error and the SSco mass accretion rate and WD mass prove to be substantially smaller.," The WD will undergo core collapse and will not explode as a Ia, unless the current models about accreting ONeMg WDs are significantly in error and the Sco mass accretion rate and WD mass prove to be substantially smaller." + It is interesting to note that theoretical studies (e.g. Hachisu et 22000: Livio 2000: Thoroughgood et al., It is interesting to note that theoretical studies (e.g. Hachisu et 2000; Livio 2000; Thoroughgood et al. + 2002: see also Justham and Podsiadlowski 2008; Walder et al., 2002; see also Justham and Podsiadlowski 2008; Walder et al. + 2010) have always looked at SSco and all RNe as likely progenitors of type la supernovae., 2010) have always looked at Sco and all RNe as likely progenitors of type Ia supernovae. + However. observational works on this class of objects seem to show the opposite. 1.8. that recurrent novae are not viable IIa progenitors.," However, observational works on this class of objects seem to show the opposite, i.e. that recurrent novae are not viable Ia progenitors." + On one hand. Della Valle and Livio (1996) have shown that the frequency of RNe in the Milky Way. M31 and the LMC is significantly smaller (by ~ I- orders of magnitude) than the supernova Ia rate deduced for these same galaxies.," On one hand, Della Valle and Livio (1996) have shown that the frequency of RNe in the Milky Way, M31 and the LMC is significantly smaller (by $\sim$ 1-2 orders of magnitude) than the supernova Ia rate deduced for these same galaxies." + On the other hand. Selvelli et ((2008) have provided observational evidence that PPyx ejects more material than it accretes and therefore it cannot explode as a Ha. This paper concludes that SSco. hosting a massive ONeMg WD. cannot explode as a Ha either.," On the other hand, Selvelli et (2008) have provided observational evidence that Pyx ejects more material than it accretes and therefore it cannot explode as a Ia. This paper concludes that Sco, hosting a massive ONeMg WD, cannot explode as a Ia either." +" Therefore. among RNe. only symbiotic recurrent novae ""survive"" as the possible progenitors of Ia (Justham and Podsiadlowski 2008: Di Stefano 2010). explaining at least some of the observed Ila (Patat et 22011: Di Stefano 2010)."," Therefore, among RNe, only symbiotic recurrent novae “survive” as the possible progenitors of Ia (Justham and Podsiadlowski 2008; Di Stefano 2010), explaining at least some of the observed Ia (Patat et 2011; Di Stefano 2010)." + Still. the ultimate fate of OOph. the prototype object of the symbiotic RNe. remains uncertain (e.g. Osborne et 22006; Justham and Podsiadlowski 2008).," Still, the ultimate fate of Oph, the prototype object of the symbiotic RNe, remains uncertain (e.g. Osborne et 2006; Justham and Podsiadlowski 2008)." + While the question of how many different stellar systems produce type la supernovae remains unsolved. it has been proven critical to establish not only the mass of the WD and the ejecta. but also the primary star composition in candidate IIa progenitors.," While the question of how many different stellar systems produce type Ia supernovae remains unsolved, it has been proven critical to establish not only the mass of the WD and the ejecta, but also the primary star composition in candidate Ia progenitors." + In the case of RNe. in particular. it will be important to establish whether an ONeMg WD is peculiar to SSco or rather common to the RNe of the same type or to all recurrent novae. as suggested by Webbink (1990).," In the case of RNe, in particular, it will be important to establish whether an ONeMg WD is peculiar to Sco or rather common to the RNe of the same type or to all recurrent novae, as suggested by Webbink (1990)." +superflat image combining the scientific images.,superflat image combining the scientific images. + Then. the images were corrected by superflat in order to correct for second order sky structures not removed by twilight flats. which are usually present in wide field images.," Then, the images were corrected by superflat in order to correct for second order sky structures not removed by twilight flats, which are usually present in wide field images." + The calibration of the broad-band image was obtained using several Landolt fields., The calibration of the broad-band image was obtained using several Landolt fields. + For the narrow-band filter spectrophotometric stars were observed., For the narrow-band filter spectrophotometric stars were observed. + Fluxes were then Yormalized to the AB magnitude system. following Theuns Warren (1997).," Fluxes were then normalized to the AB magnitude system, following Theuns Warren (1997)." +" A detailed description of the calibration steps and the relation between AB magnitudes and the ""m(5007)7 OIII] magnitude introduced by Jacoby (1989) are given in Arnaboldi et al. (", A detailed description of the calibration steps and the relation between AB magnitudes and the “m(5007)” [OIII] magnitude introduced by Jacoby (1989) are given in Arnaboldi et al. ( +2002).,2002). + For the filters used in the present observations. the relation between the AB magnitudes and n(5007) is given by: m(5007)=m(AB)+3.02.," For the filters used in the present observations, the relation between the AB magnitudes and m(5007) is given by: m(5007)=m(AB)+3.02." + Arnaboldi et al. (, Arnaboldi et al. ( +1996) detected for the first time 3 PNe in the Virgo cluster with different radial velocity from that of the nearby M86 galaxy.,1996) detected for the first time 3 PNe in the Virgo cluster with different radial velocity from that of the nearby M86 galaxy. + This difference in the radial velocity pointed to the fact that these PNe were not bound to any galaxy and they were free flying in the Virgo cluster potential., This difference in the radial velocity pointed to the fact that these PNe were not bound to any galaxy and they were free flying in the Virgo cluster potential. + This demonstrates that the diffuse light in clusters can be traced by the detection of ICPNe., This demonstrates that the diffuse light in clusters can be traced by the detection of ICPNe. + This method has been used for the Fornax (Theuns Warren 1997). several fields in the Virgo cluster (Arnaboldi et al.," This method has been used for the Fornax (Theuns Warren 1997), several fields in the Virgo cluster (Arnaboldi et al." + 2002. 2003: Aguerri et al.," 2002, 2003; Aguerri et al." + 2005: Feldmeier et al., 2005; Feldmeier et al. + 1998. 2003a. 2004a). and for several nearby galaxy groups (M81. Feldmeier et al.," 1998, 2003a, 2004a), and for several nearby galaxy groups (M81, Feldmeier et al." + 2003b. and Leo. Rodrigguez et al.," 2003b, and Leo, guez et al." + 2003)., 2003). + The detection of the ICPNe ts based on the strong emission of these objects in the 5007À {OLLI} line., The detection of the ICPNe is based on the strong emission of these objects in the $\AA$ [OIII] line. + PNe are detected using the so-called ON-OFF band technique (Jacoby et al., PNe are detected using the so-called ON-OFF band technique (Jacoby et al. + 1990)., 1990). + This observational technique requires two images of the field., This observational technique requires two images of the field. + One image is taken through a narrow-band filter (on-band filter) centered at the wavelength of the [OIILL15007À emission at the redshift of galaxy group or cluster under study. and the other image Is taken through a broad-band filter (off-band filter) not containing the [OIILL15007À emission.," One image is taken through a narrow-band filter (on-band filter) centered at the wavelength of the $\lambda 5007 +\AA$ emission at the redshift of galaxy group or cluster under study, and the other image is taken through a broad-band filter (off-band filter) not containing the $\lambda 5007 +\AA$ emission." + Then. the photometric IGPN candidates are those objects detected in the on-band filter and not detected in off-band filter.," Then, the photometric IGPN candidates are those objects detected in the on-band filter and not detected in off-band filter." + They should also be point-like objects. because PNe at the distance of galaxy clusters or groups can not be resolved.," They should also be point-like objects, because PNe at the distance of galaxy clusters or groups can not be resolved." + Our group has developed an automatic procedure for the detection of ICPNe candidates in the Virgo cluster (see Arnaboldi et al., Our group has developed an automatic procedure for the detection of ICPNe candidates in the Virgo cluster (see Arnaboldi et al. + 2002 and Aguern et al., 2002 and Aguerri et al. + 2005 for a full description of the method). which can be applied to HCG 44.," 2005 for a full description of the method), which can be applied to HCG 44." + This technique is based on the classification of the detected objects in the on- and off-band images according to their positions in a color-magnitude diagram (CMD)., This technique is based on the classification of the detected objects in the on- and off-band images according to their positions in a color-magnitude diagram (CMD). + We measure the on- and off-band photometry of all objects located in the images., We measure the on- and off-band photometry of all objects located in the images. + This was done using SExtractor (Bertin Arnouts 1996)., This was done using SExtractor (Bertin Arnouts 1996). +" All objects were plotted in the CMD ΠΠ—mmy vs nts. being wz, and ai, the narrow and broad band magnitudes of each object. respectively."," All objects were plotted in the CMD $m_{n}-m_{b}$ vs $m_{n}$, being $m_{n}$ and $m_{b}$ the narrow and broad band magnitudes of each object, respectively." + The most reliable IGPNe photometric candidates are point-like sources with no detected continuum emission and observed EW greater than 100 after convolution with the photometric errors as a function of magnitude (see Arnaboldi et al., The most reliable IGPNe photometric candidates are point-like sources with no detected continuum emission and observed EW greater than 100 after convolution with the photometric errors as a function of magnitude (see Arnaboldi et al. + 2002; Aguerri et al., 2002; Aguerri et al. + 2005)., 2005). + We selected only objects with EW greater than 100 tto avoid contamination from [OLI] emitters at ςz0.35 whose emission falls into the [OIII] filter for HCG 44. and we must properly take into account the photometric errors in order to avoid contamination by continuum objects (see the discussion in Arnaboldi et al.," We selected only objects with EW greater than 100 to avoid contamination from [OII] emitters at $z\approx 0.35$ whose emission falls into the [OIII] filter for HCG 44, and we must properly take into account the photometric errors in order to avoid contamination by continuum objects (see the discussion in Arnaboldi et al." + 2002 and Aguerri et al., 2002 and Aguerri et al. + 2005)., 2005). +"would require in case of screc""s (ely)>1 mag) very broad PDFs with ogg>| which would imply Mach uunbers M21500 far above the ones measured in the ISM of our galaxy.",would require in case of screens $\left>1~{\rm mag}$ ) very broad PDFs with $\sigma_{\ln\xi}>4$ which would imply Mach numbers $M>1500$ far above the ones measured in the ISM of our galaxy. + The analysis shows that a tirbuleut distant screen can naturally explain not ouly the flatter curvature but also a weak absorption feature a 2175 of the Calzetti-curve if within a certain οςunin density its carriers are destroved by the strong UV-radiation in star-burstf ealaxies., The analysis shows that a turbulent distant screen can naturally explain not only the flatter curvature but also a weak absorption feature at 2175 of the Calzetti-curve if within a certain column density its carriers are destroyed by the strong UV-radiation in star-burst galaxies. + The feature is effücietly reduced by more than of its intriusje value iftιο following cicunistauces are fulfilled for typical extinction values measured for star burst galaxies GA~1 nae): The condition for the staidard deviation of the loe-ual distribution of the cohuun deusitv is in agreement with he Mach uuuber of the c‘old neutral iiediua (which implies στο~ 6) Mf the thickless is not sufficieutlv larger han a few turbulent leneth scales., The feature is efficiently reduced by more than of its intrinsic value if the following circumstances are fulfilled for typical extinction values measured for star burst galaxies $A_V\sim 1~{\rm mag}$ ): The condition for the standard deviation of the log-normal distribution of the column density is in agreement with the Mach number of the cold neutral medium (which implies $\sigma_{\rho/\left<\rho\right>}\sim 6$ ) if the thickness is not sufficiently larger than a few turbulent length scales. + A fractal deusitv structure can also enhance the xobabilitv for the carriers survival as they become ocated iu optical thick clouds aud therefore save agaiust παμοι destruction by a strong UV-feld., A fractal density structure can also enhance the probability for the carriers' survival as they become located in optical thick clouds and therefore save against further destruction by a strong UV-field. +in the case of a compact. massive protoplauctary disk which is uaturally prone to gravitational instability.,"in the case of a compact, massive protoplanetary disk which is naturally prone to gravitational instability." + Firthermore. gravitational perturbations induced by a close stellar companion cau trigeer the imstability even though the disk itself is not unstable to its own gravity (Boss2006).," Furthermore, gravitational perturbations induced by a close stellar companion can trigger the instability even though the disk itself is not unstable to its own gravity \citep{boss06}." +. On the other land. cousideriug the loug survival timescale aud slim chances of gravitational instabilities. disks located within wide binaries aud around single stars are good candidates to form plaucts via the core accretion model iu their iuner regious (6.8..Boley 2009).," On the other hand, considering the long survival timescale and slim chances of gravitational instabilities, disks located within wide binaries and around single stars are good candidates to form planets via the core accretion model in their inner regions \citep[e.g.,][]{boley09}." +. While a violent process is iost likely responsible for the formation of planets in tight binaries. it is however unclear whether alb plancts in wide binaries forma through a single mechanism," While a violent process is most likely responsible for the formation of planets in tight binaries, it is however unclear whether all planets in wide binaries form through a single mechanism." + Iudoeed. it is also conceivable that ligh-mass planets (2 Mj) iostly form) via disk fragmentation. while lower mass plaucts are prefercutially the result of core accretion.," Indeed, it is also conceivable that high-mass planets $\gtrsim M_J$ ) mostly form via disk fragmentation, while lower mass planets are preferentially the result of core accretion." + This scenario would naturally alleviate the difficulty of the core accretion model to form the lighest-mass plaucts iu less than a few Myr., This scenario would naturally alleviate the difficulty of the core accretion model to form the highest-mass planets in less than a few Myr. + This hypothesis has the additional advantage that it could also apply to tight binaries., This hypothesis has the additional advantage that it could also apply to tight binaries. +" Tudeed. since a stellar companion located within less than LOOAAT dramatically shortens the disk lifetime. core accretion is essentiallv prevented frou, occurriug. accounting for the absence of low-mass (5241) eas eiut planets in tight binaries."," Indeed, since a stellar companion located within less than AU dramatically shortens the disk lifetime, core accretion is essentially prevented from occurring, accounting for the absence of low-mass $< 2 M_J$ ) gas giant planets in tight binaries." + Plauetesiuals cau prestunably foxiu iu either scenario. accounting for the observations regarding the debris disks phenomenon.," Planetesimals can presumably form in either scenario, accounting for the observations regarding the debris disks phenomenon." +" In πλαν, it remains to be determined whether the treuds ciseussed here indicate an actual dichotomy between the main plauct formation theories or a mere change of the relative importance of the two models as a function of the location of the stellar companion."," In summary, it remains to be determined whether the trends discussed here indicate an actual dichotomy between the main planet formation theories or a mere change of the relative importance of the two models as a function of the location of the stellar companion." + huproviug the statistical significance of the various trends discussed here and determining the exact properties of disks within tieht PAIS binaries will help shed further light these two possibilities., Improving the statistical significance of the various trends discussed here and determining the exact properties of disks within tight PMS binaries will help shed further light these two possibilities. + I am grateful to Silvia Alencar and Jane Curegorio-IIoteum for organizing aud inviting 1e to “Special Session T oat the TAU 27th General Assembly held in Rio de Janeiro. where this work was first preseuted. as well as to Aune Eeecnherecr. Deepak Raghavan. David Rodriguez and Peter Plavchan for invaluable input regarding exoplaucts aud debris disks.," I am grateful to Silvia Alencar and Jane Gregorio-Hetem for organizing and inviting me to “Special Session 7” at the IAU 27th General Assembly held in Rio de Janeiro, where this work was first presented, as well as to Anne Eggenberger, Deepak Raghavan, David Rodriguez and Peter Plavchan for invaluable input regarding exoplanets and debris disks." + The work preseuted here has been funded in part by the Aecuce Nationale de la Recherche through coutract ANR-07-BLAN-0221., The work presented here has been funded in part by the Agence Nationale de la Recherche through contract ANR-07-BLAN-0221. +Dased on surveys made with modern large telescopes. the number of observed Lyman-break galaxies (LBCs:e.g.Stei-del.Pettini.&Hamilton1995). has reached about 1000 (Steidelunet∣⋅⋅al.2003). by now. uproviding ia unique. window studying carly galaxy. formation.,"Based on surveys made with modern large telescopes, the number of observed Lyman-break galaxies \citep[LBGs; e.g.][]{Steidel95} has reached about $\sim 1000$ \citep{Ste03} by now, providing a unique window for studying early galaxy formation." +" ↓⊀In these observations. .massive a large sample of LBG-cancliclates... is onfirst selected as ""drop-outs” in certain sets of colour-colour planes (e.g. C, Covs. C— H0. and then later spectroscopic follow-up observations ‘are !performed. to obtain‘ the redshifts of the identified candidates."," In these observations, a large sample of LBG-candidates is first selected as ``drop-outs'' in certain sets of colour-colour planes (e.g. $\U-G$ vs. $G-R$ ), and then later spectroscopic follow-up observations are performed to obtain the redshifts of the identified candidates." + Most. surveys to date have been carried. out at optical wavelengths. corresponding to the rest-frame far ultra-violet (UV) at redshift 2=3.," Most surveys to date have been carried out at optical wavelengths, corresponding to the rest-frame far ultra-violet (UV) at redshift $z=3$." + The LBGs found in this way show strong clustering (Acelbereeretal.1998:Cii-avaliscoetal.1998:Steidelct 1998).. which has generally been interpreted. as indirect. evidence that LDCGs reside in dark. matter halos.," The LBGs found in this way show strong clustering \citep{Ade98, Giavalisco98, Steidel98}, which has generally been interpreted as indirect evidence that LBGs reside in massive dark matter halos." + Several studies. of. LBCs⋅ based∖⋅⋝ for semi-analvtic mocels.⋅ for galaxy⋅ formation agree. with theDp massive. dark matter halo hypothesis. (e.g.Alo&White 1909).. but à numerical study by Jing&Suto(1998) using. collisionless2. N-body⇁ simulations.. expressed some concerns whether the clustering. of⋅ dark matter halos of «lO7f1241M. can explain: the observed clustering: strength ∪⊔⇀∐≺∶≱∖," Several studies of LBGs based on semi-analytic models for galaxy formation agree with the massive dark matter halo hypothesis \citep[e.g.][]{Mo96, Bau98, Kau99, Mo99}, but a numerical study by \citet{Jing} using collisionless N-body simulations expressed some concerns whether the clustering of dark matter halos of $<10^{12}\himsun$ can explain the observed clustering strength of LBGs." +⋡∐∩∖∖⋎∢⊾���⇁∢⋅↓⋅⊳⋜↧↓⋜⋯⊾↓⋅⊀↓⊔∖⇁⋖⋅⊳∖↿⊲↓∙≟⋜∐⊲↓∪⊔∣⋡∖⇁↓∖⊥⋜↧⇂∠⊳↓↓⋖⋅↓⋅↓↥⊏↥⇂⇂↕≻⇂ argued that the ;CDM models have no dillieultv in explaining the strong observed:. clustering," However, a later investigation by \citet{KHW99} argued that the CDM models have no difficulty in explaining the strong observed clustering" +"Massive stars (M,>8M.) can have a significant impact upon their environment. despite the fact they are less numerous than their lower mass counterparts.","Massive stars $\mathrm{M_{\star}\ga 8\,M_{\odot}}$ ) can have a significant impact upon their environment, despite the fact they are less numerous than their lower mass counterparts." + Massive stars can dominate their host galaxy's luminosity and inject prodigious amounts of energy into the interstellar medium (ISM)., Massive stars can dominate their host galaxy's luminosity and inject prodigious amounts of energy into the interstellar medium (ISM). + This injection of energy can regulate subsequent star formation. and provides a key source of heating and turbulence in the ISM.," This injection of energy can regulate subsequent star formation, and provides a key source of heating and turbulence in the ISM." + Furthermore. the enriched material injected into the ISM by supernovae accompanying the demise of massive stars forms a crucial component in subsequent generations of stars and planets.," Furthermore, the enriched material injected into the ISM by supernovae accompanying the demise of massive stars forms a crucial component in subsequent generations of stars and planets." + Therefore. massive stars are important from galactic to planetary seales (2)..," Therefore, massive stars are important from galactic to planetary scales \citep{ZinneckerandYorke2007}." + However. despite their importance. our knowledge of how massive stars form is less complete than in the case of solar miss stars.," However, despite their importance, our knowledge of how massive stars form is less complete than in the case of solar mass stars." + There has been considerable theoretical uncertainty over the ormation of massive stars., There has been considerable theoretical uncertainty over the formation of massive stars. + A young massive star is expected o attain the luminosity of a main sequence OB star while it is still accreting material (accordingtoanextrapolationofthestandardlowmassstarformationscenarioof 2)...," A young massive star is expected to attain the luminosity of a main sequence OB star while it is still accreting material \citep[according to an extrapolation of the standard low mass +star formation scenario of][]{Shu1987}." + As a result. it ws been thought that the immense luminosity of massive stars could provide suthcient radiation pressure to reverse the in-fall of material (222)..," As a result, it has been thought that the immense luminosity of massive stars could provide sufficient radiation pressure to reverse the in-fall of material \citep{Larson1971,Kahn1974,Wolfire1987}." + Consequently. alternative modes of massive star ormation have been proposed. for example competitive accretion and stellar mergers (22)..," Consequently, alternative modes of massive star formation have been proposed, for example competitive accretion and stellar mergers \citep{Bonnell1998,Bally2005}." + However. recent 3D. hydrodynamic simulations demonstrate that radiation pressure does not prevent dise accretion forming stars of at least ~50M. (2)..," However, recent 3D hydrodynamic simulations demonstrate that radiation pressure does not prevent disc accretion forming stars of at least $\mathrm{\sim50\,M_{\odot}}$ \citep{Krumholz2009}." + The key detail being that accretion is confined to an equatorial disc. shielding the accreting material from the brunt of the radiation. and channeling the radiation pressure into the polar regions (22?)..," The key detail being that accretion is confined to an equatorial disc, shielding the accreting material from the brunt of the radiation, and channeling the radiation pressure into the polar regions \citep{YorkeandSonnhalter2002,Krumholz2009,Vaidya2009}." + However. relating theoretical models to observations is challenging.," However, relating theoretical models to observations is challenging." + The Kelvin-Helmholtz timescale. the time taken for à proto-star to convert its potential energy to thermal energy and begin nuclear fusion. is approximately 10* years for a massive star. compared to ~107 years fora star of |M...," The Kelvin-Helmholtz timescale, the time taken for a proto-star to convert its potential energy to thermal energy and begin nuclear fusion, is approximately $\mathrm{10^4}$ years for a massive star, compared to $\mathrm{\sim10^7}$ years for a star of $\mathrm{1\,M_{\odot}}$." + This short timescale. in conjunction with the innate rarity of massive stars. makes it ditficult to catch a massive star in the act of forming.," This short timescale, in conjunction with the innate rarity of massive stars, makes it difficult to catch a massive star in the act of forming." + In addition. this," In addition, this" +still consistent. [,still consistent. [ +Ar/Fe] and [S/Fe] are closer to the data but are still overpredicted and only marginally consistent with the observations. [,Ar/Fe] and [S/Fe] are closer to the data but are still overpredicted and only marginally consistent with the observations. [ +Si/Fe] and [Ca/Fe] remain in good agreement.,Si/Fe] and [Ca/Fe] remain in good agreement. +" Finally, [Ni/Fe] shows no variation with the binary fraction parameter A, which is reassuring as both elements are predominantly produced by SNIa."," Finally, [Ni/Fe] shows no variation with the binary fraction parameter $A$, which is reassuring as both elements are predominantly produced by SNIa." +" In the case of [Mg/Fe], the model ratios can be raised by increasing the Mg yield in stars above 20Mo,, a common practice with the WW95 yields (see,e.g.,?).."," In the case of [Mg/Fe], the model ratios can be raised by increasing the Mg yield in stars above 20, a common practice with the WW95 yields \citep[see, e.g., ][]{Francois04}." +" In Paper I there was no need for such a modification, but in this case increasing the Mg yield by a factor of 2.5 brings the ICM abundance ratio into good agreement with the data, while still maintaining an observationally consistent [Mg/Fe] in the galaxies’ stellar component."," In Paper I there was no need for such a modification, but in this case increasing the Mg yield by a factor of 2.5 brings the ICM abundance ratio into good agreement with the data, while still maintaining an observationally consistent [Mg/Fe] in the galaxies' stellar component." +" A slightly higher factor would give a better match for the ICM, but in that case the stellar abundance ratios would be too high."," A slightly higher factor would give a better match for the ICM, but in that case the stellar abundance ratios would be too high." + Models with a boosted magnesium yield are shown in Figure 5.., Models with a boosted magnesium yield are shown in Figure \ref{2xMg}. +" In principle, the same exercise could be done with the yields of other elements that are underpredicted (Ne) or overpredicted (Si, Ar)."," In principle, the same exercise could be done with the yields of other elements that are underpredicted (Ne) or overpredicted (Si, Ar)." +" However this should not be considered a solution, but simply a tentative constraint on nucleosynthesis from the chemical evolution models."," However this should not be considered a solution, but simply a tentative constraint on nucleosynthesis from the chemical evolution models." +" Also, we have assumed that the different elements in the ICM either have no radial gradients at all or that they have the same gradient as iron (for which there are fairly good measurements)."," Also, we have assumed that the different elements in the ICM either have no radial gradients at all or that they have the same gradient as iron (for which there are fairly good measurements)." + This simple assumption might not be strictly true and a more accurate correction for gradients could bring the models and the data into better agreement., This simple assumption might not be strictly true and a more accurate correction for gradients could bring the models and the data into better agreement. + Future observations of gradients of elements other than iron in the ICM would shed some light on this matter., Future observations of gradients of elements other than iron in the ICM would shed some light on this matter. +" We have introduced a fairly significant modification to our model — the deposition of the majority of the newly produced metals into the hot halo gas, instead of into the cold interstellar gas."," We have introduced a fairly significant modification to our model — the deposition of the majority of the newly produced metals into the hot halo gas, instead of into the cold interstellar gas." + It is important to check whether this change has an impact on the properties of galaxies that we used to calibrate our previous models., It is important to check whether this change has an impact on the properties of galaxies that we used to calibrate our previous models. +" In Figure 6 we show the same three models as in the previous section (Paper I fiducial, SAM-PI; hot enrichment with A=0.03, SAM— hota; and hot recycling with A=0.04, SAM— Ποίν)."," In Figure \ref{gxs} we show the same three models as in the previous section (Paper I fiducial, SAM-PI; hot enrichment with $A=0.03$, $\mathrm{SAM-hot_a}$ ; and hot recycling with $A=0.04$, $\mathrm{SAM-hot_b}$ )." +" We show the metallicity, [a/Fe] ratio, and SN Ia rate of galaxies, and compare them with the same data samples from the local Universe as in Paper I. We remind the reader that the fiducial model from Paper I had A=0.03."," We show the metallicity, $\alpha$ /Fe] ratio, and SN Ia rate of galaxies, and compare them with the same data samples from the local Universe as in Paper I. We remind the reader that the fiducial model from Paper I had $A=0.03$." + The metallicities of early-type galaxies are not significantly affected by this change and remain in agreement with the observations (panel A)., The metallicities of early-type galaxies are not significantly affected by this change and remain in agreement with the observations (panel A). +" However, galaxies in models with “hot enrichment” have their [a/Fe] increased (especially the most massivegalaxies)."," However, galaxies in models with “hot enrichment” have their $\alpha$ /Fe] increased (especially the most massivegalaxies)." + A higher value of the, A higher value of the +First we consider that the imediuu is isotropic aud the source is a resolved ellipsoid with no nou-sciutillatiug base component.,First we consider that the medium is isotropic and the source is a resolved ellipsoid with no non-scintillating base component. + Because of the conversion estimates we are uakiug to treat the isotropic theory in a wav to account or auisotropy. the results will also be those for the case in which the observed anisotropy is due to the medium. but he source itself is à partially resolved isotropic source.," Because of the conversion estimates we are making to treat the isotropic theory in a way to account for anisotropy, the results will also be those for the case in which the observed anisotropy is due to the medium, but the source itself is a partially resolved isotropic source." + From the above cousideratious of the effect of source size we fiud f!=tj 0057hhnrs., From the above considerations of the effect of source size we find $t^\star= t^{\rm o}/35=0.057$ hrs. + We note that Lere We associate twice the timescales measured aid oeseuted. in Table 3 with the time required im the ormnula. aud the augular scales as correspouding to the diameter of the source.," We note that here we associate twice the timescales measured and presented in Table \ref{tab:res} with the time required in the formula, and the angular scales as corresponding to the diameter of the source." + Frou the preceeding discussion. we associate f with £ aud 0 with 0. in the formulae given at the beeimmine of Sect.," From the preceeding discussion, we associate $t$ with $t^\star$ and $\theta$ with $\theta^\star_F$ in the formulae given at the beginning of Sect." + 9., 9. +" Using e-51kku/s. ""7-0. 1. pUm5GOGGIIE in these formmlac, we find Qp= 25pas."," Using $v$ km/s, $m^{\rm o}$ =0.4, $\nu^{\rm o}$ GHz in these formulae, we find $\theta_F^\star$ = $\mu$ as." + At GGIIz the source is then Ops15&(7TAS δύθμας.," At GHz the source is then $\theta_F^\star \times 15 +\times (\nu^\star/\nu)^{0.5} =860\mu$ as." +" The source has a uiean fiux deusitv of nuudy. resulting ina brielituess temperature Z5=252/a2,1.3.1010 Ix. Tu this case the screen is extremely stroug (C.E165,9 29/5). 4id nearby ( Lppe). which results in the larger augle subteuded bv the scattering disks."," The source has a mean flux density of mJy, resulting in a brightness temperature $T_B= 2 +S\lambda^2/\pi k\theta_S^2 =1.3\times10^{10}$ K. In this case the screen is extremely strong $_N^2 \approx 165 m^{-20/3}$ ), and nearby $\sim$ pc), which results in the larger angle subtended by the scattering disks." + This iu turn considerably lowers the brightucss temperature from that caleulatec in Paper I. We now cousider the case of the maxi possible fiux density in a non-sciutillatiue compoucut., This in turn considerably lowers the brightness temperature from that calculated in Paper I. We now consider the case of the maximum possible flux density in a non-scintillating component. +" Although the modulation index is 0.lL. we know that 2105€ of the source is scintillating. bv the regular imiuiua at ~ uu,Jy."," Although the modulation index is 0.4, we know that $>$ of the source is scintillating, by the regular minima at $\sim$ mJy." + We therefore consider. in a sinülar manner o Paper I a nou-scintillating base-level determined bv this value.," We therefore consider, in a similar manner to Paper I a non-scintillating base-level determined by this value." + From Fig. ll((, From Fig. \ref{fig:mean}( ( +a) we take wuJy iu the scintillating coniponeut.,a) we take mJy in the scintillating component. + However our approach here differs from Paper I not just ue to our revised velocity. aud c:culated anisotropy. but because we take iuto account that this scintillating component nist also be somewhat resolved.," However our approach here differs from Paper I, not just due to our revised velocity, and calculated anisotropy, but because we take into account that this scintillating component must also be somewhat resolved." + The reason for this is that the moclulatic1 -]wlex ds not 0.7. as would be expected from scintillation of a li0nuuJv poit source at the critical frequency. on a nowscintillating component of GO0inuuJw.," The reason for this is that the modulation index is not 0.7, as would be expected from scintillation of a mJy point source at the critical frequency, on a non-scintillating component of mJy." +" The observed modulation iudex of the smaller component. 1e. if we remove the base component. . isan?/—m""οfr. where wis. the fraction of the total flux density in the scintillating component."," The observed modulation index of the smaller component, i.e. if we remove the base component, is ${m^{\rm o}}^\prime=m^{\rm o}/x$, where $x$ is the fraction of the total flux density in the scintillating component." +" We use i?)of in place of in"" in the foruulae eiven iu the preceding sectionis.", We use ${m^{\rm o}}^\prime$ in place of $m^{\rm o}$ in the formulae given in the preceding sections. +" Again using κκ», ο and pU-—5GCGIIz. we obtain a GGIIz a source size of Ἰθθμας and brightuess temperature of 7«1p I. The scattering screen is L2ppe away with C$= Πα.onda"," Again using km/s, $t^{\rm o}$ hrs, and $\nu^{\rm o}$ GHz, we obtain at GHz a source size of $\mu$ as and brightness temperature of $7\times10^{11}$ K. The scattering screen is pc away with $_N^2=0.5$ $^{-20/3}$." + We have presented the boundary scenarios: the reality may lie somewhere in between., We have presented the boundary scenarios: the reality may lie somewhere in between. + Fig., Fig. + 16. shows the two extreme cases discussed above (r=l and 0.7). as well as the intermediary cases.," \ref{fig:limits} shows the two extreme cases discussed above $x$ =1 and 0.7), as well as the intermediary cases." + We note that the size quoted is the effective diameter. so for au axial ratio of 6:1. the source would be νοz2.5 times this in the direction of the elongation. aud 1/6=0.E times this orthogoually to it.," We note that the size quoted is the effective diameter, so for an axial ratio of 6:1, the source would be $\sqrt 6 \approx 2.5$ times this in the direction of the elongation, and $1/\sqrt 6 \approx 0.4$ times this orthogonally to it." +" Our observed z"" at around SCCz falls near to the critical frequency predicted from contributions to scattering from the Galaxy Walker(1998)... but this 1uust. be coimcicdental because. aside from the reasons oeiven in this section. the peculiar velocity rules out a coutributious from a very extended material. as does the VAope of the structure function."," Our observed $\nu^{\rm o}$ at around GHz falls near to the critical frequency predicted from contributions to scattering from the Galaxy \cite{wal98}, but this must be coincidental because, aside from the reasons given in this section, the peculiar velocity rules out a contributions from a very extended material, as does the slope of the structure function." + We calculate a high critical requeucy of between 13 and GCGITz (0.710° kan. aud. at a uiininimn (1... ignoring racdiation-induced warping. etc.).," The total radius of the accretion disk is $\ga 10^5$ km, and, at a minimum (i.e., ignoring radiation-induced warping, etc.)," +" he thickuess of the accretion disk should increase as IH=~aR. where a(00?0.13 ίσιο,Franketal. 1995)."," the thickness of the accretion disk should increase as $H \approx \alpha R$, where $\alpha \sim (10^{-3} - 0.1)$ \citep[e.g.,][]{fkr95}." +. Therefore. the outer aceretion disk has [7>107 sun. ancl is casily thick cuough to obscure the iain X-ray cutting region for a system with au inclination 7757.," Therefore, the outer accretion disk has $H \ga 10^2$ km, and is easily thick enough to obscure the main X-ray emitting region for a system with an inclination $>$." +. À raction of the X-ray cussion also origiuates 1n a corona of hot plasina above the accretion disk., A fraction of the X-ray emission also originates in a corona of hot plasma above the accretion disk. + The scale height of this emission is large enough that part of it is visible even from systems observed nearly edec-ou. as is thought to be the case for several LAINBs that are referred to as accretion disk corona sources (Parmaretal.2000:Ivall-manctal. 2003).," The scale height of this emission is large enough that part of it is visible even from systems observed nearly edge-on, as is thought to be the case for several LMXBs that are referred to as accretion disk corona sources \citep{par00, kal03}." +. The partial-coveriug absorption (Fig., The partial-covering absorption (Fig. + and Tab. 2))., \ref{fig:spectra} and Tab. \ref{tab:spectra}) ). + could be produced because the upper lavers of the outer accretion disk are not quite optically tlic- to electron scattering τη 1)., could be produced because the upper layers of the outer accretion disk are not quite optically thick to electron scattering $\tau \sim 1$ ). + Dips. similar to those seen in Figure 2.. are caused by discrete structures that rise above the outer accretiou disk aud obscure the N-rav cussion for a small fraction of the binary orbit.," Dips, similar to those seen in Figure \ref{fig:lc}, are caused by discrete structures that rise above the outer accretion disk and obscure the X-ray emission for a small fraction of the binary orbit." + Such structures form. for example. at the point where the material lost by. the companion star first mnapacts the accretion disk.," Such structures form, for example, at the point where the material lost by the companion star first impacts the accretion disk." + Since most of the absorption results from the incident X-rays photoiouizine the iuterveniug iaterial. the dips should be most prominent at low-cnergics.," Since most of the absorption results from the incident X-rays photoionizing the intervening material, the dips should be most prominent at low-energies." + This is the case in about half of all edec-on LAINBs1997)., This is the case in about half of all edge-on LMXBs. +. However. in the other half the depths of the dips are indepedeut of ener:ie (Whiteetal.198E:Parmar1999:Tavia2001).. as in Figure 3..," However, in the other half the depths of the dips are indepedent of energy \citep{whi84,par99,iar01}, as in Figure \ref{fig:prof}." + This is probably beciuse either (1) the dips result frou cucrev-independent clectron scattering by highh-ionized or metalceficicut material. or (2) the mean enerev of the X-ravs enütted from the coroua decreases ax a function of height. so that απο of the cooler flux remains unobscured durius the dips.," This is probably because either (1) the dips result from energy-independent electron scattering by highly-ionized or metal-deficient material, or (2) the mean energy of the X-rays emitted from the corona decreases as a function of height, so that much of the cooler flux remains unobscured during the dips." + Should the evidence that we fud for softeniug durius the dips in Figure 3. be confined. some combination of these options can be constructed to reproduce the spectral evolution of the dip.," Should the evidence that we find for softening during the dips in Figure \ref{fig:prof} be confirmed, some combination of these options can be constructed to reproduce the spectral evolution of the dip." + The fact that lis a compact object accreting from ai low-inass coneuion ds indicated bv the 7.9 h orbital period of the binary (Fig. 2)).," The fact that is a compact object accreting from a low-mass companion is indicated by the 7.9 h orbital period of the binary (Fig. \ref{fig:lc}) )," + aud by the faintuess of the infrared companion (Fig. 7))., and by the faintness of the infrared companion (Fig. \ref{fig:irzoom}) ). + The short orbital period can accommodate amass donor with a radius of zz0.8 FÉ. (Frank. Nine. Raine 1995. eq.," The short orbital period can accommodate a mass donor with a radius of $\approx 0.8$ $R_\odot$ (Frank, King, Raine 1995, eq." + L10)., 4.10). +" The only high-nass stars that are this compact are in the WolfRavet νάνο,", The only high-mass stars that are this compact are in the Wolf-Rayet phase. + For D28 kpe and Ay=3.2 (Reid 11999: Tan Draine 2003) a WolfRavet star would have A-—(9.11). aud would have been casily detectable iu our νους images.," For $D=8$ kpc and $A_K = 3.2$ (Reid 1999; Tan Draine 2003) a Wolf-Rayet star would have $K = (9-14)$, and would have been easily detectable in our Keck images." + Iu coutrast. if the few LAINBs that have con Inowitored iu the infrared during their outburstswere placed at the Galactic center. they would have had )oak intensities of Az(15.17) (Jainetal.2001:Chatyetal.2003:Buxton&Bailwn 2001).," In contrast, if the few LMXBs that have been monitored in the infrared during their outburstswere placed at the Galactic center, they would have had peak intensities of $K \approx (15-17)$ \citep{jai01,cha03,bb04}." +. The fainter LAINBs would have been barely detectable iu our 2003 Neck nuages., The fainter LMXBs would have been barely detectable in our 2003 Keck images. + Therefore. the short orbital period aud the lacks of a counterpart with A<15 in Figure 7 indicates that the mass donor in lis a low-mass star that over-fills its Roche lobe.," Therefore, the short orbital period and the lack of a counterpart with $K < 15$ in Figure \ref{fig:irzoom} indicates that the mass donor in is a low-mass star that over-fills its Roche lobe." + The nature of the compact object is not vet clear., The nature of the compact object is not yet clear. + We did not observe either thermomuclear bursts from the surface of the compact object. or colerent pulsations that can be naturally associated with a spin period.," We did not observe either thermonuclear bursts from the surface of the compact object, or coherent pulsations that can be naturally associated with a spin period." + Either of these would iudicate that the source is a neutron star., Either of these would indicate that the source is a neutron star. + However. the lack of theses signals is not surprising. because the recurrence tines of bursts are often longer than 100 Xs aud the time resolution of the ACTS data was too coarse to detect pulsatious faster than 10 s. Ou the other hand. bright radio emission is much more conmnuion from black hole LAINBs than neutron star ones (Feuder&Walkers 2001).. which suggests that the primary in ccould be a black hole.," However, the lack of theses signals is not surprising, because the recurrence times of bursts are often longer than 100 ks and the time resolution of the ACIS data was too coarse to detect pulsations faster than 10 s. On the other hand, bright radio emission is much more common from black hole LMXBs than neutron star ones \citep{fk01}, which suggests that the primary in could be a black hole." + One unusual aspect of the outburst from lis that it is quite faint., One unusual aspect of the outburst from is that it is quite faint. + The history of its N-rav huninosity between 1999 and 2001 is displaved in Figure 5.., The history of its X-ray luminosity between 1999 and 2004 is displayed in Figure \ref{fig:hist}. +" During 19992003. deletected a qmareinally-significaut excess in the source counts within oof 290031... with an average huninosity of ~107? 1,, "," During 1999–2003, detected a marginally-significant excess in the source counts within of , with an average luminosity of $\sim 10^{32}$ ." +This emission is probably froma nearby voung. cussion Lue stars.," This emission is probably from nearby young, emission line stars." + Therefore. we consider 107 aas the upper lait to the bhuninositv of dauinues that time period.," Therefore, we consider $10^{32}$ as the upper limit to the luminosity of during that time period." + This is typical for an ΠλΌ in, This is typical for an LMXB in +Fig 5 shows the (0D) versus (D1) diagrams for determining the interstellar extinction. using the probable cluster memboers.,Fig 5 shows the $(U-B)$ versus $(B-V)$ diagrams for determining the interstellar extinction using the probable cluster members. + We fit the intrinsic zero-age main-sequence (ZXMS) given by Schmidt-Ixaler (1982). valid. for stars of luminosity class V to the MS stars of spectral type earlier than AO assuming the slope of reddening £(ΟΙV) as 0.72., We fit the intrinsic zero-age main-sequence (ZAMS) given by Schmidt-Kaler (1982) valid for stars of luminosity class V to the MS stars of spectral type earlier than A0 assuming the slope of reddening $E(U-B)/E(B-V)$ as 0.72. + In the cluster Bascl 4. ZAMS given by Schmidt-IExaler (1082) is not fitting well for the stars of spectral tvpe AX. LE and €. Excess in (UI) colour is clearly visible for the of stars(D.V)>0.50 mag.," In the cluster Basel 4, ZAMS given by Schmidt-Kaler (1982) is not fitting well for the stars of spectral type A, F and G. Excess in $(U-B)$ colour is clearly visible for the stars of $(B-V) > 0.50$ mag." + This indicates that the cluster is metal deficient., This indicates that the cluster is metal deficient. + Phe UV excess 0(023) determined with respect to Llvaces MS turns out to be ~ 0.1 mag., The UV excess $\delta(U-B)$ determined with respect to Hyades MS turns out to be $\sim$ 0.1 mag. + Using the Fefll] versus (€D) relation of Carney (1979). we estimated Fe/1] —0.35 which correspond to Z 0.005., Using the [Fe/H] versus $\delta(U-B)$ relation of Carney (1979) we estimated [Fe/H] $\sim -0.35$ which correspond to Z $\sim$ 0.008. + To estimating the reddening in the direction of this cluster we therefore fitted the ZAAIS given by Schaerer et al. (, To estimating the reddening in the direction of this cluster we therefore fitted the ZAMS given by Schaerer et al. ( +1993) for Z = 0.008 which is shown bv short dash lines in the two colour diagram of Basel 4.,1993) for Z $=$ 0.008 which is shown by short dash lines in the two colour diagram of Basel 4. + Ehe ZAMS of Z = 0.008 fits nicely and. provide the reddening 0\5)0445x0.05 for this cluster which is in agreement with the earlier findings (see ‘Table 1)., The ZAMS of Z $=$ 0.008 fits nicely and provide the reddening $E(B-V) = 0.45\pm0.05$ for this cluster which is in agreement with the earlier findings (see Table 1). + Unlike Basel 4. in the cluster NGC 7067. ZAMS given by Schmidt-Ixaler (1982) for the solar metallicity fits both carly and late tvpe stars.," Unlike Basel 4, in the cluster NGC 7067, ZAMS given by Schmidt-Kaler (1982) for the solar metallicity fits both early and late type stars." + Phe fitted values of £(2V) vary from 0.70 to 0.80 mag., The fitted values of $E(B-V)$ vary from 0.70 to 0.80 mag. + The mean value is £(D.—V)= 0.7540.05 mag., The mean value is $E(B-V)= 0.75\pm$ 0.05 mag. + Our mean reddening estimate for the imaged region agree fairly well with values estimated earlier by others (see ‘Table 1)., Our mean reddening estimate for the imaged region agree fairly well with values estimated earlier by others (see Table 1). + We investigate the nature of interstellar extinction law towards the clusters. by considering the stars having spectral ἵνρο earlier: than AO.," We investigate the nature of interstellar extinction law towards the clusters, by considering the stars having spectral type earlier than A0." + This has been selected from their position in the (C.D) versus (21) and apparent CM cliagrams which reveals that bright stars with V« 16.0 mag and (2B V)«0.60 mag in Basel 4 and with V« 16.5 mag and (DV)«0.75 mag in NGC 7067 are needed stars., This has been selected from their position in the $(U-B)$ versus $(B-V)$ and apparent CM diagrams which reveals that bright stars with $V$$<$ 16.0 mag and $(B-V)$$<$ 0.60 mag in Basel 4 and with $V$$<$ 16.5 mag and $(B-V)<0.75$ mag in NGC 7067 are needed stars. + The number of such stars are 11 and 12 in Basel 4 and NGC 7067 respectively., The number of such stars are 11 and 12 in Basel 4 and NGC 7067 respectively. + Ehe intrinsic colours for these stars have been determined using CDY photometric Q-method (cf., The intrinsic colours for these stars have been determined using $UBV$ photometric Q-method (cf. + Johnson Morgan 1953: Sagar Joshi 1979) and the calibrations eiven by Caldwell et al. (, Johnson Morgan 1953; Sagar Joshi 1979) and the calibrations given by Caldwell et al. ( +1993) for (8δω (V2)o and (VD) with(2Voy.,"1993) for $(U-B)_{0}$, $(V-R)_{0}$ and $(V-I)_{0}$ with $(B-V)_{0}$." + The mean values of the colour excess ratios derived in this way are listed in Table 7 for both the clusters., The mean values of the colour excess ratios derived in this way are listed in Table 7 for both the clusters. + They indicate that the law of interstellar extinction in the direction of the clusters under cliscussion is normal., They indicate that the law of interstellar extinction in the direction of the clusters under discussion is normal. + )v using the optical ancl infrared. data. we estimated. the interstellar extinction for both clusters uncer studs.," By using the optical and infrared data, we estimated the interstellar extinction for both clusters under study." + “Phere are 65 and 44 common stars in the cluster Basel 4 and NGC 067 within the cluster radius respectively., There are 65 and 44 common stars in the cluster Basel 4 and NGC 7067 within the cluster radius respectively. + Fig., Fig. + 6 shows the (J N)vs (VAN) diagrams and Lit à ZAXMS for metallicity Z = 0.008 taken from Sehaerer ct al. (, 6 shows the $(J-K)$ vs $(V-K)$ diagrams and fit a ZAMS for metallicity Z = 0.008 taken from Schaerer et al. ( +1993) in the cluster Jasel 4 and Z = 0.02 taken from Schaller et al. (,1993) in the cluster Basel 4 and Z = 0.02 taken from Schaller et al. ( +1992) in the cluster NGC 7067.,1992) in the cluster NGC 7067. + This gives ECAIN) = 0.3040.20 mag and L(VA) = 1.6040.20 mag for the cluster Basel 4 and AtAK) = 0.400.20 mag and (YAv) = 2.1040.20 mag for the cluster NGC 7067., This gives $E(J-K)$ = $\pm$ 0.20 mag and $E(V-K)$ = $\pm$ 0.20 mag for the cluster Basel 4 and $E(J-K)$ = $\pm$ 0.20 mag and $E(V-K)$ = $\pm$ 0.20 mag for the cluster NGC 7067. + Por both clusters the ratio BEBalbiΑι 20-E0.30 is in σου agreement with the normal interstellar extinction value 0.19 suggested by Cardelli et al. (, For both clusters the ratio $\frac{E(J-K)}{E(V-K)}$ $\sim$ $\pm$ 0.30 is in good agreement with the normal interstellar extinction value 0.19 suggested by Cardelli et al. ( +1989).,1989). + However. scattering is larger due to the error size in Jit data.," However, scattering is larger due to the error size in $JHK$ data." +hole mass and observed. Ht ancl X-ray luminosity of Ciroup 1 ΑΝ.,hole mass and observed IR and X-ray luminosity of Group 1 AGN. + Studies of stellar and σας kinematics in the centers of nearby galaxies (and indeed our own) reveal the presence of supermassive black holes (Ixormendy&Richstone1995)., Studies of stellar and gas kinematics in the centers of nearby galaxies (and indeed our own) reveal the presence of supermassive black holes \citep{b9}. +. Estimates of the central black bole mass from. kinematics correlate. with host galaxy properties. such as the velocity dispersion of stars in the bulge as well as bulge luminosity. (seoe.g.Llopkinsetal.2007.andreferencestherein).," Estimates of the central black hole mass from kinematics correlate with host galaxy properties, such as the velocity dispersion of stars in the bulge as well as bulge luminosity \citep[see e.g.][and references +therein]{b39}." +" ]t has therefore. become possible to measure (vith large uneertainty) central black hole masses in AGN (and. in normal ealaxies) based on observed values of a, palctal.2005). and bulge luminosity (e.g.Winterct WO).", It has therefore become possible to measure (with large uncertainty) central black hole masses in AGN (and in normal galaxies) based on observed values of $\sigma_{\ast}$ \citep[e.g.][]{b91} and bulge luminosity \citep[e.g.][]{b56}. + Black hole mass in AGN can also be estimated. via reverberation mapping (e.g.Peterson1993: W4).. but see also criticism of the claimed accuracy VOL).," Black hole mass in AGN can also be estimated via reverberation mapping \citep[e.g.][]{b14,b58}, but see also criticism of the claimed accuracy \citep{b20}." + Of the AGN in our sample. some 154 had. estimates of black hole mass in the literature (from references. to ‘Table 1)).," Of the AGN in our sample, some 154 had estimates of black hole mass in the literature (from references to Table \ref{tab:sample}) )." + Where there are significant. dillerences between black hole masses estimated for the same AGN. we used the value estimated. using σε. since there is svstematic error in bulge luminosity estimates in spiral galaxies. due to bulge-disk decomposition techniques (e.g.Gultekinetal. 2009)..," Where there are significant differences between black hole masses estimated for the same AGN, we used the value estimated using $\sigma_{\ast}$, since there is systematic error in bulge luminosity estimates in spiral galaxies, due to bulge-disk decomposition techniques \citep[e.g.][]{b19}. ." + 50 our Alex estimates will be biased in favour of those AGN in host galaxies where e. can be accurately deduced., So our $M_{BH}$ estimates will be biased in favour of those AGN in host galaxies where $\sigma_{\ast}$ can be accurately deduced. + 1n ligure 2. we plot the mean observed 12]. Ht luminosity. versus the mean observed 2-10keV. X-ray luminosity. for Group 1 AGN. coloured according to estimated black hole mass.," In Figure \ref{fig:mass1} we plot the mean observed $\micron$ IR luminosity versus the mean observed 2-10keV X-ray luminosity for Group 1 AGN, coloured according to estimated black hole mass." + From Fig. 2.," From Fig. \ref{fig:mass1}," + average X-rav and LR luminosities end to increase with black hole mass. although for a given black hole mass. luminosities seem to span two Or hree orders of magnitude (~10.1—10 Εμ].," average X-ray and IR luminosities tend to increase with black hole mass, although for a given black hole mass, luminosities seem to span two or three orders of magnitude $\sim 10^{-4}-10^{-1} L_{edd}$ )." + However here is considerable uncertainty in the estimated values of Xdack hole mass in the literature., However there is considerable uncertainty in the estimated values of black hole mass in the literature. + Dilflerent. methods used o estimate black hole masses in the same AGN generally agree within a [factor of few. but can diller by more than an order of magnitude (e.g.Satvapaleteretal. 2009).," Different methods used to estimate black hole masses in the same AGN generally agree within a factor of few, but can differ by more than an order of magnitude \citep[e.g.][]{b91,b56}." + Reverberation mapping may involve. uncertainties a factor of ~3 ereater than estimated by authors (Ixrolik2001)., Reverberation mapping may involve uncertainties a factor of $\sim 3$ greater than estimated by authors \citep{b20}. +". Intrinsic dispersion in the correlation with m, as well as bulge-disk decomposition errors. (Crultekinctal.2009) are further sources of uncertainty in black hole mass estimates via the Aloo, relation and bulge Luminosity respectively.", Intrinsic dispersion in the correlation with $\sigma_{\ast}$ as well as bulge-disk decomposition errors \citep{b19} are further sources of uncertainty in black hole mass estimates via the $M-\sigma_{\ast}$ relation and bulge luminosity respectively. + 1n order to reduce the clleet of relatively large uncertainties in measurements of black hole masses. we simply divided. our sample of ΑΝ. into. low mass (<10 AL.) and high mass (>107.) populations.," In order to reduce the effect of relatively large uncertainties in measurements of black hole masses, we simply divided our sample of AGN into low mass $<10^{7} +M_{\odot}$ ) and high mass $>10^{8} M_{\odot}$ ) populations." + Estimated uncertainties in the measured mass of black holes generally do not exceed a factor of 10. so this strategy should enable us to assemble two distinct populations with few or no overlapping members.," Estimated uncertainties in the measured mass of black holes generally do not exceed a factor of 10, so this strategy should enable us to assemble two distinct populations with few or no overlapping members." + The T-test reveals that low and high mass Group 1 AGN do not have significantly dillerent mean ratios of HX to. X-ray luminosity (2;5j; x) at à confidence level of ~99%., The T-test reveals that low and high mass Group 1 AGN do not have significantly different mean ratios of IR to X-ray luminosity $R_{IR/X}$ ) at a confidence level of $\sim 99\%$. + So Group 1 AGN appear to maintain a narrow range of Ryyey across 3-4 orders of magnitude of Meu., So Group 1 AGN appear to maintain a narrow range of $R_{IR/X}$ across 3-4 orders of magnitude of $M_{BH}$. + Now we investigate the role of host galaxy classification in the observed 1. anc X-ray. luminosities of Group 1 AGN., Now we investigate the role of host galaxy classification in the observed IR and X-ray luminosities of Group 1 AGN. + We follow other galaxy surveys by simply. splitting AGN host galaxies into 3 groups: elliptical ancl lenticular (bulge-dominated). spiral (clisk-clominatecl) and. disrupted (peculiar morphology due to merging or tidal interaction).," We follow other galaxy surveys by simply splitting AGN host galaxies into 3 groups: elliptical and lenticular (bulge-dominated), spiral (disk-dominated) and disrupted (peculiar morphology due to merging or tidal interaction)." + We separate bulge-dominated: (rom. disk-dominated: hosts at Hubble stage Y=0.5 (e.g. Ixochaneketal. (2001))). so that a galaxv classed as ολο! (1= 1) for example. is bulge dominated. Cearlv but SAQ/a (7= 0) is clisk-clominated Clate’).," We separate bulge-dominated from disk-dominated hosts at Hubble stage $T=-0.5$ (e.g. \citet{b35}) ), so that a galaxy classed as SA0+ $T=-1$ ) for example, is bulge dominated ('early') but SA0/a $T=0$ ) is disk-dominated ('late')." + We are )therefore sensitive to classification error among (SO|.S0/a) galaxies.," We are therefore sensitive to classification error among (S0+,S0/a) galaxies." + Llowever ealaxies in these two stages are <10% of our sample., However galaxies in these two stages are $<10\%$ of our sample. + ‘Table 2. lists the number of AGN in oursample according (ο NED classification of their hosts as bulge-dominated. or disrupted.," Table \ref{tab:host} lists the number of AGN in oursample according to NED classification of their hosts as bulge-dominated, disk-dominated or disrupted." + In Figure 3. we plot the mean observed. 12jun. LR luminosity versus mean observed 2-I0keV. X-ray [uminosiE [or the Group 1 ΔΝ from Table 2..colour coded according," In Figure \ref{fig:class1} we plot the mean observed $\micron$ IR luminosity versus mean observed 2-10keV X-ray luminosity for the Group 1 AGN from Table \ref{tab:host}, colour coded according" +The conversion of the source pixel position to right ascension à and declination 9 was then carried out.,The conversion of the source pixel position to right ascension $\alpha$ and declination $\delta$ was then carried out. + The four CCDs of the WFC maintain a fixed geometrical pattern relative to the camera rotator centre however. the prime focus corrector of the INT introduces a cubie radial distortion term to the plate scale of the form where tyre 1s the actual radial distance in radians from the field centre. r is the measured radial distance and & is a constant.," The four CCDs of the WFC maintain a fixed geometrical pattern relative to the camera rotator centre however, the prime focus corrector of the INT introduces a cubic radial distortion term to the plate scale of the form where $r_{true}$ is the actual radial distance in radians from the field centre, $r$ is the measured radial distance and $k$ is a constant." + For the WFC. & was measured to be 220.0 7 (Irwin. private communication).," For the WFC, $k$ was measured to be 220.0 $^{-2}$ (Irwin, private communication)." + The astrometry is split into two stages., The astrometry is split into two stages. + Initially... each individual CCD frame is calibrated independently by roughly matching objects in the images with objects in the corresponding Digitised Sky Survey images (2)..," Initially, each individual CCD frame is calibrated independently by roughly matching objects in the images with objects in the corresponding Digitised Sky Survey images \cite{Lasker}." + Matched objects are then used to converge upon an astrometric fit for each frame via an iterative process., Matched objects are then used to converge upon an astrometric fit for each frame via an iterative process. + This is performed using the ASTROM package which relates the measured .r.jy to the true à.ὁ coordinates by fitting a six coefficient transformation. which includes orientation of the images. plate scale and radial distortions.," This is performed using the ASTROM package which relates the measured $x,y$ to the true $\alpha,\delta$ coordinates by fitting a six coefficient transformation, which includes orientation of the images, plate scale and radial distortions." +" These fits gave rms residuals of the order of 1"" for each frame.", These fits gave rms residuals of the order of $1^{\prime\prime}$ for each frame. + The large residuals were due to uncertainties in the exact position of the corrector axis relative to the field rotation centre on the sky., The large residuals were due to uncertainties in the exact position of the corrector axis relative to the field rotation centre on the sky. + To compensate for this. the four CCD frames from each pointing were considered as a whole and were matched to the more accurate data of the United States Naval Observatory (USNO) A2.0 astrometric catalogue (2)..," To compensate for this, the four CCD frames from each pointing were considered as a whole and were matched to the more accurate data of the United States Naval Observatory (USNO) A2.0 astrometric catalogue \cite{usno}." + During this matching process. the field centre was allowed to shift using the transformations derived in the initial stage. until the astrometric differences between the ODT and USNO catalogues (see figure 8) were minimised. thus ascertaining a more accurate estimate of the true field centre.," During this matching process, the field centre was allowed to shift using the transformations derived in the initial stage, until the astrometric differences between the ODT and USNO catalogues (see figure \ref{fig:astromscatter}) ) were minimised, thus ascertaining a more accurate estimate of the true field centre." + The final residuals for a single CCD frame were found to be typically ~0.3” where figure 9. shows an example of the rms residuals for the V. band astrometry., The final residuals for a single CCD frame were found to be typically $\sim 0.3^{\prime\prime}$ where figure \ref{fig:astromhist} shows an example of the rms residuals for the $V$ band astrometry. + Producing a final catalogue with consistent photometry throughout requires each contiguous field to have a common zeropoint., Producing a final catalogue with consistent photometry throughout requires each contiguous field to have a common zeropoint. + At this stage. the individual zeropoints derived in section 4.1. will each have a residual uncertainty due to differing observing conditions and airmass and extinction variations between observations.," At this stage, the individual zeropoints derived in section \ref{sec:photo} + will each have a residual uncertainty due to differing observing conditions and airmass and extinction variations between observations." + Many observations were taken in non-photometrie conditions., Many observations were taken in non-photometric conditions. + In order to achieve homogeneity in the photometric calibration. the zeropoints of the individual frames must be adjusted relative to a common zeropoint adopted for the whole survey.," In order to achieve homogeneity in the photometric calibration, the zeropoints of the individual frames must be adjusted relative to a common zeropoint adopted for the whole survey." + This was carried out in two stages. where the first involved using the V band as the calibrator band (see section 6.19) and considering the magnitude differences between common objects in the overlap regions of the V band pointings.," This was carried out in two stages, where the first involved using the $V$ band as the calibrator band (see section \ref{sec:overlap}) ) and considering the magnitude differences between common objects in the overlap regions of the $V$ band pointings." + The photometric zeropoints could then be corrected relative to a chosen calibrator frame. effectively creating a common zeropoint across the 1 band data.," The photometric zeropoints could then be corrected relative to a chosen calibrator frame, effectively creating a common zeropoint across the $V$ band data." + Following this. the zeropoints of all the other bands were corrected relative to the V band via stellar locus fitting (see section 6.29).," Following this, the zeropoints of all the other bands were corrected relative to the $V$ band via stellar locus fitting (see section \ref{sec:stell}) )." + This was done by examining the colours of stars in each frame and adjusting their zeropoints unti the stars had the expected colours of the stellar main sequence., This was done by examining the colours of stars in each frame and adjusting their zeropoints until the stars had the expected colours of the stellar main sequence. + To ensure a common photometric zeropoint for the Y band. the approach introduced by ?. was adopted whereby the magnitudes of objects common to overlapping images are compared in order to ascertain the difference in their zeropoints.," To ensure a common photometric zeropoint for the $V$ band, the approach introduced by \scite{glazebrook} was adopted whereby the magnitudes of objects common to overlapping images are compared in order to ascertain the difference in their zeropoints." + Objects in the overlap regions of adjacent fields were matched with a tolerance of, Objects in the overlap regions of adjacent fields were matched with a tolerance of +"Like the CN radical. the value of Q,,,. 1s similar to the values observed in Halley's comet from November 1985. ground-based observations (2).. which had a fainter absolute magnitude than for Echeclus.","Like the CN radical, the value of $_{max}$ is similar to the values observed in Halley's comet from November 1985, ground-based observations \citep{almeida:1992}, which had a fainter absolute magnitude than for Echeclus." + Consequently the gas-to-dust ratio is much lower than in the cometary comae (if molecular species are present in the Echeclus? coma)., Consequently the gas-to-dust ratio is much lower than in the cometary comae (if molecular species are present in the Echeclus' coma). + The event that happened to Echeclus looks like a cometary outburst., The event that happened to Echeclus looks like a cometary outburst. + Some other planetary bodies are now known to have suffered a similar event at large heltocentric distance (above 5 AU). nevertheless this outburst presents unusual characteristics that deserve a more detailed discussion: (1) it is unique by its amplitude (about 7 magnitudes); (11) the heliocentric distance is important for this type of event (12.9 AU): (111) the coma appears distinct from the object itself for a long time (at least several months): and (iv) the brightness distribution is compatible with a diffuse source.," Some other planetary bodies are now known to have suffered a similar event at large heliocentric distance (above 5 AU), nevertheless this outburst presents unusual characteristics that deserve a more detailed discussion: (i) it is unique by its amplitude (about 7 magnitudes); (ii) the heliocentric distance is important for this type of event (12.9 AU); (iii) the coma appears distinct from the object itself for a long time (at least several months); and (iv) the brightness distribution is compatible with a diffuse source." + Two different hypotheses might explain these characteristics: (1) the coma is created by a fragment ejected from Echeclus. or (11) it is created by a previously unknown satellite.," Two different hypotheses might explain these characteristics: (i) the coma is created by a fragment ejected from Echeclus, or (ii) it is created by a previously unknown satellite." + We examine the first hypothesis (a fragment ejected from Echeclus) in more detail., We examine the first hypothesis (a fragment ejected from Echeclus) in more detail. + First. no point-like object appears in this coma.," First, no point-like object appears in this coma." + From this observational fact. it is possible to derive an upper limit for a point-like object that would be responsible for this cometary activity.," From this observational fact, it is possible to derive an upper limit for a point-like object that would be responsible for this cometary activity." + We have added the image of a point-like object in the center of the coma with a two-sigma intensity (compared to the standard deviation of the intensity in this area)., We have added the image of a point-like object in the center of the coma with a two-sigma intensity (compared to the standard deviation of the intensity in this area). + This intensity corresponds to a magnitude of =25 (R-band)., This intensity corresponds to a magnitude of $\simeq$ 25 (R-band). + This magnitude. with a geometric albedo of 0.04. corresponds to a diameter of 8.3 km for the considered geocentric and heliocentric distances.," This magnitude, with a geometric albedo of 0.04, corresponds to a diameter of 8.3 km for the considered geocentric and heliocentric distances." + With a 1-s1gma detection level and a geometric albedo of 0.1 the upper limit for the diameter would be 3.6 km., With a 1-sigma detection level and a geometric albedo of 0.1 the upper limit for the diameter would be 3.6 km. + The diameter of Echeclus is estimated to be 83.6415 kkm. and its visual geometric albedo to 3.837) (?)..," The diameter of Echeclus is estimated to be $\pm15$ km, and its visual geometric albedo to $^{+1.89}_{-1.08}$ \citep{stansberry:2007}." + These upper limits for a fragment seems to be realistic and of the order of magnitude for a cometary nucleus., These upper limits for a fragment seems to be realistic and of the order of magnitude for a cometary nucleus. + The problems raised by a fragment are: (1) the fact that the surface brightness variation does not seem compatible with a poimt-like source (it does not follow a I/p law): and (11) the event responsible for the ejection of this fragment., The problems raised by a fragment are: (i) the fact that the surface brightness variation does not seem compatible with a point-like source (it does not follow a $\rho$ law); and (ii) the event responsible for the ejection of this fragment. + The point (1) probably implies a fragmentation process. as already pointed out by the color changes with cometocentric distance.," The point (i) probably implies a fragmentation process, as already pointed out by the color changes with cometocentric distance." + Perhaps the matter ejected from the nucleus is more similar to a swarm of dust particules than to an ice fragment., Perhaps the matter ejected from the nucleus is more similar to a swarm of dust particules than to an ice fragment. + We also examine the hypothesis of a previously unknown satellite more carefully., We also examine the hypothesis of a previously unknown satellite more carefully. + With reasonable parameters. i.e. a diameter of 83.6 km. a volumetric mass of 1000 kg.m7*. and a axis of 60 000 km (the minimum possible distance. because it 15 the projected distance on the sky). the third Kepler's law implies an orbital period P=20 years.," With reasonable parameters, i.e. a diameter of 83.6 km, a volumetric mass of 1000 $^{-3}$, and a semi-major axis of 60 000 km (the minimum possible distance, because it is the projected distance on the sky), the third Kepler's law implies an orbital period $\simeq$ 20 years." + This period could be shorter in the case of a highly eccentric orbit with a smaller semi-major axis. but such an eccentricity would be very unusual.," This period could be shorter in the case of a highly eccentric orbit with a smaller semi-major axis, but such an eccentricity would be very unusual." + A larger semi-major axis cannot be excluded and would lead to a longer, A larger semi-major axis cannot be excluded and would lead to a longer + , +investigate the correlation between (he positions of 5-rav sources aud the arrival directions ol VHECRs measured by the PAO.,investigate the correlation between the positions of $\gamma$ -ray sources and the arrival directions of UHECRs measured by the PAO. + Our goal is to unveil if specific tvpes of y-ray sources might be driving any correlation and at what angular separations these correlations become significant., Our goal is to unveil if specific types of $\gamma$ -ray sources might be driving any correlation and at what angular separations these correlations become significant. + In §2 we describe the datasets we use., In \ref{sec:data} we describe the datasets we use. + In 83. we describe our cross-correlation method., In \ref{sec:method} we describe our cross-correlation method. + In 84 we list the results of our cross-correlation analvsis when applied to the different subsamples of the IFGL and ΗΛ catalogs., In \ref{sec:results} we list the results of our cross-correlation analysis when applied to the different subsamples of the 1FGL and 1LAC catalogs. + We discuss the implications of our results in 85.., We discuss the implications of our results in \ref{sec:disc}. + In particular. we list the potential 75-rav loud” UNECR accelerators ancl discuss (heir properties in 85.1..," In particular, we list the potential $\gamma$ -ray loud” UHECR accelerators and discuss their properties in \ref{sec:sites}." + Section 6. closes with our concluding remarks., Section \ref{sec:end} closes with our concluding remarks. + We base our analvsis on the distribution of arrival directions of UIIECTs with energies exceeding 5.7xLO!eV. collected by the surface array of PAO between 1. January. 2004 and 31 August 2007. with an integrated exposure of 9.0x10*kan?srvear 2007. 2008)..," We base our analysis on the distribution of arrival directions of UHECRs with energies exceeding $5.7 \times 10^ {19} \ {\rm eV}$, collected by the surface array of PAO between 1 January, 2004 and 31 August 2007, with an integrated exposure of $9.0 \times 10^3 \ {\rm km}^2 \ {\rm sr \ year}$ \citep{pa, palong}. ." + This data set corresponds to 27 events wilh zenith angles smaller than 607 and angular resolution of z1? (Ave2007).., This data set corresponds to 27 events with zenith angles smaller than $60^\circ$ and angular resolution of $\approx 1^\circ$ \citep{padirs}. + To search for the potential astrophysical sources of UITECRs. we use the LAT First Source List (LFGL: Abdoοἱal. 2010a)) and the First LAT AGN Catalog (LLAC: 2010b)) of 5-rav sources produced alter the first eleven months of operation of Fermi.," To search for the potential astrophysical sources of UHECRs, we use the LAT First Source List (1FGL; \citealt{1fgl}) ) and the First LAT AGN Catalog (1LAC; \citealt{1lac}) ) of $\gamma$ -ray sources produced after the first eleven months of operation of ." + source detection is based on the average flux over the 1-month period corresponding to a statistical significance higher than to., Source detection is based on the average flux over the 11-month period corresponding to a statistical significance higher than $4\sigma$. + The IFGL consists of the 1451 sources detected and characterized in the LOO MeV to LOO GeV range., The 1FGL consists of the 1451 sources detected and characterized in the 100 MeV to 100 GeV range. + A subset of the IFGL consisting of 671 sources constitutes the LLAC., A subset of the 1FGL consisting of 671 sources constitutes the 1LAC. + 1037 sources in the LFGL are within the PAO field of view., 1037 sources in the 1FGL are within the PAO field of view. + Abdoetal.(20102) provides identifications or plausible associations of these 5-ray sources wilh objects in other astronomical catalogs: 93 of them correspond to Galactic sources (pulsars. pulsar wind nebulae. supernova remnants. X-rav binaries and globular clusters) and 453 (ο AGNs in ihe ILAC.," \citet{1fgl} provides identifications or plausible associations of these $\gamma$ -ray sources with objects in other astronomical catalogs: 93 of them correspond to Galactic sources (pulsars, pulsar wind nebulae, supernova remnants, X-ray binaries and globular clusters) and 453 to AGNs in the 1LAC." + Of the LLAC AGNs. 367 are blazars. 69 are AGNs of uncertain (vpe and 17 are non-blazar AGNs that include. for example. the radio galaxies M87. Centaurus A and ος 207.0 (Abdoetal.2010b)..," Of the 1LAC AGNs, 367 are blazars, 69 are AGNs of uncertain type and 17 are non-blazar AGNs that include, for example, the radio galaxies M87, Centaurus A and 3C 207.0 \citep{1lac}." + 490 LFGL sources could not be associated with any counterpart., 490 1FGL sources could not be associated with any counterpart. + Most of the unassociated sources are near (he Galactic plane. and could not be identified because of a combination of Galactic extinction ancl source confusion 2010a.b)..," Most of the unassociated sources are near the Galactic plane, and could not be identified because of a combination of Galactic extinction and source confusion \citep{0fgl, 1fgl, 1lac}." + Fieure |. shows the skv map in Galacticcoordinates of theUIIECTIU events together with the IFGL and LLAC sources., Figure \ref{aitoff} shows the sky map in Galacticcoordinates of theUHECRs events together with the 1FGL and 1LAC sources. + Also shown is the supergalactie plane along which nearby, Also shown is the supergalactic plane along which nearby +"1 and —1: σ(ϐ)=$(A-a(8)+Ai(8)), or ff(8)do(8)=3C(1)+f(-D), for any continuous f.","$1$ and $-1$: $\sigma(\beta) = \frac{1}{2}(\Delta_{-1}(\beta)+\Delta_1(\beta))$, or $ + \int f(\beta) d\sigma(\beta) = \frac{1}{2} (f(1) + f(-1)), +$ for any continuous $f$." +" The prey appears with equal probability (this symmetry can be easily changed, though) at either end of the interval."," The prey appears with equal probability (this symmetry can be easily changed, though) at either end of the interval." +" Contrary to what it might seem, this problem is far from being trivial."," Contrary to what it might seem, this problem is far from being trivial." +" It has a rich and classical history, going back at least to Wiener, Wintner, Erdóss and others in the 1930's."," It has a rich and classical history, going back at least to Wiener, Wintner, Erdöss and others in the 1930's." + Present knowledge can be summed up in the Let o(8)=i(A.a(B)+A1(B))., Present knowledge can be summed up in the Let $\sigma(\beta) = \frac{1}{2}(\Delta_{-1}(\beta)+\Delta_1(\beta))$. +" For any 6, µ is of pure type."," For any $\delta$, $\mu$ is of pure type." +" It is singular continuous, supported on a Cantor set, ifó«i."," It is singular continuous, supported on a Cantor set, if $\delta < \frac{1}{2}$." +" When 6=i, µ ds the Lebesque measure on [—1,1]."," When $\delta = \frac{1}{2}$, $\mu$ is the Lebesque measure on $[-1,1]$ ." +" There exist two constructive, countable sets of values of 6>i for which j is singular continuous, and absolutely continuous, respectively."," There exist two constructive, countable sets of values of $\delta> \frac{1}{2}$ for which $\mu$ is singular continuous, and absolutely continuous, respectively." + For almost all ó>i µ is absolutely continuous.," For almost all $\delta> \frac{1}{2}$, $\mu$ is absolutely continuous." +" It is just the case to remark here that this theorem collect significant results obtained along more than seventy years of research, see [4,19] for lists ofreferences."," It is just the case to remark here that this theorem collect significant results obtained along more than seventy years of research, see \cite{borw,solom} for lists ofreferences." + It is easy to understand what happens in the case ó« i., It is easy to understand what happens in the case $\delta < \frac{1}{2}$ . + Consider eq. (4)), Consider eq. \ref{dens3}) ) +" and let p(uo) be the uniform density on [—1,1]."," and let $\rho(\mu_0)$ be the uniform density on $[-1,1]$." +" It follows by direct computationthat (μι) is a piece-wise constant function for any n, which takes values 23153 on a set of 2” disjoint intervals of equal length 25”, and zero otherwise."," It follows by direct computationthat $\rho(\mu_n)$ is a piece–wise constant function for any $n$, which takes values $2^{-n-1} \delta^{-n}$ on a set of $2^n$ disjoint intervals of equal length $2 \delta^n$, and zero otherwise." +" These intervals constitute the usual generations in the hierarchical construction of a Cantor set (take ó—i to obtain the classical, ternary Cantor set)."," These intervals constitute the usual generations in the hierarchical construction of a Cantor set (take $\delta=\frac{1}{3}$ to obtain the classical, ternary Cantor set)." +" Clearly, the sequence p(fin) does not tend to any function and this is a remarkable example where measures converge while densities do not."," Clearly, the sequence $\rho(\mu_n)$ does not tend to any function and this is a remarkable example where measures converge while densities do not." +" The bounded variation norm is particularly suited to illustrate this point: we have that||p(us)|pv.=97"" and ||p(Hn)—p(us-i)lpv=25""(05 1)."," The bounded variation norm is particularly suited to illustrate this point: we have that$\|\rho(\mu_n)\|_{BV} = \delta^{-n}$ and $\|\rho(\mu_n)-\rho(\mu_{n-1})\|_{BV} = 2 \delta^{-n}(\frac{1}{2 \delta} +-1)$ ." + Both quantitiesdiverge as n— oo., Both quantitiesdiverge as $n \rightarrow \infty$ . + This provides a second test for algorithm, This provides a second test for algorithm +The seven allowed textures of the neutrino mass matrices with Frampton. Glashow ancl Marfatia (FGM) texture zero structure have been summarized in Table 1.,"The seven allowed textures of the neutrino mass matrices with Frampton, Glashow and Marfatia (FGM) texture zero structure have been summarized in Table 1." + For neutrino mass matrices of tvpe ly. we have," For neutrino mass matrices of type $A_1$, we have" +to measure the displacements may underestimate the velocity magnitudes.,to measure the displacements may underestimate the velocity magnitudes. +" Moreover, outside the moat one can easily find velocities larger than that."," Moreover, outside the moat one can easily find velocities larger than that." + The point is that this particular threshold makes in our case more evident the existence of a well organized radial outflows around the sunspots in comparison with the rest of the FOV., The point is that this particular threshold makes in our case more evident the existence of a well organized radial outflows around the sunspots in comparison with the rest of the FOV. + Lower values (even zero) for the threshold do not extend the areas of organized flows around the sunspots but produce maps with a very dense and noisy granules representation of arrows where (explodingthe outline of the everywhere)frontiers of the moats becomes more difficult., Lower values (even zero) for the threshold do not extend the areas of organized flows around the sunspots but produce maps with a very dense and noisy (exploding granules everywhere) representation of arrows where the outline of the frontiers of the moats becomes more difficult. +" Figures 2 to 6 show within the moats, only those velocity vectors with de-projected magnitudes above 0.3 kmss~!."," Figures \ref{F:2} to \ref{F:6} show within the moats, only those velocity vectors with de-projected magnitudes above 0.3 $^{-1}$ ." + In Figure 7 we extend this representation to the entire granulation field showing that large velocities are also present outside the moat., In Figure \ref{F:7} we extend this representation to the entire granulation field showing that large velocities are also present outside the moat. + These velocities are generally grouped and associated with exploding granules., These velocities are generally grouped and associated with exploding granules. + Our sunspot sample includes different penumbral configurations as a key factor to establish the moat-penumbra relation in a robust way., Our sunspot sample includes different penumbral configurations as a key factor to establish the moat-penumbra relation in a robust way. + Firstly we focus on granulation regions that display moat flows., Firstly we focus on granulation regions that display moat flows. +" Close inspection of Figures 2 - 7, andof the upper panel of Figure 9 reveals that the velocity vectors in the moats are oriented following the direction of the penumbral filaments."," Close inspection of Figures \ref{F:2} - \ref{F:7} , andof the upper panel of Figure \ref{F:9} reveals that the velocity vectors in the moats are oriented following the direction of the penumbral filaments." +" Nevertheless, the completeness of the velocity vectors (density of arrows) in the flow maps depends on the threshold previously imposed, as expected."," Nevertheless, the completeness of the velocity vectors (density of arrows) in the flow maps depends on the threshold previously imposed, as expected." + This can be seen in Figure 5 where the left-hand side penumbra does not seem to be strictly associated with large flows in the granulation region., This can be seen in Figure \ref{F:5} where the left-hand side penumbra does not seem to be strictly associated with large flows in the granulation region. +" However, this penumbral part has in fact an associated moat flow similar to the other penumbral regions which is not visible in the representation since the magnitude of the velocities is slightly lower than the threshold of 0.3 ss-!."," However, this penumbral part has in fact an associated moat flow similar to the other penumbral regions which is not visible in the representation since the magnitude of the velocities is slightly lower than the threshold of 0.3 $^{-1}$." + Next we consider granulation regions close to the sunspots that do not display moat flows., Next we consider granulation regions close to the sunspots that do not display moat flows. +" All sunspots of our sample, except $3, have parts of umbral core in direct contact with granulation regions without intervening penumbrae."," All sunspots of our sample, except S3, have parts of umbral core in direct contact with granulation regions without intervening penumbrae." + In all these granulation regions we do not detect systematic large-scale outflows that fulfill our criteria for moat flows., In all these granulation regions we do not detect systematic large-scale outflows that fulfill our criteria for moat flows. + Finally there are also granulation regions in the vicinity of penumbrae that lack significant moat flows.," Finally, there are also granulation regions in the vicinity of penumbrae that lack significant moat flows." +" To study these cases in more detail we mark in Figures 2,, 4,,5 and 6 peculiar regions ofinterest with rectangular white boxes."," To study these cases in more detail we mark in Figures \ref{F:2}, \ref{F:4}, \ref{F:5} and \ref{F:6} peculiar regions ofinterest with rectangular white boxes." + These regions are represented as close-ups in Figure 8.., These regions are represented as close-ups in Figure \ref{F:8}. +" In the three upper panels, the penumbral filaments display significant curvature such that they are not radially oriented with respect to the sunspot centre but they extend in a direction tangential to the sunspot border (as marked with black lines in the overview images Figures 2,, 4 and 6))."," In the three upper panels, the penumbral filaments display significant curvature such that they are not radially oriented with respect to the sunspot centre but they extend in a direction tangential to the sunspot border (as marked with black lines in the overview images Figures \ref{F:2}, \ref{F:4} and \ref{F:6}) )." + The lower panel in Figure 8 shows a penumbra extending radially from the umbra., The lower panel in Figure \ref{F:8} shows a penumbra extending radially from the umbra. + 'The surrounding photosphere exhibits moat flows only in the direction of the penumbral filaments (also see Figure 5))., The surrounding photosphere exhibits moat flows only in the direction of the penumbral filaments (also see Figure \ref{F:5}) ). + In a few cases we found small pores in the vicinity of penumbrae in a region where we would expect moat flows., In a few cases we found small pores in the vicinity of penumbrae in a region where we would expect moat flows. +" Such cases are seen around coordinates (19,29) in Figure 2 and coordinates (29,11) in Figure 6.."," Such cases are seen around coordinates (19,29) in Figure \ref{F:2} and coordinates (29,11) in Figure \ref{F:6}." + For these regions the measured proper motions are less reliable since we have a FWHM-1/0 tracking window acting on a region of only a few arc seconds (~ 2-3) between the pore and penumbra., For these regions the measured proper motions are less reliable since we have a $1\farcs0$ tracking window acting on a region of only a few arc seconds $\sim$ 2-3) between the pore and penumbra. + Another possibility is that the pores themselves are somehow blocking the large outflows changing the expected behavior., Another possibility is that the pores themselves are somehow blocking the large outflows changing the expected behavior. +" In the case presented in Figure 6 the most plausible explanation for the absence of moats is the presence of a neutral line close to coordinates (29,11) as we shall describe in 3.2.."," In the case presented in Figure \ref{F:6} the most plausible explanation for the absence of moats is the presence of a neutral line close to coordinates (29,11) as we shall describe in \ref{sec:neutral}. ." + 'The findings described above suggest a link between the moat flows and the Evershed flows in penumbrae., The findings described above suggest a link between the moat flows and the Evershed flows in penumbrae. + We come back to this relation in 4.., We come back to this relation in \ref{sec:dis}. + Only one of the sunspots we study displays a complete regular and well-developed penumbra surrounding completely the umbral core., Only one of the sunspots we study displays a complete regular and well-developed penumbra surrounding completely the umbral core. +" Figure 9 shows the flow map calculated for this active region, plotting the horizontal velocities surrounding the sunspot with deprojected magnitudes > 0.3 kmss~!."," Figure \ref{F:9} shows the flow map calculated for this active region, plotting the horizontal velocities surrounding the sunspot with deprojected magnitudes $>$ 0.3 $^{-1}$." + Large outflows are not found in a certain part of the right-hand side of the spot in the black squared region in the upper panel ofFigure 9.., Large outflows are not found in a certain part of the right-hand side of the spot in the black squared region in the upper panel ofFigure \ref{F:9}. . +" Following the findings of 3.1, we would expect to find a moat flow in thisregion."," Following the findings of \ref{sec:flowmaps}, , we would expect to find a moat flow in thisregion." + The penumbral, The penumbral +flares although they were clearly seen with Swift/BAT.,flares although they were clearly seen with Swift/BAT. + We will discuss the faint flares later on., We will discuss the faint flares later on. + We found that the data point of outburst 8 follows the empirical relation reported in Yuetal.(2007).. as shown in the inset panel of Fig 1..," We found that the data point of outburst 8 follows the empirical relation reported in \citet{Yu07}, as shown in the inset panel of Fig \ref{fig_pkwt}." + The deviation from the empirical relation is only -0.034 crab., The deviation from the empirical relation is only -0.034 crab. +" The linear Pearson’s correlation coefficient for all the 7 data points is 0.997, again indicating a nearly linear relation between the hard X-ray peak flux F, and the waiting time T,."," The linear Pearson's correlation coefficient for all the 7 data points is 0.997, again indicating a nearly linear relation between the hard X-ray peak flux $\rm F_p$ and the waiting time $\rm T_w$." +" A linear fit to this relation gives F,=(9.25+0.06)x107T,—(0.039+ 0.005). where E, is in unit of crab and T, in units of days."," A linear fit to this relation gives $\rm F_p=(9.25\pm0.06)\times +10^{-4}{\rm T_w}-(0.039\pm0.005)$ , where $\rm F_p$ is in unit of crab and $\rm T_w$ in units of days." + This updated relation is almost identical to the one reported in Yuetal.(2007)., This updated relation is almost identical to the one reported in \citet{Yu07}. +". The intrinsic scattering of the data is 0.014 crab. which defines a 40.014 crab bound ""Sof the linear relation."," The intrinsic scattering of the data is 0.014 crab, which defines a $\pm$ 0.014 crab bound of the linear relation." +" The intercept of the best-fitting linear model on the waiting time axis is T,=42 days when F,=0 crab."," The intercept of the best-fitting linear model on the waiting time axis is $\rm +T_w=42$ days when $\rm F_p=0$ crab." +" Considering the intrinsic scattering and the model uncertainty.= we obtained an intercept Ty,=42520 days."," Considering the intrinsic scattering and the model uncertainty, we obtained an intercept $\rm T_w= 42\pm 20$ days." + This means that the hard X-ray peak of any outburst should be at least 42+20 days after the end of the previous outburst. which ts determined eds the hard X-ray peak corresponding to the HS-to-LH transition.," This means that the hard X-ray peak of any outburst should be at least $42\pm 20$ days after the end of the previous outburst, which is determined as the hard X-ray peak corresponding to the HS-to-LH transition." + The refined empirical relation enables us to approximately estimate the hard X-ray peak flux (10-day average) for the next bright outburst in GX 339-4., The refined empirical relation enables us to approximately estimate the hard X-ray peak flux (10-day average) for the next bright outburst in GX 339-4. +" The updated relation gives the peak flux of the next bright outburst as Fy),=9.25x crab. where Dayay is the number of days in 2009 when a future outburst starts and Ty is the rise time in unit of day for the next outburst to reach its initial hard X-ray peak."," The updated relation gives the peak flux of the next bright outburst as $\rm F_{p,n}=9.25\times10^{-4}~({\rm +Day_{09}}+{\rm T_{rise}})+0.44$ crab, where $\rm Day_{09}$ is the number of days in 2009 when a future outburst starts and ${\rm +T_{rise}}$ is the rise time in unit of day for the next outburst to reach its initial hard X-ray peak." + The hard X-ray peak flux can be predicted almost as soon as the next outburst occurs because the rise time is nearly a small constant compared with the waiting time., The hard X-ray peak flux can be predicted almost as soon as the next outburst occurs because the rise time is nearly a small constant compared with the waiting time. + The source has remained inactive for about 750 days since the end of the 2007 outburst., The source has remained inactive for about 750 days since the end of the 2007 outburst. + This gives that the hard X-ray peak flux of the next outburst should be at least 0.65 crab (Fig 3)). making it the second brightest outburst since 1991. brighter than all the outbursts except outburst 6.," This gives that the hard X-ray peak flux of the next outburst should be at least 0.65 crab (Fig \ref{fig_pred}) ), making it the second brightest outburst since 1991, brighter than all the outbursts except outburst 6." + Again notice that only for an outburst brighter than about 0.12 crab can such a prediction be made based on the empirical relation., Again notice that only for an outburst brighter than about 0.12 crab can such a prediction be made based on the empirical relation. + We have shown that the empirical relation holds if faint hard X-ray flares are ignored., We have shown that the empirical relation holds if faint hard X-ray flares are ignored. + Por example the flare of about 0.08 crab in March 2006 does not affect the peak flux of the 2007 outburst., For example the flare of about 0.08 crab in March 2006 does not affect the peak flux of the 2007 outburst. + This suggests that the flare of about 0.1 crab in March 2009 will not affect the hard X-ray peak flux of next bright outburst significantly., This suggests that the flare of about 0.1 crab in March 2009 will not affect the hard X-ray peak flux of next bright outburst significantly. + The negligible effect of the faint flares on the empirical relation is also consistent with the consideration of the actual value range of T4., The negligible effect of the faint flares on the empirical relation is also consistent with the consideration of the actual value range of $\rm T_w$. + The intersection of the best-fitting linear empirical relation on the time axis indicates that the hard X-ray peak of a major. bright outburst must occur more than 42+20 days after the hard X-ray peak during the decay phase of the previous outburst.," The intersection of the best-fitting linear empirical relation on the time axis indicates that the hard X-ray peak of a major, bright outburst must occur more than $42\pm20$ days after the hard X-ray peak during the decay phase of the previous outburst." + However as discussed in (2007).. the sum of the decay time of the LH state in the previous outburst and the rise time of the LH state in the next outburst is normally about 100-150 days.," However as discussed in \citet{Yu07}, the sum of the decay time of the LH state in the previous outburst and the rise time of the LH state in the next outburst is normally about 100–150 days." +" Therefore m reality the minimal T, for bright outbursts. as defined by Yuet (2007).. would be 100-150 days."," Therefore in reality the minimal $\rm T_w$ for bright outbursts, as defined by \citet{Yu07}, would be 100–150 days." +" This corresponds to F, in the range of ~0.04—0.12 crab. which indicates a lower limit of F, for any outburst that should be considered in the empirical relation."," This corresponds to $\rm F_{p}$ in the range of $\sim0.04-0.12$ crab, which indicates a lower limit of $\rm F_{p}$ for any outburst that should be considered in the empirical relation." + This might suggest that after an outburst. GX 339- can subsequently rise up to ~0.12 crab without returning quiescence.," This might suggest that after an outburst, GX 339-4 can subsequently rise up to $\sim0.12$ crab without returning quiescence." + Because of their low luminosities. the faint flares," Because of their low luminosities, the faint flares" +the absorbed energv is split between the dillerent grain sizes. ancl Jg(A.0) is the spectral shape of the spectrum emitted by the erains with radius à.,"the absorbed energy is split between the different grain sizes, and $\mathcal{F}_{\rm IR}(\lambda,a)$ is the spectral shape of the spectrum emitted by the grains with radius $a$." +" The simplest situation is when (he spectrum emitted by all grains has approximately (he same spectral shape (e.. Ay,(A.0) is independent of o)."," The simplest situation is when the spectrum emitted by all grains has approximately the same spectral shape (i.e., $\mathcal{F}_{\rm IR}(\lambda,a)$ is independent of $a$ )." + In this case. the spectral shape of the IR SED of the envelope will be similar to (he spectral shape of the individual grains. regarcless of how the absorbed energv is split between the different. grains.," In this case, the spectral shape of the IR SED of the envelope will be similar to the spectral shape of the individual grains, regardless of how the absorbed energy is split between the different grains." + A somewhat similar situation occurs when a particular range of grain sizes. with a similar emission spectrum. completely dominates the emission.," A somewhat similar situation occurs when a particular range of grain sizes, with a similar emission spectrum, completely dominates the emission." + [lere. even if the spectral shape of the other erain sizes is different. it does not affect the envelope IR. SED.," Here, even if the spectral shape of the other grain sizes is different, it does not affect the envelope IR SED." + An important difference from the first situation is that. here. the manner in which the absorbed energy is distributed between (he grain sizes is important.," An important difference from the first situation is that, here, the manner in which the absorbed energy is distributed between the grain sizes is important." + For both these cases. we expect a close similarity lo the corresponding single-szed erain model.," For both these cases, we expect a close similarity to the corresponding single-sized grain model." + An opposite situation occurs when clillerent erain sizes emit a dillerent spectral shape with similar integrated emissions., An opposite situation occurs when different grain sizes emit a different spectral shape with similar integrated emissions. + In (his case. the envelope IR SED can no longer be described using a single erain size mocel.," In this case, the envelope IR SED can no longer be described using a single grain size model." + What controls Jig(A.e) is the spectral shape of the absorption elliciencies ancl (he erain temperature.," What controls $\mathcal{F}_{\rm IR}(\lambda,a)$ is the spectral shape of the absorption efficiencies and the grain temperature." + From the conditions of AIL it is evident that the grain sizes with similar emission spectra will be the ones that comply with conditions 1 and 3.," From the conditions of AI, it is evident that the grain sizes with similar emission spectra will be the ones that comply with conditions 1 and 3." + The fist condition requires all grain sizes of the distribution must be smaller than a maximuni size. given bv eq. (1)).," The first condition requires all grain sizes of the distribution must be smaller than a maximum size, given by eq. \ref{eq1}) )." + The third condition implies that all grain sizes must have similar equilibrium temperatures., The third condition implies that all grain sizes must have similar equilibrium temperatures. + llowever. owing to their different absorption efficiencies. different grain sizes can have very different. equilibrium temperatures.," However, owing to their different absorption efficiencies, different grain sizes can have very different equilibrium temperatures." + This effect can be inlerred. [vom the second. column of Table 1:: different grain sizes have clifferent condensation radii. which indicates that. if these erains were (o coexist al the same point in space. (he grain sizes wilh larger condensation radii will be hotter than those with lower condensation radii.," This effect can be inferred from the second column of Table \ref{tab1}: different grain sizes have different condensation radii, which indicates that, if these grains were to coexist at the same point in space, the grain sizes with larger condensation radii will be hotter than those with lower condensation radii." + Recently. Wolf.(2003). studied the condensation temperature of the individual grain sizes in a mixture ol different. grains sizes. both in 1-D and 2-D dust shells. and found that the temperature difference spans a range of up to 22250 Ix. although (his value is highly dependent of the choice of the dust properties.," Recently, \citet{wol03} studied the condensation temperature of the individual grain sizes in a mixture of different grains sizes, both in 1-D and 2-D dust shells, and found that the temperature difference spans a range of up to $\approx 250$ K, although this value is highly dependent of the choice of the dust properties." + It is easy to show Chat. in the Monte Carlo radiative equilibrium scheme. the temperature T(a) of the grains wilh radius à al a given point of the envelope will depend on (he number of photons absorbed by these grains. Ia(G1). and on the Planck mean opacity. &p(1.«) (see Djorkman&Wood(2001).. eq. |," It is easy to show that, in the Monte Carlo radiative equilibrium scheme, the temperature $T(a)$ of the grains with radius $a$ at a given point of the envelope will depend on the number of photons absorbed by these grains, $N_{\rm abs}(a)$, and on the Planck mean opacity, $\kappa_{\rm P}(T,a)$ (see \citet{bjo01}, eq. [" +5]). The number of absorbed photons is proportional to the absorption cross section averaged,"5]), The number of absorbed photons is proportional to the absorption cross section averaged" +added to the helitun core is itself proportional to the luminosity. this means that throughout red eiant evolution tie helitun core mass and the lIunminosity increase at an ever faster rate.,"added to the helium core is itself proportional to the luminosity, this means that throughout red giant evolution the helium core mass and the luminosity increase at an ever faster rate." + The oue exception to this is at the RGB bump. where the sudden Change in chemical composition causes the growth in luiinosity to pause temporarily. while the |eliui core continues to galli nass.," The one exception to this is at the RGB bump, where the sudden change in chemical composition causes the growth in luminosity to pause temporarily, while the helium core continues to gain mass." + The probability of observing a star in a given luminosity range ou the RGB is inversely proportional to the ra eat whic stars evolve at tlat luinosity., The probability of observing a star in a given luminosity range on the RGB is inversely proportional to the rate at which stars evolve at that luminosity. + In observed οobularm uster ciagrams. herefore. we find that the 1tuber o“observed stars steadily dec‘eases aloug the RGB. except at tl 'ecd giat Dump.," In observed globular cluster color-magnitude diagrams, therefore, we find that the number of observed stars steadily decreases along the RGB, except at the red giant bump." + Iu fact. the ciffe|ntial luminosity fnction oCa globular cluster. showing the 1aber NV of observed stars as a fuirctiou of maguitucle. descens along the RGB as a nearly. stral line i ile e-logSeN plane.," In fact, the differential luminosity function of a globular cluster, showing the number $N$ of observed stars as a function of magnitude, descends along the RGB as a nearly straight line in the $\log N$ plane." + The slope of this liue indicates |OW the rate of evolution i‘reases along the RGB., The slope of this line indicates how the rate of evolution increases along the RGB. + Globular cluster luinosity [tuctlous provide an important test of the accuracy of stelar evolution models., Globular cluster luminosity functions provide an important test of the accuracy of stellar evolution models. + The number of sals observed as a functioi of luminosiy indicates the relative timescale of stellar evoion. which u turn conveys information abou the internal cliemical structure of stars.," The number of stars observed as a function of luminosity indicates the relative timescale of stellar evolution, which in turn conveys information about the internal chemical structure of stars." + A great deal of alention has been paiL for example. to the total uum)er of stars on the RGB cOLipared to the 1ialli sedeuce ΕΕ region.," A great deal of attention has been paid, for example, to the total number of stars on the RGB compared to the main sequence turn-off region." + Seve‘al authors (Bolte1991:Larson&dePropris1998:Langer.BolteSandquist2000) |ave found a discrepancy in this quautity betweοι observed. lunilosity fiictions for the elobular clisters ALS ancl M30 and tlle predictions «X stellar evolution theory.," Several authors \citep{bolte,van98,langer} + have found a discrepancy in this quantity between observed luminosity functions for the globular clusters M5 and M30 and the predictions of stellar evolution theory." + Vadenberg.Larso1&deP‘opris(1998) take this discrepancy {ο 5ους the presence of ‘apidly rotating cores in red giants. while take it to indicate the possibiity of a chemica —ixiug p'ocess deep iu the stellar juterlo1.," \citet{van98} + take this discrepancy to suggest the presence of rapidly rotating cores in red giants, while \citet{langer} take it to indicate the possibility of a chemical mixing process deep in the stellar interior." + Tje magitide of the RGB bimp in observed globular cluse* serves to indicate the depth of he chemical cliscoutiinuity left by he convective envelope at 1S j»oiut of deepest extent. near the JASE O ‘the RGB., The magnitude of the RGB bump in observed globular clusters serves to indicate the depth of the chemical discontinuity left by the convective envelope at its point of deepest extent near the base of the RGB. + In oie of the first extensive studies of the red [n]eiit bump. FusiPeccietal.(1990) compared observatjonal determinatlous of the bump maguittce i 11 globular clusters to theoretical jyredieious.," In one of the first extensive studies of the red giant bump, \citet{fusi} compared observational determinations of the bump magnitude in 11 globular clusters to theoretical predictions." +" They fouxd that. taker yeative to the horizouta b""alch magnitude. theoretical values oL the bump magnuitude are higher han observed values by Hibou O0.I1 mag."," They found that, taken relative to the horizontal branch magnitude, theoretical values of the bump magnitude are higher than observed values by about 0.4 mag." +" However. LOο recent studies usine upcatece stellar evolulo1 models aud improve ¢ervations (C'assisl&Salaris1997:Zoccalietal.1999:Riello200:) iave [ound io cliscrepaicy between theory auk obse""vallons."," However, more recent studies using updated stellar evolution models and improved observations \citep{cas3,zoccali,riello} have found no discrepancy between theory and observations." + Cassisi&Salaris(1997) have sjed how uncertainties 1 ije most Important in]Nrictual stellar evolution parameters impact the m:iglitude of the red giai bump., \citet{cas3} have studied how uncertainties in the most important individual stellar evolution parameters impact the magnitude of the red giant bump. + They look at tle equation of state. mixing leugth. mass loss alotD>oO he RGB. opacities. ad the V-baud bolometjc correction.," They look at the equation of state, mixing length, mass loss along the RGB, opacities, and the $V$ -band bolometric correction." + Iu addition. Cassisi.deelInnocenti&Salaris(1997) stuclied the impact of elemeul diffusion in detail.," In addition, \citet{cas1} studied the impact of element diffusion in detail." + The effects of overshooting from the convective envel[9]ye have been considered by (1991).., The effects of overshooting from the convective envelope have been considered by \citet{alongi}. + This paper preseuts a comprehensive study of incorporatiug all the relevant uncertainties to firmly esta)ish the agreement between stancard stellar models aud observatious of the red giant. bump., This paper presents a comprehensive study of incorporating all the relevant uncertainties to firmly establish the agreement between standard stellar models and observations of the red giant bump. + , +consistent with sinusoidal modulation at the orbital period with a semiamplitude of about 0.2—0.3 mag. suggesting the presence of an irradiated companion.,"consistent with sinusoidal modulation at the orbital period with a semiamplitude of about $-$ 0.3 mag, suggesting the presence of an irradiated companion." + From the observed Δι we estimate a color excess of E(B—V)=0.74+0.07 mag.," From the observed $N_H$, we estimate a color excess of $E(B-V)=0.74 \pm 0.07$ mag." + The observed optical/NIR quiescent luminosity. derived from our multiband photometry. can be modeled with an irradiated companion star providing a good agreement with the observed data.," The observed optical/NIR quiescent luminosity, derived from our multiband photometry, can be modeled with an irradiated companion star providing a good agreement with the observed data." + The presence of a residual dise component. even if possible. is not necessary for our model.," The presence of a residual disc component, even if possible, is not necessary for our model." +" The required irradiating luminosity is 4xI0?6x107 Gauss.," If we assume this value as a lower limit for the spin-down luminosity, then the magnetic field of the neutron star results to be $> 6 \times 10^7$ Gauss." + As remarked for SAX J1808.4-3658 by Burderi et al. (, As remarked for SAX $-$ 3658 by Burderi et al. ( +2003) and Campana et al. (,2003) and Campana et al. ( +2004). the only source of energy available within the system that can supply such luminosity is the rotational energy of the neutron star emitted in the form of a relativistic particle wind.,"2004), the only source of energy available within the system that can supply such luminosity is the rotational energy of the neutron star emitted in the form of a relativistic particle wind." + However. a direct detection of millisecond pulsations in the radio band for IGR JO029145934 could be dificult for free-free absorption effects. due to the mass coming from the companion star and swept away by the radiation pressure of the pulsar.," However, a direct detection of millisecond pulsations in the radio band for IGR J00291+5934 could be difficult for $-$ free absorption effects, due to the mass coming from the companion star and swept away by the radiation pressure of the pulsar." + A search at high frequencies could be a solution to overcome this effect (see also Campana et al 1998. Burderi et al.," A search at high frequencies could be a solution to overcome this effect (see also Campana et al 1998, Burderi et al." + 2003 and Campana et al., 2003 and Campana et al. + 2004)., 2004). +2010).,. +. This suggested that the observed dust eloud and the nucleus were (he result of an impact between (wo previously unknown asteroids: the dust cloud is a plume of dust and the nucleus is what remains [rom the largest of the asteroids that collided., This suggested that the observed dust cloud and the nucleus were the result of an impact between two previously unknown asteroids: the dust cloud is a plume of dust and the nucleus is what remains from the largest of the asteroids that collided. + Owing to its cometary-like aspect and orbital parameters. P/2010 A2 can be classified as a Main-Delt. Comet (MDC.IIsieh&Jewitt2006).," Owing to its cometary-like aspect and orbital parameters, P/2010 A2 can be classified as a Main-Belt Comet \citep[MBC,][]{Hsieh06}." +. In contrast with the other known AIDCS. however. P/2010 A2 has a significantly smaller semi-major axis (2.29 AU versus 2.7 AU and —3.2 AU).," In contrast with the other known MBCs, however, P/2010 A2 has a significantly smaller semi-major axis (2.29 AU versus 2.7 AU and $\sim$ 3.2 AU)." +" Until now. the activity observed in MDCs was found to be compatible with a water-ice driven activation mechanism suggesting that those asteroids retained ice lavers below their surface and. under certain conditions. become ""activated asteroids”."," Until now, the activity observed in MBCs was found to be compatible with a water-ice driven activation mechanism suggesting that those asteroids retained ice layers below their surface and, under certain conditions, become “activated asteroids”." + The presence of water-ice on the surface of 24 Themis. the parent asteroid of the Themis family MBCs (Campinsοἱal.2010:Rivkin&Emery2010) stronely support this.," The presence of water-ice on the surface of 24 Themis, the parent asteroid of the Themis family MBCs \citep{Campins10,RivkinEmery10} strongly support this." + One of the activation mechanisms could be a collision between two asteroids., One of the activation mechanisms could be a collision between two asteroids. + Collisions are known to take place regularly. but (μον are so rare that. none of the dust plumes that they should generate has ever been seen.," Collisions are known to take place regularly, but they are so rare that none of the dust plumes that they should generate has ever been seen." + If P/2010 A? is the debris of a collisional event. this would be the first time that the ejecta from such a collision is observed soon after it happened.," If P/2010 A2 is the debris of a collisional event, this would be the first time that the ejecta from such a collision is observed soon after it happened." + It would provide a unique opportunity to learn something about asteroid collision processes and about the internal composition of asteroids., It would provide a unique opportunity to learn something about asteroid collision processes and about the internal composition of asteroids. + Alternatively. if Che observed aclivily is sustained in (nme as in comets. (his leaves open (wo interesting problems: (1) if water-ice sublimation is the activation mechanism. how does water-ice survive in an asteroid with such a small semi-major axis: or (2) is there any other mechanism capable of ejecting dust in a similar manner as water-ice sublimation does?," Alternatively, if the observed activity is sustained in time as in comets, this leaves open two interesting problems: (1) if water-ice sublimation is the activation mechanism, how does water-ice survive in an asteroid with such a small semi-major axis; or (2) is there any other mechanism capable of ejecting dust in a similar manner as water-ice sublimation does?" + In this paper we present and analvze images of P/2010 A2 obtained with three telescopes al the Roque de los Muchachos Observatory (ORAL). La Palma. Spain.," In this paper we present and analyze images of P/2010 A2 obtained with three telescopes at the Roque de los Muchachos Observatory (ORM), La Palma, Spain." + In. Sect., In Sect. + 2 the observations and data reduction are presented., 2 the observations and data reduction are presented. + In Sect., In Sect. + 3 we analvze (he combined images using the inverse Monte Carlo dust tail fitting method (e.g.Morenoetal.2009) to study possible ejection scenarios.," 3 we analyze the combined images using the inverse Monte Carlo dust tail fitting method \citep[e.g.][]{Moreno04, Moreno09} to study possible ejection scenarios." + The conclusions are presented in Sect., The conclusions are presented in Sect. + 4., 4. + Images of P/2010 A2 were obtained in January 2010 with the Optical System [for Imaging and low Resolution Integrated Spectroscopy (OSIRIS:Cepaetal.2000: camera-spectrograph αἱ the Gran Teleseopio Canarias (GTC). with the Auxiliary. spectrograph CACAM) at the William Ilerschel Telescope (WIT). and with the Andalucia Faint Object Spectrograph and Camera (ALFOSC) at the Nordic Optical Telescope (NOT) all located at the ORAL.," Images of P/2010 A2 were obtained in January 2010 with the Optical System for Imaging and low Resolution Integrated Spectroscopy \citep[OSIRIS;][]{Cepa00, Cepa10} camera-spectrograph at the Gran Telescopio Canarias (GTC), with the Auxiliary camera-spectrograph (ACAM) at the William Herschel Telescope (WHT), and with the Andalucia Faint Object Spectrograph and Camera (ALFOSC) at the Nordic Optical Telescope (NOT) all located at the ORM." +stars.,stars. + The CNO effect dominates on the SCD. and Πο effect on the NB.," The CNO effect dominates on the SGB, and He effect on the HB." + ILowever. in this scenario the DIID should also be brighter than the RIID. which is nof observed (ee. Salarisctal. 2008)). G," However, in this scenario the BHB should also be brighter than the RHB, which is not observed (e.g. \citealt{sal08}) ). (" +i) A merging of two GCs differing in age (although this does not excludeprior? a difference in the total CNOJ).,iii) A merging of two GCs differing in age (although this does not exclude a difference in the total CNO). + Tn this scenario. one of the CC Gucluding some of the stars) would be responsible for the bright. vounecr (possible less conuceutrated) SGD. of the MR (less concentrated) RGB. aud of the vounger RUB.," In this scenario, one of the GC (including some of the stars) would be responsible for the bright, younger (possibly less concentrated) SGB, of the MR (less concentrated) RGB, and of the younger RHB." + The other GC (including some of the stars} would be responsible of the faint. older (possibly more concentrated) SOB. of the MP. (minore. conceutrated) RGB. and of the older BIB.," The other GC (including some of the stars) would be responsible of the faint, older (possibly more concentrated) SGB, of the MP (more concentrated) RGB, and of the older BHB." + Iu this case. the two SGBs can be fitted by isochrones differing iu age by ~1.5 Car. if the same CNO coutent is assumed for both GCs. aud the difference in Fe is as derived from the MP aud AIR RGB components.," In this case, the two SGBs can be fitted by isochrones differing in age by $\sim 1.5$ Gyr, if the same CNO content is assumed for both GCs, and the difference in Fe is as derived from the MP and MR RGB components." + Should the solution (i) be the right one. the age clifference that we ueed (~11.5 Cir) is not uulikelv if the clusters were born iu a dSphl (see e.2.. he case of the Fornax dSph GCs. Buonannoetal.1998. 1999)).," Should the solution (iii) be the right one, the age difference that we need $\sim 1-1.5$ Gyr) is not unlikely if the clusters were born in a dSph (see e.g., the case of the Fornax dSph GCs, \citealt{buo98, buo99}) )." + As a consistency check. we explored Lees diagram IIB-type vs [Fe/II|] (seo c.g. Fig.," As a consistency check, we explored Lee's diagram HB-type vs [Fe/H] (see e.g., Fig." + 9 in Reyetal.20013) uusing the average values of ietallicity [Fe/T=1.20 (c=0.03 dex) and |Fe/TMJ=1.12 (6=0.03 dex) for the MP aud MP. components. respectively.," 9 in \citealt{rey01}) using the average values of metallicity $=-1.20$ $\sigma=0.03$ dex) and $=-1.12$ $\sigma=0.03$ dex) for the MP and MP components, respectively." + If we tentatively adopt for the two the IB type of NGC 288 (0.98) and NGC 362v (-0.87).nile componentsthe diagram shows that the MIR component may be about 1-1.5 Gyr vounecr then the MP onc.," If we tentatively adopt for the two components the HB type of NGC 288 (0.98) and NGC 362 (-0.87), the diagram shows that the MR component may easily be about 1-1.5 Gyr younger then the MP one." + Au additional coustraint comes from thle ratio between the abundances of s andr process clements., An additional constraint comes from the ratio between the abundances of $s-$ and $r-$ process elements. + Fie., Fig. + 6 shows the |Da/Eu| ratio as a function of metallicity for the 13 stars with UVES spectra., \ref{f:fig5} shows the [Ba/Eu] ratio as a function of metallicity for the 13 stars with UVES spectra. + This ratio is close to that expected from a pure-1 component for MP. stars. while it indicates a larger coutribution by —5 process for the MIR ones.," This ratio is close to that expected from a $r$ component for MP stars, while it indicates a larger contribution by $-s$ process for the MR ones." + The treud with [Fe/TI] is even cleaner when using the average from Ba. La. and Ce.," The trend with [Fe/H] is even cleaner when using the average from Ba, La, and Ce." + It sugecsts a lavecr contribution of polluters of sinaller masses for the MIR component. which fits well with the proposed age difference.," It suggests a larger contribution of polluters of smaller masses for the MR component, which fits well with the proposed age difference." + To conclude. we note that Carballo-Dello&Martinez-Deleado|(2010). reported the existence of a distinct metal-poor main sequence around the GCs NGC 1551 and NGC 1901. which they interpreted as ἃ very low surface brightuess stellar svstem.," To conclude, we note that \cite{carb10} reported the existence of a distinct metal-poor main sequence around the GCs NGC 1851 and NGC 1904, which they interpreted as a very low surface brightness stellar system." + This is maybe consistent with the structure ideutified by Olszewskictal.(2009)x in the form of a halo of mmai-sequenee stars surrounding NGC 1851 up to a distance of 250 pc., This is maybe consistent with the structure identified by \cite{ols09} in the form of a halo of main-sequence stars surrounding NGC 1851 up to a distance of 250 pc. + Both these observatious sugecst the existence of a residual structure that uuelt be what is left by the destruction of the ancestral dwarf where the progenitor of NGC 1851 originated., Both these observations suggest the existence of a residual structure that might be what is left by the destruction of the ancestral dwarf where the progenitor of NGC 1851 originated. + A really clear-cut test for the preseuce of two distiuct GCs is to probe the Na-O auticorrelation among TB stars., A really clear-cut test for the presence of two distinct GCs is to probe the Na-O anticorrelation among HB stars. + If the merecr hypothesis is correct. each one of the IID (comune frou individual GCs) should presentνους the Na-O auticorrelation. as we find in the MR and AIP components of the ROB.," If the merger hypothesis is correct, each one of the HB populations (coming from individual GCs) should present the Na-O anticorrelation, as we find in the MR and MP components of the RGB." + Ou the contrary. for a single proto-cluster scenario. we should expect the RIB stars be almost all O-rich. with the O-poor stars only confined to the DBIIB.," On the contrary, for a single proto-cluster scenario, we should expect the RHB stars be almost all O-rich, with the O-poor stars only confined to the BHB." + Specific proposals of obscrvatious ainied to perform this test have been alreacky πατος., Specific proposals of observations aimed to perform this test have been already submitted. + Partial funding come from the PRIN MIUR 2007 CRA 1.06.07.05. PRIN INAF 2007 CRA 1.06.10.01. the DFC cluster of excellence “Origiu and Structure of the Universe”," Partial funding come from the PRIN MIUR 2007 CRA 1.06.07.05, PRIN INAF 2007 CRA 1.06.10.04, the DFG cluster of excellence ”Origin and Structure of the Universe”." +mass distributions. by adding the effects of mass at scales »vond that of the Local Group. or testing its validity using numerical simulations (see.e.g..2277????7).,"mass distributions, by adding the effects of mass at scales beyond that of the Local Group, or testing its validity using numerical simulations \citep[see, e.g.,][]{Peeb89,FT91,Val93,P94,P01,SF05,Loeb05,LW07,vdM07}." +. One of the most intriguing developments. stemming rom the various studies of the Local Group is an estimate of the transverse velocity. of Andromeda., One of the most intriguing developments stemming from the various studies of the Local Group is an estimate of the transverse velocity of Andromeda. + Dy. emploving he action principle to the motions of galaxies within ane near (<20 Alpe) the Local Group. ? concluded that the ransverse velocity of Andromeda is less than 200," By employing the action principle to the motions of galaxies within and near $<20$ Mpc) the Local Group, \citet{P01} concluded that the transverse velocity of Andromeda is less than $200$." +" Using the well measured. transverse velocity of M33. (7) and numerical simulations that tracked the potential tidal disruption curingM33s past encounters with Ancronicela,. ? [ound an even smaller estimate. ~LOOL.. for the transverse velocity."," Using the well measured transverse velocity of M33 \citep{Bru05} and numerical simulations that tracked the potential tidal disruption duringM33's past encounters with Andromeda, \citet{Loeb05} found an even smaller estimate, $\sim 100$, for the transverse velocity." + While future astrometric observations using ancl will be able to accurately measure the proper motion of Andromeda. the low values favored by these papers suggests that the Local. Coup is. indeed: a gravitationally bound syslem.," While future astrometric observations using and will be able to accurately measure the proper motion of Andromeda, the low values favored by these papers suggests that the Local Group is indeed a gravitationally bound system." + Provided that the Local Group is gravitationally bound. and that the Milkv Way and Andromeda. are. heading towards cach other. one must admit the possibility that they will eventually interact and merge.," Provided that the Local Group is gravitationally bound, and that the Milky Way and Andromeda are heading towards each other, one must admit the possibility that they will eventually interact and merge." + This outcome appears inevitable given. the massive halos of dark matter that likely surround the Alilky Way and Andromeda., This outcome appears inevitable given the massive halos of dark matter that likely surround the Milky Way and Andromeda. + Numerical experiments have robusthy concluded that dark matter halos can exert significant dynamical friction. and are sponges that soak up energy and angular momentum leacing to a rapid merger (?)..," Numerical experiments have robustly concluded that dark matter halos can exert significant dynamical friction, and are sponges that soak up energy and angular momentum leading to a rapid merger \citep{B88}." + Even though the eventual merger. between the Milky Way and Xndromeda is common lore in Astronomy. the merecr process has not been addressed by a comprehensive numerical study.," Even though the eventual merger between the Milky Way and Andromeda is common lore in Astronomy, the merger process has not been addressed by a comprehensive numerical study." + The one exception is a paper by 7 that presented. a viable model for the Local Group and numerically simulated. the eventual merger between the Milky Wavy and Ancromeca., The one exception is a paper by \citet{Dub96} that presented a viable model for the Local Group and numerically simulated the eventual merger between the Milky Way and Andromeda. + However. 2 utilized this Local Group model and its numerical evolution to study the ooduction of tidal tails curing such an encounter and the »ossibility to use the structure of this tical material to probe he dark matter potential.," However, \citet{Dub96} utilized this Local Group model and its numerical evolution to study the production of tidal tails during such an encounter and the possibility to use the structure of this tidal material to probe the dark matter potential." + While the study by 2? provided he first enticing picture of the future encounter. between he Milky Way anc Andromeda. (foramorerecentandueherresolutionversionofthissimulation.sec 2).. it was neither designed to detail the merger dynamics including intergalactic material. nor outline the possible outcomes for he dynamics of our Sun. nor quantify properties of the merger remnant.," While the study by \citet{Dub96} provided the first enticing picture of the future encounter between the Milky Way and Andromeda, \citep[for a more recent and higher +resolution version of this simulation, see][]{Dub06}, it was neither designed to detail the merger dynamics including intergalactic material, nor outline the possible outcomes for the dynamics of our Sun, nor quantify properties of the merger remnant." + In addition. the last decade has producd a number of improved. models for the structure of the Milky. Way ancl Andromeda as well as the properties of the intragroup mecium.," In addition, the last decade has produced a number of improved models for the structure of the Milky Way and Andromeda as well as the properties of the intragroup medium." + In this paper we quantitatively predict when the interaction and merger of the Milky Way and Xnedromeda will likely occur and forecast the probable dynamics of the Sun during this event., In this paper we quantitatively predict when the interaction and merger of the Milky Way and Andromeda will likely occur and forecast the probable dynamics of the Sun during this event. + We achieve this goal by constructing a mocdel for the Local Croup in refsec:imodel that) satisfies. all. observational constraints., We achieve this goal by constructing a model for the Local Group in \\ref{sec:model} that satisfies all observational constraints. + We then evolve. this model using a self-consistent body/hvdrodynamie simulation. as described inrefsec:ipmeths.," We then evolve this model using a self-consistent N-body/hydrodynamic simulation, as described in." +. “Phe generic properties of the merger. including the merger timescale. the possible evolution. ofour Solar System. ancl properties of the merger remnant. ave outlined in refsec:results..," The generic properties of the merger, including the merger timescale, the possible evolution ofour Solar System, and properties of the merger remnant, are outlined in \\ref{sec:results}." + Finally. we conclude in re[seciconc..," Finally, we conclude in \\ref{sec:conc}." + The distribution of mass within our Local Group of galaxies has been a longstanding question in astrophivsies., The distribution of mass within our Local Group of galaxies has been a long–standing question in astrophysics. + I is clear that much of the matter is associated with the two largest ealaxies in the Local Group: the Milky Way and Andromeda., It is clear that much of the matter is associated with the two largest galaxies in the Local Group: the Milky Way and Andromeda. + Moreover. these two spiral galaxies are likely to be embedded in an ambient medium of dark matter and gas.," Moreover, these two spiral galaxies are likely to be embedded in an ambient medium of dark matter and gas." + There are a number of different models for both the Milky Wav and Andromeda galaxies (see.e.7TT?T.androfer-encetherein)...," There are a number of different models for both the Milky Way and Andromeda galaxies \citep[see, e.g.,][and reference therein] {KZS02,WD05,SBB07}." + These studies generally enlist a myriad. of observational data to infer the clistribution of barvons. while the dark matter. which dominates the gravitationa potential. is set to match. distributions extracted. from cosmological N-body simulations (e.g..2)..," These studies generally enlist a myriad of observational data to infer the distribution of baryons, while the dark matter, which dominates the gravitational potential, is set to match distributions extracted from cosmological N-body simulations \citep[e.g.,][]{NFW96}." + Together. these models specify the total mass distribution out to the viria raclius (~200300 kpe).," Together, these models specify the total mass distribution out to the virial radius $\sim200-300$ kpc)." + In our model of the Local Group we start by. adopting the models for the Milkv Way and Andromeda: favore by 7.., In our model of the Local Group we start by adopting the models for the Milky Way and Andromeda favored by \citet{KZS02}. + Within these models. the barvons are. containe entirely. within the rotationally supported exponential disk and central bulge.," Within these models, the baryons are contained entirely within the rotationally supported exponential disk and central bulge." + These components are then surrouncdec by à massive dark.matter halo. which has nearly 20 times 10 mass as the barvons. as specified by the mass fractions. ny and m. defined as the bulge and disk mass. respectively. divided bv the total mass.," These components are then surrounded by a massive dark–matter halo, which has nearly 20 times the mass as the baryons, as specified by the mass fractions, $m_b$ and $m_d$ , defined as the bulge and disk mass, respectively, divided by the total mass." + Ehe exponential disk. of racial disk scale radius A4. also contains a set fraction f of its mass in collisional gas that can cool and form stars.," The exponential disk, of radial disk scale radius $R_d$, also contains a set fraction $f$ of its mass in collisional gas that can cool and form stars." + Both the bulge ancl dark halo components are assumed to follow the 7/— profile., Both the bulge and dark halo components are assumed to follow the \citet{H90} profile. + The bulge scale radius e is fixed to be of the radial cisk scale. radius Z2;., The bulge scale radius $a$ is fixed to be of the radial disk scale radius $R_d$. + Phe darkmatter profile is defined. by its concentration c. spin parameter A. and total virial mass Aou) ancl virial circular velocity Voug fat the radius rego where the average interior density is 200 times the critical cosmic density today. ros=]07?ecm 7) which are all listed. in Table 1..," The dark–matter profile is defined by its concentration $c$, spin parameter $\lambda$, and total virial mass $M_{200}$ and virial circular velocity $V_{200}$ (at the radius $r_{200}$ where the average interior density is 200 times the critical cosmic density today, $rho_{\rm crit}= 10^{-29}~{\rm g~cm^{-3}}$ ), which are all listed in Table \ref{tab:galps}." + The numerical construction of these models employs. methods commonly used to construct equilibrium clisk galaxies (see.e.g.P2222)," The numerical construction of these models employs methods commonly used to construct equilibrium disk galaxies \citep[see, +e.g.,][]{H93,SW99,Sp00,Cox06,SdMH05}." + Given the adopted: parameters of the two Largest. galaxics in the Local Croup. we must now define their orbital parameters and any ambient medium in which the system will be embedded.," Given the adopted parameters of the two largest galaxies in the Local Group, we must now define their orbital parameters and any ambient medium in which the system will be embedded." + “Phere are a few empirical. constraints that must be considered., There are a few empirical constraints that must be considered. + First. at the current epoch. theseparation between the Milky Was ancl Anclromeca is TSO kpe (??)..," First, at the current epoch, theseparation between the Milky Way and Andromeda is 780 kpc \citep{McC05,Rib05}. ." + Second. the Milky Way ancl Andromeda are approaching each other at a radial speed of 120 assuming a local circular. speec of 220," Second, the Milky Way and Andromeda are approaching each other at a radial speed of 120 , assuming a local circular speed of 220" + Second. the Milky Way ancl Andromeda are approaching each other at a radial speed of 120 assuming a local circular. speec of 220.," Second, the Milky Way and Andromeda are approaching each other at a radial speed of 120 , assuming a local circular speed of 220" +"and the phase speeds of the first three phases, as well as the comparisons of W1 and W2 wavelengths, and of P1 to P3 speeds.","and the phase speeds of the first three phases, as well as the comparisons of W1 and W2 wavelengths, and of P1 to P3 speeds." + The last issue that needs to be addressed in this section is related to the wave period determined from the above analysis., The last issue that needs to be addressed in this section is related to the wave period determined from the above analysis. +" The period is about 1 hour, and the interval of the LASCO C2 or C3’s observations are both approximately 30 minutes."," The period is about 1 hour, and the interval of the LASCO C2 or C3's observations are both approximately 30 minutes." +" Thus, the data are sampled at roughly the Nyquist rate."," Thus, the data are sampled at roughly the Nyquist rate." +" This raises the issue of possible aliasing and incorrect determination of the period if the actual oscillation period is shorter than 30 minutes example, 20 minutes)."," This raises the issue of possible aliasing and incorrect determination of the period if the actual oscillation period is shorter than 30 minutes (for example, 20 minutes)." + The issue is addressed from the (forfollowing two aspects of argument., The issue is addressed from the following two aspects of argument. +" Firstly, the concerned imaging areas of the two LASCO coronagraphs are overlapping between 4 to 8 and the combination of the two sets of observations Ro,results in an effective exposure interval of 12 minutes mostly, as read from the exposure instants listed in Figures 2 and 4."," Firstly, the concerned imaging areas of the two LASCO coronagraphs are overlapping between 4 to 8 $R_\odot$, and the combination of the two sets of observations results in an effective exposure interval of 12 minutes mostly, as read from the exposure instants listed in Figures 2 and 4." +" Secondly, for an oscillation period as small as, say, 30 minutes, the average phase speed is 965 km s! with a wavelength of 2.5 Ro."," Secondly, for an oscillation period as small as, say, 30 minutes, the average phase speed is 965 km $^{-1}$ with a wavelength of 2.5 $R_\odot$." +" As will be discussed in the discussion section of this paper, this means an Alfvénn speed in the slow wind surrounding the plasma sheet significantly faster than that estimated from previous relevant theoretical calculations (e.g., Wang et al.,"," As will be discussed in the discussion section of this paper, this means an Alfvénn speed in the slow wind surrounding the plasma sheet significantly faster than that estimated from previous relevant theoretical calculations (e.g., Wang et al.," +" 1998; Suess et al,"," 1998; Suess et al.," +" 1999; Chen Hu, 2001, 2002; Hu et al.,"," 1999; Chen Hu, 2001, 2002; Hu et al.," +" 2003; Li et al.,"," 2003; Li et al.," + , 2006). +"According to these calculations, the plasma ( should 2006).be no less than 0.1 in the slow wind regime surrounding the plasma sheet above the streamer cusp, this yields an Alfvénn speed less than 575 km s! assuming an isothermal temperature of 1MK for both electrons and protons."," According to these calculations, the plasma $\beta$ should be no less than 0.1 in the slow wind regime surrounding the plasma sheet above the streamer cusp, this yields an Alfvénn speed less than 575 km $^{-1}$ assuming an isothermal temperature of 1MK for both electrons and protons." +" Therefore, we conclude that the value of the deduced wave period is unlikely affected by the aliasing issue raised above."," Therefore, we conclude that the value of the deduced wave period is unlikely affected by the aliasing issue raised above." +" As mentioned at the start of Section 2, the CME eruption that drives the streamer wavy motion seems to originate from the backside of the sun."," As mentioned at the start of Section 2, the CME eruption that drives the streamer wavy motion seems to originate from the backside of the sun." +" To provide more information on the magnetic topology of the CME source and the associated streamer, we show two images of the coronal magnetic fields calculated using the photospheric fields for Carrington Rotation 2018 with the Solar Software package PFSS (CR)(Potential Field Source Surface, Schatten(SSW) et al.,"," To provide more information on the magnetic topology of the CME source and the associated streamer, we show two images of the coronal magnetic fields calculated using the photospheric fields for Carrington Rotation (CR) 2018 with the Solar Software (SSW) package PFSS (Potential Field Source Surface, Schatten et al.," + 1969)., 1969). +" The central meridians of the two images are taken to be the Carrington longitudes of 205.5° (left) and 26.8° (right), corresponding to the Carrington times of July 06 20:00, 2004 and July 20 08:00, 2004."," The central meridians of the two images are taken to be the Carrington longitudes of $^{\circ}$ (left) and $^{\circ}$ (right), corresponding to the Carrington times of July 06 20:00, 2004 and July 20 08:00, 2004." +" The closed field lines are colored black, and the open outward (inward) field lines are represented with purple (green) lines."," The closed field lines are colored black, and the open outward (inward) field lines are represented with purple (green) lines." +" If assuming the global magnetic topology does not change significantly during the CR, we can regard the left image as the front side one and the right as the backside one at the time of the relevant CME occurrence."," If assuming the global magnetic topology does not change significantly during the CR, we can regard the left image as the front side one and the right as the backside one at the time of the relevant CME occurrence." + We see that the most probable CME source region is the active region group in the southeastern quadrant of the backside., We see that the most probable CME source region is the active region group in the southeastern quadrant of the backside. + This is consistent with the brightness asymmetric feature of the eruption., This is consistent with the brightness asymmetric feature of the eruption. +" The concerned streamer is also mainly rooted in the backside, which nominally connects with the suggested CME source region through a highly inclined loop system."," The concerned streamer is also mainly rooted in the backside, which nominally connects with the suggested CME source region through a highly inclined loop system." + This configuration allows the CME ejecta to hit directly on the streamer stalk from the flank without causing any observable disruption of the streamer., This configuration allows the CME ejecta to hit directly on the streamer stalk from the flank without causing any observable disruption of the streamer. +" An earlier CME, first present in the C2 FOV at 23:06 UT on July 5th, is also observed to drive apparent streamer wavy motions."," An earlier CME, first present in the C2 FOV at 23:06 UT on July 5th, is also observed to drive apparent streamer wavy motions." +" The overall process of this earlier streamer wave event is presented in Figure 7 by four RDIs, where the familiar DB-BD features are observed."," The overall process of this earlier streamer wave event is presented in Figure 7 by four RDIs, where the familiar DB-BD features are observed." + The deflection and bouncing of the streamer is evident from the first and the second images., The deflection and bouncing of the streamer is evident from the first and the second images. +" The third image indicates that the streamer waves backwards in the direction of the CME deflection, and the streamer bounces again to the opposite direction in the last image."," The third image indicates that the streamer waves backwards in the direction of the CME deflection, and the streamer bounces again to the opposite direction in the last image." + It is seen that only one complete wavelength of the streamer wave is observable., It is seen that only one complete wavelength of the streamer wave is observable. + And the streamer wave feature is not as clear as the one discussed in detail., And the streamer wave feature is not as clear as the one discussed in detail. +" A preliminary evaluation shows that the wave period is also about 1 hour, the wave amplitude, the wavelength, and the propagation phase speed are about 0.2 Ro, 2-4 Ro, and 400 km s~!, respectively."," A preliminary evaluation shows that the wave period is also about 1 hour, the wave amplitude, the wavelength, and the propagation phase speed are about 0.2 $_\odot$, 2-4 $_\odot$, and 400 km $^{-1}$, respectively." +" In this paper, we conduct an observational study on the phenomena of streamer wave, which is excited by the CME impact and represents one of the largest wave"," In this paper, we conduct an observational study on the phenomena of streamer wave, which is excited by the CME impact and represents one of the largest wave" +Despite. three decades. of 2.intensive. study. the mechanism. producing pulsar radio emission is poorlv understood.,"Despite three decades of intensive study, the mechanism producing pulsar radio emission is poorly understood." + H. . . B ↓⊲↓⋯⇍⋯⋜⊔↓∪⊔⊳∖↓↓⊔↓↥⋖⊾↓⊔∩⋅⊔⊳∖⊔∙∖⇁∪∣⇂↥⋖⊾↓⋅⋯∐∪↓⋅⋯⊔⋜∐↓∪⊔↓≻↓⋅∪∖⇁⊔⇂⋖⊾. η. . important constraints on plausible mechanisms., Fluctuations in the intensity of the radio radiation provide important constraints on plausible mechanisms. + Single-pulse studies of bright pulsars detect a variety of patterns. in the intrinsic intensity Duetuations. including nulling an drifting phenomena.," Single-pulse studies of bright pulsars detect a variety of patterns in the intrinsic intensity fluctuations, including nulling and drifting phenomena." + The distribution of integrated: pulse energies. rowever. has only a modest. dispersion.," The distribution of integrated pulse energies, however, has only a modest dispersion." + Johnston et al., Johnston et al. + showed that in the Vela pulsar. of al pulses are within a factor of 3 of the mean Lux density. C5 and that the histogram of pulse energies is a Gaussian when plotted in the log.," \nocite{jvkb01} + showed that in the Vela pulsar, of all pulses are within a factor of 3 of the mean flux density, $\langle S \rangle$ and that the histogram of pulse energies is a Gaussian when plotted in the log." + This distribution seems typical for mos pulsars (?:?)..," This distribution seems typical for most pulsars \cite{hw74,rit76}." + In contrast. the Crab pulsar emits pulses with [lux densities 220 Ss. extending up to 2107685 (2) which were instrumental in the original detection of the Crab (2)...," In contrast, the Crab pulsar emits pulses with flux densities $> 20 \times \langle S \rangle$ , extending up to $> 2 \times 10^3 +\langle S \rangle$ \cite{lcu+95} which were instrumental in the original detection of the Crab \cite{sr68}." + These giant. pulses are tvpically broadband 2) and of short duration. with widths of order a few rs and structure down to LO ns (7)..," These giant pulses are typically broadband \cite{mof97,sbh+99} + and of short duration, with widths of order a few $\mu$ s and structure down to 10 ns \cite{han96b}." + They are localized to the main and interpulse phase windows and follow an intensity distribution. best characterized. as a power lw with. index. 59xr2n, They are localized to the main and interpulse phase windows and follow an intensity distribution best characterized as a power law with index $\sim 3-3.5$. + The discovery of similar. pulses from the millisecond pulsar PSR. D193721 (7:7) was surwising.," The discovery of similar pulses from the millisecond pulsar PSR B1937+21 \cite{sb95,cstt96} was surprising." + The pulses are extremely short (7 0.3568) events οςfined to small phase windows trailing the main pulse ancl interpulse. again with an approximately power-law distribution of pulse energies (?)..," The pulses are extremely short $\tau < 0.3 \mu$ s) events confined to small phase windows trailing the main pulse and interpulse, again with an approximately power-law distribution of pulse energies \cite{kt00}." + Since PSR D937|21 is the only known radio pulsar with an estimated magnetic field at the light evlinder larger than that of the Crab. it has been suggested that this is a kev parameter controlling. the giant. pulse phenomenon (?)..," Since PSR B1937+21 is the only known radio pulsar with an estimated magnetic field at the light cylinder larger than that of the Crab, it has been suggested that this is a key parameter controlling the giant pulse phenomenon \cite{cstt96}." +ο Johnston et MSal., Johnston et al. + haveAYO recentlypoco ⇁⋅found that⊳ a⊳ small⊳ subset of pulse phases from the Vela pulsar have à very wide distribution of peak Iluxes., \nocite{jvkb01} have recently found that a small subset of pulse phases from the Vela pulsar have a very wide distribution of peak fluxes. + “Phe pulses are localized. to a phase window 1 ms prior to the bulkof the integrated pulse emission. are of short duration and are highly. polarized.," The pulses are localized to a phase window $\sim$ 1 ms prior to the bulk of the integrated pulse emission, are of short duration and are highly polarized." + Johnston et al. (, Johnston et al. ( +2001) called. these giant. micro-pulses.,2001) called these giant micro-pulses. + {4 is not clear if these events are related to true giant pulses: 1 largest’ Vela pulses observed. to date have 9<0S. ut these narrow. pulses have peak Buxes exceeding 40 16 integrated peak intensity.," It is not clear if these events are related to true giant pulses; the largest Vela pulses observed to date have $ S < 10\langle S \rangle$, but these narrow pulses have peak fluxes exceeding $40\times$ the integrated peak intensity." + Ixramer.. Johnston Van Straten have shown that these giant micro-pulses lave a power-law distribution and the extended ail of the ‘istribution may continue ino the true giant pulse regime.," Kramer, Johnston Van Straten \nocite{kjv01} have shown that these giant micro-pulses have a power-law distribution and the extended tail of the distribution may continue into the true giant pulse regime." + Cairns. Johnston Das (2001).. in contrast. recently showed wt a log-normal distribution provided an excellent. fit to 1e Hux densities in individual phase bins across the main »ealkk of the Vela profile.," Cairns, Johnston Das \nocite{cjd01}, in contrast, recently showed that a log-normal distribution provided an excellent fit to the flux densities in individual phase bins across the main peak of the Vela profile." + I0 seems likely that. the same istribution is also applicable to other pulsars., It seems likely that the same distribution is also applicable to other pulsars. + 1jerefore a »»tentialni discriminatorijscriminz- of ofgiant. pulse ∙activity is the ∙∙⊳∙∙change roni a log-normal distribution to a power-law one., Therefore a potential discriminator of giant pulse activity is the change from a log-normal distribution to a power-law one. + ‘To explore the connection between the giant. pulses in he €‘rab and PSR DBI937|21 and the large individual pulses in the Vela pulsar. we obtained fast time-samplecd cata for several voung ancl milliseconcl pulsars.," To explore the connection between the giant pulses in the Crab and PSR B1937+21 and the large individual pulses in the Vela pulsar, we obtained fast time-sampled data for several young and millisecond pulsars." + In an earlier paper (?) we reported the detection of giant pulses from the milli.second pulsar with the next highestknown light evlincer," In an earlier paper \cite{rj01} + we reported the detection of giant pulses from the millisecond pulsar with the next highestknown light cylinder" +"that the [S aand [N fflux ratios for the vvaried together in the same way as in the WIM and they concluded that the variations in flux ratios were due to variations inΤο, with the WIM being significantly warmer than the mmaterial.","that the [S and [N flux ratios for the varied together in the same way as in the WIM and they concluded that the variations in flux ratios were due to variations in, with the WIM being significantly warmer than the material." + They established that the pattern of the line ratios was quite different for the H II regions they had sampled and the aand WIM., They established that the pattern of the line ratios was quite different for the H II regions they had sampled and the and WIM. + The difference was in the sense that the [S II] to rratio was much weaker in the H II regions at the same value of the [N II] to rratios., The difference was in the sense that the [S II] to ratio was much weaker in the H II regions at the same value of the [N II] to ratios. +" Moreover, they noted that the [S II] 6716 oover [N IT] 6583 fflux ratio was both larger than in their H II regions and increased only slightly with surface brightness inHa,, with an average value near 0.8."," Moreover, they noted that the [S II] 6716 over [N II] 6583 flux ratio was both larger than in their H II regions and increased only slightly with surface brightness in, with an average value near 0.8." + The value of this ratio was about 0.4 in their low surface brightness H II regions., The value of this ratio was about 0.4 in their low surface brightness H II regions. + It is important to determine the physical conditions in the Barnard's Loop and the iin order to understand both the nature of these objects and their origin., It is important to determine the physical conditions in the Barnard's Loop and the in order to understand both the nature of these objects and their origin. +" As we will see, there is a fundamental problem when trying to explain the line ratios (which reflect the conditions of ionization and excitation) with the mechanism of direct stellar photoionization by the hottest star in the region, but, we have been able to develop a model consistent with all the available observational material."," As we will see, there is a fundamental problem when trying to explain the line ratios (which reflect the conditions of ionization and excitation) with the mechanism of direct stellar photoionization by the hottest star in the region, but, we have been able to develop a model consistent with all the available observational material." +or angular monmentuni is lost from the binary. the time scales for the mass trausfer aud for changes iu the orbital »eriod are set by the expansion time scale of the donor. MAL—PP~RR.,"or angular momentum is lost from the binary, the time scales for the mass transfer and for changes in the orbital period are set by the expansion time scale of the donor, $M/\dot M\sim P/\dot P\sim R/\dot R$." +" The time averaged mass rausfer rate of AL~LE&10.WAL, erived above. aud the ini of the period change P/P<3<10S 31 aye both conrpatible with the expansion rate of a subeiaw donor star."," The time averaged mass transfer rate of $\dot M\simeq 1.4\times10^{-10} M_{\odot}$ $^{-1}$ derived above, and the limit of the period change $\dot P/P<3\times10^{-8}$ $^{-1}$ are both compatible with the expansion rate of a subgiant donor star." +" The low mass transter rate furthermore Πιοσατος that [um μαinie scale for angular momentum loss from the binary xough magnetic braking is louger than 1012 vr,", The low mass transfer rate furthermore indicates that the time scale for angular momentum loss from the binary through magnetic braking is longer than $\sim 10^{10}$ yr. +" An alternative explanation for an expanded donor star NOIL be that the donor still coutaims a fair amount of iernual cuerey left over from its capture bv the joutron stab (οι, Verbuut 1991)."," An alternative explanation for an expanded donor star would be that the donor still contains a fair amount of thermal energy left over from its capture by the neutron star (e.g., Verbunt 1994)." + Since the life time of such a source would be set bv its thermal time scale. this οκτν is less probable a priori: aud the argunueuts above show that it is not necessary as all the properties of the low-mass X-ray binary may be explained with au ordinary subeiaut donor.," Since the life time of such a source would be set by its thermal time scale, this possibility is less probable a priori; and the arguments above show that it is not necessary as all the properties of the low-mass X-ray binary may be explained with an ordinary subgiant donor." + The transition profiles iu aare remarkably stable. when compared to other LAINBs.," The transition profiles in are remarkably stable, when compared to other LMXBs." + lueress aud egress durations range from -30 το with respect to the average., Ingress and egress durations range from -30 to with respect to the average. + In ENO 0718-676. for instance. the variation is (NVOMT et al.," In EXO 0748-676, for instance, the variation is (Wolff et al." + 2002)., 2002). + The stability may be due to either a relative stabilitv of magnetic activity on the secondary. or a relative sanootliness of the accretion process (aud associated rav irradiation of the secondary).," The stability may be due to either a relative stability of magnetic activity on the secondary, or a relative smoothness of the accretion process (and associated X-ray irradiation of the secondary)." + We observed a difference in the eclipse duration at 25 keV and 520 keV energies aud 1n0odeled Εαν by assuming anu isothermal spherical atimosphere in hivdrostatic equilibria where the density is an exponential fiction of height., We observed a difference in the eclipse duration at 2–5 keV and 5–20 keV energies and modeled this by assuming an isothermal spherical atmosphere in hydrostatic equilibrium where the density is an exponential function of height. + This simple model reproduces the eclipse duration difference for a scale height. as projected on the path of the neutron star line of sight through the atmosphere. of 2.0«LO? km for the iugress and 2.5«107 lan for the eeress.," This simple model reproduces the eclipse duration difference for a scale height, as projected on the path of the neutron star line of sight through the atmosphere, of $2.0\times10^3$ km for the ingress and $2.8\times10^3$ km for the egress." + The model reproduces the curvature on both euds of the ransition profiles aud the spectral change over the transition., The model reproduces the curvature on both ends of the transition profiles and the spectral change over the transition. + The true scale heigh depends on the precise inclination auele., The true scale height depends on the precise inclination angle. + If the primary aud secondary are T. laud 015 M. respectively. the inclination angle would be 71755. the secondary radius 1.2 B... aud the true scale height 1.2«10? kin.," If the primary and secondary are 1.4 and 0.8 $_\odot$ respectively, the inclination angle would be 5, the secondary radius 1.2 $_\odot$ and the true scale height $1.2\times10^3$ km." + This is about 2 times larecr than expected. but this could be explained by Nav radiation of the secondary.," This is about 2 times larger than expected, but this could be explained by X-ray irradiation of the secondary." + The zx differeuce between the average ingress and eeress duration has not been reported before i iu other LAINB eclipser., The $\approx25$ difference between the average ingress and egress duration has not been reported before in any other LMXB eclipser. + Perhaps the relative stability of the transitions is what makes this measureimenut yossible in this particular source., Perhaps the relative stability of the transitions is what makes this measurement possible in this particular source. + The difference is indicative of a similar difference in the atinosphere's scale height between the leading aud trailing hemisphere of the secondary., The difference is indicative of a similar difference in the atmosphere's scale height between the leading and trailing hemisphere of the secondary. + Dax et al (, Day et al. ( +1988) predicted such a scale height difference. iu he same sense. froma Coriolis force acting ou supersouic flows on the secondary’s surface as invoked by N-rav radiation.,"1988) predicted such a scale height difference, in the same sense, from a Coriolis force acting on supersonic flows on the secondary's surface as invoked by X-ray irradiation." + This will increase the scale height on the railing lemisphere while decreasing it on the leading ienisphere., This will increase the scale height on the trailing hemisphere while decreasing it on the leading hemisphere. + Whether this model is viable to ls hard o verify without the detection of the secoucdary star (note that the secondaries have been detected iu the well-doctumented eclipses Her δις AINB 1658-298 and ENO 0718-GTG).," Whether this model is viable to is hard to verify without the detection of the secondary star (note that the secondaries have been detected in the well-documented eclipsers Her X-1, MXB 1658-298 and EXO 0748-676)." + The first-time detection of tvpe-I ταν bursts unanbieuouslv proves that the conrpact object in jis a neutron star., The first-time detection of type-I X-ray bursts unambiguously proves that the compact object in is a neutron star. + This leaves ΑΡΤ in AILS as the sole bright LAINB in a Calactic globular cluster for which uo nature has been determined of the compact object., This leaves AC211 in M15 as the sole bright LMXB in a Galactic globular cluster for which no nature has been determined of the compact object. + Finding bursts in this object is goiug to be at least as difficult as for1717-312.. because it also is a high-inclination svstem.," Finding bursts in this object is going to be at least as difficult as for, because it also is a high-inclination system." + Iu fact. the ceutral source is obscured by the accretion disk rinthine (e... Tlovaisky et al.," In fact, the central source is obscured by the accretion disk rim (e.g., Ilovaisky et al." + 1993) aud bursts can only be detected indirectly through scattered X-rays., 1993) and bursts can only be detected indirectly through scattered X-rays. + Another complication for AC211 is that it is accompanied by another bright aud bursting LAINB at a distauce of ouly 2777 (White Augeliui 2001) so that only Chandra and NMM-Nexwtou will be able to localize bursts accurately enough., Another complication for AC211 is that it is accompanied by another bright and bursting LMXB at a distance of only 7 (White Angelini 2001) so that only Chandra and XMM-Newton will be able to localize bursts accurately enough. + All seven bursts rom aare relatively slor sugecstingOO that the flashes occur in a lydrogen-poor/helmm-rich laver which. according to burst theory (Fujimoto e al.," All seven bursts from are relatively short suggesting that the flashes occur in a hydrogen-poor/helium-rich layer which, according to burst theory (Fujimoto et al." +" 1981). must have beeu formed by stable lydrogen ""son."," 1981), must have been formed by stable hydrogen fusion." + For that to happen. the accretion rate must be higher than about of Eddington.," For that to happen, the accretion rate must be higher than about of Eddington." + This value is cousisteut with the observations., This value is consistent with the observations. + The highest observed peak flux translates to a luminosity of (2.3!13)«HUS ffor a distance of T2 kpe (Iuullers et al., The highest observed peak flux translates to a luminosity of $(2.3^{+1.9}_{-1.1})\times10^{38}$ for a distance of $^{+3.3}_{-2.5}$ kpc (Kuulkers et al. + 2003)., 2003). + This value is consistent with the Eddington liit. as expected for a hvdrogeuaich atinosphliere., This value is consistent with the Eddington limit as expected for a hydrogen-rich atmosphere. + The four bursts that were well measured with the PCA have the following interestiug characteristics:, The four bursts that were well measured with the PCA have the following interesting characteristics: +HF only marginally in agreement with our result.,", only marginally in agreement with our result." + In. (Trea&Ixoopmians2002) it is obtained fy=59P43kms+Alpe modelling PG 1115ΤΟΝΟ with two different components so as to describe the Luminous part and the dark halo. ancl using information by stellar civnamics.," In \cite{Treu-Koopmans} it is obtained $H_{0}=59_{-7}^{+12}{\pm} 3 +\hspace{0.1 cm} \textrm{km} \hspace{0.05 cm} \textrm{s}^{-1} +\textrm{Mpc}^{-1}$ , modelling PG 1115+080 with two different components so as to describe the luminous part and the dark halo, and using information by stellar dynamics." + In this paper we have presented a numerical method able to estimate lensing parameters and. Hubble constant for a wide class of models., In this paper we have presented a numerical method able to estimate lensing parameters and Hubble constant for a wide class of models. + The model parameters as well as the Hubble constant have been estimated using as constraints the image positions and the time delay ratios., The model parameters as well as the Hubble constant have been estimated using as constraints the image positions and the time delay ratios. + We used. (svo classes of models: separable elliptical models ancl constant [light ratio profiles. adding an external shear to take into account the presence of an external eroup of galaxy.," We used two classes of models: separable elliptical models and constant light ratio profiles, adding an external shear to take into account the presence of an external group of galaxy." + For these models we solved. the system composed. by the combinations of lens equations and. two ime clelay ratios. selecting the solutions by means of suitable physical constraints.," For these models we solved the system composed by the combinations of lens equations and two time delay ratios, selecting the solutions by means of suitable physical constraints." + For each model and each parameter. we obtain an ensemble of values: we used the mean as better estimate and a confidence level of 684. as error.," For each model and each parameter, we obtain an ensemble of values: we used the mean as better estimate and a confidence level of $68\%$ as error." + In. order o reduce the uncertainty due to the lens models on the estimation of the Hubble constant. wemergimalized over all he models collecting the complete data set anc obtained a final estimate of {1ο and its error. which does not result dramatically underestimated. in this way. because of an choice of the model.," In order to reduce the uncertainty due to the lens models on the estimation of the Hubble constant, we over all the models collecting the complete data set and obtained a final estimate of $H_0$ and its error, which does not result dramatically underestimated, in this way, because of an choice of the model." + To test the code we created simulated svstems. being able to recover the correct. values of parameters.," To test the code we created simulated systems, being able to recover the correct values of parameters." + After the encouraging testing of the codes. we have then applied them to two real svstems for which a measure of time delays has been possible: PG 1115050 and RA J0911|055.," After the encouraging testing of the codes, we have then applied them to two real systems for which a measure of time delays has been possible: PG 1115+080 and RX J0911+055." + For PG 1115|OSO it was possible to get an estimate of Ly=DNI.Tkms!Mpe consistent with other results in the literature. obtained using cilferent techniques.," For PG 1115+080 it was possible to get an estimate of $H_{0}= 58 {\pm} 27 \hspace{0.1 +cm} \textrm{km} \hspace{0.1 cm}\textrm{s}^{-1} \textrm{Mpc}^{-1}$ , consistent with other results in the literature, obtained using different techniques." + For example. (Courbinetal.1997:Weeton&IxochanekLOOT) show that the isothermal ancl pseudoisothermal. models. predict. low values of ££). while the constant Light ratio ones generate higher values.," For example, \cite{Courbin97,Ke-Ko97} show that the isothermal and pseudoisothermal models predict low values of $H_{0}$, while the constant light ratio ones generate higher values." + We can verify these results. using Llubble and. de Vaucouleurs models. finding that a simple elliptical isothermal model as2 predicts a very. low value of fy. in agreement with the value —40kms.Alpe+ obtained in (Impoeyetal.1998).," We can verify these results using Hubble and de Vaucouleurs models, finding that a simple elliptical isothermal model as predicts a very low value of $H_{0}$, in agreement with the value $\sim 40 \hspace{0.1 cm} +\textrm{km} \hspace{0.1 cm}\textrm{s}^{-1} \textrm{Mpc}^{-1}$ obtained in \cite{Impey-et-al98}." + For RA J0011|0551. only the elliptical. profile allows to fit the image configuration.," For RX J0911+0551, only the elliptical profile allows to fit the image configuration." + These trends are also confirmed by the simulations., These trends are also confirmed by the simulations. + As previously said. we “mareinalize” over ve models since we do not know the “correct” form of the lens mocel. and hence we have thought to overcome this cilliculty in this wav.," As previously said, we “marginalize” over the models since we do not know the “correct” form of the lens model, and hence we have thought to overcome this difficulty in this way." + The combination of the two final distribution can help to reduce the uncertainties and to obtain more information [rom more lens systems. thus should avoid the problems in the fitting of the single svstems.," The combination of the two final distribution can help to reduce the uncertainties and to obtain more information from more lens systems, thus should avoid the problems in the fitting of the single systems." + The combined estimate is Πυ—56423kms!Mpe3 The uncertainty in the final estimate can be further reduced adding other models and including in the statistics other lensed systems. consistently with the uncertainty obtained using other methods (see. for instance. (Williams 2000)).," The combined estimate is $H_{0}= 56 {\pm} 23 \hspace{0.1 cm} +\textrm{km} \hspace{0.1 cm}\textrm{s}^{-1} \textrm{Mpc}^{-1}$ The uncertainty in the final estimate can be further reduced adding other models and including in the statistics other lensed systems, consistently with the uncertainty obtained using other methods (see, for instance, \cite{Wi-Saha2000}) )." + LE we consider re contribution of the smoothness parameter à. the change in {ως can be very high and comparable with uncertainty in our estimates of Ho., If we consider the contribution of the smoothness parameter $\tilde{\alpha}$ the change in $H_{0}$ can be very high and comparable with uncertainty in our estimates of $H_{0}$. + For example. the variability. for αν 091110551. is ~3040% (using these particular cosmological mocels). with a comparable uncertainty in modelling.," For example, the variability for RX J0911+0551 is $\sim 30-40\%$ (using these particular cosmological models), with a comparable uncertainty in modelling." + The general method. developed. in this paper can be used to do more. allowing to obtain an estimate of {1ο that is assumed for hypothesis as the ‘same’ for all the lensed systems (see (Saha&Williams 2004))).," The general method developed in this paper can be used to do more, allowing to obtain an estimate of $H_0$ that is assumed for hypothesis as the `same' for all the lensed systems (see \cite{SW2004}) )." + We can in fact. fit simultaneously the (wo svstems. using a general elliptical potential with a not fixed angular part ancl a shared 45.," We can in fact fit simultaneously the two systems, using a general elliptical potential with a not fixed angular part and a shared $H_{0}$." +" The final estimate is Z4)=497,I&m+Alpe+. lower than the result obtained by means of the mareinalization of the 5 models already. analyzed in the paper. but in agreement within the uncertainties."," The final estimate is $H_{0}=49_{-11}^{+6} \ +\textrm{Km} \ \textrm{s}^{-1}\ \textrm{Mpc}^{-1}$, lower than the result obtained by means of the marginalization of the 5 models already analyzed in the paper, but in agreement within the uncertainties." + The hypothesis of a common Lfy is ambitious ancl very strong. since we don't know if cillerent lens svstem can be fitted in the same manner by. using the same lens model and the same Zo.," The hypothesis of a common $H_0$ is ambitious and very strong, since we don't know if different lens system can be fitted in the same manner by using the same lens model and the same $H_0$." + In fact. fitting cillerent lens models. we have seen that different ones for the two lensed svstems give us different values of 4/5.," In fact, fitting different lens models, we have seen that different ones for the two lensed systems give us different values of $H_0$." +" But we think that à 7""more-svstem mocdel can help to obtain a reasonable estimate.", But we think that a “more-system” model can help to obtain a reasonable estimate. + Further improvements are possible., Further improvements are possible. + Lt will possible to use other different models. for which it is not possible to write the potential in a simple form. such as NEW profiles ((Navarro.Frenk&White1996:Navarro. 1907))). or more complex ones (also realizing more-svstenir models).," It will possible to use other different models, for which it is not possible to write the potential in a simple form, such as NFW profiles \cite{Navarro96,Navarro97}) ), or more complex ones (also realizing more-system models)." + To take into account the cdilferent. components of the lensing galaxy. we can use different profiles to describe their components: for example. it can be used. a nearly isothermal model to describe the dark halo and a de Vaucouleurs one to describe the luminous profile.," To take into account the different components of the lensing galaxy, we can use different profiles to describe their components; for example, it can be used a nearly isothermal model to describe the dark halo and a de Vaucouleurs one to describe the luminous profile." + Phen. we could also use an exponential profile to account for a thin disk. that elliptical galaxies sometimes seem to have.," Then, we could also use an exponential profile to account for a thin disk, that elliptical galaxies sometimes seem to have." +" Lt is necessary à more accurate modelling of RA 091110551 in order to give à better bound on the estimated. Z4, for this system.since we checked that it furnish a little information and a little statistical weight."," It is necessary a more accurate modelling of RX J0911+0551 in order to give a better bound on the estimated $H_0$ for this system,since we checked that it furnish a little information and a little statistical weight." + Then. it is possible to shape," Then, it is possible to shape" +its well-known shell system and previously undetected faint features.,its well-known shell system and previously undetected faint features. +" Even though our ab initio simulation was not constrained to reproduce NGC 7600 in any way, the observations and the simulation are strikingly similar, suggesting that such systems arise naturally in the CDM model."," Even though our ab initio simulation was not constrained to reproduce NGC 7600 in any way, the observations and the simulation are strikingly similar, suggesting that such systems arise naturally in the CDM model." + The movie shows how the simulated system is formed in a major (3: merger between a ~10!?M halo and its brightest satellite1) at z~0.4.," The movie shows how the simulated system is formed in a major $3:1$ ) merger between a $\sim 10^{12}\, \mathrm{M_{\sun}}$ halo and its brightest satellite at $z\sim0.4$." +" At z=0, our semi-analytic model predicts that this halo hosts an ellipsoidal galaxy (bulge-to-total mass ratio B/T= 0.85) of total stellar mass 1.3x101?Mo."," At $z=0$, our semi-analytic model predicts that this halo hosts an ellipsoidal galaxy (bulge-to-total mass ratio $B/T=0.85$ ) of total stellar mass $1.3\times10^{10}\,\mathrm{M_{\odot}}$." + Three still frames from our movie are shown in Fig 1., Three still frames from our movie are shown in Fig 1. +" 'The model follows the formation of the entire galaxy (disk, bulge, halo; see C10 for details), but the movie shows only the evolution of the stars formed in (and stripped out of) all progenitors of the final galaxy the main progenitor."," The model follows the formation of the entire galaxy (disk, bulge, halo; see C10 for details), but the movie shows only the evolution of the stars formed in (and stripped out of) all progenitors of the final galaxy the main progenitor." + Stars formed — those that would make up all of the disk and part of the bulge — arenot included in our particle-tagging procedure and are shown., Stars formed – those that would make up all of the disk and part of the bulge – are included in our particle-tagging procedure and are shown. + The movie begins with the close encounter of two dark matter haloes at z—4., The movie begins with the close encounter of two dark matter haloes at $z=4$. + These haloes merge after ~2.5 Gyr (z=2.7)., These haloes merge after $\sim2.5$ Gyr $z=2.7$ ). + Both are surrounded by a number of dwarf galaxies and the debris of earlier mergers., Both are surrounded by a number of dwarf galaxies and the debris of earlier mergers. + The halo entering the picture from below is the more massive., The halo entering the picture from below is the more massive. +" As the haloes coalesce, their cores oscillate radially about the center of the potential, creating a series of compact shells causticsattheapocentersofapproxi-mately(densityradialstellarorbits; ][1984)."," As the haloes coalesce, their cores oscillate radially about the center of the potential, creating a series of compact shells \citep[density caustics at the apocenters of approximately radial + stellar orbits;][]{Quinn84}." +". This merger establishes the main halo, on [Quinnwhich the movie is centered for the remainder of the simulation."," This merger establishes the main halo, on which the movie is centered for the remainder of the simulation." + The shells propagate rapidly outwards and by z—2 have phase-mixed into a diffuse bow-tie-shaped cloud., The shells propagate rapidly outwards and by $z=2$ have phase-mixed into a diffuse bow-tie-shaped cloud. +" In the next phase of the movie (z—20.5, spanning ~5 Gyr - see the topmost panel of Fig."," In the next phase of the movie $z=2-0.5$, spanning $\sim5$ Gyr – see the topmost panel of Fig." + 1) the halo is bombarded by a number of smaller satellites on high-angular-momentum orbits., 1) the halo is bombarded by a number of smaller satellites on high-angular-momentum orbits. +" Tidal forces disrupt many of these satellites, leaving behind streams of debris that crisscross the halo."," Tidal forces disrupt many of these satellites, leaving behind streams of debris that crisscross the halo." +" As with the shells seen earlier, the stars in these streams pile up at the apocenters of their orbits."," As with the shells seen earlier, the stars in these streams pile up at the apocenters of their orbits." +" Where the stream progenitor crosses the center of the halo perpendicular to the line of sight, it appears as an ‘umbrella’: a broad arc at the end of a thin stream (e.g.B010)."," Where the stream progenitor crosses the center of the halo perpendicular to the line of sight, it appears as an `umbrella': a broad arc at the end of a thin stream \citep[e.g.][]{MD10}." +". These features are rapidly erased by phase-mixing, perturbations to the potential and the decay of satellite orbits through dynamical friction."," These features are rapidly erased by phase-mixing, perturbations to the potential and the decay of satellite orbits through dynamical friction." + The final and most spectacular stage of the movie begins at z—0.4., The final and most spectacular stage of the movie begins at $z=0.4$. + As shown in the central panel of Fig., As shown in the central panel of Fig. +" 1, a bright satellite appears in the upper right of the frame."," 1, a bright satellite appears in the upper right of the frame." +" The satellite (whose stellar mass of ~7x109Ms at z=0.4 is only ~0.1% of the stellar mass of the main galaxy at that time, although its dark matter halo is 1/3 of the main dark matter halo) seems much brighter than the central galaxy because only starsaccreted by the central galaxy are shown —GALFORM predicts that the majority of its stars form in situ, and these are not tagged by dark matter particles in our model C10)."," The satellite (whose stellar mass of $\sim7\times10^{6}\,\mathrm{M_{\odot}}$ at $z=0.4$ is only $\sim0.1$ of the stellar mass of the main galaxy at that time, although its dark matter halo is $1/3$ of the main dark matter halo) seems much brighter than the central galaxy because only stars by the central galaxy are shown – predicts that the majority of its stars form in situ, and these are not tagged by dark matter particles in our model (see C10)." +" The satellite galaxy brings with it its own extensive(see stellar halo and set of companions, one of which is already being disrupted into a wide stream when its host arrives in the main halo."," The satellite galaxy brings with it its own extensive stellar halo and set of companions, one of which is already being disrupted into a wide stream when its host arrives in the main halo." + The bright satellite makes two pericentric passages as the angular momentum is drained from its orbit., The bright satellite makes two pericentric passages as the angular momentum is drained from its orbit. + These early passages strip the satellite of its stellar halo and its companions., These early passages strip the satellite of its stellar halo and its companions. +" Meanwhile, the stellar halo of the main galaxy is distorted and mixed by the new arrival, destroying pre-existing tidal features."," Meanwhile, the stellar halo of the main galaxy is distorted and mixed by the new arrival, destroying pre-existing tidal features." +" What happens next (z~0.27, lowest panel of Fig "," What happens next $z\sim0.27$, lowest panel of Fig 1.)" +is crucial for understanding NGC 7600., is crucial for understanding NGC 7600. + The bright satellite1.) is now on an approximately radial orbit and will pass through the center of the potential at subsequent pericenters., The bright satellite is now on an approximately radial orbit and will pass through the center of the potential at subsequent pericenters. + Material is stripped from the satellite on, Material is stripped from the satellite on +The thin aceretion disk is the model most commonly employed in explaining gravitational energy release in active galactic nuclei (AGN) and X-ray binaries.,The thin accretion disk is the model most commonly employed in explaining gravitational energy release in active galactic nuclei (AGN) and X-ray binaries. + In the original formulation (Shakura Sunyaev 1973. Novikov Thorne 1973 NT73). both the mechanical structure of the disk and the thermal spectrum which it radiates Were solved together. self consistently.," In the original formulation (Shakura Sunyaev 1973, Novikov Thorne 1973 NT73), both the mechanical structure of the disk and the thermal spectrum which it radiates were solved together, self consistently." +" More recently. the nature of the anomalous ""-viscosity"". required for angular momentum transport. has been revealed to be MHD turbulence driven by the magnetorotational instability (MRI. Balbus Hawley 1991)."," More recently, the nature of the anomalous $\alpha$ -viscosity”, required for angular momentum transport, has been revealed to be MHD turbulence driven by the magnetorotational instability (MRI, Balbus Hawley 1991)." + Spectral models taking into account reprocessing of X-ray photons. along with the implied reflection features (Lightman White 1988. Guilbert Rees 1988). have proven to be very useful tools in diagnosing the variability and geometrical properties of such flows.," Spectral models taking into account reprocessing of nonthermal X-ray photons, along with the implied reflection features (Lightman White 1988, Guilbert Rees 1988), have proven to be very useful tools in diagnosing the variability and geometrical properties of such flows." + Further. the idea that the broad-band X-ray power-law continuum results from thermal Comptonization of soft seed disk photons by a hot diffuse corona (Haardt Maraschi 1991) qualitatively reproduces the observed X-ray continuum in both AGN and X-ray binaries.," Further, the idea that the broad-band X-ray power-law continuum results from thermal Comptonization of soft seed disk photons by a hot diffuse corona (Haardt Maraschi 1991) qualitatively reproduces the observed X-ray continuum in both AGN and X-ray binaries." + Despite these advances. progress towards our understanding of the mechanies and radiative processes of accretion flows have occurred separately with little quantitative connection between the two.," Despite these advances, progress towards our understanding of the mechanics and radiative processes of accretion flows have occurred separately with little quantitative connection between the two." + We propose that bulk Comptonization of soft thermal disk photons by the turbulent motions themselves. in other words turbulent Comptonization. may substantially alter the dynamics and the emitted spectrum concurrently.," We propose that bulk Comptonization of soft thermal disk photons by the turbulent motions themselves, in other words turbulent Comptonization, may substantially alter the dynamics and the emitted spectrum concurrently." + Thus. turbulent Comptonization allows for a direct concrete link between the details of the disk dynamics and the observed spectrum.," Thus, turbulent Comptonization allows for a direct concrete link between the details of the disk dynamics and the observed spectrum." + Turbulent Comptonization is not an entirely new ZeVdovich. Hlarionov. and Sunyaev (1972) derived a general formulation in which turbulent Comptonization could be applied within a cosmological context.," Turbulent Comptonization is not an entirely new Zel'dovich, Illarionov, and Sunyaev (1972) derived a general formulation in which turbulent Comptonization could be applied within a cosmological context." + Thompson (1994) considered Alfvénnic reconnection-limited turbulent Comptonization while calculating the spectral energy distribution (SED) of a 5-ray burst fireball model., Thompson (1994) considered Alfvénnic reconnection-limited turbulent Comptonization while calculating the spectral energy distribution (SED) of a $\gamma$ -ray burst fireball model. + At the same time. Thompson conjectured that this effeet may be responsible for producing the Comptonized power-law continuum in AGN and X-ray binaries.," At the same time, Thompson conjectured that this effect may be responsible for producing the Comptonized power-law continuum in AGN and X-ray binaries." +" Rather than in a corona, we consider here the possibility that turbulent Comptoniz: occurs above the effective photosphere. the body of the disk itself."," Rather than in a corona, we consider here the possibility that turbulent Comptonization occurs above the effective photosphere, the body of the disk itself." + The organization of this paper is as follows., The organization of this paper is as follows. + In section 2 we outline the basic hydrodynamic principles governing turbulei= Comptonization in accretion disks while defining and estimatingT important spectral parameters such as the turbulent wave temperature and v-parameter., In section 2 we outline the basic hydrodynamic principles governing turbulent Comptonization in accretion disks while defining and estimating important spectral parameters such as the turbulent wave temperature and $y$ -parameter. + In section 3. we estimate a characteristic timescale for turbulent Comptonization from the Kompan'eets equation in terms of fundamental thin disk parameters.," In section 3, we estimate a characteristic timescale for turbulent Comptonization from the Kompan'eets equation in terms of fundamental thin disk parameters." + We show the results of Monte Carlo calculations in section 4 in order to demonstrate how turbulent Comptonization alters the emergent disk spectrum., We show the results of Monte Carlo calculations in section 4 in order to demonstrate how turbulent Comptonization alters the emergent disk spectrum. + We consider how turbulent Comptonization may observationally manifest itself in AGN and X-ray binaries in nonthermapection 5 and we summarize our conclusions in section 6., We consider how turbulent Comptonization may observationally manifest itself in AGN and X-ray binaries in section 5 and we summarize our conclusions in section 6. + In black hole aceretion disks. the turbulent velocity of the flow may be larger than the thermal velocity of the electrons in the inner-most regions.," In black hole accretion disks, the turbulent velocity of the flow may be larger than the thermal velocity of the electrons in the inner-most regions." + As a result. electrons moving at the turbulent velocity will be able to Compton up-scatter soft photons to higher energy. potentially deforming the observed spectrum.," As a result, electrons moving at the turbulent velocity will be able to Compton up-scatter soft photons to higher energy, potentially deforming the observed spectrum." + Here. we parameterize the turbulent motions in terms of a wave temperature Τρ. which should be compared to the local electron thermal temperature of the disk 7; in order to see whether turbulent or thermal Comptonization determines the radiative transfer.," Here, we parameterize the turbulent motions in terms of a wave temperature $T_w$, which should be compared to the local electron thermal temperature of the disk $T_e$ in order to see whether turbulent or thermal Comptonization determines the radiative transfer." + At the same time. we deduce an effective turbulent y-parameter. allowing us to estimate the contribution to the resulting non-thermal spectrum.," At the same time, we deduce an effective turbulent $y$ -parameter, allowing us to estimate the contribution to the resulting non-thermal spectrum." +" MRI turbulence is fundamentally magnetic in behavior with a characteristic velocity given by the Alfvénn speed v4 which is less than the local sound speed c,.", MRI turbulence is fundamentally magnetic in behavior with a characteristic velocity given by the Alfvénn speed $v_A$ which is less than the local sound speed $c_s$. +" Close to the hole. where the radiation pressure is dominant. c, is given by the radiation sound speed. which is larger than the sound speed of the gas."," Close to the hole, where the radiation pressure is dominant, $c_s$ is given by the radiation sound speed, which is larger than the sound speed of the gas." + Thus. it is possible for the MRI turbulence to begas.," Thus, it is possible for the MRI turbulence to be." + We propose that supersonic MRI eddies in the inner radiation pressure dominated region of thin accretion disks Compton up-scatter soft thermal photons arising from viscous dissipation., We propose that supersonic MRI eddies in the inner radiation pressure dominated region of thin accretion disks Compton up-scatter soft thermal photons arising from viscous dissipation. + IPürder for this to take place. the electron bulk velocity which corresponds to the turbulent velocity must be greater than the local electron thermal velocity.," In order for this to take place, the electron bulk velocity which corresponds to the turbulent velocity must be greater than the local electron thermal velocity." +in the core. (he superconducting state of protons determines in part the mutual friction on neutron vortex lines.,"in the core, the superconducting state of protons determines in part the mutual friction on neutron vortex lines." + A type II superconductor corresponds to the strong-drag. limit. with vortices entangled in a dense array. of magnetic flix tubes (Link2003): For a type I superconductor. instead. both the weak- ancl strong-drag limits have been suggested 2006).," A type II superconductor corresponds to the strong-drag limit, with vortices entangled in a dense array of magnetic flux tubes \citep{lin03}; for a type I superconductor, instead, both the weak- and strong-drag limits have been suggested \citep{sed05,jon06}." +. To date. (he microscopic nature of the proton superconductor is far from seltled: therefore. both scenarios of weak and strong mutual [riction in the core should be taken into account in the study of glitehes.," To date, the microscopic nature of the proton superconductor is far from settled; therefore, both scenarios of weak and strong mutual friction in the core should be taken into account in the study of glitches." + Post-eliteh models. however. are not affected by (his (theoretical uncertainty. since (hey involve mostly vortices in (he equatorial regions. Iving entirely in (he inner crust.," Post-glitch models, however, are not affected by this theoretical uncertainty, since they involve mostly vortices in the equatorial regions, lying entirely in the inner crust." +" A (vpical neutron star has total momentum of inertia 4447:LO’ ο οι”. while its inner crust has fe22LO24,4."," A typical neutron star has total momentum of inertia $I_{\rm tot}\approx10^{45}$ g $^2$, while its inner crust has $I_{\rm ic}\approx10^{-2}I_{\rm tot}$." + The accidental coincidence of the ratio {ως with the early observations οἱ AQz10?O and with fact that about L.7% of the Vela spin-down is reversed during a gliteh. led to consider glitches as related to crust vorticity alone. and thence to the assumption of disconnected neutron superfIuids.," The accidental coincidence of the ratio $I_{\rm ic}/I_{\rm tot}$ with the early observations of $\Delta\dot{\Omega}_{\rm gl}\approx10^{-2}\dot{\Omega}$ and with fact that about $1.7\%$ of the Vela spin-down is reversed during a glitch, led to consider glitches as related to crust vorticity alone, and thence to the assumption of disconnected neutron superfluids." + This scenario. however. has direct implications on the glitehi energetics.," This scenario, however, has direct implications on the glitch energetics." + Iideed. since vortex lines in the core are strongly coupled to the normal component. being magnetized by entrainment effects 1984c).. Che normal crust comprises most of the star and J.2 Ji.," Indeed, since vortex lines in the core are strongly coupled to the normal component, being magnetized by entrainment effects \citep{alp84c}, the normal crust comprises most of the star and $I_{\rm c}\approx I_{\rm tot}$ ." + This implies that the angular momentum transferred during the glitch is AL.)=J.A\Qu210! erg s. and the corresponding glitch energy is AR=.NLQO2LOM erg: both values appear too large.," This implies that the angular momentum transferred during the glitch is $\Delta L_{\rm gl}=I_{\rm c}\Delta\Omega_{\rm gl}\approx10^{41}$ erg s, and the corresponding glitch energy is $\Delta E_{\rm gl}=\Delta L_{\rm gl}\Omega\approx10^{43}$ erg; both values appear too large." + On the one hand. 10!! erg s corresponds to the difference in angular momentum of the entire inner crust between glitches. (hus requiring some unlikely mechanism (hat freezes (he vorticitv. in the crust for about 3 vears. and (hen releases it simultaneously.," On the one hand, $10^{41}$ erg s corresponds to the difference in angular momentum of the entire inner crust between glitches, thus requiring some unlikely mechanism that freezes the vorticity in the crust for about 3 years, and then releases it simultaneously." + On the other hand. observations of the power wind nebula surrounding Vela indicate an upper limit of ~LO” erg to the glitch οποιον (Ποαμαοἱal.2001).," On the other hand, observations of the power wind nebula surrounding Vela indicate an upper limit of $\sim10^{42}$ erg to the glitch energy \citep{hel01}." +. In (his letter we present the first realistic (wilh several approximations. but still preserviadye the essential physics) and consistent model to determine where in (he star the vorticity 1s pinned. how much of it. ancl for how long.," In this letter we present the first realistic (with several approximations, but still preserving the essential physics) and consistent model to determine where in the star the vorticity is pinned, how much of it, and for how long." + The model has been tested against observations using realistic equations of state (E05) for dense matter and implementing general relativistic hydrostatic equilibrium. (Pizzochero. Seveso Ilaskell. in preparation).," The model has been tested against observations using realistic equations of state (EoS) for dense matter and implementing general relativistic hydrostatic equilibrium (Pizzochero, Seveso Haskell, in preparation)." + Moreover. initial dynamical simulations based on the multifluid formalism of Andersson&Comer(2006) confirm (he main assumptions and predictions of the model (Ilaskelletal.2011).," Moreover, initial dynamical simulations based on the multifluid formalism of \citet{ac06} confirm the main assumptions and predictions of the model \citep{hps11}." +. Here. however. we will discuss a fully analviical. Newtonian version of ihe model: it vields the correct orders of magnitude [ονall relevant variables. but. provides deeper insight than any numerical treatment.," Here, however, we will discuss a fully analytical, Newtonian version of the model: it yields the correct orders of magnitude forall relevant variables, but provides deeper insight than any numerical treatment." +parameters.,parameters. + Numerically. combining the tonizing continuum inferred from the spectrum of knot C with =1.2 10! 5m the highest density compatible with the FIR[NeV]| doublet (Table 3.3)). yields [~0.5 at r=10 pe from the AGN. an ionization parameter far too large for the production of low excitation species.," Numerically, combining the ionizing continuum inferred from the spectrum of knot C with $n$ $\,10^4$ $^{-3}$, the highest density compatible with the FIR[NeV] doublet (Table \ref{diagnostic}) ), yields $U\!\simeq\!0.5$ at $r$ =10 pc from the AGN, an ionization parameter far too large for the production of low excitation species." + Not surprisingly therefore. all the models so far developed for the high excitation lines (O94.. M96.. B97)) predict that [SII] should peak much farther out and have a much lower surface brightness than that observed.," Not surprisingly therefore, all the models so far developed for the high excitation lines \cite{O94}, \cite{M96}, \cite{B97}) ) predict that [SII] should peak much farther out and have a much lower surface brightness than that observed." + A simple and indeed natural solution ts to assume that the low excitation lines are formed in dusty clouds., A simple and indeed natural solution is to assume that the low excitation lines are formed in dusty clouds. + At these large tonization parameters dust dominates the absorption of UV tonizing photons and. therefore. quenches the Helll and HII Strómmgegren spheres.," At these large ionization parameters dust dominates the absorption of UV ionizing photons and, therefore, quenches the HeIII and HII gren spheres." + Consequently. the X-ray dominated partially ionized region starts at much smaller radii. and ts also slightly hotter than in the dust free model (cf.," Consequently, the X–ray dominated partially ionized region starts at much smaller radii, and is also slightly hotter than in the dust free model (cf." + Fig 9))., Fig \ref{modelnuc}) ). + Therefore. dusty clouds have a [SII] peak much closer to the nucleus and à >10 times higher surface brightness than dust-free clouds.," Therefore, dusty clouds have a [SII] peak much closer to the nucleus and a $>$ 10 times higher surface brightness than dust–free clouds." + It should be noted. however. that the total luminosity of low excitation optical lines is similar in the two cases. fundamentally because the available luminosity of soft X-rays is the same.," It should be noted, however, that the total luminosity of low excitation optical lines is similar in the two cases, fundamentally because the available luminosity of soft X–rays is the same." + Although the combined emission of dusty and dust-free clouds can account for the observed emission of low ionization and coronal species. it falls short by large factors in producing [OLIV] and other relatively low ionization species which form within the Helll sphere.," Although the combined emission of dusty and dust–free clouds can account for the observed emission of low ionization and coronal species, it falls short by large factors in producing [OIV] and other relatively low ionization species which form within the HeIII sphere." +" This is an intrinsic limitation of ""compact models"" such as those of Fig. 9.."," This is an intrinsic limitation of “compact models” such as those of Fig. \ref{modelnuc}," + and can be understood as follows., and can be understood as follows. +" Compact models are characterized by large ""ionization parameters"" (cf.", Compact models are characterized by large “ionization parameters” (cf. + Sect., Sect. + 3 of Oliva 1997. for a critical discussion on this parameter) and therefore have large fluxes of OIV tonizing photons which keep oxygen in higher ionization stages (mostly OVI and OVID at all radii inside the HellI Strómmgren sphere., 3 of Oliva \cite{oliva_china97} for a critical discussion on this parameter) and therefore have large fluxes of OIV ionizing photons which keep oxygen in higher ionization stages (mostly OVI and OVII) at all radii inside the HeIII Strömmgren sphere. + Outside the Helll region. on the contrary. oxygen cannot be ionized above OIL because most of the OIL ionizing photons have already been absorbed by Hell.," Outside the HeIII region, on the contrary, oxygen cannot be ionized above OIII because most of the OIII ionizing photons have already been absorbed by HeII." + Therefore. OIV can only exist in a very narrow range of radii. just at the edge of the Helll sphere. and its relative abundance is therefore very low.," Therefore, OIV can only exist in a very narrow range of radii, just at the edge of the HeIII sphere, and its relative abundance is therefore very low." + In practice. we found it impossible to construct a single model which simultaneously produces a compact coronal line region. such as that observed in |FeXI] (O94)). and which comes anywhere close to the A550077-0.3 observed ratio.," In practice, we found it impossible to construct a single model which simultaneously produces a compact coronal line region, such as that observed in [FeXI] \cite{O94}) ), and which comes anywhere close to the $\simeq$ 0.3 observed ratio." + We did indeed construct nany thousands of randomly generated dusty and dust-free models. and attempted an approach similar to that used for knot C (Sect. 4.2) ," We did indeed construct many thousands of randomly generated dusty and dust–free models, and attempted an approach similar to that used for knot C (Sect. \ref{details_photion}) )" +but. in no case. could we find a model which satisfies these contradictory constraints.," but, in no case, could we find a model which satisfies these contradictory constraints." + It should also be noted that B97 independently come to a similar conclusion.," It should also be noted that \cite{B97} + independently come to a similar conclusion." +" The main conclusion therefore is that. regardless of the details of the models. the nuclear spectrum and line spatial distribution can only be modeled by adding a third ""diffuse"" component (e.g. with a lower filling factor) to the dusty anc dust-free clouds discussed above and depicted in Fig. 9.."," The main conclusion therefore is that, regardless of the details of the models, the nuclear spectrum and line spatial distribution can only be modeled by adding a third “diffuse” component (e.g. with a lower filling factor) to the dusty and dust–free clouds discussed above and depicted in Fig. \ref{modelnuc}." + Giver the large number of free parameters. we abandoned the idea of using photoionization models to constrain abundances anc other physical properties of the gas. We made some attempt to verify that a mixture of clouds exposed to the same continuum. and with the same abundances as Model #11 of knot C (Table 4 and Fig. 7) ," Given the large number of free parameters, we abandoned the idea of using photoionization models to constrain abundances and other physical properties of the gas, We made some attempt to verify that a mixture of clouds exposed to the same continuum, and with the same abundances as Model 1 of knot C (Table \ref{tab_modelKNC} and Fig. \ref{agn_cont}) )" +could reasonably well reproduce the observed properties of the nuclear spectrum., could reasonably well reproduce the observed properties of the nuclear spectrum. + However. the results are not too encouraging and. apart from the much improved [SII surface brightness and [ΟΙΥΙΟΙ ratio. the solutions are not significantly better than those already discussed by M96. anc B97.. and are not therefore discussed here.," However, the results are not too encouraging and, apart from the much improved [SII] surface brightness and [OIV]/[OIII] ratio, the solutions are not significantly better than those already discussed by \cite{M96} and \cite{B97}, and are not therefore discussed here." + An analysis similar to that used for knot C was also applied to the other extra-nuclear knots using the more limited number of lines available in their spectra., An analysis similar to that used for knot C was also applied to the other extra–nuclear knots using the more limited number of lines available in their spectra. + The results can be summarized as follows., The results can be summarized as follows. + The abundances derived in the Seyfert-type knots A. B. D. G. F (cf.," The abundances derived in the Seyfert-type knots A, B, D, G, F (cf." + Fig. 6)), Fig. \ref{knotdiag}) ) + are similar those found in knot C but affected by much larger errors because of the more limited. numbers of lines available for the analysis., are similar those found in knot C but affected by much larger errors because of the more limited numbers of lines available for the analysis. + In. particular. the. density sensitive [ArIV| doublet and the U-sensitive [ArV] line is not detected in any of these knots. and the reddening correction for [OII|AA3727 could be very uncertain in the high extinction regions (cf.," In particular, the density sensitive [ArIV] doublet and the U–sensitive [ArV] line is not detected in any of these knots, and the reddening correction for $\LL3727$ could be very uncertain in the high extinction regions (cf." + note b of Table 2))., note $b$ of Table \ref{tab_obs2}) ). + We also attempted to verify if the observed line ratios in these knots could be explained as photoionization by the same AGN continuum seen by knot C but could not find any satisfactory solution using radiation bounded clouds exposed to the same continuum., We also attempted to verify if the observed line ratios in these knots could be explained as photoionization by the same AGN continuum seen by knot C but could not find any satisfactory solution using radiation bounded clouds exposed to the same continuum. + Adding matter bounded clouds alleviates the problem (as already stressed by B96)) but requires an choice of their photoelectric opacities. re. the radius at which the ionization structure ts cut.," Adding matter bounded clouds alleviates the problem (as already stressed by \cite{B96}) ) but requires an choice of their photoelectric opacities, i.e. the radius at which the ionization structure is cut." + In particular. explaining," In particular, explaining" +for which mid-infrared colours indicate significant emission from an AGN.,for which mid-infrared colours indicate significant emission from an AGN. + We thus find no strong evidence for buried AGN in the SMGs., We thus find no strong evidence for buried AGN in the SMGs. + Having said this. we note that deep X-ray (e.g. Vignati et al.," Having said this, we note that deep X-ray (e.g. Vignati et al." + 1999: Netzer et al., 1999; Netzer et al. + 2005) and infrared spectroscopy (e.g. Lutz et al., 2005) and infrared spectroscopy (e.g. Lutz et al. + 2003: Armus et al., 2003; Armus et al. + 2006) observations of NGC 6240 show that this galaxy does in fact host a highly obscured AGN but that the energetics are dominated by the starburst., 2006) observations of NGC 6240 show that this galaxy does in fact host a highly obscured AGN but that the energetics are dominated by the starburst. + This leaves open the possibility that many of the SMGs contain buried AGN which are not powerful enough to dominate over the starburst in the infrared., This leaves open the possibility that many of the SMGs contain buried AGN which are not powerful enough to dominate over the starburst in the mid-infrared. + We have shown that the number counts of SMGs with flux densities ~2. tmiy inthe ~2 arcmin diameter fields surrounding our X-ray absorbed QSOs is higher than that found for a blank field., We have shown that the number counts of SMGs with flux densities $\sim2-4$ mJy in the $\sim 2$ arcmin diameter fields surrounding our X-ray absorbed QSOs is higher than that found for a blank field. + Tost of these galaxies have mid-infrared colours very similar to he local ULIRG Arp 220 if it were placed at 1<23., Most of these galaxies have mid-infrared colours very similar to the local ULIRG Arp 220 if it were placed at $1 Q)", An alternative scenario is oblique magnetic field to the shock normal in this region $\theta_{\rm u} > 0^\circ$ ). + For simplicity. we neglect the back reaction of accelerated particle. (hen the compression ratio becomes 4 for strong shock limit.," For simplicity, we neglect the back reaction of accelerated particle, then the compression ratio becomes 4 for strong shock limit." +" The allowed region of 6, is given from the eq.(8)) as: Thus the magnetic fiekd in upstream near the filaments is almost perpendicular.", The allowed region of $\theta_{\rm u}$ is given from the \ref{xi_B}) ) as; Thus the magnetic field in upstream near the filaments is almost perpendicular. +" Assuming 6,=907. r= 4. and D, = 10 j(G. Ey is given from eq.(6)). When particles are accelerated. very. efficiently. their back reactions to the shock can nol be ienored hence r becomes larger than 4."," Assuming $\theta_{\rm u} = 90^\circ$, $r = 4$ , and $B_{\rm u}$ = 10 $\mu$ G, $E_{\rm max}$ is given from \ref{Emax}) ), When particles are accelerated very efficiently, their back reactions to the shock can not be ignored hence $r$ becomes larger than 4." +" Even if the compression ratio 1s the largest ol ry=7 (Ellison.Berezhko.&Daring2000:Berezhkoetal.2002).. the allowed range is 0,>80°."," Even if the compression ratio is the largest of $r=7$ \citep{ellison,berezhko}, the allowed range is $\theta_{\rm u} > 80^\circ$." + Therelore. we can salely predict (hat the magnetic field in the NE shell of SN 1006 is nearly perpendicular to the shock normal.," Therefore, we can safely predict that the magnetic field in the NE shell of SN 1006 is nearly perpendicular to the shock normal." + As lor the downstream region. the observed spatial profile seems to be incompatible with the solution derived by Dlandford&Ostriker(1973).," As for the downstream region, the observed spatial profile seems to be incompatible with the solution derived by \citet{blandford1978}." +. The maximum electron energy Lus would be determined by the balance of the time scales between (he accelerating and the svnchrotron cooling., The maximum electron energy $E_{\max}$ would be determined by the balance of the time scales between the accelerating and the synchrotron cooling. + These time scales may depend on the structure and the fluctuation ol the magnetic field along the shock normal: both time scales become smaller with larger magnetic field. while the former becomes also smaller with larger fluctuation of the magnetic [ield.," These time scales may depend on the structure and the fluctuation of the magnetic field along the shock normal; both time scales become smaller with larger magnetic field, while the former becomes also smaller with larger fluctuation of the magnetic field." + The shock flow may conmpresses ancl partly stretches the magnetic field in the radial direction. which may produce highly disordered magnetic field with small fraction of radial component. as discussed by Revnolds&Gilmore(1993) with the radio polarization data. who reported that only of the magnetic-lield οποιον in SN 1006 NE shell in radial polarization. and most of the magnetic field is disordered with the scale smaller than 0.2 pc.," The shock flow may compresses and partly stretches the magnetic field in the radial direction, which may produce highly disordered magnetic field with small fraction of radial component, as discussed by \citet{reynolds1993} with the radio polarization data, who reported that only of the magnetic-field energy in SN 1006 NE shell in radial polarization, and most of the magnetic field is disordered with the scale smaller than 0.2 pc." + To determine the magnetic field in downstream. we thus need require more complicated processes such as the history of the shock propagation ancl the non-linear effect. ancl many assumptions. which is bevond this paper and would leave fora future study.," To determine the magnetic field in downstream, we thus need require more complicated processes such as the history of the shock propagation and the non-linear effect, and many assumptions, which is beyond this paper and would leave fora future study." +electrons and free-free emission fromLUI regions.,electrons and free-free emission from regions. + Only massive stars (1.60. Al SAL.) ionise the regions and. produce supernovae. whose remnants accelerate most of the relativistic electrons.," Only massive stars (i.e. $M~ \gsimeq~ 5 M_{\odot}$ ) ionise the regions and produce supernovae, whose remnants accelerate most of the relativistic electrons." + Such massive stars aave Lifetimes much shorter than the Llubble time. so the current radio luminosity is proportional to yw recent star formation rate (Condon 1992).," Such massive stars have lifetimes much shorter than the Hubble time, so the current radio luminosity is proportional to the recent star formation rate (Condon 1992)." + The supernova rate Is directly related to the non.therm radio luminosity. which at 1.4 CLlz is dominant over 1 thermal component (see Condon Yin 1990 for he most reliable derivation of this relation. calibrate with Galactic supernova remnants).," The supernova rate is directly related to the non–thermal radio luminosity, which at $1.4$ GHz is dominant over the thermal component (see Condon Yin 1990 for the most reliable derivation of this relation, calibrated with Galactic supernova remnants)." + Moreover. since all stars more massive than A=5M. become radio supernovae. the radio supernova rate is determine directly by the star formation rate.," Moreover, since all stars more massive than $M = 5 M_{\odot}$ become radio supernovae, the radio supernova rate is determined directly by the star formation rate." + Thus. the star formation rate can be obtained by nonthermal radio luminosity. following Condon (1992): where v is the [frequency and à is the nonthermal radio spectral index (as defined: above).," Thus, the star formation rate can be obtained by non–thermal radio luminosity, following Condon (1992): where $\nu$ is the frequency and $\alpha$ is the non--thermal radio spectral index (as defined above)." + If weassume a Salpeter initial mass function. (LAL: pe(M)xM OL125 A.) we obtain for the total star formation rate In Figures 5.. 6. we convert our racio luminosity densities (Table 3... row 3. correction /1) to star formation rates together with that from the RSA sample (Table 3.. row 1).," If weassume a Salpeter initial mass function (IMF; $\psi(M)\propto M^{-2.35}$, $0.1-125$ $M_\odot$ ) we obtain for the total star formation rate In Figures \ref{fig:sfr1}, \ref{fig:sfr2} we convert our radio luminosity densities (Table \ref{tab:lumden}, row 3, correction $l1$ ) to star formation rates together with that from the RSA sample (Table \ref{tab:lumden}, row 1)." + lt is instructive to compare with the U-band luminosity clensities at redshifts 2.©1. from ‘Trever ct al. (," It is instructive to compare with the U-band luminosity densities at redshifts $z\stackrel{<}{_\sim}1$, from Treyer et al. (" +1998) and the Canada-Erance Redshift Survey (CERS. Lilly et al.,"1998) and the Canada-France Redshift Survey (CFRS, Lilly et al." + 1996)., 1996). + For the ultraviolet CODVOESIODS We asse taken from Trever et al. (, For the ultraviolet conversions we assume taken from Treyer et al. ( +1998) and Cowie ct al. (,1998) and Cowie et al. ( +1997) respectively.,1997) respectively. + In. Figure 5 we do not apply a reddening correction. in Figure ο the luminosity densities are cle-recdeleneck following Trever οἱ al. (," In Figure \ref{fig:sfr1} we do not apply a reddening correction, in Figure \ref{fig:sfr2} the luminosity densities are de-reddened following Treyer et al. (" +1998).,1998). + Also plotted are the Ho. luminosity densities from. the CERS (Lresse Maddox 1997) the IXISS sample (Cromwell 1998) and from the local (2= 0) sample of Gallego et al. (, Also plotted are the $\alpha$ luminosity densities from the CFRS (Tresse Maddox 1997) the KISS sample (Gromwell 1998) and from the local $z=0$ ) sample of Gallego et al. ( +1995). converted to total star formation rates for this IME using from Macau et al. (,"1995), converted to total star formation rates for this IMF using from Madau et al. (" +1996).,1996). + Both Lla luminosity densities were corrected. for reddening using Balmer decrements ancl assuming a simple dust. screen. in ligure 5. we remove the average reddening correction ~] mag (CIresse Macidox. 1997).," Both $\alpha$ luminosity densities were corrected for reddening using Balmer decrements and assuming a simple dust screen, in Figure \ref{fig:sfr1} we remove the average reddening correction $\sim1$ mag (Tresse Maddox 1997)." +" A priori we would have expected. the ΕΕ, o provide a higher estimate of the star-formation rate than an un-reddenecd optical estimate.", A priori we would have expected the 1.4GHz to provide a higher estimate of the star-formation rate than an un-reddened optical estimate. + This is recause the radio should be measuring the total star-ormation rate which the optical onlv measures the un-obsceured rate., This is because the radio should be measuring the total star-formation rate which the optical only measures the un-obscured rate. + At the low redshift (0=0.240 has a radio luminosity at 5GGllz of logeL,zLOMores sugeesting that this is a Ligh energy peak BL-Lac (sec Figure Ta of Fossati et al."," Source 4 at $z=0.240$ has a radio luminosity at GHz of $\log \nu L_\nu\approx10^{40}\,\rm erg\,s^{-1}$ suggesting that this is a High energy peak BL-Lac (see Figure 7a of Fossati et al." + 1998)., 1998). + Phe estimated racio luminosity is also consistent with the steep X-ray. spectral index of this source in Table 2 (see Figure 11 of Fossati et al., The estimated radio luminosity is also consistent with the steep X-ray spectral index of this source in Table 2 (see Figure 11 of Fossati et al. + 1998)., 1998). + We also note that absorption line svstems with properties similar to those of source #44 have been identified in previous X-ray. surveys with available radio observations (Gunn et al., We also note that absorption line systems with properties similar to those of source 4 have been identified in previous X-ray surveys with available radio observations (Gunn et al. + 2003: Brusa et al., 2003; Brusa et al. + 2003)., 2003). + Three sources in Figure 5. lie close to the ‘normal’ ealaxy region of the Stocke et al. (, Three sources in Figure \ref{fig_aox} lie close to the `normal' galaxy region of the Stocke et al. ( +1991) classification scheme.,1991) classification scheme. +" ""Two of these sources are the “normal galaxy candidates showing narrow emission line optical spectra.", Two of these sources are the `normal' galaxy candidates showing narrow emission line optical spectra. + The third source is #33 in Tables 1: and 2 exhibiting both narrow emission and absorption optical lines., The third source is 3 in Tables 1 and 2 exhibiting both narrow emission and absorption optical lines. + The evidence above combined with the fact that this svstem cleviates from. the Ranalli et al. (, The evidence above combined with the fact that this system deviates from the Ranalli et al. ( +2003). Lyfy relation in Figure 4 suggest an ADA or a LLAG,2003) $L_X-L_{1.4}$ relation in Figure \ref{fig_lxl14} suggest an ADAF or a LLAGN. + Droad optical emission line svstems ancl double lobe sources in Figure 5.r occupy the radio loud ane the racio quiet AGN space., Broad optical emission line systems and double lobe sources in Figure \ref{fig_aox} occupy the radio loud and the radio quiet AGN space. + We note that the one double lobe source associated with the X-ray cluster is not plotted here since its X-ray emission is not due to the central AGN., We note that the one double lobe source associated with the X-ray cluster is not plotted here since its X-ray emission is not due to the central AGN. + One ofthe two speetroscopically unclassified sources (2111) in the present sample has eox and ago consistent with those of BL-Lacs., One of thetwo spectroscopically unclassified sources 11) in the present sample has $\alpha_{OX}$ and $\alpha_{RO}$ consistent with those of BL-Lacs. + This is inconsistent. however. with the relatively hard X-rav spectral properties of this source in Table 2 suggesting 107 for P=1.9.," This is inconsistent however, with the relatively hard X-ray spectral properties of this source in Table 2 suggesting $\rm N_H\approx1.5\times10^{22}$ for $\Gamma=1.9$." + The second. spectroscopically unclassified: source 110) lies in the border line between radio loud. QSOs ancl BL-Lacs., The second spectroscopically unclassified source 10) lies in the border line between radio loud QSOs and BL-Lacs. + A detailed description of individual sources is presented in Appendix ??.., A detailed description of individual sources is presented in Appendix \ref{app1}. + The classification of the present. sample into different classes is performed. on the basis. of their optical spectroscopic (i.e. spectral features). photometric (i.c. resolved. or point-like sources) ancl X-ray properties (i.c. Nerav luminositv. X-raytooptical [lux ratio. X-rav spectral properties).," The classification of the present sample into different classes is performed on the basis of their optical spectroscopic (i.e. spectral features), photometric (i.e. resolved or point-like sources) and X-ray properties (i.e. X-ray luminosity, X-ray–to–optical flux ratio, X-ray spectral properties)." + More. information about. the source classification can be found in Appendix. ??.., More information about the source classification can be found in Appendix \ref{app1}. + The present sample of X-rav/radio matches comprises: 3 broad emission line AGNs 2. 6. 9). 2 sources with double lobe radio morphology also indicating GN activity (3555. 12). 1double lobe source (3411) associated with X- cluster emission. 2 systems with optical spectra dominated by the host galaxy. (ic. absorption and/or narrow emission lines) and X-ray/optical properties. suggesting," The present sample of X-ray/radio matches comprises: 3 broad emission line AGNs 2, 6, 9), 2 sources with double lobe radio morphology also indicating AGN activity 5, 12), 1double lobe source 1) associated with X-ray cluster emission, 2 systems with optical spectra dominated by the host galaxy (i.e. absorption and/or narrow emission lines) and X-ray/optical properties suggesting" +surface temperatures when in quiescence as dwarf nova systems aud the potential discovery of Te WDs through their pulsations (Arrasetal.2006).,surface temperatures when in quiescence as dwarf nova systems and the potential discovery of He WDs through their pulsations \citep{arras06}. +.escribing Tn §5.. we explore details of the individual novae. « he physics of the convective burning phase in &5.l.. aud the conrposition of the nova ejecta in 85.2.. which is nof eulanced iu CNO nuclei due to the lack of a reservoir of uuderlviug C/O as iu normal CNe (Starrfieldetal.1972:σσetal. 1998).," In \ref{sec:indiv}, we explore details of the individual novae, describing the physics of the convective burning phase in \ref{sec:conv}, and the composition of the nova ejecta in \ref{sec:comp}, which is not enhanced in CNO nuclei due to the lack of a reservoir of underlying C/O as in normal CNe \citep{stsk72,gehrz98}." +". The CN event leaves a remnant burning envelope ou the surface of the WD. allowing for a xolouged stable burning phase (Sharaetal.1993). that we detail in 85.3.. which may explain the few P,= ble oue-lived sitporsoft sources (8883)."," The CN event leaves a remnant burning envelope on the surface of the WD, allowing for a prolonged stable burning phase \citep{shara93} that we detail in \ref{sec:supersoft}, which may explain the few $\porb \lesssim 4 $ hr long-lived supersoft sources (SSSs)." + We conclude in 86. by üuehliehtiug where future CV. aud CN observations nav reveal the long-lost heliuui core WDs in mass transferring nnuaries., We conclude in \ref{sec:conclusions} by highlighting where future CV and CN observations may reveal the long-lost helium core WDs in mass transferring binaries. + The conuunon cuvelope eveut that exposes the Ie WD leaves a wide range of WD and donor masses (Mj). oulv a fraction of which will become stable mass-transfering binaries once the donor comes mto contact (deΊνου1992:Politauo199," The common envelope event that exposes the He WD leaves a wide range of WD and donor masses $M_d$ ), only a fraction of which will become stable mass-transferring binaries once the donor comes into contact \citep{dek92, pol96,hnr01}." +"6:Tlowelletal.2001).. Table 1 shows the parametersof those pre-CVs with probable Πο WDs whose courpaiious will overflow their Roche lobes in ty,<20 Cyr. under the assuniptiou of aneulay momentum losses due to eravitational waves."," Table \ref{tab:preCVs} shows the parametersof those pre-CVs with probable He WDs whose companions will overflow their Roche lobes in $t_{\rm in}< 20$ Gyr, under the assumption of angular momentum losses due to gravitational waves." +" The prevalence of low-mass (Af,<0.25 M.) iain sequence eonmrpauious is likely due to their slower inspiral under gravitational wave losses compared to those with more massive (M,20.25 A.) companions that would have stellar wind braking(Schreiber&Gausicke2003).", The prevalence of low-mass $M_d<0.25 \msol$ ) main sequence companions is likely due to their slower inspiral under gravitational wave losses compared to those with more massive $M_d>0.25 \msol$ ) companions that would have stellar wind braking \citep{sch03}. +. As we will show iu the following sections. all biuaries iu Table 1 will likely transfer matter stably after coutact. leading to the accretion of cosiiic-nüx material onto a Πο WDat Af=t1«10HΑινιt," As we will show in the following sections, all binaries in Table \ref{tab:preCVs} will likely transfer matter stably after contact, leading to the accretion of cosmic-mix material onto a He WD at $\mdot = 1-4 \E{-11} \smpy$." + When the main sequence star comes into contact. the possibility exists for dvuamically unstable mass transfer. which occurs when the donors Roche radius shrinks faster or expands slower than the donors radial response to adiabatic changes (Webbiuk1985:ITjelluung&Web-biuk 1987). ," When the main sequence star comes into contact, the possibility exists for dynamically unstable mass transfer, which occurs when the donor's Roche radius shrinks faster or expands slower than the donor's radial response to adiabatic changes \citep{web85,hw87}. ." +"Low-iass main sequence stars have small radiative cores and large convective envelopes that make up >50% of the sti mass. and stars with M,«0.3AZ. are nearly fully convective."," Low-mass main sequence stars have small radiative cores and large convective envelopes that make up $>50\%$ of the star's mass, and stars with $M_d<0.3 \msol$ are nearly fully convective." +"s The adiabatic response of the radius of a fully couvective star to dass loss is dlufü;/dluMj|,=1/35. and usns the Paczvüsli approximation to the donors Roche radius vields dluRyfdludAly,=5/3|24. where gq=ALY/AL."," The adiabatic response of the radius of a fully convective star to mass loss is $ \left. d \ln R_d / d \ln M_d \right|_s=-1/3$, and using the \cite{pac67} approximation to the donor's Roche radius yields $ d \ln +R_{L} / d \ln M_d = -5/3+2q$, where $q \equiv M_d/M$." + Thus. cvnaucally uustable mass transfer occurs if the donor is fully convective aud has a ass ratio Ady/AL>2/3.," Thus, dynamically unstable mass transfer occurs if the donor is fully convective and has a mass ratio $M_d/M > 2/3$." + For the maximum mass He WD with AJ=0.5 AL... this restricts the main sequence donor mass to M«0.33M. in order to avoid dynamical mass trausfer.," For the maximum mass He WD with $M = 0.5 \msol$ , this restricts the main sequence donor mass to $M_d< 0.33 \msol$ in order to avoid dynamical mass transfer." + If the more exact Roche radius formula from Eeeleton(1983) is used. the limit changes only slightly to AZ;/M.«," If the more exact Roche radius formula from \cite{egg83} is used, the limit changes only slightly to $M_d/M< 0.63$." +" Binaries just at the lait of stability would have donors fill their Roche lobes as main sequence stars CM,=d""AudSAL.Ry=0.33 Ro: Ribasetal. 2008)) with Po,2: "," Binaries just at the limit of stability would have donors that fill their Roche lobes as main sequence stars $M_d=0.33 \msol, +R_d=0.33 \ R_\odot$ ; \citealt{ribas08}) ) with $ \porb = 3$ hr." +"doatiug of such à donor could drive £24, slishtlv longer. potentially to the 3.501 hr seen iu a few supersoft SOWrCCS, as we discuss in 85."," Any bloating of such a donor could drive $\porb$ slightly longer, potentially to the $3.5-4$ hr seen in a few supersoft sources, as we discuss in \ref{sec:supersoft}." +"3 All the pre-CVs in Table 1. have Mj/Mithe=0.63 aud will become stable mass trausfer svstenis when Vv Cole iuto contact a fine ty, from now.", All the pre-CVs in Table \ref{tab:preCVs} have $M_d/M \lesssim 0.63$ and will become stable mass transfer systems when they come into contact a time $t_{\rm in}$ from now. + We derive their mass transfer rates in 82.2.., We derive their mass transfer rates in \ref{sec:cvmdot}. +" There are certainly We WD post-colmmon euvelope svstenis with less extreme mass ratios that would trigger a ανασα. mass transfer event at the ouset of Roche lobe πιο,", There are certainly He WD post-common envelope systems with less extreme mass ratios that would trigger a dynamical mass transfer event at the onset of Roche lobe filling. + These vield a red eiaut configuration. ax the supply of freshly accreted IT leads to a rejuvenation of the IT burning shell typical of a We core on the firstascent of the red eiaut brauch.," These yield a red giant configuration, as the supply of freshly accreted H leads to a rejuvenation of the H burning shell typical of a He core on the firstascent of the red giant branch." + Our focus here is ou those svsteis that uudergo stable niass transfer. with the WD accunmlatius mass over time and then ejecting most of it durius the CN.," Our focus here is on those systems that undergo stable mass transfer, with the WD accumulating mass over time and then ejecting most of it during the CN." +" We start with a total mass AM;=AL,|M aud orbital angular momentum J=MjM(GGa/Mj)U? for an orbital separation a.", We start with a total mass $M_t=M_d+M$ and orbital angular momentum $J=M_dM(Ga/M_t)^{1/2}$ for an orbital separation $a$. + Mass trauster is driven by the rate of orbital aneular monmoeutui loss. J. via Since CNe lead to ejection of material from the binary. we must account for nues loss.," Mass transfer is driven by the rate of orbital angular momentum loss, $\dot J$, via Since CNe lead to ejection of material from the binary, we must account for mass loss." + We define a excavation factor f bv setting M;=fA. so that f=1 means the WD. on average. keeps a constant mass (ie. the CNe eject the amount of matter that is accreted). aud f=0 mcaus that the WD keeps all the accreted mass.," We define an excavation factor $f$ by setting $\dot M_t=f\dot M_d$, so that $f=1$ means the WD, on average, keeps a constant mass (i.e., the CNe eject the amount of matter that is accreted), and $f=0$ means that the WD keeps all the accreted mass." +" The resulting relation is then Presumius that the donor always fills its Roche lobe. and using the Paczvnsli(1967) formulation. we obtain We need the response of the donor stars radius to mass loss.Q4=dluRBfdhiM,;. which initially occurs ou a timescale longer than the Ielvin-IHehuholtz time. allowing the star to stay close to the main sequence (e.g. Gy~ 1)."," The resulting relation is then Presuming that the donor always fills its Roche lobe, and using the \cite{pac67} formulation, we obtain We need the response of the donor star's radius to mass loss, $\zeta_d= +d \ln R_d / d \ln M_d $, which initially occurs on a timescale longer than the Kelvin-Helmholtz time, allowing the star to stay close to the main sequence (e.g., $\zeta_d\approx 1$ )." + However. the increase of the Nelvin-Ueluholtz time as AL; decreases leads to a nearly adiabatie response ο 3) late in the binary evolution (Ixolb 1999).," However, the increase of the Kelvin-Helmholtz time as $M_d$ decreases leads to a nearly adiabatic response $\zeta_d\approx -1/3$ ) late in the binary evolution \citep{kolbbar99}." + The resulting mass trausfer rate is then where we use the work of Kolb&Daraffe(1999) to obtain RCM) aud cj., The resulting mass transfer rate is then where we use the work of \cite{kolbbar99} to obtain $R_d(M_d)$ and $\zeta_d$. + Their RiMa) relation was calculated sclfconsistently for a M=also0.6AL. WD with eravitational wave losses alouc., Their $R_d(M_d)$ relation was calculated self-consistently for a $M=0.6 \msol$ WD with gravitational wave losses alone. + We presume that eravitationalwave losses sot J aud consider a few specific scenarios in Figure L.., We also presume that gravitational-wave losses set $\dot J$ and consider a few specific scenarios in Figure \ref{fig:mdotplot}. . + The two solid lines labeledA aud D are the two scenarioswe will discuss at length in &l.., The two solid lines labeledA and B are the two scenarioswe will discuss at length in \ref{sec:fullscenario}. . +" Scenario A beeins with a AM,=0.2AL. donor. while scenario D beeius with a AZ,=0.05AZ. donor."," Scenario A begins with a $M_d=0.2\msol$ donor, while scenario B begins with a $M_d=0.05 \msol$ donor." + Both asstuue that all matter accreted onto the WD is ejected during the CN event., Both assume that all matter accreted onto the WD is ejected during the CN event. + The resulting accretion rates are knots., The morphological correspondence between radio and X-rays is not close as in the other 3 knots. + Iu ⋅∖, In fig. + ]∐⊔≻∪↴∖↴↴∖↴↕⊓∖∙ , \ref{fig:k80} we show the relevant maps. +detected structures are concerned. the situation of the N-rays being slightly displaced wpstreainof he bulk of the radio cussion is very siuülu to hat iu the outer knot iu the jet of PKS1127-115 (Sicuuginowska et al.," Insofar as the detected structures are concerned, the situation of the X-rays being slightly displaced upstream of the bulk of the radio emission is very similar to that in the outer knot in the jet of PKS1127-145 (Siemiginowska et al." + 2002)., 2002). +" The three values of S. in Table 2) are consistent with à,0.8.", The three values of $_x$ in Table \ref{tab:fluxden} are consistent with $\alpha_{rx}$ =0.8. + As ‘or the imer knots. the results of section L leave ittle doubt that the x-rays come from svuchrotrou CLUSSIOLL.," As for the inner knots, the results of section \ref{sec:emis} leave little doubt that the x-rays come from synchrotron emission." + S-ray↽⊲≻↱⋅∖∢⋅⋈ cutission from k25 remainslo a puzzle., The X-ray emission from k25 remains a puzzle. + valuesthe only ad-hoc models which we can suggest relativistic distinct spectral populations of relativistic ⋅↴⋅ ⊀≚↴∖↴↴, The only ad-hoc models which we can suggest involve distinct spectral populations of relativistic electrons. +∖↴∐∪↖↖⇁∐↕∐⊺⋜∏⋝↕↸∖≺∖↔↑∐↸∖↥⋅↕⊔⋜↧↕↸∖⊔↕↴∖∷∖↴↕∪↓⊔∪∩∖↕↴∖↴ ∫⇀∪↥⋅↸∖↕↑∑↕⋟⋜↧↸⊳↑∪↥⋅↴∖↴∪↕⋡↷↴∶↕∩∣↑∪∐∣⋉⋖↴∖↴↸∖↸∖↑⋜∏⋝↕↸∖⋅↱≻∪↕⋡ ⋜↧∏⋜↧↴∖↴⋉∖↸⊳⊓⋅⋯⊔↸⊳∪∐∏≻∪∐↸∖∐↑↸∖↘↑↸∖∐≼∐∐∶↴⋁↑∪↸∖↸∖↸⊳⊓," For synchrotron emission, this would be a flat spectrum component extending to electron Lorentz factors of $\gamma=10^7$ to $10^8$ (see table 5 of HHSSV)." +⋅∪↕ ∐∐≋≋∖⊽⋝∙⋀∖⊽∪↑↸∖∐∪↖↖↽↸∖↖↽↸∖↥⋅↑∐⋜↧↑↘⇁⋜⊔∐↴∖↴↑↕∐↸⊳↑↴∖↴⋉∖↸⊳⊓⋅⋜↧↕ bopyopulation need not indicate a separate. shock for its⋅ eeuesis., Note however that “a distinct spectral population” need not indicate a separate shock region for its genesis. + Denier! & ⋅ . 5 ∙∙ ⋅ ⋅ ↖↖⇁↕∐↸⊳↕↸⊳⋜⋯↻↥⋅∪≼↧⋯⊳↸∖↴∖↴↻↸∖↸⊳⊓⋅⋜↧↕∐⋜∐⋅≼∐∖⋯∐∶↴⋁⋜↧↑↕∐∶↴∙⊾↕ ↸∖∐↸∖↥⋅∶↴∙⊾↕↸∖↴∖↴∐↸∖⋜∐⋅↑∐↸∖↸⊳∏↑∪↕−↥∙⋜⋯≼∟∖↕↸∖∐∐↸∖↸⊳∙∖↽⋅ ⋅ ⇁⋅⋅ ↻↴∖↴↾↕⋅∪∖↖⊽↴∖↴∖⊽↕≼⋮∪∪⊔∐≷↧↖⊽↸∖⋯⋅∪⋔∐≱↸∖↸∐⋯⊔↸∖⊔↸⋟≷↧↕ sinnlations for what they call realistic magnetic field structures in relativistic shocks that can provide both relatively flat particle and even flatter high cnerey tails distributionsfor energies below the cutoff.," Dermer Atoyan (2002) have described $^2$ loss conditions which can produce spectral hardening at high energies near the cutoff, and Niemiec Ostrowski (2004) have produced numerical simulations for what they call 'realistic' magnetic field structures in relativistic shocks that can provide both relatively flat particle distributions and even flatter high energy tails for energies below the cutoff." + For IC/CMD with beanüng. the parameters derived above could be relaxed if an additional. steep. spectrum distribution of electrons existed below >=2000 (see section 5.2 of artis aud Iyrawezyusii we102).," For IC/CMB with beaming, the parameters derived above could be relaxed if an additional, steep spectrum distribution of electrons existed below $\gamma=2000$ (see section 5.2 of Harris and Krawczynski 2002)." + A GOks observation with Chandra has been approved for AOG., A 60ks observation with Chandra has been approved for AO6. + When these data are available we should obtain more ⋜↧↸⊳↸⊳↿∐⋅⋜↧↑↸∖⊸∖≓↥⋅⋜↧⋅↖↽↴∖↴↻↸∖↸⊳⊓⋅⋜, When these data are available we should obtain more accurate X-ray spectral parameters. +↧↕↻⋜∐⋅⋜↧⋯↸∖↑↸∖↥⋅↴∖↴∙- Although oue of. us (DEID has been a lone and ardent supporter of the classical view: T he spectrum is nof concave dowuward. it is no svuchrotrou enüssion'. if is now our view tha here is strous evidence for marked deviations roni this scenario.," Although one of us (DEH) has been a long and ardent supporter of the classical view: “If the spectrum is not concave downward, it is not synchrotron emission”, it is now our view that there is strong evidence for marked deviations from this scenario." +" It should be remembered a his point. that there are many other kuots in jets or Which a,100$ higher than current observational data suggest. + This mechauisui ust not be he only primary mechauisu that worked in the Calactic ido., This mechanism must not be the only primary mechanism that worked in the Galactic halo. + Other primary mcchanisus like superbubbles that supply light clemeuts regardless of SN type are required o reproduce the observed abuudance ratios such as De/Fe., Other primary mechanisms like superbubbles that supply light elements regardless of SN type are required to reproduce the observed abundance ratios such as Be/Fe. + These SNe Ic can produce Li with more than oue order of magnitude smaller amounts than indicated w observations., These SNe Ic can produce Li with more than one order of magnitude smaller amounts than indicated by observations. + However. lack of information ou the Li abundances in the metallicity range of 2X <1 prevents us from deducing a fiii conclusion.," However, lack of information on the Li abundances in the metallicity range of $-2\ltsim$ $\ltsim -1$ prevents us from deducing a firm conclusion." + SNe are suggested to be associated with aspherical explosions., SNe are suggested to be associated with aspherical explosions. + The deviation from spherical svuuuctry will be able to increase the mass of ejecta with enough cucreies for spallation reactions for a given Γον)λέω because M(€) is proportional to the ~231 3.6 power of this value., The deviation from spherical symmetry will be able to increase the mass of ejecta with enough energies for spallation reactions for a given $E_{\rm ex}/M_{\rm ej}$ because $M(>\epsilon)$ is proportional to the $\sim3.4$ —3.6 power of this value. + To illustrate this effect. a simplified situation will be considered.," To illustrate this effect, a simplified situation will be considered." + Suppose the enerev injected iu the direction with a solid ausle of z steradian is euhauced by a factor of two and the energv iu the other directions is reduced by a factor of 1.5. then the empirical formula for the mass Af(oe) indicates that this mass will iucrease by a factor of ~2)!«U/Lου while the total cucrev will be unchanged.," Suppose the energy injected in the direction with a solid angle of $\pi$ steradian is enhanced by a factor of two and the energy in the other directions is reduced by a factor of $1.5$ , then the empirical formula for the mass $M(>\epsilon)$ indicates that this mass will increase by a factor of $\sim 2^{3.4}\times 1/4 + (2/3)^{3.4}\times3/4\sim 2.8$ while the total energy will be unchanged." + Applviug the enipirical formula obtained from the spherically sviunietric calculations to this situation nüeht lead to au erroneous result., Applying the empirical formula obtained from the spherically symmetric calculations to this situation might lead to an erroneous result. + Thus to further explore SNe Ic as a production site for light clements. we need to perforii multi-dimieusioual relativistic lvdrodvuamuc calculations for SNe Ic that can trace the motion of the outermost ejecta with a suffiicicut accuracy such as the calculations presentedhere.," Thus to further explore SNe Ic as a production site for light elements, we need to perform multi-dimensional relativistic hydrodynamic calculations for SNe Ic that can trace the motion of the outermost ejecta with a sufficient accuracy such as the calculations presentedhere." +"ο Though the agreement is not comprehensive, the analytic forms are an adequate description of the global distribution of simulated stars for the majority of the systems evolution.","] Though the agreement is not comprehensive, the analytic forms are an adequate description of the global distribution of simulated stars for the majority of the systems evolution." +" Unsurprisingly, the simple profiles of (21)) and (B1]) fail to describe the simulated system at early times, before an ordered galactic system has formed."," Unsurprisingly, the simple profiles of \ref{RadialProfile}) ) and \ref{rquarter}) ) fail to describe the simulated system at early times, before an ordered galactic system has formed." +" 'The fact that adheres, atall times, to the fitting forms that are really only appropriate to recent times (z« 2) is clearly a valid criticism of this technique."," The fact that adheres, at times, to the fitting forms that are really only appropriate to recent times $z<2$ ) is clearly a valid criticism of this technique." +" However, as long as such forms are indeed a good description of low-redshift systems, then the only way their earlier misjudgements can significantly mislead the predictions of the model is in the early time star formation rates (Fig.??))"," However, as long as such forms are indeed a good description of low-redshift systems, then the only way their earlier misjudgements can significantly mislead the predictions of the model is in the early time star formation rates \ref{SFtimescale})" +" However, as long as such forms are indeed a good description of low-redshift systems, then the only way their earlier misjudgements can significantly mislead the predictions of the model is in the early time star formation rates (Fig.??)),"," However, as long as such forms are indeed a good description of low-redshift systems, then the only way their earlier misjudgements can significantly mislead the predictions of the model is in the early time star formation rates \ref{SFtimescale})" +for A(BV)>0.15 mag and viesfECD)»10 for K(D.V)«0.15 mag.,"for $\overline{E(B-V)}>0.15$ mag and $\sigma_{E(B-V)}~/~ +\overline{E(B-V)}>1.0$ for $\overline{E(B-V)}<0.15$ mag." + However. following Barmbyetal. (2000).. we emphasize that the rules adopted here for rejecting reddening values are quite arbitrary.," However, following \citet{bh00}, we emphasize that the rules adopted here for rejecting reddening values are quite arbitrary." + In total. 443 reliable reddening values were determined in this paper. which are listed in Table 5..," In total, 443 reliable reddening values were determined in this paper, which are listed in Table \ref{t5.tab}." + Columns |. 3. 5. 7. and 9 list the names of the GCs. using the nomenclature adopted by Galletietal.(2004).," Columns 1, 3, 5, 7, and 9 list the names of the GCs, using the nomenclature adopted by \citet{gall04}." +.. From Sections 3.1 and 3.2 we find that the reddening values for the Galactic GCs obtained from different relations are internally consistent., From Sections 3.1 and 3.2 we find that the reddening values for the Galactic GCs obtained from different relations are internally consistent. + However. for ΜΟΙ GCs this is not always the case.," However, for M31 GCs this is not always the case." + For some GCs and GC candidates the reddening values. based on different relations. are inconsistent.," For some GCs and GC candidates the reddening values, based on different relations, are inconsistent." + Reasons for this may include hat for Galactic GCs. the photometric data are accurate. but for some M31 GCs and GC candidates (particularly the fainter objects) his may not be the case.," Reasons for this may include that for Galactic GCs, the photometric data are accurate, but for some M31 GCs and GC candidates (particularly the fainter objects) this may not be the case." + Therefore. when we average the reddening values for each object. we reject reddening values that are clearly statistical outliers: these are defined as those values that differ from he mean value fora given object by more than 1o.," Therefore, when we average the reddening values for each object, we reject reddening values that are clearly statistical outliers: these are defined as those values that differ from the mean value for a given object by more than $1\sigma$." + Fig., Fig. + 3 shows the distribution of the reliable reddening values isted in Table 5.., \ref{fig3} shows the distribution of the reliable reddening values listed in Table \ref{t5.tab}. + From Fig., From Fig. + 3. we tind that slightly more than half of the reddening values are (D.V)«0.2 mag., \ref{fig3} we find that slightly more than half of the reddening values are $E(B-V) < 0.2$ mag. + The distribution of the 443 reiable reddening values has a mean of f(bV)—0.28SuULBTi WI4h a standard deviation of @=0.17 mag. compared with (51)2022:60=0.19 mag of Barmbyetal.(2000).," The distribution of the 443 reliable reddening values has a mean of $E(B-V) = 0.28_{-0.14}^{+0.23}$ with a standard deviation of $\sigma=0.17$ mag, compared with $E(B-V)=0.22; \sigma=0.19$ mag of \citet{bh00}." +.. Fig., Fig. + 4 shows the reddening values as a function of position., \ref{fig4} shows the reddening values as a function of position. + The large ellipse represents the boundary of the M31 dise defined by Racine(1991). and the small ellipses on the northwestern and southeastern sides of the major axis are the os diameters of the M31 companion galaxies NGC 205 and M32. respectively.," The large ellipse represents the boundary of the M31 disc defined by \citet{rac91} and the small ellipses on the northwestern and southeastern sides of the major axis are the $D_{25}$ diameters of the M31 companion galaxies NGC 205 and M32, respectively." + The distribution appears reasonable in that the objects with low reddening values are spread across the dise and halo. while those with high reddening values are mainly concentrated in the galactic disc.," The distribution appears reasonable in that the objects with low reddening values are spread across the disc and halo, while those with high reddening values are mainly concentrated in the galactic disc." + However. from Fig. +.," However, from Fig. \ref{fig4}," + we can also see that a substantial number of objects outside the “halo” boundary have (DM)>>0.1 mag. r.e.. greater than the Galactic foreground reddening in the direction of M31. as estimated by many authors (see.e.g..vandenBergh1969:McClure&RacineFrogeletal. 1980).," we can also see that a substantial number of objects outside the “halo” boundary have $E(B-V)>0.1$ mag, i.e., greater than the Galactic foreground reddening in the direction of M31, as estimated by many authors \citep[see, +e.g.,][]{van69,McRa69,Frogel80}." +. In fact. Barmbyetal.(2000) also noted this phenomenon.," In fact, \citet{bh00} also noted this phenomenon." +They suggested a number of plausible explanations. which include that (1) this could be caused by the large uncertainties inherent to the method: or," They suggested a number of plausible explanations, which include that (i) this could be caused by the large uncertainties inherent to the method; or" +listed In Table 3.,listed In Table 3. + In Fig., In Fig. + 4 we plot. for both filters. the racial profile of the detection. limits averaged. for the 15 fields.," 4 we plot, for both filters, the radial profile of the detection limits averaged for the 15 fields." +" The average detection limit for compact (dilfuse) sources is lLig=25.0(24.4) at an angular separation of 0.56""(0.79) from the quasar. improving to ILyg=25.5(224.8) at large angular separations."," The average detection limit for compact (diffuse) sources is ${\mathrm H_{AB}}=25.0\, (24.4)$ at an angular separation of $0.56\arcsec\, (0.79\arcsec)$ from the quasar, improving to ${\mathrm H_{AB}}=25.5\, (24.8)$ at large angular separations." + All the magnitudes. of the candidates (section 3.2) are quoted as aperture magnitudes i.c. we have simply summed the counts within the aperture and no aperture correction has been applied: (aperture Corrections are. nevertheless. discussed in section 3.2.1).," All the magnitudes of the candidates (section 3.2) are quoted as aperture magnitudes i.e. we have simply summed the counts within the aperture and no aperture correction has been applied (aperture corrections are, nevertheless, discussed in section 3.2.1)." + We have not attempted. to extrapolate to total magnitudes. since this would be unreliable for the faint sources.," We have not attempted to extrapolate to total magnitudes, since this would be unreliable for the faint sources." + The use of aperture magnitudes makes it very simple to compute whether or not a hypothetical galaxy of specified surface brightness profile ancl impact parameter would have been detected in a particular Geld., The use of aperture magnitudes makes it very simple to compute whether or not a hypothetical galaxy of specified surface brightness profile and impact parameter would have been detected in a particular field. + One first. computes the aperture magnitude of the galaxy. for the small and large apertures.," One first computes the aperture magnitude of the galaxy, for the small and large apertures." + For the hypothesised impact parameter. one CONLPares the two aperture magnituces against the detection limits provided in Table 3 for the field in question., For the hypothesised impact parameter one compares the two aperture magnitudes against the detection limits provided in Table 3 for the field in question. + Lf the ealaxy were brighter than either detection limit. it. would have been included in our catalogue., If the galaxy were brighter than either detection limit it would have been included in our catalogue. + The catalogue of detections is provided. in Table 4., The catalogue of detections is provided in Table 4. + For each quasar [field the candidates are listed in order of angular separation from the quasar., For each quasar field the candidates are listed in order of angular separation from the quasar. + Listed in the first hree columns of Table 4 are the quasar number. quasar name. and the candidate number.," Listed in the first three columns of Table 4 are the quasar number, quasar name, and the candidate number." + The candidate numbering scheme is explained as follows., The candidate numbering scheme is explained as follows. +" Taking as example candidate -15-3C. the N. stands for NICMOS (we will provide a similar list ""S for the STIS images). 15 is the quasar number. the 3 indicates that it is the third nearest candidate o the quasar in that. field. and the € states that it is compact."," Taking as example candidate N-15-3C, the `N' stands for NICMOS (we will provide a similar list `S' for the STIS images), 15 is the quasar number, the 3 indicates that it is the third nearest candidate to the quasar in that field, and the C states that it is compact." + We find a total of41 candidates., We find a total of 41 candidates. + The magnitudes and impact parameters are compared. against the average detection limits in Fig., The magnitudes and impact parameters are compared against the average detection limits in Fig. + 4., 4. + Phe positions of the candidates are illustrated) in the Dinding charts in the right-hand panels in Figs 5S., The positions of the candidates are illustrated in the finding charts in the right-hand panels in Figs $5-8$. + Phe remaining columns in Table 4 list successively the coordinates. aperture magnitucle. detection S/N. angular separation from the quasar. and the position angle from the quasar.," The remaining columns in Table 4 list successively the coordinates, aperture magnitude, detection $S/N$, angular separation from the quasar, and the position angle from the quasar." + Phe NICAIOS data header files contain an astrometric solution that. provides coordinates that are accurate in à relative sense. for the small angular separations with which we are concerned.," The NICMOS data header files contain an astrometric solution that provides coordinates that are accurate in a relative sense, for the small angular separations with which we are concerned." + The coordinates were shifted to absolute values by adopting for the coordinates of the quasar the value measured. from. the DSS plate. listed in Table 2.," The coordinates were shifted to absolute values by adopting for the coordinates of the quasar the value measured from the DSS plate, listed in Table 2." + For the brighter candidates we have measured the deconvolyed surface brightness profile using the techniques described. by Warren ct al (1996)., For the brighter candidates we have measured the deconvolved surface brightness profile using the techniques described by Warren et al (1996). +" We use the Sersic model where the surface brightness as a function of radius rds XV=MoexplBon)(yfy""1]bB."," We use the Sersic model where the surface brightness as a function of radius $r$ is $\Sigma=\Sigma_e +\exp\{-B(n)\lbrack(r/r_e)^{1/n}-1\rbrack\}$." + The parameter n characterises the shape of the profile: »=1 is the exponential profile anc à?=4 the de Vaueoulcurs profile., The parameter $n$ characterises the shape of the profile: $n=1$ is the exponential profile and $n=4$ the de Vaucouleurs profile. + This parameterisation is particularly useful. therefore. as the value of 0 can be usec to classify faint galaxies into Cenrlv and ας tvpes.," This parameterisation is particularly useful, therefore, as the value of $n$ can be used to classify faint galaxies into “early” and “late” types." +" The parameter ry is the hall-light radius. X, is the surface brightness at the hall-light radius. ancl D(n) is a constant for particular n."," The parameter $r_e$ is the half-light radius, $\Sigma_e$ is the surface brightness at the half-light radius, and $B(n)$ is a constant for particular $n$." +" Ciotti and Bertin (1999) provide the series asymptotic solution for 20). and we used the approximation provided by the first four terms Bin)=2n1/3]4/405)|46402551507) which is accurate to better than one part in 10"" over the range of η of interest."," Ciotti and Bertin (1999) provide the series asymptotic solution for $B(n)$, and we used the approximation provided by the first four terms $B(n)=2n-1/3+4/(405n)+46/(25515n^2)$ which is accurate to better than one part in $10^6$ over the range of $n$ of interest." + We created a psf using the software. with pixels. one-third. the size of the NIC. pixels. to. ensure adequate sampling.," We created a psf using the software, with pixels one-third the size of the NIC2 pixels, to ensure adequate sampling." + The fitting proceeds by creating a two-dimensional galaxy surlace-brightness profile with the same small pixel size. convolving with the psf. rebinning to theull pixel size and. computing the \7 of the fit.," The fitting proceeds by creating a two-dimensional galaxy surface-brightness profile with the same small pixel size, convolving with the psf, rebinning to thefull pixel size and computing the $\chi^2$ of the fit." + The best it is found by X47 minimisation on the seven parameters boy Mo. rss n. orientation. ancl ellipticity.," The best fit is found by $\chi^2$ minimisation on the seven parameters $x$, $y$ , $\Sigma_e$, $r_e$, $n$, orientation, and ellipticity." + In. Table 5 we wovicle the details of the fits to all the candidates in Table d with S/N7LS., In Table 5 we provide the details of the fits to all the candidates in Table 4 with $S/N>18$. + Also listed there are the total magnitudes. computed by extrapolating the mocels to infinite radius. and he aperture corrections Lc. the dillerence between the total and aperture magnitudes.," Also listed there are the total magnitudes, computed by extrapolating the models to infinite radius, and the aperture corrections i.e. the difference between the total and aperture magnitudes." + Le is of interest to compare the aperture corrections for these galaxies with the values for a point source., It is of interest to compare the aperture corrections for these galaxies with the values for a point source. + For a point source the aperture correction for the small aperture (used for compact objects) is 0.444 mag., For a point source the aperture correction for the small aperture (used for compact objects) is 0.444 mag. + Exclucling the two point sources listed in Table 5. there are seven compact objects. for which the mean aperture correction is 0.66 mag..," Excluding the two point sources listed in Table 5, there are seven compact objects, for which the mean aperture correction is 0.66 mag.," +. with a scatter of 0.16 mag., with a scatter of 0.16 mag. + For a point source the aperture correction for the large aperture (used for dilluse objects) is 0.134 mae., For a point source the aperture correction for the large aperture (used for diffuse objects) is 0.134 mag. + There are four cdilluse objects listed in Table 5. for which the mean aperture correction is 0.6040.17 mae.," There are four diffuse objects listed in Table 5, for which the mean aperture correction is $0.60\pm0.17$ mag." + We now comment on the results for the individual fields in turn., We now comment on the results for the individual fields in turn. + Vhe spectrum of this source shows a LLS at 215502 and a DLA at 2=2.0713 (Vable 1). but no candidate counterparts were found in this field.," The spectrum of this source shows a LLS at $z=1.8862$ and a DLA at $z=2.0713$ (Table 1), but no candidate counterparts were found in this field." + There is a strong DLA line ab oz=2.7771 in the spectrum of this quasar., There is a strong DLA line at $z=2.7771$ in the spectrum of this quasar. + Bearing in münd the small impact parameters of the few confirmed DLA counterparts we consider the nearest. candidate. N-2-1C which lies at an angular separation of2” (to be the most likely of the four candidate counterparts listed in ‘Table 4.," Bearing in mind the small impact parameters of the few confirmed DLA counterparts we consider the nearest candidate, N-2-1C which lies at an angular separation of, to be the most likely of the four candidate counterparts listed in Table 4." + Phe Large. ellipticitv. 0.70. of the canecliclate 4D suggests that this is a late-tvpe galaxy. viewed at a high inclination angle.," The large ellipticity, 0.70, of the candidate N-2-4D suggests that this is a late-type galaxy viewed at a high inclination angle." + The orientation of the imageis only 10 from the line joining the quasar to the galaxy., The orientation of the imageis only $^{\circ}$ from the line joining the quasar to the galaxy. + Therefore a possible alternative explanation of the DLA line is the presence of an extended gaseous disk around this galaxy., Therefore a possible alternative explanation of the DLA line is the presence of an extended gaseous disk around this galaxy. + Vhe redshift of theDLA is close to the redshift ofthe quasar z= .022., The redshift of theDLA $z=1.9342$ is close to the redshift ofthe quasar $z=1.922$ . + The, The +were merged together for this image: the data taken in the PV-phase of the sub-group around NGC 4839 (Neumann et al.,were merged together for this image: the data taken in the PV-phase of the sub-group around NGC 4839 (Neumann et al. + 2001) and the observations described here., 2001) and the observations described here. + The PV-phase data (latest pipeline processing) were treated in the same way as the Coma relic observations., The PV-phase data (latest pipeline processing) were treated in the same way as the Coma relic observations. + Figure | is vignetting-corrected and background-subtracted using the above-mentioned blank sky observations., Figure \ref{xmm1} is vignetting-corrected and background-subtracted using the above-mentioned blank sky observations. + As ca be seen from the image. the X-ray emission around the sub-group extends into the radio relic region and shows a strikingly similar outer boundary.," As can be seen from the image, the X-ray emission around the sub-group extends into the radio relic region and shows a strikingly similar outer boundary." + It 1s clear that the X-ray emission 1 the relic region comes from the sub-group., It is clear that the X-ray emission in the relic region comes from the sub-group. + It cannot originate from the Coma cluster itself. as seen when extrapolating the beta-model derived by Briel. Henry Bohhringer (1992).," It cannot originate from the Coma cluster itself, as seen when extrapolating the beta-model derived by Briel, Henry Böhhringer (1992)." + In fact. the Coma cluster emission at these radii is more then 20 times fainter than what is observed.," In fact, the Coma cluster emission at these radii is more then 20 times fainter than what is observed." + To check for the presence of a shock wave and of non-thermal emission. we selected two regions for the spectral analysis (Fig. 2)):," To check for the presence of a shock wave and of non-thermal emission, we selected two regions for the spectral analysis (Fig. \ref{xmm2}) ):" + one ellipse of 600 x 330 kpc in the relic region (1) and another ellipse of 310 x 190 kpe- to the NE of the relic towards the Coma cluster (2)., one ellipse of 600 $\times$ 330 $^2$ in the relic region (1) and another ellipse of 310 $\times$ 190 $^2$ to the NE of the relic towards the Coma cluster (2). + The total number of source photons in the 0.3-10 keV band in regions (1) and (2) is 13520 and 10620. respectively.," The total number of source photons in the 0.3-10 keV band in regions (1) and (2) is 13520 and 10620, respectively." + In these regions. the source count-rate in the 0.3-10 keV energy band is similar to the background count-rate.," In these regions, the source count-rate in the 0.3-10 keV energy band is similar to the background count-rate." + Table ] shows the results of the spectral fitting analysis with XSPEC., Table \ref{tab:spec} shows the results of the spectral fitting analysis with XSPEC. + For this study. we used the latest response matrix files avalable at ESA’s XMM-Newton homepage and the on-axis auxiliary reponse files describing the effective area of each camera as a function of photon energy.," For this study, we used the latest response matrix files avalable at ESA's XMM-Newton homepage and the on-axis auxiliary reponse files describing the effective area of each camera as a function of photon energy." + We chose the corresponding background regions in the same detector coordinates., We chose the corresponding background regions in the same detector coordinates. + There is an intensity variability in the instrumental background of XMM-Netwon., There is an intensity variability in the instrumental background of XMM-Netwon. + To correct for this effect. we compared the source and background count-rates in the 10-12 keV (12-14) keV energy band for the MOS (pn) cameras over each entire camera (see Majerowiez et al.," To correct for this effect, we compared the source and background count-rates in the 10-12 keV (12-14) keV energy band for the MOS (pn) cameras over each entire camera (see Majerowicz et al." + 2004 for details)., 2004 for details). + The ratio of the count-rates is used as the normalization factor of the background to the source spectrum., The ratio of the count-rates is used as the normalization factor of the background to the source spectrum. + The normalization value in our case Is about 1.2. which indicates that the instrumental background in our observation is higher than the instrumental background in the blank sky observations.," The normalization value in our case is about 1.2, which indicates that the instrumental background in our observation is higher than the instrumental background in the blank sky observations." + The chosen background normalization of 1.2 provides the lowest y results., The chosen background normalization of 1.2 provides the lowest $\chi^2$ results. + Varying the normalization factor. the changes of the spectral fitting results are always within the error bars.," Varying the normalization factor, the changes of the spectral fitting results are always within the error bars." + We fit both a thermal model and a combined thermal/non- model with à fixed power law index of 2.2. derived," We fit both a thermal model and a combined thermal/non-thermal model with a fixed power law index of 2.2, derived" +From the radial velocities of the IWC and LYC. ancl assuming an inclination angle of (to the line of sieht and a distance of ppc to13.. then over the time period between the observations the Hs LVC and IVC should have moved by ((12 AU) and ((38 AU) on the sky. while the [Fe i1] feature should have moved by ((53 AU).,"From the radial velocities of the HVC and LVC, and assuming an inclination angle of to the line of sight and a distance of pc to, then over the time period between the observations the $_2$ LVC and HVC should have moved by (12 AU) and (38 AU) on the sky, while the [Fe ] feature should have moved by (53 AU)." + Clearly. only the Ls LVC has a PM consistent with the observed radial velocity.," Clearly, only the $_2$ LVC has a PM consistent with the observed radial velocity." + such consisteney. is expected if. [or example. the gas is accelerated bv a fast-moving shock front in a heavy jet.," Such consistency is expected if, for example, the gas is accelerated by a fast-moving shock front in a heavy jet." + The apparent lack of movement of the IIl» IVC could result from: (1) the larger errors associated. wilh the positional measurements of (his fainter. more extended feature: (2) blending of component 2 with component 3 (Table 1)) in the lower-spatial-resolution data. so that the overall peak appears shifted downwind: or (3) the [act that the time interval between the observations is comparable to the molecular cooling time ancl therefore the timescale For morphological change. which could introduce unknown errors on the PM measurements.," The apparent lack of movement of the $_2$ HVC could result from: (1) the larger errors associated with the positional measurements of this fainter, more extended feature; (2) blending of component 2 with component 3 (Table \ref{table1}) ) in the lower-spatial-resolution data, so that the overall peak appears shifted downwind; or (3) the fact that the time interval between the observations is comparable to the molecular cooling time and therefore the timescale for morphological change, which could introduce unknown errors on the PM measurements." + The lack of a measurable PM in the [Fe Π peak is more difficult to explain., The lack of a measurable PM in the [Fe ] peak is more difficult to explain. + If the [Fe Π peak was associated with ejectecl clumps or bullets. then one would perhaps expect to see additional components along the flow axis (as is the case in I3).," If the [Fe ] peak was associated with ejected clumps or bullets, then one would perhaps expect to see additional components along the flow axis (as is the case in $_2$ )." + Instead. (he [Fe 11] is confined to a single. very compact peak at the jet base.," Instead, the [Fe ] is confined to a single, very compact peak at the jet base." + The [Fe ii| could be associated with a stationary. collimating shock. similar (ο that described in the models of (1994).," The [Fe ] could be associated with a stationary, collimating shock, similar to that described in the models of \citet{ouy94}." +. If this is indeed the case. the collimation point would be at a distance of 20 AAU," If this is indeed the case, the collimation point would be at a distance of $\sim 20$ AU" +"(Masonetal.2006,2008),, although higher resolution simulations suggest that the alignment saturates at small scales 2011).","\citep{mason06,mason08}, although higher resolution simulations suggest that the alignment saturates at small scales \citep{beresnyak11}." +". To date, there has not been a measurement of the spectral index parallel to the local magnetic field in simulations."," To date, there has not been a measurement of the spectral index parallel to the local magnetic field in simulations." + Measurements of the perpendicular spectral index in the solar wind and in simulations are also not always in agreement., Measurements of the perpendicular spectral index in the solar wind and in simulations are also not always in agreement. + It is important to be sure that the same quantities are being measured in both the solar wind and simulations and the subject of this paper is such a comparative study., It is important to be sure that the same quantities are being measured in both the solar wind and simulations and the subject of this paper is such a comparative study. +" We apply a similar analysis technique to both solar wind data and reduced MHD (RMHD) simulations, to make direct comparison of the anisotropic scaling."," We apply a similar analysis technique to both solar wind data and reduced MHD (RMHD) simulations, to make a direct comparison of the anisotropic scaling." +" In Section 2 we presenta the solar wind analysis, in Section 3 we present the simulation analysis, in Section 4 we compare the local and global mean field methods and in Section 5 we present our conclusions."," In Section \ref{sec:sw} we present the solar wind analysis, in Section \ref{sec:sim} we present the simulation analysis, in Section \ref{sec:localvsglobal} we compare the local and global mean field methods and in Section \ref{sec:conc} we present our conclusions." +" In this section, we apply the multispacecraft method of Chenetal.(2010a) to obtain the power and spectral index anisotropy of inertial range turbulence in the slow solar wind at 1 AU."," In this section, we apply the multispacecraft method of \citet{chen10b} to obtain the power and spectral index anisotropy of inertial range turbulence in the slow solar wind at 1 AU." +" The technique is applied to 65 1-hour intervals of data from the Cluster spacecraft (Escoubetetal.2001) from December 2005 to April 2006, when the typical separation between the four spacecraft was ~ 10,000 km."," The technique is applied to 65 1-hour intervals of data from the Cluster spacecraft \citep{escoubet01} from December 2005 to April 2006, when the typical separation between the four spacecraft was $\sim$ 10,000 km." + The selected intervals are from the parts of the Cluster orbit where the spacecraft were in the free solar wind upstream of the bow shock at geocentric distances of between 15 Re and 20 ΚΕ., The selected intervals are from the parts of the Cluster orbit where the spacecraft were in the free solar wind upstream of the bow shock at geocentric distances of between 15 $R_E$ and 20 $R_E$. +" They contain no evidence of ion foreshock activity: signatures typical of the ion foreshock, such as enhanced magnetic field fluctuations and high-energy ions, are not present."," They contain no evidence of ion foreshock activity: signatures typical of the ion foreshock, such as enhanced magnetic field fluctuations and high-energy ions, are not present." + The time series were also inspected visually to ensure that they are approximately stationary and do not contain shocks or magnetic clouds., The time series were also inspected visually to ensure that they are approximately stationary and do not contain shocks or magnetic clouds. +" In the analysis, weuse 4 s measurements of the magnetic field from the fluxgate magnetometer (FGM) (Baloghetal.2001) and velocity and density moments from the Cluster ion spectrometer (CIS) (Rémeetal. 2001).."," In the analysis, weuse 4 s measurements of the magnetic field from the fluxgate magnetometer (FGM) \citep{balogh01} and velocity and density moments from the Cluster ion spectrometer (CIS) \citep{reme01}. ." + The mean values of various parameters for the 65 intervals are given in Table 1.., The mean values of various parameters for the 65 intervals are given in Table \ref{tab:parameters}. +" The geometric mean is used for the ion beta, temperature anisotropy, gyroradius and ratio."," The geometric mean is used for the ion beta, temperature anisotropy, gyroradius and ratio." + The intervals are in slow solar wind with a speed < 550 km Ss., The intervals are in slow solar wind with a speed $<$ 550 km $^{-1}$. +" The rratio is the ratio of energy in the velocity u to the magnetic field in uunits b, and can be calculated spectrally, ra—E""/Eb where E"" and E? are the power spectra of u and b."," The ratio is the ratio of energy in the velocity $\mathbf{u}$ to the magnetic field in units $\mathbf{b}$ , and can be calculated spectrally, $r_A=E^u/E^b$ , where $E^u$ and $E^b$ are the power spectra of $\mathbf{u}$ and $\mathbf{b}$." +" We calculate the average ra in the spacecraft frequency range 2x10? Hz to 1x10? Hz, which roughly corresponds to scales 36,000 km to 180,000 km under Taylor’s hypothesis (Taylor1938)."," We calculate the average $r_A$ in the spacecraft frequency range $2\times 10^{-3}$ Hz to $1\times 10^{-2}$ Hz, which roughly corresponds to scales 36,000 km to 180,000 km under Taylor's hypothesis \citep{taylor38}." +". While this is at larger scales than the following anisotropy measurements, itis in the range where noise does not appear to dominate the velocity spectra."," While this is at larger scales than the following anisotropy measurements, itis in the range where noise does not appear to dominate the velocity spectra." + The value slightly lessthan unity that we obtain (e 0.7) is consistent with previous measurements (e.g.Matthaeus2007;Salemetal. 2009).," The value slightly lessthan unity that we obtain $\approx$ 0.7) is consistent with previous measurements \citep[e.g.][]{matthaeus82a,marsch90a,podesta07a,bruno07,salem09}." +". We also calculate the normalised cross helicity, where E and E~ are the power spectra of the Elsasser variables z=u+b."," We also calculate the normalised cross helicity, where $E^+$ and $E^-$ are the power spectra of the Elsasser variables $\mathbf{z}^\pm=\mathbf{u}\pm\mathbf{b}$." + The average value for each interval is calculated over the same range as the rratio., The average value for each interval is calculated over the same range as the ratio. + The usual convention is used: the Elsasser variables are defined such that positive values of o; correspond to ppropagation away from the Sun., The usual convention is used: the Elsasser variables are defined such that positive values of $\sigma_c$ correspond to propagation away from the Sun. + A histogram of 0; (Fig. 1)), A histogram of $\sigma_c$ (Fig. \ref{fig:nch}) ) +" shows a range of values with a non-Gaussian distribution: there is a large outward population (0;> 0.5), a balanced population (σε7:0), and a few inward intervals (σ.« —0.5)."," shows a range of values with a non-Gaussian distribution: there is a large outward population $\sigma_c > 0.5$ ), a balanced population $\sigma_c \approx 0$ ), and a few inward intervals $\sigma_c < -0.5$ )." +" For each interval, pairs of points from the time series of the four spacecraft are used to calculate second-order structure functions at different angles to the local magnetic field, as described by Chenetal. (20102)."," For each interval, pairs of points from the time series of the four spacecraft are used to calculate second-order structure functions at different angles to the local magnetic field, as described by \citet{chen10b}." +". The second-order structure function is defined as where Bj is the ith component of the magnetic field, 1 is theseparation vector, and the angular brackets denote an ensemble average over positions r."," The second-order structure function is defined as where $B_i$ is the $i$ th component of the magnetic field, $\mathbf{l}$ is theseparation vector, and the angular brackets denote an ensemble average over positions $\mathbf{r}$." +" The local mean magnetic field at scale lis defined as We calculate the structure functions of the localperpendicular magneticfield component B, , which corresponds to the ffluctuations, at a variety of separations l."," The local mean magnetic field at scale $\mathbf{l}$ is defined as We calculate the structure functions of the localperpendicular magneticfield component $\mathbf{B}_{\perp}$ , which corresponds to the fluctuations, at a variety of separations $\mathbf{l}$ ." +" The structure function values are binned according toscale parallel, J, and perpendicular, /, , to Biocal."," The structure function values are binned according toscale parallel, $l_{\para}$ , and perpendicular, $l_{\perp}$ , to $\mathbf{B}_{\text{local}}$ ." + Nine linearly spaced, Nine linearly spaced +The data base of rotational measurements used in this paper is described. in section. 2.,The data base of rotational measurements used in this paper is described in section 2. + Section 3 presents the analvsis methods. used. in this work., Section 3 presents the analysis methods used in this work. + The results are presented in section 4 and discussed in section 5., The results are presented in section 4 and discussed in section 5. + The ONC is among the best studied. star forming regions and the premier cluster for investigating star formation and early stellar evolution., The ONC is among the best studied star forming regions and the premier cluster for investigating star formation and early stellar evolution. + Lt is relatively nearby. very voung (392+ 34ppc. c1 2MMyr.— Jelfries. 2007: 389 2lppe Sandstrom et al.," It is relatively nearby, very young $392\pm 34$ pc, $\simeq$ Myr – Jeffries 2007; $389^{+24}_{-21}$ pc -- Sandstrom et al." + 2007) and contains a large population of stars and brown cwarfs covering the entire (sub)stellar mass spectrum (0:01«AZ/AZ.300 see Hillenbrand. 1997: Slesnick. Hillenbrand Carpenter 2004).," 2007) and contains a large population of stars and brown dwarfs covering the entire (sub)stellar mass spectrum $0.013$ Myr) stars appears to be absent from the rotation sample. + A Ixolmogorov-Smirnov (Ix-8) test sugeests that there is à «1 per cent probability that the two age distributions are consistent., A Kolmogorov-Smirnov (K-S) test suggests that there is a $<1$ per cent probability that the two age distributions are consistent. + This selection. effect arises chiellv from the bias towards brighter targets., This selection effect arises chiefly from the bias towards brighter targets. + Some of the age bias might be thought to arise because older. smaller objects could have unresolveable esin? (see Rebull. Wolff Strom 2004).," Some of the age bias might be thought to arise because older, smaller objects could have unresolveable $v \sin i$ (see Rebull, Wolff Strom 2004)." + However. the H-It. diagram-based age distribution for objects which have unresolved: Ομ but otherwise match the sample selection criteria is in fact similar to that of the rotation sample.," However, the H-R diagram-based age distribution for objects which have unresolved $v +\sin i$ but otherwise match the sample selection criteria is in fact similar to that of the rotation sample." + Stars in the rotation sample are classified as CTS or, Stars in the rotation sample are classified as CTTS or +(another solar analog staudard) for the determination of color terms.,(another solar analog standard) for the determination of color terms. + Ground-based JiIV photometry for NICMOS standards comes frou Perssonetal.(1998)., Ground-based $JHK$ photometry for NICMOS standards comes from \citet{per98}. +. Our definition of J. 1 aud A zeropoiuts i9 based ou different apertures and sky auuuli for each baud. to match the noticeable increase in FWIIM. as a function of wavelength.," Our definition of $J$, $H$ and $K$ zeropoints is based on different apertures and sky annuli for each band, to match the noticeable increase in FWHM as a function of wavelength." + Table 2 lists our clioices of aperture radius aud inner and outer sky annul for cach ofthe three baudpasses., Table 2 lists our choices of aperture radius and inner and outer sky annuli for each of the three bandpasses. + Iu the case of the drizzled ΑΠΟ P160NV nuages. which have twice the spatial resolution. all radii were mereased by a factor of two in pixcl units so they would subteud the same angular size.," In the case of the drizzled M101 F160W images, which have twice the spatial resolution, all radii were increased by a factor of two in pixel units so they would subtend the same angular size." + Marcia Ricke kindly provided us with svuthetic (TinyTim) stellar images as well as NICMOS observations of P330-E. which we used to derive the magnitude zoropoiuts for our choices of aperture aud sky aunuuli.," Marcia Rieke kindly provided us with synthetic (TinyTim) stellar images as well as NICMOS observations of P330-E, which we used to derive the magnitude zeropoints for our choices of aperture and sky annuli." + First. we computed the ratio of TinyTia counts to observed NICAIOS count rates for P330-E as a function of aperture radius.," First, we computed the ratio of TinyTim counts to observed NICMOS count rates for P330-E as a function of aperture radius." +" We found this ratio to be constant. at the.. levels for ΕΟΝ, E160 and F205W. respectively. over a large rauge in radius (525 pixels)."," We found this ratio to be constant, at the, and levels for F110W, F160W and F205W, respectively, over a large range in radius (5–25 pixels)." + This confined that the TinwTim nuage was a good representation of the actual svstem PSF., This confirmed that the TinyTim image was a good representation of the actual system PSF. +" We then re-scaled the TiuvTuu nuage (n arbitrary units) to match the actua mean observed count rate of P330-E: this produced :(| svuthetic image of P330-E that could be used to perorn aperture measurements ou a ""porfect image free ο| defects; cosnule ravs. or ally other source of scatter fouud iu real nuages."," We then re-scaled the TinyTim image (in arbitrary units) to match the actual mean observed count rate of P330-E; this produced a synthetic image of P330-E that could be used to perform aperture measurements on a “perfect” image free of defects, cosmic rays, or any other source of scatter found in real images." + Next. we ran DAOPIIOT' rotifiue on the svuthetie P330-E inages using the ssame aperure and skv annuli as for the Cepheid photometry.," Next, we ran DAOPHOT's routine on the synthetic P330-E images using the same aperture and sky annuli as for the Cepheid photometry." + DAOPHOT quoted measurement errors of 0.001 mag for tjiese Inaenitudes., DAOPHOT quoted measurement errors of 0.004 mag for these magnitudes. + Lastly. we combined the Perssonetal.(1998). standard magnitudes and the DAOPHOT NICMOS Προ magnitudes for P330-E to arrive at our mmaenitude zeropoiuts.τα listed in Table 2.," Lastly, we combined the \citet{per98} standard magnitudes and the DAOPHOT NICMOS instrumental magnitudes for P330-E to arrive at our magnitude zeropoints, listed in Table 2." + Since the NICMOS filters are uot exact matches to the standard filters. color term corrections had to be determined.," Since the NICMOS filters are not exact matches to the standard filters, color term corrections had to be determined." + Svuthetie spectra of the NICMOS standards were created based ou [Eurucz latest solu-abundance models., Synthetic spectra of the NICMOS standards were created based on Kurucz' latest solar-abundance models. + These model spectra were convolved with two sets of transmission curves: one contained the NICMOS filter responses plus the quantum efficiency of camera 2. while the other was based on standard filter responses plus au atmospheric transmission curve.," These model spectra were convolved with two sets of transmission curves: one contained the NICMOS filter responses plus the quantum efficiency of camera 2, while the other was based on standard filter responses plus an atmospheric transmission curve." + This allowed us to predict FII10W. F1G0W. F205W. J. IT and A maguitudes for the NICAIOS standards.," This allowed us to predict F110W, F160W, F205W, $J$, $H$ and $K$ magnitudes for the NICMOS standards." + We then compared our results with published values (Perssouctal.L998) aud found uceleible offsets of 0.002-E0.003 mae for J aud 11 aud a small offset of 0.022+0.001 nae for A., We then compared our results with published values \citep{per98} and found negligible offsets of $0.002\pm0.003$ mag for $J$ and $H$ and a small offset of $0.022\pm0.001$ mag for $K$. + We used the same mocel atmospheres aud transmission curves deseribed above to generate svuthetic spectra for a varicty of spectral types (F. Ce and Iv) aud. luninositv classes (Land V).," We used the same model atmospheres and transmission curves described above to generate synthetic spectra for a variety of spectral types (F, G and K) and luminosity classes (I and V)." +" We compared the values of GPLLOT7} and CFIGOUTFF) as a function of «ΕΤΗ—F160115 as well as the values of CF2051YA) as a function of (PLGOTTΕΟΓ,"," We compared the values of $\langle F110W-J +\rangle$ and $\langle F160W-H \rangle$ as a function of $\langle +F110W-F160W\rangle$ as well as the values of $\langle F205W-K\rangle$ as a function of $\langle F160W-F205W\rangle$." + We found The mean values of the corrections were 0.230.11 mag for CFII0ITJ). 0.05+0.02 imag for CF1601T—IT; aud 0.010.0δ mag for (F205M/—Aj.," We found The mean values of the corrections were $0.23\pm0.11$ mag for $\langle +F110W-J\rangle$, $0.05\pm0.02$ mag for $\langle F160W-H\rangle$ and $-0.04\pm0.08$ mag for $\langle F205W-K\rangle$." + Note that au exact correction for «ΕΙTj was ouly applied to the stars in the 11613. M31. MIOLI-Iuner aud. MIOT-Outer fields.," Note that an exact correction for $\langle F160W-H\rangle$ was only applied to the stars in the 1613, M31, M101-Inner and M101-Outer fields." + The other fields were observed oulv in FIGOW aud therefore only an average IL--baud correction of 0.03 mag could be applied. based on a mean Cepheid ΕΟΟ color of 0.16 mae.," The other fields were observed only in F160W and therefore only an average H-band correction of $0.03$ mag could be applied, based on a mean Cepheid $\langle F110W-F160W\rangle$ color of $0.46$ mag." + The dense nature of most of our fields makes it difficult to obtain accurate values of the local sky around cach object and to perform unbiased magnitude measurements., The dense nature of most of our fields makes it difficult to obtain accurate values of the local sky around each object and to perform unbiased magnitude measurements. + This effect is couunoulv referred to as “crowding”., This effect is commonly referred to as “crowding”. + Iu order to characterize its mipact on our nieasurenients. we injected. artificial stars mto each field and compared their input maenitudes with the recovered values;," In order to characterize its impact on our measurements, we injected artificial stars into each field and compared their input magnitudes with the recovered values." + We used the poiut-spread functions derived for cach feld to geucrate the artificial stars. which were placed randomly across cach field.," We used the point-spread functions derived for each field to generate the artificial stars, which were placed randomly across each field." + The objects spanned a maguitude range Πιοπιαπας that euconipassed by the variables., The objects spanned a magnitude range including that encompassed by the variables. + Iu the case of the AMILOL fields. we injected artificial stars iuto the originalresolution mosaics as well as the ligher-resolution ones created by drizzling.," In the case of the M101 fields, we injected artificial stars into the original-resolution mosaics as well as the higher-resolution ones created by drizzling." + We rea our photometry programs ou the new images aud searched the new star lists to locate the artificial stars., We re-ran our photometry programs on the new images and searched the new star lists to locate the artificial stars. + The results of the tests are stunmarized in Table 3 aud displaved in Figures 2a-b. Figure 2a coutains plots of the difference. between iuput and recovered magnitudes as a function of magnitude for cach field., The results of the tests are summarized in Table 3 and displayed in Figures 2a-b. Figure 2a contains plots of the difference between input and recovered magnitudes as a function of magnitude for each field. + Figure 2b shows the strong correlation that exists between the crowding bias and the stellar density of cach field., Figure 2b shows the strong correlation that exists between the crowding bias and the stellar density of each field. + The effect ranges from 0.01 mag for the least crowded fields to 0.09 mag for the denser ones., The effect ranges from 0.01 mag for the least crowded fields to 0.09 mag for the denser ones. + All maguitudes were corrected for this effect., All magnitudes were corrected for this effect. + Iu addition to these “crowding” tests. we also undertook simulations to estimate the contamination of Cepheid magnitudes by unresolved nearby stars.," In addition to these “crowding” tests, we also undertook simulations to estimate the contamination of Cepheid magnitudes by unresolved nearby stars." +" These ""bleudiug tests are presented in 85.", These “blending” tests are presented in 5. + We performed several internal and external photometry checks το ensure. the accuracy and precision of our inaguitudes., We performed several internal and external photometry checks to ensure the accuracy and precision of our magnitudes. + We tested our aperture correction technique by comparing our corrected magnitudes against “standard” aperture magnitudes for stars m the IC 1613 fields., We tested our aperture correction technique by comparing our corrected magnitudes against “standard” aperture magnitudes for stars in the IC 1613 fields. + We found no significant differeuce (<0.01 mae), We found no significant difference $<0.01$ mag) +"Sokolov.Marscher.&Alellarcdy(2004.hereafterPaper1).. (Antonucci1993). T~1000IX (Peterson.1993). ~0.LLET,,pe {μ.ο LO’ergstA"" ","\citet*[hereafter Paper I]{paper1}, \citep{ant93} + $\sim$ $T\sim1000\,\mbox{K}$ \citep{pet93} $\sim0.1L_{{{}} uv,42}^{1/2}\,\mbox{pc}$ $L_{{{}} uv,42}$ $10^{42}\,\mbox{erg}\,\mbox{s}^{-1}\,\mbox{\AA}^{-1}$ " +identified an isolated unresolved: mid-infrared object. associated. with the jet that is likely to be responsible for the excitation of IRAS 16547-4247.,identified an isolated unresolved mid-infrared object associated with the jet that is likely to be responsible for the excitation of IRAS $-$ 4247. + If the luminosity of IRAS comes from a single object it would have the spectral (ype Os., If the luminosity of IRAS 16547--4247 comes from a single object it would have the spectral type O8. + The finding of a jet and collimated flow: towards such a massive object supports the accretion scenario for the formation of stars across the entire mass spectrum., The finding of a jet and collimated flow towards such a massive object supports the accretion scenario for the formation of stars across the entire mass spectrum. + We thank Vanessa Doublier. Rachel Johnson. Nathan Smith and Michael Sterzik lor their help with observations ancl data reduction.," We thank Vanessa Doublier, Rachel Johnson, Nathan Smith and Michael Sterzik for their help with observations and data reduction." + The ISAAC data were obtained through the ESO Directors Discretionary Time Program., The ISAAC data were obtained through the ESO Director's Discretionary Time Program. + This work has been partly fanded bv the Chilean Centro de Astroffssica FONDAP N?15010003., This work has been partly funded by the Chilean Centro de sica FONDAP $^o$ 15010003. +valid.,valid. + In the case that. for example. (NCA))>>| but (N(B)) I. equation (8) is still valid. and rate equations may be used. (," In the case that, for example, $\langle N(A) \rangle >> 1$ but $\langle N(B) \rangle << 1$ , equation (8) is still valid, and rate equations may be used. (" +An assumption to this effect was made by Stantcheva et al.,An assumption to this effect was made by Stantcheva et al. + 2002. in treating species such as CO using deterministic rates).," 2002, in treating species such as CO using deterministic rates)." + In such cases. reactions involving species B would have only a small effect on the population state of species A. making any (anti-correlation very weak.," In such cases, reactions involving species $B$ would have only a small effect on the population state of species $A$, making any (anti-)correlation very weak." + In the case where both (N(A))] and (N(B))<1 are deemed to be in the (NG))>>| regime. whilst species with «ΝΟ»«| are deemed to be in the (N(/)<<| regime.," To apply these conditions, species with $\langle N(i) \rangle \geq 1$ are deemed to be in the $\langle N(i) \rangle >> 1$ regime, whilst species with $\langle N(i) \rangle < 1$ are deemed to be in the $\langle N(i) \rangle << 1$ regime." + Modifications are therefore made only when (N(A».(NCB)) |.," Modifications are therefore made only when $\langle N(A) \rangle,\langle N(B)\rangle < 1$ ." + This is. of course. a gross simplification: however. the tests to follow demonstrate that any resultant inaccuracies are small.," This is, of course, a gross simplification; however, the tests to follow demonstrate that any resultant inaccuracies are small." + As a further restriction on the new rates. it is asserted that under no circumstances may the modified production rate exceed the standard rate-equation value. following the argument of Section 2.1.," As a further restriction on the new rates, it is asserted that under no circumstances may the modified production rate exceed the standard rate-equation value, following the argument of Section 2.1." + It is therefore required that: Thus. if à modified production. rate exceeds the deterministic rate. the deterministic rate Is used.," It is therefore required that: Thus, if a modified production rate exceeds the deterministic rate, the deterministic rate is used." + This basic formulation is tested against the simplest. of grain-surface systems. in which atomic hydrogen is the only reactive species.," This basic formulation is tested against the simplest of grain-surface systems, in which atomic hydrogen is the only reactive species." + Barzel Biham (2007b) investigated this system for various gram sizes. at a temperature of 10 K. They conducted rate-equation. master-equation. and moment-equation simulations. run to steady state in the population of atomic hydrogen.," Barzel Biham (2007b) investigated this system for various grain sizes, at a temperature of 10 K. They conducted rate-equation, master-equation, and moment-equation simulations, run to steady state in the population of atomic hydrogen." +" Calculations were made using either a high or a low flux of acereting H-atoms: R,..(H)=2.75*LOSS s! or RI)=1x107!S sv! where S is the number of surface binding sites."," Calculations were made using either a high or a low flux of accreting H-atoms; $R_{acc}(H)=2.75 \times 10^{-8} S$ $^{-1}$ or $R_{acc}(H)=1 \times 10^{-11} S$ $^{-1}$, where $S$ is the number of surface binding sites." + Details of this system are given in Tables | 2., Details of this system are given in Tables 1 2. + Barzel&Biham(2007b) detail all other relevant values., \cite{barzel2} detail all other relevant values. + Solving for H populations and H» production rates requires the solution of the equation: dowhere ΑΠ») is defined according to the stipulations of Section 3.1., Solving for H populations and $_2$ production rates requires the solution of the equation: where $R_{prod}($ $_{2})$ is defined according to the stipulations of Section 3.1. + Obtaining an analytical solution is trivial., Obtaining an analytical solution is trivial. + Figures | and 2 show grain-surface atomic hydrogen populations and H» production rates calculated in this way for various values of S. using low and high H-fluxes. respectively.," Figures 1 and 2 show grain-surface atomic hydrogen populations and $_2$ production rates calculated in this way for various values of $S$, using low and high H-fluxes, respectively." + Solid black lines show the results when modified rates are employed according to the stipulations of the modification scheme of Section 3.1., Solid black lines show the results when modified rates are employed according to the stipulations of the modification scheme of Section 3.1. + Dashed lines represent standard rate-equation results: dotted lines represent results obtained from equations (11) and (12)., Dashed lines represent standard rate-equation results; dotted lines represent results obtained from equations (11) and (12). + Indicated 1n red are the master-equation results of Barzel&Biham(2007b).. with crosses marking the individual data points.," Indicated in red are the master-equation results of \cite{barzel2}, with crosses marking the individual data points." + The master-equation results may be regarded as a true representation of the system., The master-equation results may be regarded as a true representation of the system. + Rates and populations calculated using standard. rate equations rise linearly with increasing S., Rates and populations calculated using standard rate equations rise linearly with increasing $S$. + At large grain sizes these are the exact solutions. but become inaccurate for small grains.," At large grain sizes these are the exact solutions, but become inaccurate for small grains." + Similarly. populations calculated purely with equations (11) and (12) may diverge from the rate equations for large grain sizes.," Similarly, populations calculated purely with equations (11) and (12) may diverge from the rate equations for large grain sizes." + The simple modification scheme demonstrates near-perfect agreement with the master-equation populations and production rates calculated by Barzel Biham. at both the large- and smiall-grain extremes of the system. for each H-flux value.," The simple modification scheme demonstrates near-perfect agreement with the master-equation populations and production rates calculated by Barzel Biham, at both the large- and small-grain extremes of the system, for each H-flux value." + Approaching the stochastic-deterministic threshold. where deterministic rates become accurate. results vary marginally from the exact master-equation values; the match is otherwise perfect.," Approaching the stochastic–deterministic threshold, where deterministic rates become accurate, results vary marginally from the exact master-equation values; the match is otherwise perfect." + Whilst modification using equations (10) — (13). along with the stipulations of Section. 3.1. is accurate in the case of simple. highly prescribed systems. the purpose of this work is to fashion à modification scheme that is more universally," Whilst modification using equations (10) – (13), along with the stipulations of Section 3.1, is accurate in the case of simple, highly prescribed systems, the purpose of this work is to fashion a modification scheme that is more universally" +rate and optimizations for transient detection in the non-Gaussian domain.,rate and optimizations for transient detection in the non-Gaussian domain. + Figure 2 shows how the apparent SNR of four techniques scales with SNR per baseline for a 27-element array like the VLA., Figure \ref{snrtheory} shows how the apparent SNR of four techniques scales with SNR per baseline for a 27-element array like the VLA. +" The apparent bispectrum SNR scales as s?, giving it a strong response to bright sources and very little response to faint sources."," The apparent bispectrum SNR scales as $s^3$, giving it a strong response to bright sources and very little response to faint sources." +" However, the effective bispectrum SNR, defined according to a Gaussian false-positive rate, would be less sensitive for large s."," However, the effective bispectrum SNR, defined according to a Gaussian false-positive rate, would be less sensitive for large $s$." + Our simulations suggest that the effective bispectrum SNR. never exceeds that of coherent beamforming., Our simulations suggest that the effective bispectrum SNR never exceeds that of coherent beamforming. +" The bottom panel of Figure 2. shows the effective 5c fflux limit for an array with n, eelements and sensitivity like the VLA.", The bottom panel of Figure \ref{snrtheory} shows the effective $\sigma$ flux limit for an array with $n_a$ elements and sensitivity like the VLA. +" For the beamforming techniques, this plot essentially shows how the lines in the top panel intersect SNR=5 aas the array size changes."," For the beamforming techniques, this plot essentially shows how the lines in the top panel intersect $\rm{SNR}=5$ as the array size changes." +" For the bispectrum, the effective flux limit is shown by correcting for sensitivity loss due to non-Gaussianity, as measured in our simulations."," For the bispectrum, the effective flux limit is shown by correcting for sensitivity loss due to non-Gaussianity, as measured in our simulations." +" Generally, since large arrays are sensitive to pulses with SNR per baseline much less than one, coherent beamforming and imaging become more sensitive than the bispectrum as n, iincreases."," Generally, since large arrays are sensitive to pulses with SNR per baseline much less than one, coherent beamforming and imaging become more sensitive than the bispectrum as $n_a$ increases." +" For large nq, the bispectrum and incoherent beamforming techniques scale similarly (sοςna1/ so the bispectrum is always more sensitive than the incoherent3, techniques."," For large $n_a$, the bispectrum and incoherent beamforming techniques scale similarly $s\propto n_a^{-1/2}$ ), so the bispectrum is always more sensitive than the incoherent techniques." + To interpret the bispectrum as the brightness of a transient requires subtracting the signature of constant emission from the visibilities., To interpret the bispectrum as the brightness of a transient requires subtracting the signature of constant emission from the visibilities. + Proper subtraction requires that the visibility fringe does not change over background subtraction time., Proper subtraction requires that the visibility fringe does not change over background subtraction time. + The maximum fringe rate is equal to the product of the rate of change of the longest baseline in the plane and the largest direction cosine., The maximum fringe rate is equal to the product of the rate of change of the longest baseline in the ) plane and the largest direction cosine. +" In units of (u,v))radians per day, the maximum fringe rate is TOmaxO¢.0.v./A, where bx iis the longest baseline, ro... iis the field of view in radians, and A iis the wavelength."," In units of radians per day, the maximum fringe rate is $\pi \, b_{\rm{max}} \, \theta_{\rm{f.o.v.}} / \lambda$, where $b_{\rm{max}}$ is the longest baseline, $\theta_{\rm{f.o.v.}}$ is the field of view in radians, and $\lambda$ is the wavelength." +" More precisely, the error from subtracting visibilities leaves residual errors proportional to the brightness of sources in the field."," More precisely, the error from subtracting visibilities leaves residual errors proportional to the brightness of sources in the field." + Thompsonetal.(2001) quantify the effect of time smearing as a reduction in the peak brightness of a source., \citet{tms} quantify the effect of time smearing as a reduction in the peak brightness of a source. +" For small changes, we can parametrize this in terms of a 1.4 GHz VLA A"," For small changes, we can parametrize this in terms of a 1.4 GHz VLA A" +The first step of our caleulation is the hydrodvuauuical siuulation of the explosion with a 2D Eulerian lvdvodvuamical code based ou BRocs scheme (Hachisu 1992. 1991).,"The first step of our calculation is the hydrodynamical simulation of the explosion with a 2D Eulerian hydrodynamical code based on Roe's scheme (Hachisu 1992, 1994)." + Eulers equations are solved with a constant adiabatie index 5 = 1/3. which is a good approximation if the pressure ds raciation-domunated.," Euler's equations are solved with a constant adiabatic index $\gamma$ = 4/3, which is a good approximation if the pressure is radiation-dominated." + The effect of nuclear reactions on the lyvdrodvuamics 1s uceleible since the explosion cucrey is large., The effect of nuclear reactions on the hydrodynamics is negligible since the explosion energy is large. + We use 120<120 meshes on a cylindrical (+.2) coordinate system.," We use $120 \times 120$ meshes on a cylindrical $(r,z)$ coordinate system." + The mesh size is linearly zoned aud decreases nsvard. which eives a high resolution of the hydrodvuamic evolition of the central regions where explosive nucleosvuthesis takes place.," The mesh size is linearly zoned and decreases inward, which gives a high resolution of the hydrodynamic evolution of the central regions where explosive nucleosynthesis takes place." + We follow 190 test particles initially iu the Si laver and 2250 particles initially iu the C|O laver. tracking their density aud teniperature histories.," We follow 190 test particles initially in the Si layer and 2250 particles initially in the C+O layer, tracking their density and temperature histories." + These histories are then used to caleulate the change in the chemical composition. using a reaction network incliding 222 isotopes up to “Ce (Thiclemannu 1996).," These histories are then used to calculate the change in the chemical composition, using a reaction network including 222 isotopes up to $^{71}$ Ge (Thielemann 1996)." + We construct several asvinimetric explosion models for various combinations of the model parameters (Table 3)., We construct several asymmetric explosion models for various combinations of the model parameters (Table 3). + We use as progenitor the 16 AL.. We core of a 10. AL. star (Nomoto Tlashimoto 1988)., We use as progenitor the 16 $M_\odot$ He core of a 40 $M_\odot$ star (Nomoto Hashimoto 1988). + This has a 13.5 AL. οτο core. the same as that used in Iwamoto (1998).," This has a 13.8 $M_\odot$ C+O core, the same as that used in Iwamoto (1998)." +" We test three values of the final kinetic energv: E—1«1003, 1107, and ὃς10° eres."," We test three values of the final kinetic energy: $E = 1 \times 10^{51}$, $1 \times 10^{52}$, and $3 \times 10^{52}$ ergs." + The lydrodyuamical sinmlation is started by depositing the cnerey below the mass cut that divides the cjecta from the collapsing core., The hydrodynamical simulation is started by depositing the energy below the mass cut that divides the ejecta from the collapsing core. + The enerey deposited is divided between thermal aud kinetic ΟΠΟΙΟΥ. with various ratios.," The energy deposited is divided between thermal and kinetic energy, with various ratios." + The asvuuuetry is eenerated by distributing the initial kinetic cucreyv dn an axisviunetric wav., The asymmetry is generated by distributing the initial kinetic energy in an axisymmetric way. + This is done bv muposiug different initial velocities in different directions: e;=a: in the jet direction aud C.=9r on the equatorial plane., This is done by imposing different initial velocities in different directions: $v_z = \alpha \; z$ in the jet direction and $v_r = \beta \; r$ on the equatorial plane. + The ratio a/o ranges from 16:1 to 1:1 (spherical case)., The ratio $\alpha/\beta$ ranges from 16:1 to 1:1 (spherical case). +" The mass cut is set at AL,=2.1AL... so that the ejected mass of 7?Ni is ~ 0.1 AL. to reproduce the peak of the light curve (Nakamura 2001a) in models A. B. €. E. aud F. Figure d aud 2 show respectively the post-shock peak temperatures aud densities for the asvuunetric liviperuova model € in the direction of the jet and. perpendicular to it (with those for the spherically svuumetric hvperuova model EF also shown for comparison). and the isotopic composition of the ejecta of model C. Iu the z-direction. where the ejecta carry more kinetic energw. the shock is stronecr and post-shock temperatures are higher. so that explosive uucleosvuthesis takes place d more exteuded. lower density resious compared with the r-direction."," The mass cut is set at $M_r = 2.4M_\odot$, so that the ejected mass of $^{56}$ Ni is $\sim$ 0.4 $M_\odot$ to reproduce the peak of the light curve (Nakamura 2001a) in models A, B, C, E, and F. Figure 1 and 2 show respectively the post-shock peak temperatures and densities for the asymmetric hypernova model C in the direction of the jet and perpendicular to it (with those for the spherically symmetric hypernova model F also shown for comparison), and the isotopic composition of the ejecta of model C. In the $z$ -direction, where the ejecta carry more kinetic energy, the shock is stronger and post-shock temperatures are higher, so that explosive nucleosynthesis takes place in more extended, lower density regions compared with the $r$ -direction." + Therefore. larger amounts of a-rich freeze-out clements. such as Πο aud 79Nà (which decays iuto Fe via °° Co) are produced in the :-directiou than in the r-direction.," Therefore, larger amounts of $\alpha$ -rich freeze-out elements, such as $^4$ He and $^{56}$ Ni (which decays into $^{56}$ Fe via $^{56}$ Co) are produced in the $z$ -direction than in the $r$ -direction." + Also. the expansion velocity of newly svuthesized heavy elements is much higher in the :-direction.," Also, the expansion velocity of newly synthesized heavy elements is much higher in the $z$ -direction." + The velocity of clemeuts ejected in the <:-direction in model € is actually simular to the result of a spherical explosion with E~3<10% eres (Nakaumera 20015). although the integrated kinetic energy is ouly E=1<107? eres.," The velocity of elements ejected in the $z$ -direction in model C is actually similar to the result of a spherical explosion with $E +\sim 3 \times 10^{52}$ ergs (Nakamura 2001b), although the integrated kinetic energy is only $E = 1 \times 10^{52}$ ergs." + Tn contrast. along the r-dizection °ONi is produced only in the deepest lavers. and clemeuts ejected in this direction are ijostlv the product of hydrostatic nuclear burning (CO). with some explosive oxvecu-buruing products (Si. S. etc).," In contrast, along the $r$ -direction $^{56}$ Ni is produced only in the deepest layers, and elements ejected in this direction are mostly the product of hydrostatic nuclear burning (O), with some explosive oxygen-burning products (Si, S, etc)." + The expansion velocities are much lower than in the :- direction., The expansion velocities are much lower than in the $z$ -direction. + Figure 3 shows the 2D distribution of °°Ni aud 1O in model € in the homologous expansion plase., Figure 3 shows the 2D distribution of $^{56}$ Ni and $^{16}$ O in model C in the homologous expansion phase. + Near the z-axis the shock is stronger aud a low deusity. 'We-rich region is produced.," Near the $z$ -axis the shock is stronger and a low density, $^4$ He-rich region is produced." + 79 Ni is distributed prefercutially iu this direction. but it is mostly located slightly off of it because the shock propagates laterally as it penetrates the stellar envelope.," $^{56}$ Ni is distributed preferentially in this direction, but it is mostly located slightly off of it because the shock propagates laterally as it penetrates the stellar envelope." + As a result. the distribution of heavy clemets is elongated in the z-direction. whilea that of 0Ο is less aspherical.," As a result, the distribution of heavy elements is elongated in the $z$ -direction, while that of $^{16}$ O is less aspherical." + On the other hand. because the ejecta move more slowly in the r-direction. densities im this direction are higher than in the z-direction.," On the other hand, because the ejecta move more slowly in the $r$ -direction, densities in this direction are higher than in the $z$ -direction." +" Tables 1 aud 2 give respectively the detailed vields aud the abundances of major stable isotopes relative to the solar values for model € (iu Table 2. ΑΟ)=logy,(A/B) |. where A aud D are nuclear mass fractious)."," Tables 1 and 2 give respectively the detailed yields and the abundances of major stable isotopes relative to the solar values for model C (in Table 2, $\rm{[A/B]} \equiv \log_{10}\rm{(A/B)} - +\log_{10}\rm{(A/B)}_\odot$ , where A and B are nuclear mass fractions)." + The main characteristics can be stunarized as follows (see also Nomoto et al., The main characteristics can be summarized as follows (see also Nomoto et al. + 20015). (, 2001b). ( +1) The complete Si-burning region is more extended for larger explosion enereies.,1) The complete Si-burning region is more extended for larger explosion energies. + The aspherical explosion causes a region of ligher cutropy along the + axis. which offers better conditions for the a-ich freezeout (Fie.," The aspherical explosion causes a region of higher entropy along the $z-$ axis, which offers better conditions for the $\alpha$ -rich freezeout (Fig." + 1)., 1). +" The high entropy inhibits the production of Να, ", The high entropy inhibits the production of $^{56}$ Ni. +Much Πο is left after the freezeout. so that the elemeuts produced through ‘Tle capture are very abundant in the deepest region along he :-axis (Fig.," Much $^4$ He is left after the freezeout, so that the elements produced through $^{4}$ He capture are very abundant in the deepest region along the $z$ -axis (Fig." + 2)., 2). + This results in the cnhancemenut of he clements svuthesized in the deepest regiou. such as Hu (produced. as IUD ΤΙ (as P'Cr) and elements jeavier than A~Se.," This results in the enhancement of the elements synthesized in the deepest region, such as $^{44}$ Ca (produced as $^{44}$ Ti), $^{48}$ Ti (as $^{48}$ Cr), and elements heavier than $A \sim 58$." +" Because of the cuhauccment of hese clemeuts and the simultancous suppression of ""Ni. he abundances of these clements relative to ion (e.g... Hus τα, 617 Τομ) are ereatly euhanced."," Because of the enhancement of these elements and the simultaneous suppression of $^{56}$ Ni, the abundances of these elements relative to iron (e.g., $^{44}$ Ca, $^{48}$ Ti, $^{64}$ Zn /Fe]) are greatly enhanced." + For more asvuuuetric explosion. the effect of a-vich freezeout is even arecr. (," For more asymmetric explosion, the effect of $\alpha$ -rich freezeout is even larger. (" +2) Incomplete Si-buruiug aud O-buruiug regions are nore extended for larger explosion euergies (Nakamura ct al.,2) Incomplete Si-burning and O-burning regions are more extended for larger explosion energies (Nakamura et al. + 200110)., 2001b). +" This results in the culiancement of 285i, 72$, IU. 028. (produced as 2 Foy, ?! Fo, and iu the reduction of ο. Asphericity has little effect on the production of these elements."," This results in the enhancement of $^{28}$ Si, $^{32}$ S, $^{40}$ Ca, $^{52}$ Cr (produced as $^{52}$ Fe), $^{54}$ Fe, and in the reduction of O. Asphericity has little effect on the production of these elements." + The most pronounced effect of asphericity is that elements produced bv the strong a-rich freezeout are greatly cuhanuced relative to iron (e.c... [Ti/Fe]).," The most pronounced effect of asphericity is that elements produced by the strong $\alpha$ -rich freezeout are greatly enhanced relative to iron (e.g., [Ti/Fe])." + For other explosive burning products. the effect of a large explosion energv usually dominates over that of asplericity.," For other explosive burning products, the effect of a large explosion energy usually dominates over that of asphericity." + Tn order to verify the observable consequences of au axisviunietrie explosion. we calculated the profiles of the 1| blend aud of ΕΙ for models ÀA-C. Line eimissivities were obtained from à 1D NLTE uebular code (Mazzali et al.," In order to verify the observable consequences of an axisymmetric explosion, we calculated the profiles of the ] blend and of ] for models A-G. Line emissivities were obtained from a 1D NLTE nebular code (Mazzali et al." + 2001). and the cohuun doeusities of the various elements along different lines of sight were derived frou the clement distribution obtained frou our 2D explosion models.," 2001), and the column densities of the various elements along different lines of sight were derived from the element distribution obtained from our 2D explosion models." + Because we asstme that the nebula is optically thin. the blended nature of the ciissious is automatically," Because we assume that the nebula is optically thin, the blended nature of the emissions is automatically" +we used this value for the external extinction to predict the reddened aand mmagnitudes of the central star.,we used this value for the external extinction to predict the reddened and magnitudes of the central star. + Where necessary. we applied. the interstellar reddening law given. by Pottasch (LOSL)..," Where necessary, we applied the interstellar reddening law given by Pottasch \cite{c2:book:pot}." + A comparison of the calculated values with the literature values taken from Acker et citec2:ack:cat is given in δ.., A comparison of the calculated values with the literature values taken from Acker et \\cite{c2:ack:cat} is given in \ref{mag:tab}. + The predicted. magnitudes. are slightly fainter than observed. but still in remarkable good agreement. considering t16 fact that we use a blackbocv approximation to determine these values.," The predicted magnitudes are slightly fainter than observed, but still in remarkable good agreement, considering the fact that we use a blackbody approximation to determine these values." + Given the fact that a blackbody of a given temperature has more ionizing photons than a realistic spectrum with the same effective temperature. one can expect that in the best-fit mocel the total luminosity will be underestimated to compensate for this ellect.," Given the fact that a blackbody of a given temperature has more ionizing photons than a realistic spectrum with the same effective temperature, one can expect that in the best-fit model the total luminosity will be underestimated to compensate for this effect." + Llowever. we find that this effect is only very modest and this can be uncerstood from the fact that we include the clust emission in the modelling.," However, we find that this effect is only very modest and this can be understood from the fact that we include the dust emission in the modelling." +el Cuains can be heated very elliciently. by jalmer continuum photons. as well as by Lyman continuum. photons.," Grains can be heated very efficiently by Balmer continuum photons, as well as by Lyman continuum photons." + Tjerefore. the fluxes give a good constraint on the Balmer continuum flux.," Therefore, the fluxes give a good constraint on the Balmer continuum flux." + This counteracts the previously mentioned underestimation ol the total luminosity and explains the remarkable accuracy of our stellar broadband [uxes., This counteracts the previously mentioned underestimation of the total luminosity and explains the remarkable accuracy of our stellar broadband fluxes. + In our model assumptions we assume the distance to be a fixed number., In our model assumptions we assume the distance to be a fixed number. + However. our method can easily be changed in such à way that the distance would be a free parameter.," However, our method can easily be changed in such a way that the distance would be a free parameter." + When this is done. the best-fit model would also. give an estimate for the distance.," When this is done, the best-fit model would also give an estimate for the distance." + We have investigated the possibility. to determine the distance this way (van Hoof Van de Steene 1996)., We have investigated the possibility to determine the distance this way (van Hoof Van de Steene 1996). + We found that. though possible in principle. the spread in the resulting distance determinations is large.," We found that, though possible in principle, the spread in the resulting distance determinations is large." + The distance determination is vulnerable to various observational errors. but. especially to. the error. in the determination of the angular diameter.," The distance determination is vulnerable to various observational errors, but especially to the error in the determination of the angular diameter." + Since the angular diameter is notoriously hard to measure. this sensitivity makes the results very uncertain.," Since the angular diameter is notoriously hard to measure, this sensitivity makes the results very uncertain." + When we determined the distances to the bulge nebulae in our sample with this method. we found the spread in the values to be larger than what is obtained from a statistical method (Van de Steene Zijlstra 1995).," When we determined the distances to the bulge nebulae in our sample with this method, we found the spread in the values to be larger than what is obtained from a statistical method (Van de Steene Zijlstra 1995)." + Closer investigation reveals that this moethoc of etermining cisances is in essence identical to the method escribed in Pjdllips Pottasch (1984)..., Closer investigation reveals that this method of determining distances is in essence identical to the method described in Phillips Pottasch \cite{c2:phillips}. + They alreacly onclhuded that this method. is unreliable., They already concluded that this method is unreliable. + The use of à wrong value for he clistance not only influences the distance ependent parameters but also some distance independent parameters. as was already discussed. in. Paper 1. We verelore do. no recommend this method. and advise the use of separately determined. distances.," The use of a wrong value for the distance not only influences the distance dependent parameters but also some distance independent parameters, as was already discussed in Paper I. We therefore do not recommend this method, and advise the use of separately determined distances." + We applied our method which enables a fully self-consistent determination of the physical parameters of a PN. using the spectrum. the aand radio Uuxes and the angular ciameter of the nebula. to a sample of five galactic bulge PNe.," We applied our method which enables a fully self-consistent determination of the physical parameters of a PN, using the spectrum, the and radio fluxes and the angular diameter of the nebula, to a sample of five galactic bulge PNe." + Comparison of t distance independent physical. parameters. with published data shows that the stellar. temperatures. generally are in good agreement and can be considered. reliable., Comparison of the distance independent physical parameters with published data shows that the stellar temperatures generally are in good agreement and can be considered reliable. + E, The + (e...7).," \citep[e.g.,][]{Chevalier:2005}." + (72). (7). (ee.2).," \citep{Blair:2000} \citep{Hughes:2000} + \citep[e.g.,][]{Woosley:1988}." +" >-ravs νὰ, 1000 +. (222), (??).."," $\gamma$ $^{56}$ $4000$ $^{-1}$ \citep{Arnett:1989,Witteborn:1989,Utrobin:2004}. \citep{Heger&Woosley:2008,Hirschi:2008}." + jas a lower opacity than solarauetallicity eas aud. lacks initial seed nuclei for the CNO cvcle. leading to inefficient ivdrosen burning and a very dense hwdrosen shell of ow entropv in the presuperunova stars.," has a lower opacity than solar-metallicity gas and lacks initial seed nuclei for the CNO cycle, leading to inefficient hydrogen burning and a very dense hydrogen shell of low entropy in the presupernova stars." + ? predicted hat ligher amounts of fallback are expected for more conrpact progenitors.," \citet{Chevalier:1989} + predicted that higher amounts of fallback are expected for more compact progenitors." + In a recent paper. ? used their onc-diniensiounal Evlerian code to determine the remnant masses left behind by the supernova models calculated in surveys by 7/— and ?..," In a recent paper, \citet{Zhang:2008} used their one-dimensional Eulerian code to determine the remnant masses left behind by the supernova models calculated in surveys by \citet{Woosley&Heger:2007} and \citet{Heger&Woosley:2008}." + They found that zevo-lnetallicity supernovae experienced more fallback and left behind larger compact remmauts than their solar metallicity counterparts., They found that zero-metallicity supernovae experienced more fallback and left behind larger compact remnants than their solar metallicity counterparts. + For example. the baryouic remnant masses left delim bv 25 sstars of zero aud solar mctallicity were [16 and 2.09AL... respectively.," For example, the baryonic remnant masses left behind by 25 stars of zero and solar metallicity were 4.16 and 2.09, respectively." + Different ΕΕ structures. arising from differences dm stellar iuass and ΤΠ determine where Ravleigh-Tavlor instabilities occur aud the exteut o which they erow.," Different presupernova structures, arising from differences in stellar mass and metallicity, determine where Rayleigh-Taylor instabilities occur and the extent to which they grow." + An initially static. incompressible Πίοis unstable if the pressure eradieut poiuts opposite o the density gradient. ic. when (LPfdi)(dpfdyi)«0 (e.g.?7)..," An initially static, incompressible fluidis unstable if the pressure gradient points opposite to the density gradient, i.e., when $(dP/dr)(d\rho/dr) < 0$ \citep[e.g.][]{Chevalier:1976,Benz:1990}." + The location of these density iuversious varies with time as the forward and reverse shocks propagate hrough the star., The location of these density inversions varies with time as the forward and reverse shocks propagate through the star. + Particularly iuportaut are regions where the forward shock encounters au increasing value or pr. where pis the deusity aud r. the radius (2)..," Particularly important are regions where the forward shock encounters an increasing value for $\rho r^3$, where $\rho$ is the density and $r$, the radius \citep{Herant&Woosley:1994}." + The ine scale also depends upon the initial stellar structure., The time scale also depends upon the initial stellar structure. + Iu particular. a more compact star will experieuce faster shock propagation. leaving less time for instabilities to erow.," In particular, a more compact star will experience faster shock propagation, leaving less time for instabilities to grow." + Because SN 1987À was so well observed. most previous studies of Ravleigh-Tavlor κας iu core collapse supernovae (27777777) have been in the context of that event.," Because SN 1987A was so well observed, most previous studies of Rayleigh-Taylor mixing in core collapse supernovae \citep{Arnett:1989,Fryxell:1991,Muller:1991,Hachisu:1990,Hachisu:1992,Herant:1991,Herant&Benz:1992,Kifonidis:2006} have been in the context of that event." + Others have studied red supergiantprogenitors(7).. Except for Ieraut aud Woosley.thesestudies all usedred aud blue superegiauts of 15 to 20," Others have studied red supergiantprogenitors\citep{Herant&Woosley:1994}.. Except for Herant and Woosley,thesestudies all usedred and blue supergiants of 15 to 20" +in their equations (C3) and (C9). respectively.,"in their equations (C3) and (C9), respectively." +" Lines of constant BRi,g are also plotted in Figure 2..", Lines of constant $\Ri_{\eff}$ are also plotted in Figure \ref{sdh_fig}. + Recall that for a continuous dust distribution. Ri«1/4 is a necessary (but not sufficient) condition for the development of the IKIE instability.," Recall that for a continuous dust distribution, $\Ri < 1/4$ is a necessary (but not sufficient) condition for the development of the KH instability." + For our discrete three-Iaver distribution. Rig=const. is a good proxy for the stability limit of both even and odd modes at fixed Αα. but only at low δνδρ.," For our discrete three-layer distribution, $\Ri_{\eff} = const.$ is a good proxy for the stability limit of both even and odd modes at fixed $k_y H_d$ , but only at low $\Sigma_d / \Sigma_g$." +" Fork,I,= 2/4. we lind that the critical Rigg70.3 al X,/X,0.01. close to the Ri=1/4 result of. Miles(1961). and Howard(1961)."," For$k_y H_d = \pi/4$ , we find that the critical $\Ri_{\eff} \approx +0.3$ at $\Sigma_d / \Sigma_g \lesssim 0.01$, close to the $\Ri = +1/4$ result of \citet{mil61} and \citet{how61}." +". At larger X,/X,. the laver is too heavy to be easily disturbed. by a global mode."," At larger $\Sigma_d / \Sigma_g$, the layer is too heavy to be easily disturbed by a global mode." +" In this case. with po291. the stability. limit. (for either even- or odd-svnumetry modes) is Big=hyI1,;/p."," In this case, with $\mu \gg 1$, the stability limit (for either even- or odd-symmetry modes) is $\Ri_{\eff} = k_y H_d / \mu$." +" So. al given Big and Ha/IH,. the increasingly short wavelengths that are required Lor instability with increasing X,/X, would make the disturbance only a surface phenomenon."," So, at given $\Ri_{\eff}$ and $H_d/H_g$, the increasingly short wavelengths that are required for instability with increasing $\Sigma_d / \Sigma_g$ would make the disturbance only a surface phenomenon." +" Global instabilities only become possible when //;/Il,. and hence hi,g. decreases."," Global instabilities only become possible when $H_d / H_g$, and hence $\Ri_{\eff}$, decreases." +" Garaud&Lin(2004) lind. similarly. that the critical value of Ri decreases as X;/X, increases above zz0.01. for the value of ρω)ος we adopt."," \citet{gar04} find, similarly, that the critical value of $\Ri$ decreases as $\Sigma_d / \Sigma_g$ increases above $\approx 0.01$, for the value of $v_{0,max}/c_s$ we adopt." +" For large X;/X, and fixed ,/£,. Figure 2. shows that the maximum unstable /7;/1H, has the same wavelength for both the even and odd modes."," For large $\Sigma_d / \Sigma_g$ and fixed $k_y H_d$, Figure \ref{sdh_fig} shows that the maximum unstable $H_d / H_g$ has the same wavelength for both the even and odd modes." + But the growth rates are not {he same. as shown in Figure 3..," But the growth rates are not the same, as shown in Figure\ref{shgrowth_fig}. ." + Asthe laver thickness decreases al constant surface density. even modes al a given fiftyJi will develop more rapidly (han the corresponding odd modes.," Asthe layer thickness decreases at constant surface density, even modes at a given $k_y H_d$ will develop more rapidly than the corresponding odd modes." +Tn these respects IC3328 resenibles a Sb or She galaxy very simular to M51 (Danuver 1912: Keunicut 1981). bu without obvious gas. dust or bright regions.,"In these respects IC3328 resembles a Sb or Sbc galaxy very similar to M51 (Danver 1942; Kennicutt 1981), but without obvious gas, dust or bright regions." + The surface brightucss profile derived from Zg(r) is shown in Fig. L., The surface brightness profile derived from $I_0(r)$ is shown in Fig. \ref{fig4}. +" It cau be approximated by two straigh Ines (exponentials), with the cross-over occurine at 307. which is also the place where the spiral patteru cuds."," It can be approximated by two straight lines (exponentials), with the cross-over occuring at $r \simeq 30\arcsec$ , which is also the place where the spiral pattern ends." + The end of the spiral can be seen in the flattening of he phase in Fie. 3.., The end of the spiral can be seen in the flattening of the phase in Fig. \ref{fig3}. + The R surface brightuess profile jas the same characteristics as the B profile. which has con classified as type IIIb by Diugeeli Cameron (1991. vereatter DC'91).," The $R$ surface brightness profile has the same characteristics as the $B$ profile, which has been classified as type IIIb by Binggeli Cameron (1991, hereafter BC91)." + The total appareut maguitude. Rr. computed from Ίο). is 13.17.," The total apparent magnitude, $R_T$, computed from $I_0(r)$ is $13.17$." + The half light radius rap= 1579. aud he mean surface brightness within the effective radius og=314-7 2].linuuag )7.," The half light radius $r_{\mathrm{eff}}=15\farcs 9$ , and the mean surface brightness within the effective radius $\langle \mu \rangle_{\mathrm{eff}}=21.17$ mag $^{-2}$." +" The best-fitting line (exponential) of the iuner part has a central surface tightness+ of. pOP""=19.95 πας P aud a scale eueth oS?=x77,", The best-fitting line (exponential) of the inner part has a central surface brightness of $\mu^{\mathrm{exp}}=19.95$ mag $^{-2}$ and a scale length $r^{\mathrm{exp}}=8 \farcs 7$. + Iu order to estimate the cvuamical time scales associated with the spiral pattern we need to know the distauce to aud the velocities within IC3328., In order to estimate the dynamical time scales associated with the spiral pattern we need to know the distance to and the velocities within IC3328. + There are two distauce estimates for 103328., There are two distance estimates for IC3328. + The first comes from the radial velocity which coincides with the mean velocity of the Virgo cluster., The first comes from the radial velocity which coincides with the mean velocity of the Virgo cluster. + It agrees well with the preluaminary SBF distance of MMpe (Jerjen et al., It agrees well with the preliminary SBF distance of Mpc (Jerjen et al. + in preparation)., in preparation). + At this distance 17 corresponds to 77.5 ppc., At this distance $1\arcsec$ corresponds to $77.5$ pc. + The oulv kinematic data available for IC3328 to date Isa lucasurement of the central velocity dispersion of 2T]aus (Petersou Caldwell 1993)., The only kinematic data available for IC3328 to date is a measurement of the central velocity dispersion of $\sigma_{\mathrm{c}}=27$ (Peterson Caldwell 1993). + In the absence of a proper velocity field determination we have to resort to the liebt distribution and estimates of the mass-to-light ratio. ML.," In the absence of a proper velocity field determination we have to resort to the light distribution and estimates of the mass-to-light ratio, $M/L$." +" The square of the rotational velocity. V2. cau be determined from 2zGqpr. where p(r) is the projected surface mass density,"," The square of the rotational velocity, $V_{\mathrm{c}}^2$, can be determined from $2\pi G\mu r$, where $\mu(r)$ is the projected surface mass density." + On a logarithmic scale these two quantities are related by a couvolution (Nalnajs 1999)., On a logarithmic scale these two quantities are related by a convolution (Kalnajs 1999). + Fie. shows the relation between the two quantities iu the case when ML=1., \ref{fig5} shows the relation between the two quantities in the case when $M/L=1$. + The wo VD curves correspond to the lamiting cases where the projected surface density cones from a flat or a spherical mass distribution., The two $V_{\mathrm{c}}^2$ curves correspond to the limiting cases where the projected surface density comes from a flat or a spherical mass distribution. + Fig.5 also makes it clear that the value of AZ/£ around the peak πμ is what really matters., \ref{fig5} also makes it clear that the value of $M/L$ around the peak $2\pi G\mu r$ is what really matters. + Asstuning M/L=1 eives a maxinunun disk rotation velocity. Voauax[lls 2," Assuming $M/L=1$ gives a maximum disk rotation velocity, $V_{\mathrm{c,max}}=44$ ." + A’ better estimate of 55 coles from the average mass-to-light ratio for elobular clusters (AL/£)—1.6. based on the quantities (ΑΕΓον=2.45 (Prvor Aevlan 1993) aud (V.R))=O.I7 (Peterson 1993).," A better estimate of $55$ comes from the average mass-to-light ratio for globular clusters $(M/L)_R=1.6$, based on the quantities $(M/L)_V=2.5$ (Pryor Meylan 1993) and $(V-R)_0=0.47$ (Peterson 1993)." +" Such a value does not clash with c,—2T)ns|.", Such a value does not clash with $\sigma_{\mathrm{c}}=27$. + The best option would be to measure the rotation curve., The best option would be to measure the rotation curve. + Then oue could use the above aremucuts to obtain the actual AL ratio of IC3328., Then one could use the above arguments to obtain the actual $M/L$ ratio of IC3328. +" The estimated peak rotation velocity of 55 occurs around 1.L[ kpce. which means that the angular rotation rate there is 39sο, a value comparable to the 25 tmeasured near the Sun."," The estimated peak rotation velocity of $55$ occurs around $1.4$ kpc, which means that the angular rotation rate there is $39$, a value comparable to the $25$ measured near the Sun." + Thus[C3328 has had ample time o settle into an equilibrium., ThusIC3328 has had ample time to settle into an equilibrium. + The presence of the spiral implies the presence ofa disk., The presence of the spiral implies the presence ofa disk. + If what we see is a nearly face-on disk then the small spiral, If what we see is a nearly face-on disk then the small spiral +here aud because different metallicity tracks are aliiost superimposed on cach other for our plotted scales. (,here and because different metallicity tracks are almost superimposed on each other for our plotted scales. ( +i) Druzual&Charlot19930 (dash-dotted line: see also Charlot&Bruzual 19913): Stellar population svuthesis models. caleulated for solar metallicitics and starting from the very. earvostages of evolution: «0.0001. 2. 7. 12. 17 Ci.,"iii) \cite{bruzual93} (dash-dotted line; see also \cite{charlot91}) ): Stellar population synthesis models, calculated for solar metallicities and starting from the very early stages of evolution: $\leq$ 0.0001, 2, 7, 12, 17 Gyr." + These models use a Salpeter IME with (.1<\[< 100 and are calculated for different star formation histories. that is. a single burst. an exponcutially declining SFR aud a coustaut SER model.," These models use a Salpeter IMF with $\leq$ $\leq$ 100 and are calculated for different star formation histories, that is, a single burst, an exponentially declining SFR and a constant SFR model." + On our plots we chose to represent the single burst model. for compatibility with the other models aud also because this should be the most likely situation m Sevterts.," On our plots we chose to represent the single burst model, for compatibility with the other models and also because this should be the most likely situation in Seyferts." + The Bruzual Charlot and Worthey models are offset from cach other (although the relative trends are sinuilar). this beiug due to uncertainties iu the used stellar evolutionary tracks (DeJong 1996)).," The Bruzual Charlot and Worthey models are offset from each other (although the relative trends are similar), this being due to uncertainties in the used stellar evolutionary tracks \cite{jong96c}) )." + It was indeed found that lurge discrepancies exist between different population svuthesis models. the uncertainties in stellar age for a given metallicity can be as laree as and in metallicity for a given aee of the order of (Charlotetal. 1996)).," It was indeed found that large discrepancies exist between different population synthesis models, the uncertainties in stellar age for a given metallicity can be as large as and in metallicity for a given age of the order of \cite{charlot96}) )." + That js. uncertainties in these two quantities are larger than anv effects from chaugmg IMEs or cut-offs.," That is, uncertainties in these two quantities are larger than any effects from changing IMFs or cut-offs." + The nuün effects of model uucertaiutfles are shifts -in absolute colour values. but the predicted colour eradients aud other relative trends within a galaxy or between different galaxics should be correct and iectly comparable with the observations (see DeJoug 1996).," The main effects of model uncertainties are shifts in absolute colour values, but the predicted colour gradients and other relative trends within a galaxy or between different galaxies should be correct and directly comparable with the observations (see \cite{jong96c}) )." + Let us now briefly discuss the mai conclusions rawu frou Figure 17.., Let us now briefly discuss the main conclusions drawn from Figure \ref{f10}. + Throughout this discussion. the reader should be referring to the detailed. colour profiles and two-dimensional maps shown in the Appendix of Paper III.," Throughout this discussion, the reader should be referring to the detailed colour profiles and two-dimensional maps shown in the Appendix of Paper III." + First of all. it is clear that our galaxies have very differeut profiles than those of normal spirals (shown as dotted line in Figure 16)). which were better fitted wea colubination of the Worthev aud Bruzual Charlot mocls (DeJong 1996)). (," First of all, it is clear that our galaxies have very different profiles than those of normal spirals (shown as dotted line in Figure \ref{f9}) ), which were better fitted by a combination of the Worthey and Bruzual Charlot models \cite{jong96c}) ). (" +a) Upper panels: The Sevtert 1 ealaxy on the eft panel is IRAS 13512-3731 and the two Sevfert 2s on the right paucl are ΠΑΣ 01507]0358. and 13202-5150.,a) Upper panels: The Seyfert 1 galaxy on the left panel is IRAS 13512-3731 and the two Seyfert 2s on the right panel are IRAS 04507+0358 and 03202-5150. + The first is a compact early-type galaxy: its nuclear blue colours are probably affected by he AGN aud sleltly reddened outwards through a track that is difücult to interpret eiven the larec error bars., The first is a compact early-type galaxy; its nuclear blue colours are probably affected by the AGN and slightly reddened outwards through a track that is difficult to interpret given the large error bars. + This object is redder than the rest of he Sevfert l sample: according to the Worthey or Charlot Druzual models. the cicated mean stellar ages are ~5-8 Cur.," This object is redder than the rest of the Seyfert 1 sample; according to the Worthey or Charlot Bruzual models, the indicated mean stellar ages are $\sim$ 5-8 Gyr." + The first of the two Sevfert 2s ucutioned above. IRAS 01507|0358. is also an early ype ealaxy whose colours lie within the above two sequeuces of models. indicating somewhat vounger Lea1 populations (within he model aud data uncertainties) han the Seyfert 1 salaxx.," The first of the two Seyfert 2s mentioned above, IRAS 04507+0358, is also an early type galaxy whose colours lie within the above two sequences of models, indicating somewhat younger mean populations (within the model and data uncertainties) than the Seyfert 1 galaxy." + The second Sevtert 2 ealaxv. IRAS 03202-5150. is an carly type galaxy. uost Likely interacting with a nearby companion.," The second Seyfert 2 galaxy, IRAS 03202-5150, is an early type galaxy, most likely interacting with a nearby companion." + The nain body has colours iucicative of a relatively old stellar population (a mean of 5 Cor according to the Worthey models)., The main body has colours indicative of a relatively old stellar population (a mean of 5 Gyr according to the Worthey models). + This galaxy las also a bar aud ving eatures with associated star formation (see Appendix of Paper IIT). that are seen as loops in its colour profile and as a blue jump towards the loci of (star forming) nodels of Dicaetal.1990.. (," This galaxy has also a bar and ring features with associated star formation (see Appendix of Paper III), that are seen as loops in its colour profile and as a blue jump towards the loci of (star forming) models of \cite{bica90}. (" +b) Middle panels: The Sevfert 1 galaxies ou the eft pancl are IRAS 02366-3101. 01193-6LET aud 15015|1037.,"b) Middle panels: The Seyfert 1 galaxies on the left panel are IRAS 02366-3101, 04493-6441 and 15015+1037." + Thev are all isolated. carly or intermediate type ealaxies. with progressively redder colours iu the cited order.," They are all isolated, early or intermediate type galaxies, with progressively redder colours in the cited order." + Thev all have inverse (positive) eradicuts aud their tracks are parallel and partially overlap with the Dica Alloiu tracks. indicating a very receut starburst (0.2-0.7 Cyr if the model is to be used) superposed on an older stellar population.," They all have inverse (positive) gradients and their tracks are parallel and partially overlap with the Bica Alloin tracks, indicating a very recent starburst (0.2-0.7 Gyr if the model is to be used) superposed on an older stellar population." + Civeu the size of the error bars. the colours could also fit the modelzuud a x0. Cur starburst or. less likely. a Druzual Charlot model. with mean stellar ages ~5 Car or vouneger.," Given the size of the error bars, the colours could also fit the model and a $\leq$ 0.1 Gyr starburst or, less likely, a Bruzual Charlot model, with mean stellar ages $\sim$ 5 Gyr or younger." +" The Sevtert 2 galaxies on the right panel are IRAS 03059-2309, 23250500. 02580-1136 aud 2081-5715. this beiug a range of progressively redder 1ieau colours."," The Seyfert 2 galaxies on the right panel are IRAS 03059-2309, 23254+0830, 02580-1136 and 20481-5715, this being a range of progressively redder mean colours." + The latter is an carly type ealaxy with a nearby companion., The latter is an early type galaxy with a nearby companion. + There is little change iu its colours. which show a 1-2 Car stellar population superposed ou the redder uuderlviug ealaxy.," There is little change in its colours, which show a 1-2 Gyr stellar population superposed on the redder underlying galaxy." +" IRAS 02580-1136 is an earlv-tvpe barred spiral with strong star formation associated with its ""erand design” spiral arius.", IRAS 02580-1136 is an early-type barred spiral with strong star formation associated with its “grand design” spiral arms. + Its colours are consistent with a vouug starburst —1-2 Gyr old (or 0.1-0.2 Cyr if the inodel is used). from disk to center.," Its colours are consistent with a young starburst $\sim$ 1-2 Gyr old (or 0.1-0.2 Gyr if the model is used), from disk to center." + The other two Sevfert 2 ealaxies are both later type spirals and members of strongly interacting svsteiis., The other two Seyfert 2 galaxies are both later type spirals and members of strongly interacting systems. + Both show eraud design spiral axius (and tidal tails) with knotty star forming regions., Both show grand design spiral arms (and tidal tails) with knotty star forming regions. + Their colour profiles overlap with the and Dica models. indicating recent star formation: 0.5-1 Civr for the model. or vounger by a factor of 10 for the model in IRAS 23251|0830 and 0.2-0.7 Car or vouuger in IRAS 03059-2309 (the," Their colour profiles overlap with the and Bica models, indicating recent star formation: 0.5-1 Gyr for the model, or younger by a factor of 10 for the model in IRAS 23254+0830 and 0.2-0.7 Gyr or younger in IRAS 03059-2309 (the" +stars. if seems that they tend to cluster in planetary systems.,"stars, it seems that they tend to cluster in planetary systems." + Such a conjecture is underpinned by recent observational evidence on both outer gas-giant planets €?2?) as. well as Super-Earths and dlanets with Neptune-class masses in closer orbits (??)..," Such a conjecture is underpinned by recent observational evidence on both outer gas-giant planets \citep{DoubleCatch,Marois:planet} as well as Super-Earths and planets with Neptune-class masses in closer orbits \citep{Mayor:abundance,HARPS:abundance2}." + Therefore. he detection of planets in an experiment does not correspond to independent draws from its population. but the probability of their detection around a star that is known to host planets is larger than hat of finding it around a randomly chosen star.," Therefore, the detection of planets in an experiment does not correspond to independent draws from its population, but the probability of their detection around a star that is known to host planets is larger than that of finding it around a randomly chosen star." + While Sect., While Sect. + ?. presents a theoretical framework for describing dlanet populations in view of clustering in planetary systems and specific regions of interest or sensitivity. Sect.," \ref{sec:formalism} presents a theoretical framework for describing planet populations in view of clustering in planetary systems and specific regions of interest or sensitivity, Sect." + 3 provides rough estimates for the size of planet samples required to assess the undamental functions that decribe these populations., \ref{sec:measureMF} provides rough estimates for the size of planet samples required to assess the fundamental functions that decribe these populations. + Sect., Sect. + + is devoted to planetary multiplicity. while Sect.," \ref{sec:multiplicity} is devoted to planetary multiplicity, while Sect." + 5 looks into dlanet abundance estimates arising from gravitational microlensing observations. their uncertainties. and the involved challenges.," \ref{sec:abundance} looks into planet abundance estimates arising from gravitational microlensing observations, their uncertainties, and the involved challenges." + Sect., Sect. + 6. tinally concludes the paper with a short summary and outlook., \ref{sec:outlook} finally concludes the paper with a short summary and outlook. + Only celestial bodies that are in orbit around a around a star or stellar remnant are This means that planets cannot be seen in isolation from these. and consequently planets are not well-described by just extending the stellar mass function (222) to lower masses. but a mass function decribing planets needs to link to their host stars Cor remnants).," Only celestial bodies that are in orbit around a around a star or stellar remnant are This means that planets cannot be seen in isolation from these, and consequently planets are not well-described by just extending the stellar mass function \citep{Salpeter,Scalo:IMFreview,Kroupa:Science} to lower masses, but a mass function decribing planets needs to link to their host stars (or remnants)." +" Let us consider explicitly the dependence of planetary abundance on stellar mass A/,. metallicity Z. age 7. and spin rate $2 and therefore define a differential stellar mass function £(AML.Z.7.).1 so that for à population with density functions pzlZ). peCr). and po(£2) for metallicity. age. or spin rate. respectively. one obtains a mass function where the number density of stars becomes where AJ. denotes the mass of the Sun."," Let us consider explicitly the dependence of planetary abundance on stellar mass $M_\star$, metallicity $Z$, age $\tau$, and spin rate $\Omega$ and therefore define a differential stellar mass function $\xi(M_\star,Z,\tau,\Omega)$ so that for a population with density functions $p_Z(Z)$, $p_\tau(\tau)$, and $p_\Omega(\Omega)$ for metallicity, age, or spin rate, respectively, one obtains a mass function where the number density of stars becomes where $M_{\odot}$ denotes the mass of the Sun." +" For the stars that host planets.the properties of planets can then be described by a differential planetary mass-radius-orbit function «(myruac:M,Z.T.Q). where my. ry. αν and = denote the mass. radius. orbital semi-major axis. or orbital eccentricity of the planet. respectively. and further parameters might be added."," For the stars that host planets,the properties of planets can then be described by a differential planetary mass-radius-orbit function $\varphi(m_\rmn{p},r_\rmn{p},a,\varepsilon; M_\star, Z, \tau,\Omega)$, where $m_p$, $r_\rmn{p}$, $a$, and $\varepsilon$ denote the mass, radius, orbital semi-major axis, or orbital eccentricity of the planet, respectively, and further parameters might be added." +" This amass function for planetary systems around stars with(AL,.impliesZ.7.©) given foeniby with +; being the Earth's radius and αι=1au. so that the average number of planets in such systems reads where A/) is the mass of the Earth."," This implies a mass function for planetary systems around stars with $(M_\star,Z,\tau,\Omega)$ given by with $r_\oplus$ being the Earth's radius and $a_\oplus = 1~\mbox{au}$, so that the average number of planets in such systems reads where $M_\oplus$ is the mass of the Earth." +" With f,(CAL.Z.denasr.Q)denoting the fraction of stars that host planets. the number of planets for a stellar population becomes Moreover. one finds a population-integrated planetary radius-orbit function and a corresponding planetary mass function results as so that one finds the number density of planets again as Provided that experiments in the hunt for extra-solar planets follow deterministic criteria. a mass function can be extracted that refers to the selected host stars and planetary orbits that the applied technique is sensitive to. aaverages are taken over the stellar population and the orbital parameters."," With $f_\mathrm{p}(M_\star,Z,\tau,\Omega)$ denoting the fraction of stars that host planets, the number density of planets for a stellar population becomes Moreover, one finds a population-integrated planetary mass-radius-orbit function and a corresponding planetary mass function results as so that one finds the number density of planets again as Provided that experiments in the hunt for extra-solar planets follow deterministic criteria, a mass function can be extracted that refers to the selected host stars and planetary orbits that the applied technique is sensitive to, averages are taken over the stellar population and the orbital parameters." + However. in order to answer fundamental questions such as “How frequent are planets of a given mass range in the Solar neighbourhood?.," However, in order to answer fundamental questions such as `How frequent are planets of a given mass range in the Solar neighbourhood?'," +" ""What fraction of stars in the Milky Way do have planetary systems?."," `What fraction of stars in the Milky Way do have planetary systems?'," +" or ""How many planets that could host life are there in the Universe?'."," or `How many planets that could host life are there in the Universe?'," +" one needs to trace back the deseription of planetary systems to more fundamental functions such as the differential. mass-radius-orbit function (my.rua.c:M...Z.r.O). the fraction of stars with planetary systems f,CAZ,.Z.r.OQ). and the differential stellar mass function £(M,.Z."," one needs to trace back the description of planetary systems to more fundamental functions such as the differential mass-radius-orbit function $\varphi(m_\rmn{p},r_\rmn{p},a,\varepsilon; M_\star, Z, \tau,\Omega)$, the fraction of stars with planetary systems $f_\mathrm{p}(M_\star, Z, \tau,\Omega)$, and the differential stellar mass function $\xi(M_\star,Z,\tau,\Omega)$." +T In order to obtain an estimate on how well we can measure a planetary mass function. let us consider dividing the parameter space into multi-dimensional bins.," In order to obtain an estimate on how well we can measure a planetary mass function, let us consider dividing the parameter space into multi-dimensional bins." + If rather than aiming for a precision measurement. one sets the goal at an “astronomical” accuracy of SO per cent. the assumption of Poisson statistics yields the requirement of each bin to contain at least 4 planets.," If rather than aiming for a precision measurement, one sets the goal at an 'astronomical' accuracy of 50 per cent, the assumption of Poisson statistics yields the requirement of each bin to contain at least 4 planets." +" Let p denote the number of considered parameters. and b the number of considered parameter ranges. the minimal number of planets needed to provide the desired result is Ni,=46"". which would correspond to letting the choice of parameter ranges follow the observed distribution of detected planets. in such a way that each bin contains exactly the mimimum of 4 planets."," Let $p$ denote the number of considered parameters, and $b$ the number of considered parameter ranges, the minimal number of planets needed to provide the desired result is $N_\rmn{p} = 4\,b^{p}$, which would correspond to letting the choice of parameter ranges follow the observed distribution of detected planets, in such a way that each bin contains exactly the mimimum of 4 planets." +" mw denoting the desired accuracy. one finds more generally MselectedNj,=sL7 b, "," With $\kappa$ denoting the desired accuracy, one finds more generally $N_\rmn{p} = \kappa^{-1/2}\,b^{p}$ ." +Table | shows the requirements for some cases with relative accuracies of 50 per cent or 20 per cent. 2-. 4- or 6-parameter functions. and a various," Table \ref{tab:nplanets} shows the requirements for some selected cases with relative accuracies of 50 per cent or 20 per cent, 2-, 4- or 6-parameter functions, and a various" +While we have demonstrated that the presence of finite photon-ALP coupling could lead to an easily detectable signature in the light curves of magnetars. failing to detect splitting features cannot be used to place reliable limits on g so long as the radio emission mechanism in magnetars is not well understood.,"While we have demonstrated that the presence of finite photon-ALP coupling could lead to an easily detectable signature in the light curves of magnetars, failing to detect splitting features cannot be used to place reliable limits on $g$ so long as the radio emission mechanism in magnetars is not well understood." + For example. it might be that magnetic fields in the vicinity of the radio emitting region are considerably smaller than assumed here (e.g.. if photons are emitted high above the stellar surface. in the outer parts of the magnetosphere).," For example, it might be that magnetic fields in the vicinity of the radio emitting region are considerably smaller than assumed here (e.g., if photons are emitted high above the stellar surface, in the outer parts of the magnetosphere)." + It could also mean that the photon polarization is less favorably inclined with respect to the magnetic field., It could also mean that the photon polarization is less favorably inclined with respect to the magnetic field. + Lastly. it may be that the radio emission is less beamed than implied by the pulse duration. in which case splitting effects would be suppressed (there are no observable implications for splitting of isotropically emitting sources).," Lastly, it may be that the radio emission is less beamed than implied by the pulse duration, in which case splitting effects would be suppressed (there are no observable implications for splitting of isotropically emitting sources)." + In this paper we have described the effect of photon-ALP beam splitting in the presence of an external magnetic field -- an effect which arises solely by virtue of the interaction of the particle with the EM field., In this paper we have described the effect of photon-ALP beam splitting in the presence of an external magnetic field – an effect which arises solely by virtue of the interaction of the particle with the EM field. + This effect is very different than (but physically related to) that of photon-particle oscillations which were discussed in C09. and provides a complementary means for probing axion and ALP physics in magnetized environments.," This effect is very different than (but physically related to) that of photon-particle oscillations which were discussed in C09, and provides a complementary means for probing axion and ALP physics in magnetized environments." + In this paper we focus on the observable signatures of this effect in the light curve of compact. highly magnetized objects and. in particular. the case of magnetars.," In this paper we focus on the observable signatures of this effect in the light curve of compact, highly magnetized objects and, in particular, the case of magnetars." + The formalism developed here. and applied to magnetars. is limited to the case of negligible photon and ALP mass (relative to the interaction term) or at resonance where they equate.," The formalism developed here, and applied to magnetars, is limited to the case of negligible photon and ALP mass (relative to the interaction term) or at resonance where they equate." + We have shown that. by studying the radio light-curves of magnetars. one can be sensitive to light bosons down to very low values of the coupling constant — about 3-4 orders of magnitude smaller than current CAST limits and other indirect astrophysical constraints.," We have shown that, by studying the radio light-curves of magnetars, one can be sensitive to light bosons down to very low values of the coupling constant – about 3-4 orders of magnitude smaller than current CAST limits and other indirect astrophysical constraints." + The parameter space probed by such experiments is shown in figure 3 [for various combinations of €=(f5B/10'GY(À/my] and nicely complements spectroscopic searches for photon-particle oscillation features (000).," The parameter space probed by such experiments is shown in figure \ref{prm} [for various combinations of $\zeta=(f_G B/10^{16}\,{\rm G})(\lambda/{\rm m})$ ] and nicely complements spectroscopic searches for photon-particle oscillation features (C09)." + Note that. for a given ¢. there is a maximum e beyond which one beam is attenuated (equation I] is not satisfied).," Note that, for a given $\zeta$, there is a maximum $g$ beyond which one beam is attenuated (equation \ref{prop} is not satisfied)." + In this case. one can probe pulse shifting. as discussed above.," In this case, one can probe pulse shifting, as discussed above." + The detection and verification of the splitting and shifting effects may be done by looking for a typical phase differences between pulses in the light curves of magnetars., The detection and verification of the splitting and shifting effects may be done by looking for a typical phase differences between pulses in the light curves of magnetars. + In particular. the splitting/shifting phase would be wavelength dependent and would diminish at shorter wavelengths.," In particular, the splitting/shifting phase would be wavelength dependent and would diminish at shorter wavelengths." + In addition. the fluxes and polarizations of the split pulses would be similar.," In addition, the fluxes and polarizations of the split pulses would be similar." + Split or shifted pulses are likely to have a different polarization than pulses whose photons do not mix with bosons., Split or shifted pulses are likely to have a different polarization than pulses whose photons do not mix with bosons. + Splitting and shifting effects could also depend on the rotation phase of the magnetar reflecting. perhaps. the configuration of the magnetic field along the line-of-sight.," Splitting and shifting effects could also depend on the rotation phase of the magnetar reflecting, perhaps, the configuration of the magnetic field along the line-of-sight." + The various trends discussed above provide simple yet robust tests for photon-particle mixing., The various trends discussed above provide simple yet robust tests for photon-particle mixing. + It should be noted. however. that failing to detect beam splitting and shifting cannot be used to confidently exclude part of the axion/ALP parameter space so long as our understanding of the radio emission from magnetars is incomplete.," It should be noted, however, that failing to detect beam splitting and shifting cannot be used to confidently exclude part of the axion/ALP parameter space so long as our understanding of the radio emission from magnetars is incomplete." + Finally. we wish to note that the results presented here are general and apply to all (astrophysical) settings in which beamed. long wavelength emission originates from highly magnetized regions.," Finally, we wish to note that the results presented here are general and apply to all (astrophysical) settings in which beamed, long wavelength emission originates from highly magnetized regions." + We are grateful to Konstantin Zioutas and the organizers of the PATRAS 4 workshop at DESY for a wonderful learning experience. and for continuous encouragement.," We are grateful to Konstantin Zioutas and the organizers of the PATRAS 4 workshop at DESY for a wonderful learning experience, and for continuous encouragement." + We thank Pierre Sikivie for many discussions and extensive illuminating correspondence., We thank Pierre Sikivie for many discussions and extensive illuminating correspondence. + We also thank Keith Baker. Giovanni Cantatore. Aaron Chou. Glennys Farrar. Yosi Gelfand. and Vicky Kaspi for valuable comments and suggestions.," We also thank Keith Baker, Giovanni Cantatore, Aaron Chou, Glennys Farrar, Yosi Gelfand, and Vicky Kaspi for valuable comments and suggestions." + Consider the scalar QED Lagrangian (neglecting mass terms and magnetic fields; Guendelman 2008a.b):," Consider the scalar QED Lagrangian (neglecting mass terms and magnetic fields; Guendelman 2008a,b):" +"the default JA, colors.",the default $J-K_s$ colors. + This nonintuitivo result arises because the J images have a higher signal-to-noise ratio and allow a more accurate determination of the ντο aperture size., This nonintuitive result arises because the $J$ images have a higher signal-to-noise ratio and allow a more accurate determination of the Kron aperture size. + We adopt this magnitude definition of A., We adopt this magnitude definition of $K_s$. + A snall fraction )) of the galaxies in the LCRS within our magnitude range (defined below) are müsclassified as stars in 2\LASS., A small fraction ) of the galaxies in the LCRS within our magnitude range (defined below) are misclassified as stars in 2MASS. + For these galaxies. we use the aaperture maguitudes in the point source catalog.," For these galaxies, we use the aperture magnitudes in the point source catalog." + It is miportaut to check the overall completeness of the matched LCRS-2MASS catalog used in our analysis., It is important to check the overall completeness of the matched LCRS-2MASS catalog used in our analysis. + Iu Figure 1 owe show the fraction of the galaxies iu 2MÁASS for which a successful match is made with a ealaxy in the LORS., In Figure \ref{fig-comp_lcrs} we show the fraction of the galaxies in 2MASS for which a successful match is made with a galaxy in the LCRS. + We restrict our comparison to the largest (207« 1.57) contiguous patch covered by both surveys. which inchides about 1300 ealaxies.," We restrict our comparison to the largest $20^\circ \times 1.5^\circ$ ) contiguous patch covered by both surveys, which includes about 1300 galaxies." + The LCRS is not intended to be complete. but is a random sample of a magnitude-Hinüted survey.," The LCRS is not intended to be complete, but is a random sample of a magnitude-limited survey." + The dashed line shows he effect of applying the weights necessary focorrect or this incompleteness., The dashed line shows the effect of applying the weights necessary tocorrect for this incompleteness. + At Wy>12.2 aud J>13.2. he corrected completeness is close τοL00%.," At $K_s>12.2$ and $J>13.2$, the corrected completeness is close to." +. At brighter naenitudes. the completeness drops. due primarily to the LCRS's upper magnitude cutoff (R~ 15): we therefore iuit the sample to magnitudes fainter than this lait.," At brighter magnitudes, the completeness drops, due primarily to the LCRS's upper magnitude cutoff $R \sim 15$ ); we therefore limit the sample to magnitudes fainter than this limit." + Cole (7)) show that 2\TASS is highly complete and is not uissne a substantial nuniber of low surface brightucss ealaxies., Cole \shortcite{Cole-2mass}) ) show that 2MASS is highly complete and is not missing a substantial number of low surface brightness galaxies. + By association there can be no siguificaut incompleteness in low surface briehtuess galaxies in the natched LCRS-2MASS catalog. at least to the relatively wielt lower magnitude limit of 2\LASS.," By association there can be no significant incompleteness in low surface brightness galaxies in the matched LCRS-2MASS catalog, at least to the relatively bright lower magnitude limit of 2MASS." + The 2MÁSS catalog iscomplete to Ay=13.2. aud J=1145. as shown by Cole (2)).," The 2MASS catalog iscomplete to $K_s=13.2$, and $J=14.5$, as shown by Cole \shortcite{Cole-2mass}) )." + Up to about 0.5 mae auter than these limits. the icompleteness is primarily due to misclassification of faint galaxies as stars and stall jases iu the maguitude measurements;," Up to about 0.5 mag fainter than these limits, the incompleteness is primarily due to misclassification of faint galaxies as stars and small biases in the magnitude measurements." + We mitigate some of this incompleteness by using the LORS to ideutifv ealaxies that 2\LASS has classified as stars., We mitigate some of this incompleteness by using the LCRS to identify galaxies that 2MASS has classified as stars. + Furthermore. vecause our saluple is considerably siualler than that of Coleaf... we are less concerned with svstematic blasses of order x;0.1 mag. and we can maxiize our useful sample size by considering fainter magnitude limits.," Furthermore, because our sample is considerably smaller than that of Cole, we are less concerned with systematic biasses of order $\lesssim0.1$ mag, and we can maximize our useful sample size by considering fainter magnitude limits." + Oue other say to test the completeness of oursample is by cousicdering the distribution of V/Vias., One other way to test the completeness of oursample is by considering the distribution of $V/V_{\rm max}$. +" For a galaxy at redshift ο. Vtz) is the volume between it and the lowest redshift ty, at which it would still have been selected in the sample (due to the bright magnitude luit)"," For a galaxy at redshift $z$, $V(z)$ is the volume between it and the lowest redshift $z_{\rm min}$ at which it would still have been selected in the sample (due to the bright magnitude limit)." +" Via is the volue between ty, aud naase Where naas Is the redshift at which the galaxy would drop out of the sample due to the faint maguitude Πατ,"," $V_{\rm max}$ is the volume between $z_{\rm min}$ and $z_{\rm max}$, where $z_{\rm max}$ is the redshift at which the galaxy would drop out of the sample due to the faint magnitude limit." + For a uniform spatial distribution of objects the mean value of V/Vi ix 0.5., For a uniform spatial distribution of objects the mean value of $V/V_{\rm max}$ is 0.5. + Although galaxies are clustered. we expect that over the ]arge volume surveved here the distribution cau be thought of as uuifor.," Although galaxies are clustered, we expect that over the large volume surveyed here the distribution can be thought of as uniform." + Iu Fieure 2. we show the distribution of V/V for the A baud sample. Buuited at A=13.7. and the J band sample. Iunuited at J=15.0.," In Figure \ref{fig-vvmax} we show the distribution of $V/V_{\rm max}$ for the $K_s$ band sample, limited at $K_s=13.7$, and the $J$ band sample, limited at $J=15.0$." + With these limits. the distribution. of V/V Is approximately uniform. though there is a systematic variation of about15'4.," With these limits, the distribution of $V/V_{\rm max}$ is approximately uniform, though there is a systematic variation of about." +. The mean value of V/V is about 30 luger than the value of 0.5. which it would be for a statistically complete siuupliug of a spatially uuifoiii population.," The mean value of $V/V_{\rm max}$ is about $\sigma$ larger than the value of 0.5, which it would be for a statistically complete sampling of a spatially uniform population." +" This appears to be partly due to a deficit of galaxies with V/V< 0.3. perhaps a consequence of Maliiquist. bias becoming iuportant at A,13.5."," This appears to be partly due to a deficit of galaxies with $V/V_{\rm max}<0.3$ , perhaps a consequence of Malmquist bias becoming important at $K_s>13.5$." + Indeed. moving the magnitude luit brighter bv 0.2 mae does make the distribution of Εως more wuiform.," Indeed, moving the magnitude limit brighter by 0.2 mag does make the distribution of $V/V_{\rm max}$ more uniform." +" None of the trends we discuss iu this paper are affected by decreasing the magnitude Πιτ, although the uncertainties are increased aud. consequently. the significance of the results is diminished."," None of the trends we discuss in this paper are affected by decreasing the magnitude limit, although the uncertainties are increased and, consequently, the significance of the results is diminished." + To maximize the useful sample size. we therefore restrict the Jv. sample to 12.2«ἂν13.7. which consists of 2673 galaxics Gucluding 271 cluster galaxies aud 951 eroup galaxies).," To maximize the useful sample size, we therefore restrict the $K_s$ sample to $12.2=]|40s/(256s) for the outer region of standard thin discs. —1|10s/(7—2s) for the middle region. d=]|δέν4s) for the inner region. and 3=1|55/2 for NDAEs.," By assuming that the coupling between the local outflow and inflow is weak on the accretion rate fluctuations, we obtain the following explicit expressions of $\beta$ for different disc models: $\beta = 1 + 4s/3$ for advection-dominated discs, $\beta = 1 + 40s/(25-6s)$ for the outer region of standard thin discs, $\beta = 1 + {10s}/(7-2s)$ for the middle region, $\beta = 1 + {4}{s}/({7-4s})$ for the inner region, and $\beta = 1 + 5s/2$ for NDAFs." + Phe above expressions imply that in a CRB is generally larger than that in a DIID for comparable 5., The above expressions imply that $\beta$ in a GRB is generally larger than that in a BHB for comparable $s$. + The expressions of 2 indicate the possibility of evaluating the strength of outllows by the power spectrum in X-ray binaries and GRBs., The expressions of $\beta$ indicate the possibility of evaluating the strength of outflows by the power spectrum in X-ray binaries and GRBs. + In addition. if the coupling is not negligible. the value of 2 will probably be located. between unity ane the value presented in the above expressions.," In addition, if the coupling is not negligible, the value of $\beta$ will probably be located between unity and the value presented in the above expressions." + In both BIUBs and AGN. ADAFEs are usually adopted to ceseribe the quiescent state. the TowBard state. and the corona which lies above a cold disc.," In both BHBs and AGN, ADAFs are usually adopted to describe the quiescent state, the low/hard state, and the corona which lies above a cold disc." + ADAKS may produce significant outflows. and therefore the power spectrum can deviate from f+ based on the present analysis.," ADAFs may produce significant outflows, and therefore the power spectrum can deviate from $f^{-1}$ based on the present analysis." + The exact value of s is. however. dillicult to estimate from the heoretical point of view. except for the general constraint Yesκ1 (Naravan&MeClintock. 2008)).," The exact value of ${s}$ is, however, difficult to estimate from the theoretical point of view, except for the general constraint $0 < s < 1$ \citealp{Narayan08}) )." + On the other iud. some observations indicate s0.3 (Yuanetal.2003:: Zhangetal. 2010)).," On the other hand, some observations indicate $s \sim 0.3$ \citealp{Yuan03}; \citealp{Zhang10}) )." + Taking this value. we obtain 3=1.4 for ADAEFs. which is close to 1.3. the power-law index of PSDs oesented in the low mass X-ray binary svstems (Cilfanov&Arcley 2005))-," Taking this value, we obtain $\beta=1.4$ for ADAFs, which is close to $1.3$, the power-law index of PSDs presented in the low mass X-ray binary systems \citealp{Gilfanov05}) )." + The quantitative dillerence may be relevant o the coupling between the outflow and inflow as discussed in 822.4., The quantitative difference may be relevant to the coupling between the outflow and inflow as discussed in 2.4. + If there is only outllow that operates in the accreting system. 5 should be positive.," If there is only outflow that operates in the accreting system, $s$ should be positive." + Llowever. 5 can also be negative due to the evaporation mechanism of a cold. disc.," However, $s$ can also be negative due to the evaporation mechanism of a cold disc." + For he accreting black hole in DIIDs. the observed: power-law components in the X-ray spectra are generally attributed to 100. tenuous plasmas. namely accretion disc coronae.," For the accreting black hole in BHBs, the observed power-law components in the X-ray spectra are generally attributed to hot, tenuous plasmas, namely accretion disc coronae." + Due to he high temperature in the corona. the interaction between he disc and. corona would lead to mass evaporating from. he disc to the corona (Meyerctal.200k: 2002)).," Due to the high temperature in the corona, the interaction between the disc and corona would lead to mass evaporating from the disc to the corona \citealp{Meyer00}; \citealp{Spruit02}) )." + In this case. the value of s for the corona should be negative if outllows are not strong. and therefore it is quite »ossible for 3 to be less than unity.," In this case, the value of $s$ for the corona should be negative if outflows are not strong, and therefore it is quite possible for $\beta$ to be less than unity." + Consequently. in this scenario s for the underneath cold dise should be positive.," Consequently, in this scenario $s$ for the underneath cold disc should be positive." + We thank Feng Yuan. Wen-Fei Yu. and Shan-Shan Weng for beneficial discussion. and the referee for helpful comments.," We thank Feng Yuan, Wen-Fei Yu, and Shan-Shan Weng for beneficial discussion, and the referee for helpful comments." + This work was supported by the National Basic Research Program of China under grant 20€ος591900. ancl the National Natural Science Foundation of China under grants 10833002. 11073015. and 11103015.," This work was supported by the National Basic Research Program of China under grant 2009CB824800, and the National Natural Science Foundation of China under grants 10833002, 11073015, and 11103015." +We have analysed a high-resolution cosmological simulation of the formation of a Milky Way-like halo. focusing on the properties of the satellite population at the present-day.,"We have analysed a high-resolution cosmological simulation of the formation of a Milky Way-like halo, focusing on the properties of the satellite population at the present-day." + We have found that dark-matter subhalos are often accreted in groups in our simulations., We have found that dark-matter subhalos are often accreted in groups in our simulations. +" Roughly 1/3 of the surviving subhalos with mass z2.9.10""AL. atthe present epoch share this property.", Roughly $1/3$ of the surviving subhalos with mass $\ge 2.9 \times 10^6 \msun$ at the present epoch share this property. + This is clearly a lower limit since we are not be able to identify accompanying halos below our resolution limit (this is particularly severe at high-redshift)., This is clearly a lower limit since we are not be able to identify accompanying halos below our resolution limit (this is particularly severe at high-redshift). + This group infall is apparent as an enhancement in the number of subhalos whose angular momentum orientation is similar. particularly at the time of infall.," This group infall is apparent as an enhancement in the number of subhalos whose angular momentum orientation is similar, particularly at the time of infall." + This signal is measurable also from the present-day angular momentum of subhalos. even for those accreted 8 Gyr ago.," This signal is measurable also from the present-day angular momentum of subhalos, even for those accreted 8 Gyr ago." + These groups of subhalos share coherent orbits which ean be traced back well before the accretion epoch., These groups of subhalos share coherent orbits which can be traced back well before the accretion epoch. +" The differential group mass function follows a power-law distribution dNfdlogAL|grce,xM"" with n~0.5+0.2."," The differential group mass function follows a power-law distribution $dN/d \log M|_{group} +\propto M^{n}$ with $n \sim -0.5 \pm 0.2$." + This is reminiscent of the differential mass function of subhalos in both galaxy and cluster-size halos. albeit with a shallower slope (compared to n»~0.8 as in e.g. DeLuciaetal.2004: 2004b).," This is reminiscent of the differential mass function of subhalos in both galaxy and cluster-size halos, albeit with a shallower slope (compared to $n \sim -0.8$ as in e.g. \citealt{delucia04,gao04b}) )." + We have also studied the degree of flattening of the spatial distribution of subhalos in our simulation., We have also studied the degree of flattening of the spatial distribution of subhalos in our simulation. + The mean major axis ratio c/« of the inertia tensor defined by the positions of 11 randomly selected subhalos with 300 kpe is ¢fa0.5130.12.," The mean minor-to-major axis ratio $c/a$ of the inertia tensor defined by the positions of $11$ randomly selected subhalos with $300$ kpc is $c/a \sim 0.51 \pm +0.12$." + In comparison the c/« of the 11 “classical” MW satellites is 0.18+0.01., In comparison the $c/a$ of the $11$ “classical” MW satellites is $0.18 \pm 0.01$. + Imposing the centrally concentrated MW satellite radial distribution leads to οία~0.40.1 and therefore somewhat alleviates the discrepancy with the observations (seealsoKangetal. 2005)., Imposing the centrally concentrated MW satellite radial distribution leads to $c/a \sim 0.4 \pm 0.1$ and therefore somewhat alleviates the discrepancy with the observations \citep[see also][]{kang05}. + We have explored also how this planar configuration may be obtained as a result of the infall of satellites. in. groups., We have explored also how this planar configuration may be obtained as a result of the infall of satellites in groups. + The observed correlation in the angular momentum orientation of subhalos naturally gives rise to disk-like configurations., The observed correlation in the angular momentum orientation of subhalos naturally gives rise to disk-like configurations. + For example. we tind that if all subhalos are accreted from just one group. it is almost impossible to avoid a disk-like distribution (~80% probability). while for accretion from just two groups. the likelihood of obtaining a distribution as planar as observed isθές.," For example, we find that if all subhalos are accreted from just one group, it is almost impossible to avoid a disk-like distribution $\sim$ probability), while for accretion from just two groups, the likelihood of obtaining a distribution as planar as observed is." + These results may explain the origin of the ghostly streams proposed by Lynden-Bell&(1995)., These results may explain the origin of the ghostly streams proposed by \citet{lyndenbell95}. +.. Out of the streams originally proposed. only two appear to have survived the rigour of time. after modern and accurate measurements of proper motions have become available.," Out of the streams originally proposed, only two appear to have survived the rigour of time, after modern and accurate measurements of proper motions have become available." + Palma.Majewski&John-ston(2002) confirmed the LMC-SMC-UMi-Draco stream forms a kinematic group whose angular momentum separation is «18.5.," \citet{palma02} confirmed the LMC-SMC-UMi-Draco stream forms a kinematic group whose angular momentum separation is $< +18.5^{\circ}$ ." + More recently Piateketal.(2005). ruled out with 95'4 confident level UMi as a member using proper motions., More recently \citet{piatek05} ruled out with $95\%$ confident level UMi as a member using proper motions. + The latest measurements of the Fornax proper motion by Piateketal.(2007) has apparently confirmed the Sculptor-Sextans-Fornax stream (although previous measurements led to conflicting results. see Piateketal.2002:Dinescu 2004)).," The latest measurements of the Fornax proper motion by \citet{piatek07} + has apparently confirmed the Sculptor-Sextans-Fornax stream (although previous measurements led to conflicting results, see \citealt{piatek02,dinescu04}) )." + If some of the luminous satellites are embedded in dark (subjhalos that fell in together. such coherent structures would be a naturally consequence of the hierarchical buile-up of galaxies.," If some of the luminous satellites are embedded in dark (sub)halos that fell in together, such coherent structures would be a naturally consequence of the hierarchical build-up of galaxies." + In our simulations. such groups remain coherent in angular momentum (i.e. tyey share similar orbital planes giving rise to great circle streams) for approximately 8 Gyr.," In our simulations, such groups remain coherent in angular momentum (i.e. they share similar orbital planes giving rise to great circle streams) for approximately 8 Gyr." + This implies that these groups (or satellites) should have been accreted by the Milky Way at redshifts 2~ or below., This implies that these groups (or satellites) should have been accreted by the Milky Way at redshifts $z\sim 1$ or below. + One of the possible implications of the reality of the ghostly streams is that its member galaxies formed and evolved in a similar environment before falling into the Milky Way potential., One of the possible implications of the reality of the ghostly streams is that its member galaxies formed and evolved in a similar environment before falling into the Milky Way potential. + This would have implications on the (earliest) stellar populations. of these objects. such as for example. sharing a common metallicity floor (Helmietal.2006).," This would have implications on the (earliest) stellar populations of these objects, such as for example, sharing a common metallicity floor \citep{helmi06}." +. On the other hand. this implies that there should be groups that have not been able to host any luminous satellites.," On the other hand, this implies that there should be groups that have not been able to host any luminous satellites." + This would hint at a strong dependence on environment on the ability of a subhalo to retain gas (Scannapiecoetal.2001).. or be shielded from re-ionization by nearby sources (Mashchenko.Carignan&Bouchard2004:Weinmannetal. 2007).," This would hint at a strong dependence on environment on the ability of a subhalo to retain gas \citep{scannapieco01}, or be shielded from re-ionization by nearby sources \citep{mcb04,weinmann07}." +. Recent proper motion measurements of the Large and Small Magellanic clouds by Kallivayalil.vanderMarel&Alcock(2006). as well as the simulations by Bekki&Chiba(2005). suggest that these systems may have become bound to each other only recently.," Recent proper motion measurements of the Large and Small Magellanic clouds by \citet{smc-mu}, as well as the simulations by \citet{bc05} + suggest that these systems may have become bound to each other only recently." + This would be fairly plausible in the context of our results., This would be fairly plausible in the context of our results. + The Clouds may well have been part of a recently accreted group (seeSalesetal.2007.forthelinktoLeoI). and it may not even be necessary for t1em to ever have been a binary system., The Clouds may well have been part of a recently accreted group \citep[see also][for the link to Leo I]{sales07} and it may not even be necessary for them to ever have been a binary system. + This may also have implicaions on the computations of the past trajectories of these systems. particularly if both are embedded in a larger common dark-mater envelope (Beslaetal.2007).," This may also have implications on the computations of the past trajectories of these systems, particularly if both are embedded in a larger common dark-matter envelope \citep{besla07}." +. Our analysis shows that the dynamical peculiarities of the Milky Way satellites can be understood in the context of the concordance cosmological model., Our analysis shows that the dynamical peculiarities of the Milky Way satellites can be understood in the context of the concordance cosmological model. + Their properties must be a consequence of both the environment as well as of the hierarchical nature of the build up of galactic halos., Their properties must be a consequence of both the environment as well as of the hierarchical nature of the build up of galactic halos. + We thank Felix Stoehr for providing us with the GAnew simulations and for the great support in dealing with their analysis: Smith and Simon White for stimulating discussions and suggestions., We thank Felix Stoehr for providing us with the GAnew simulations and for the great support in dealing with their analysis; Smith and Simon White for stimulating discussions and suggestions. + We are grateful to Laura Sales for a careful reading of the manuscript and for many useful discussions., We are grateful to Laura Sales for a careful reading of the manuscript and for many useful discussions. + We acknowledge financial support from the NetherlandsOrganisation for Scientific Research (NWO)., We acknowledge financial support from the NetherlandsOrganisation for Scientific Research (NWO). +merger event (e.g.. see model F in Fig.,"merger event (e.g., see model F in Fig." + 6 in Cooper et al., 6 in Cooper et al. + 2010)., 2010). + In a similar wax. the diffuse structure detected around NGC 3521 (Fig.," In a similar way, the diffuse structure detected around NGC 3521 (Fig." + IE) also contains some cliscernible substructure. such as an almost spherical cloud of debris visible on its eastern side and a laree. more elongated cloud on its western side.," 1f) also contains some discernible substructure, such as an almost spherical cloud of debris visible on its eastern side and a large, more elongated cloud on its western side." + Both structures may represent debris shells belonging io an umbrella like structure. as seen in the image of NGC! 4651 (Fig.," Both structures may represent debris shells belonging to an umbrella like structure, as seen in the image of NGC 4651 (Fig." + Id). but their [uzzier appearance could suggest that they were accreted much farther in (the past.," 1d), but their fuzzier appearance could suggest that they were accreted much farther in the past." + Our pilot survey of dal streams. associated wilh nearby galaxies has revealed (hat many spiral galaxies in (he Local Universe contain significant. numbers of gigantic stellar structures (hat resemble the features expected from hierarchical formation., Our pilot survey of tidal streams associated with nearby galaxies has revealed that many spiral galaxies in the Local Universe contain significant numbers of gigantic stellar structures that resemble the features expected from hierarchical formation. + Although we have only explored a handful of galaxies. our collection already. presents a wide spectrum of morphologies lor these stellar features.," Although we have only explored a handful of galaxies, our collection already presents a wide spectrum of morphologies for these stellar features." + Some of them mavbe have analogs in the Milky Way e.g.. (1) great are-like features (labeled in Fig.," Some of them maybe have analogs in the Milky Way — e.g., (i) great arc-like features (labeled in Fig." + 2) that resemble the Milky Was Sagittarius. Orphan and Anticenter streams (e.g. Majewski et al.," 2) that resemble the Milky Way's Sagittarius, Orphan and Anticenter streams (e.g., Majewski et al." + 2003. Belokurov οἱ al.," 2003, Belokurov et al." + 2006. 2007b. Grillmair 2006) and (i) enormous clouds of debris that resemble our current understandings of the expansive Tri-AÀnd and Virgo overdensities ancl the IHercules-Acuila cloud in the Galactic halo (Rocha-Pinto et al.," 2006, 2007b, Grillmair 2006) and (ii) enormous clouds of debris that resemble our current understandings of the expansive Tri-And and Virgo overdensities and the Hercules-Aquila cloud in the Galactic halo (Rocha-Pinto et al." + 2004. Delokurov οἱ al.," 2004, Belokurov et al." + 20072. Martinez-Delgado et al.," 2007a, Martinez-Delgado et al." + 2007. Jurie et al.," 2007, Juric et al." + 2003)., 2008). + Our observations also uncover enormous features resembling giant “wubrellas” (labeled.C in Fig., Our observations also uncover enormous features resembling giant “umbrellas” (labeled in Fig. + 2). isolated shells. eiut plumes ol debris (labeled.GP in Fig.," 2), isolated shells, giant plumes of debris (labeled in Fig." + 2). spike-like patterns (labeledS in Fig.," 2), spike-like patterns (labeled in Fig." + 2) emerging from galactic disks. long. tighlv coherent streams with a central remnant core (labeled.PD in Fig.," 2) emerging from galactic disks, long, tighly coherent streams with a central remnant core (labeled in Fig." + 2) and large-scale diffuse forms that are possibly related to the remnants of ancient. fully disrupted satellites.," 2) and large-scale diffuse forms that are possibly related to the remnants of ancient, fully disrupted satellites." +accretion time. the aceretion of the substructure on we main progenitor of the cluster itself.,"accretion time, the accretion of the substructure onto the main progenitor of the cluster itself." + Fig., Fig. + 10. shows the distribution of the accretion redshifts for the cluster substructures in our sample., \ref{fig:fig8} shows the distribution of the accretion redshifts for the cluster substructures in our sample. + Interestingly. we find that a laree fraction. of the substructures are acereted at recshift ο<1.," Interestingly, we find that a large fraction of the substructures are accreted at redshift $z<1$." + As noted above. for most. of these substructures this accretion event corresponds to the accretion onto the main cluster itself.," As noted above, for most of these substructures this accretion event corresponds to the accretion onto the main cluster itself." + Our results hint that substructures are constantly. erased. in the cluster. being replenished by newly infalling haloes.," Our results hint that substructures are constantly erased in the cluster, being replenished by newly infalling haloes." + In Fig. LL.," In Fig. \ref{fig:fig9}," + we plot the distribution of ALG=fy) lacey). Le. the ratio of the mass of the subhalo at. the oesent clay to the mass it had when it was first aceretect.," we plot the distribution of $M(t=t_0)/M(t=t_{\rm accr})$ , i.e. the ratio of the mass of the subhalo at the present day to the mass it had when it was first accreted." + The histograms show that this ratio has a quite broad clistribution. varving from a value of ~1 to ~0.1.," The histograms show that this ratio has a quite broad distribution, varying from a value of $\sim 1$ to $\sim 0.1$." + We note hat most of the subhalos that have lost only small amounts of mass have been accreted very recently., We note that most of the subhalos that have lost only small amounts of mass have been accreted very recently. + This is more clearly shown in Fig., This is more clearly shown in Fig. + 12. where we xot the average mass accretion function for the cluster subhalos in the two mass bins considered., \ref{fig:fig10} where we plot the average mass accretion function for the cluster subhalos in the two mass bins considered. + Three. ciülferent accretion redshift intervals are considered and in all cases the subhalo masses are normalised to the mass of the subhalo ab faces., Three different accretion redshift intervals are considered and in all cases the subhalo masses are normalised to the mass of the subhalo at $t_{\rm accr}$. + Lhe thick solid line shows the mean relation [or subhalos with mass ~1045TAL. while the thin line shows the relation for Alan~LOA?AΛΙ.," The thick solid line shows the mean relation for subhalos with mass $\sim 10^{11}\,h^{-1}{\rm M}_{\odot}$, while the thin line shows the relation for $M_{\rm sub} \sim 10^{12}\,h^{-1}{\rm M}_{\odot}$." + Phe mass accretion function monotonically increases for times prior to the aceretion event., The mass accretion function monotonically increases for times prior to the accretion event. + Once the substructures are accretect. ticlal stripping is effective and operates on short time scales.," Once the substructures are accreted, tidal stripping is effective and operates on short time scales." + The longer the substructure spends in a more massive halo. the larger is the destructive elect. of tidal stripping.," The longer the substructure spends in a more massive halo, the larger is the destructive effect of tidal stripping." + Substructures remaining at z=0 that were accreted at redshift larger than 1 (panel ο) have been typically stripped of ~SO per cent of their mass., Substructures remaining at $z=0$ that were accreted at redshift larger than $1$ (panel c) have been typically stripped of $\sim 80$ per cent of their mass. + There. is also a slight indication that stripping is more effective for more massive substructures: panels (a) and (b) show that more massive substructures have been stripped significantly more than Less massive substructures acerctecl at the same redshift., There is also a slight indication that stripping is more effective for more massive substructures: panels (a) and (b) show that more massive substructures have been stripped significantly more than less massive substructures accreted at the same redshift. + This οσοι does not appear in panel (ο) but note that we have very lew objects accreted in this redshift bin in our sample of more massive subhalos., This effect does not appear in panel (c) but note that we have very few objects accreted in this redshift bin in our sample of more massive subhalos. + In Fig., In Fig. + 13 we compare the mass accretion. histories of field ancl cluster subhalos., \ref{fig:fig11} we compare the mass accretion histories of field and cluster subhalos. +. We limit the analysis to substructures with mass ~101!M..," We limit the analysis to substructures with mass $\sim 10^{11}\,h^{-1}{\rm M}_{\odot}$." + Again the mass accretion function is normalised to the mass of the subhalo at the accretion time., Again the mass accretion function is normalised to the mass of the subhalo at the accretion time. + We find that field subhalos and eluster subhalos have remarkably similar histories suggesting that the ellicieney of the tidal stripping is largely independent of the mass of the parent halo., We find that field subhalos and cluster subhalos have remarkably similar histories suggesting that the efficiency of the tidal stripping is largely independent of the mass of the parent halo. + In hierarchical models of galaxy formation. galaxies ancl their associated dark matter haloes form hierarchically through merger. and aceretion processes.," In hierarchical models of galaxy formation, galaxies and their associated dark matter haloes form hierarchically through merger and accretion processes." + In this context. the terni is usually used to refer to an interaction between two objects of similar mass. while the term is used to describe the infall of small objects onto much more massive haloes.," In this context, the term is usually used to refer to an interaction between two objects of similar mass, while the term is used to describe the infall of small objects onto much more massive haloes." + Observational results and numerical simulations confirm that interactions (such as tidal truncation or collisions) play an important role in the evolution of galaxies., Observational results and numerical simulations confirm that interactions (such as tidal truncation or collisions) play an important role in the evolution of galaxies. + There is. lor example. solid evidence (22727) that at least some elliptical galaxies are the result of mergers between disk galaxies of similar mass.," There is, for example, solid evidence \citep{schweizer,whitmore,barnes} that at least some elliptical galaxies are the result of mergers between disk galaxies of similar mass." + Mergers may also, Mergers may also +(see Fig 5).,(see Fig \ref{g_z}) ). + A less prominent colour evolution is observed during phase 1) with the σ΄/—z' colour getting bluer by about Amagx0.1 between ss and ss. We cannot exclude a further less prominent colour evolution during phase 11) while the hint of colour evolution during the small rebrightenings observed during phase i1) is not statistically significant., A less prominent colour evolution is observed during phase i) with the $g^\prime-z^\prime$ colour getting bluer by about $\Delta {\rm mag}\approx 0.1$ between s and s. We cannot exclude a further less prominent colour evolution during phase iii) while the hint of colour evolution during the small rebrightenings observed during phase iii) is not statistically significant. + In order to estimate the possible effect of the host galaxy dust absorption. we extracted the optical-NIR SED of GRB 081029 at different times before and after the bump.," In order to estimate the possible effect of the host galaxy dust absorption, we extracted the optical-NIR SED of GRB 081029 at different times before and after the bump." + GRB 081029 occurred at z=3.8479. therefore both the GROND ¢’ (and partially the +’) bands are affected by the Lyman alpha absorption.," GRB 081029 occurred at z=3.8479, therefore both the GROND $g^\prime$ (and partially the $r^\prime$ ) bands are affected by the Lyman alpha absorption." + Because of the uncertain intergalactic hydrogen column density alongthe line of sight. the g’ band is excluded from the SED fits.," Because of the uncertain intergalactic hydrogen column density alongthe line of sight, the $g^\prime$ band is excluded from the SED fits." + We fitted the other six optical-NIR GROND bands (1.e.. Ky.H.J. or) assuming a simple power-law spectrum after correcting the observed fluxes for the foreground Galactic extinction of Egy=0.03 mag (Schlegel et al.," We fitted the other six optical-NIR GROND bands (i.e., $K_s, H, J, z^\prime, i^\prime, r^\prime$ ) assuming a simple power-law spectrum after correcting the observed fluxes for the foreground Galactic extinction of $E_{\rm B-V}=0.03$ mag (Schlegel et al." +" 1998) corresponding to an extinction of AG""=0.093 mag using Ry = 3.1.", 1998) corresponding to an extinction of $A_{\rm V}^{\rm Gal}= 0.093$ mag using $R_{\rm V}$ = 3.1. + Large and Small Magellanie Clouds (LMC. SMC) and Milky Way (MW) extinction laws from Pei (1992) Were Used to describe the dust reddening in the host galaxy.," Large and Small Magellanic Clouds (LMC, SMC) and Milky Way (MW) extinction laws from Pei (1992) were used to describe the dust reddening in the host galaxy." + We found that all SEDs are consistent with a negligible host galaxy dust absorption for all considered extinetion curves., We found that all SEDs are consistent with a negligible host galaxy dust absorption for all considered extinction curves. + Using a SMC extinction curve. we obtained a confidence level upper limit for the host galaxy extinction AY<0.16 mag at kks.," Using a SMC extinction curve, we obtained a confidence level upper limit for the host galaxy extinction $A_{\rm V}^{\rm host}< 0.16$ mag at ks." + The Ky.H.J.z./.i spectral index (where the standard notation f(v)cv7 is adopted) is Bo=1.067008 and the reduced y is 1.06.," The $K_s, H, J, z^\prime, i^\prime, r^\prime$ spectral index (where the standard notation $f(\nu)\propto \nu^{-\beta}$ is adopted) is $\beta_{\rm opt}=1.06^{+0.06}_{-0.05}$ and the reduced $\chi^2$ is 1.06." + In Fig., In Fig. + 6 we show the temporal evolution of the optical spectral index for each individual GROND observation., \ref{lcbeta} we show the temporal evolution of the optical spectral index for each individual GROND observation. + The colour evolution during the light-curve bump shown in Fig., The colour evolution during the light-curve bump shown in Fig. + 5 is also clearly visible in Fig., \ref{g_z} is also clearly visible in Fig. + 6 where the spectral hardening is also observed before the bump., \ref{lcbeta} where the spectral hardening is also observed before the bump. + This latter early-time colour evolutioi is consistent with the light-curve break observed around 900ss to be caused by a spectral break moving bluewards through the observed GROND bands., This latter early-time colour evolution is consistent with the light-curve break observed around s to be caused by a spectral break moving bluewards through the observed GROND bands. + The observed Ap. could be related to an incomplete passage of a cooling frequency in a wind-like profile if the shape of the cooling break were very shallow., The observed $\Delta \beta_{\rm opt}$ could be related to an incomplete passage of a cooling frequency in a wind-like profile if the shape of the cooling break were very shallow. + The slow decay rates observed during phase 1) do not agree with the standard closure relations when compared with the values of Boy (see. e.g.. Racusin et al.," The slow decay rates observed during phase i) do not agree with the standard closure relations when compared with the values of $\beta_{\rm opt}$ (see, e.g., Racusin et al." + 2009) which cast some doubts on this interpretation., 2009) which cast some doubts on this interpretation. + The nature of the optical-NIR afterglow reddening during the rebrightening will be discussed in $5.., The nature of the optical-NIR afterglow reddening during the rebrightening will be discussed in \ref{model}. + Because the optical and X-ray light-curves show a similar temporal evolution after the bump. we can analyse the combined optical to X-rays spectral energy distribution under the simple assumption that the flux observed in both bands is produced by the same mechanism.," Because the optical and X-ray light-curves show a similar temporal evolution after the bump, we can analyse the combined optical to X-rays spectral energy distribution under the simple assumption that the flux observed in both bands is produced by the same mechanism." + Following the method described in Greiner et al. (, Following the method described in Greiner et al. ( +2011). we extracted a broad-band SED around κκ.,"2011), we extracted a broad-band SED around ks." + We selected this time interval to obtain a contemporaneous GROND and XRT coverage and to avoid the presence of the small sub-flares observed during the rebrightening., We selected this time interval to obtain a contemporaneous GROND and XRT coverage and to avoid the presence of the small sub-flares observed during the rebrightening. + We find that the SED ts well fit by a single power-law connecting the NIR to the X-ray band (see Fig. 7))., We find that the SED is well fit by a single power-law connecting the NIR to the X-ray band (see Fig. \ref{sedoptx}) ). + Moreover. no host galaxy dust absorption is required in this case.," Moreover, no host galaxy dust absorption is required in this case." +" The best-fit value for rest-frame reddening is AY=0.037145—(.03 mag. the broad-band spectral index is f=1.00£0.01 with a host galaxy column density NP-79795x]10em"". which is consistent with both 5, and the values of £y and NY from the XRT spectral analysis reported in Tab."," The best-fit value for rest-frame reddening is $A_{\rm V}^{\rm host}=0.03^{+0.02}_{-0.03}$ mag, the broad-band spectral index is $\beta=1.00\pm 0.01$ with a host galaxy column density $N_{\rm H}^{\rm host}=7.9^{+6.8}_{-5.9}\times 10^{21}~{\rm cm}^{-2}$, which is consistent with both $\beta_{\rm opt}$ and the values of $\beta_{\rm X}$ and $N_{\rm H}^{\rm host}$ from the XRT spectral analysis reported in Tab." + |., 1. + The most evident peculiarity of GRB 081029 is the presence of the intense optical rebrightening that occurs around 3.5 ks after the trigger., The most evident peculiarity of GRB 081029 is the presence of the intense optical rebrightening that occurs around 3.5 ks after the trigger. + This 1s not the first case in which a late-time optical rebrighening is observed in à long GRB afterglow but the intensity of the flux increase and the steepness of the light-curve rise are unusual., This is not the first case in which a late-time optical rebrighening is observed in a long GRB afterglow but the intensity of the flux increase and the steepness of the light-curve rise are unusual. + Moreover. the density of the available data set and the possibility to contemporaneously study the temporal evolution of the rebrightening in. sever bands thanks to GROND make GRB 081029 a unique case.," Moreover, the density of the available data set and the possibility to contemporaneously study the temporal evolution of the rebrightening in seven bands thanks to GROND make GRB 081029 a unique case." + A sudden increase of optical flux was already observed iu one of the first afterglows ever detected., A sudden increase of optical flux was already observed in one of the first afterglows ever detected. + GRB 970508 showed a rebrightening of about 1.5 magnitudes in L.. R and V bands around one day after the trigger (Sahu et al.," GRB 970508 showed a rebrightening of about 1.5 magnitudes in $_c$, R and V bands around one day after the trigger (Sahu et al." + 1997: Vietri 1998: Sokolov et al., 1997; Vietri 1998; Sokolov et al. + 1998; Nardint et al., 1998; Nardini et al. + 2006)., 2006). + Other cases reported in the literature are GRB 060206 (Monfardini et al., Other cases reported in the literature are GRB 060206 (Monfardini et al. + 2006) . GRB 070311 (Guidorzi et al.," 2006) , GRB 070311 (Guidorzi et al." + 2007; Kong et al., 2007; Kong et al. + 2010). GRB 071003 (Perley et al.," 2010), GRB 071003 (Perley et al." + 2008: Ghisellini et al., 2008; Ghisellini et al. + 2009). and GRB 071010A (Covino et al.," 2009), and GRB 071010A (Covino et al." + 2008b: Kong et al., 2008b; Kong et al. + 2010)., 2010). +C. $ and NW.,"C, S and NW." +" The warm gas is distributed only within the extent of the strong, infrared enussion. except in the direction of the SNI (Figures 2eg 2i)."," The warm gas is distributed only within the extent of the strong infrared emission, except in the direction of the SNR (Figures \ref{iimap}g \ref{iimap}i i)." + It therefore seems reasonable to consider that the warm gas is heated predominantly bv the O star. since the warmest regions of the 2 km F1 and 8 km ! clouds are located within a few pe of this central source.," It therefore seems reasonable to consider that the warm gas is heated predominantly by the O star, since the warmest regions of the 2 km $^{-1}$ and 8 km $^{-1}$ clouds are located within a few pc of this central source." +" The enerev of the stellar wind [rom the central O star is estimated as 1.6x107"" ere + (see section 1).", The energy of the stellar wind from the central O star is estimated as $1.6\times10^{36}$ erg $^{-1}$ (see section 1). +" The cooling rate of a cloud with a diameter of 3 pe. density of 10? 7oE and temperature of 40 IX is estimated as LO""! erg + (Goldsmith&Langer1973).. much lower than the energv of the stellar wind."," The cooling rate of a cloud with a diameter of 3 pc, density of $10^3$ $^{-3}$ and temperature of 40 K is estimated as $\sim10^{34}$ erg $^{-1}$ \citep{gol1978}, much lower than the energy of the stellar wind." + The high temperatures of the 2 kms ! and 8S km ! clouds can therefore be explained energetically in terms of the shock heating by (he stellar winds of the central star. alüihbough the present low angular resolution is not high enough to test this possibility further bv deriving a detailed temperature distribution.," The high temperatures of the 2 km $^{-1}$ and 8 km $^{-1}$ clouds can therefore be explained energetically in terms of the shock heating by the stellar winds of the central star, although the present low angular resolution is not high enough to test this possibility further by deriving a detailed temperature distribution." + In either case. the plivsical association of the four clouds with the O star is virtually certain.," In either case, the physical association of the four clouds with the O star is virtually certain." + It is therefore reasonable that both the 2 km | cloud and cloud C are candidates for the parental cloud of the O star., It is therefore reasonable that both the 2 km $^{-1}$ cloud and cloud C are candidates for the parental cloud of the O star. + The two clouds share peak positions. suggesting that they are located nearly at the same position. and the velocity dillerence of these two clouds is ~7.5 kms J| (Table 1)). meaning that they can only move by ~2 pe within the 0.3 Mvr age of M20. which is consistent with the interpretation that these two clouds is located at the sale position.," The two clouds share peak positions, suggesting that they are located nearly at the same position, and the velocity difference of these two clouds is $\sim$ 7.5 km $^{-1}$ (Table \ref{cloudlist}) ), meaning that they can only move by $\sim$ 2 pc within the 0.3 Myr age of M20, which is consistent with the interpretation that these two clouds is located at the same position." +" On the other hand. the molecular clouds at Vi,18 km | do not seem to be directly associated with the O star. because these clouds have temperatures of 10 Ix. lower than those of the 2 km F and 8 kam | clouds."," On the other hand, the molecular clouds at $V_{\rm lsr} \sim 18$ km $^{-1}$ do not seem to be directly associated with the O star, because these clouds have temperatures of 10 K, lower than those of the 2 km $^{-1}$ and 8 km $^{-1}$ clouds." +" The clouds around Vi,~ 18 kms ! therelore appear to be located near M20 but are neither as close or as heated by M20 as the 2 kin bands km ! clouds.", The clouds around $V_{\rm lsr} \sim$ 18 km $^{-1}$ therefore appear to be located near M20 but are neither as close or as heated by M20 as the 2 km $^{-1}$ and 8 km $^{-1}$ clouds. +" Only TC3 ΤΟ cloud has a possibility to be located around AI20 as close as cloud NE. NW and ο, because studies by Lefloch&Cernicharo(2000). and Rhoetal.(2008) indicate (hat it is located at the boundary of the HII region and shocks"," Only TC3 TC4 cloud has a possibility to be located around M20 as close as cloud NE, NW and S, because studies by \citet{lef2000} and \citet{rho2008} indicate that it is located at the boundary of the HII region and shocks" +opposite polarity possess their own penumbrae at the interface where they meet.,opposite polarity possess their own penumbrae at the interface where they meet. + For NOAA AR 10930 presented in this letter. the left negative polarity umbra is significantly stronger than the right positive ones.," For NOAA AR 10930 presented in this letter, the left negative polarity umbra is significantly stronger than the right positive ones." + The interface is dominated by the penumbrae of the left umbra and the penumbrae of the right umbrae almost vanish at the interface. therefore the sheared Evershed flow of predominant one direction ts observed.," The interface is dominated by the penumbrae of the left umbra and the penumbrae of the right umbrae almost vanish at the interface, therefore the sheared Evershed flow of predominant one direction is observed." + Using MDI Dopplergrams for the 2000 July 14 X5.7 Bastille Day flare. Wangetal.(2005) measured a decrease of Doppler velocity in the outer decayed— penumbral segments and an increase in parts of the central darkened penumbral region. suggesting actual weakening/enhancing of the outer/central penumbral structure.," Using MDI Dopplergrams for the 2000 July 14 X5.7 Bastille Day flare, \citet{WangH+etal2005ApJ...627.1031W} measured a decrease of Doppler velocity in the outer decayed penumbral segments and an increase in parts of the central darkened penumbral region, suggesting actual weakening/enhancing of the outer/central penumbral structure." + The Dopplergrams measure real mass flow but only in the LOS direction., The Dopplergrams measure real mass flow but only in the LOS direction. + The measured Doppler velocity is subject to the view angle. the location of the object on the Sun. and the flow direction relative to the LOS. therefore Dopplergram alone cannot fully resolve the surface flow.," The measured Doppler velocity is subject to the view angle, the location of the object on the Sun, and the flow direction relative to the LOS, therefore Dopplergram alone cannot fully resolve the surface flow." + LCT on the other hand performs well for systematic advection motion and has been widely used to estimate solar surface flow., LCT on the other hand performs well for systematic advection motion and has been widely used to estimate solar surface flow. + We are aware. though. that LCT measured optical flow may differ from real mass flow because it is based on local contrast that can be affected by other things besides mass flows. such as thermal. oscillation. and wave effects.," We are aware, though, that LCT measured optical flow may differ from real mass flow because it is based on local contrast that can be affected by other things besides mass flows, such as thermal, oscillation, and wave effects." + Nevertheless. the same LCT technique with all the same parameters was applied to the same region. even though the measured velocities may differ from real ones. the trend of the dramatic increase we believe is reliable.," Nevertheless, the same LCT technique with all the same parameters was applied to the same region, even though the measured velocities may differ from real ones, the trend of the dramatic increase we believe is reliable." + The substantial increase of flow speed in the central region before the flare is intriguing. which may imply a precursor reconfiguration before the eruptive phase of the flare.," The substantial increase of flow speed in the central region before the flare is intriguing, which may imply a precursor reconfiguration before the eruptive phase of the flare." + We do see brightening or formation of some small loops traversing the central neutral line before the flare from the HH movie., We do see brightening or formation of some small loops traversing the central neutral line before the flare from the H movie. + More events are needed to verify if this pre-flare signature Is solid and can be used for flare forecasting., More events are needed to verify if this pre-flare signature is solid and can be used for flare forecasting. + In summary. this study indicates that besides direct vector magnetograms. high-resolution WL observations of penumbra and coupled Evershed flow can be used as an indirect way to diagnose the magnetic azimuth and inclination as well as their change in the photosphere. which ts particularly valuable for flare study even for near limb events.," In summary, this study indicates that besides direct vector magnetograms, high-resolution WL observations of penumbra and coupled Evershed flow can be used as an indirect way to diagnose the magnetic azimuth and inclination as well as their change in the photosphere, which is particularly valuable for flare study even for near limb events." += Hinode is a Japanese mission developed and launched by ISAS/JAXA. with ΝΑΟΙ as domestic partner and NASA and STFC (UK) as international partners.," Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners." + It is operated by these agencies in co-operation with ESA and NSC (Norway)., It is operated by these agencies in co-operation with ESA and NSC (Norway). + N.D. and D.P.C were supported by NASA grant NNXO8AQ32G and NSF grant ATM 05-48952., N.D. and D.P.C were supported by NASA grant NNX08AQ32G and NSF grant ATM 05-48952. + C.L. and H.W. were supported by NSF grants AGS 08-19662 and AGS 08-49453 and NASA grants NNX O8AQ90G and NNX 08AJ23G. We thank A. Cookson for carefully reading the manuscript., C.L. and H.W. were supported by NSF grants AGS 08-19662 and AGS 08-49453 and NASA grants NNX 08AQ90G and NNX 08AJ23G. We thank A. Cookson for carefully reading the manuscript. +The plateau-tail distances derived in section 3 and listed in column 2 of 3 are plotted in a Llubble diagram in 2 (except 1987X which is not in the Llubble How).,"The plateau-tail distances derived in section 3 and listed in column 2 of $\,$ 3 are plotted in a Hubble diagram in $\,$ \ref{nadezhfg2} (except $\,$ 1987A which is not in the Hubble flow)." + The eight LLP define a Hubble line with Zo=55+5kmsMpe.|.," The eight $\,$ IIP define a Hubble line with $H_0=55\pm 5\,{\mathrm{km}}\,{\mathrm{s}}^{-1}\,{\mathrm{Mpc}}^{-1}$." + Also shown in 2 are the eleven LLP for which EPAL distances have been published. (column 3 of 2).," Also shown in $\,$ \ref{nadezhfg2} are the eleven $\,$ IIP for which EPM distances have been published (column 3 of $\,$ 2)." + They deline a Llubble line of 4/4=70+4kms+Alpe+. ie. the IPM distances are smaller than the plateau-tail clistances by On average.," They define a Hubble line of $H_0=70\pm 4\,{\mathrm{km}}\,{\mathrm{s}}^{-1}\,{\mathrm{Mpc}}^{-1}$, i.e. the EPM distances are smaller than the plateau-tail distances by on average." + At this point it is not possible to decide which of the two results is more nearly correct., At this point it is not possible to decide which of the two results is more nearly correct. + Both methods. the plateau-tail distances and the EPAL distances. depend on assumptions which are dillicult to verify.," Both methods, the plateau-tail distances and the EPM distances, depend on assumptions which are difficult to verify." + The EPAL method faces the problem of the dilution factor in an expanding atmosphere and the definition of the photospheric radius which depends on the uncertainties connected with the opacity of an expanding medium., The EPM method faces the problem of the dilution factor in an expanding atmosphere and the definition of the photospheric radius which depends on the uncertainties connected with the opacity of an expanding medium. + However. it may be notec that the IZPM. distance of 1987X agrees well with the generally adopted distance of LAIC of SOkpe (IZastman. Schmidt. LIxirshner 1996) and the EPM distance of LOGSL is indistinguishable from the Cephoeid distance of 5236 (M83) (Phim et al.," However, it may be noted that the EPM distance of $\,$ 1987A agrees well with the generally adopted distance of LMC of $\,$ kpc (Eastman, Schmidt, Kirshner 1996) and the EPM distance of $\,$ 1968L is indistinguishable from the Cepheid distance of $\,$ 5236 (M83) (Thim et al." + 2003)., 2003). + The main assumption which alfects the plateau-tai distances concerns the nature of the proposed οτν correlation., The main assumption which affects the plateau-tail distances concerns the nature of the proposed $E-{\cal M}_{\mathrm{Ni0}}$ correlation. + For our simplified example of such a correlation. all the uncertainties turn out. to be cumulated in. the proportionality factor £ between the explosion energy. fo and the nickel mass .Myio.," For our simplified example of such a correlation, all the uncertainties turn out to be cumulated in the proportionality factor $\xi$ between the explosion energy $E$ and the nickel mass ${\cal M}_{\mathrm{Ni0}}$." + In 3 we have adopted a plausible value of£=I. but it cannot be excluded that £ is as low as 0.5 or as high as 2.," In $\,$ 3 we have adopted a plausible value of $\xi=1$, but it cannot be excluded that $\xi$ is as low as 0.5 or as high as 2." +" Since the Hubble constant scales as Ly~074, an average value as high as £=1.9 would be needed to bring the plateau-tail distances in general accord with the EPM distances."," Since the Hubble constant scales as $H_0\sim\xi^{0.374}$, an average value as high as $\xi=1.9$ would be needed to bring the plateau-tail distances in general accord with the EPM distances." + Such a high average value. of £ is. however. not supported. by SNe 1987 and. 1999e1.," Such a high average value of $\xi$ is, however, not supported by SNe 1987A and 1999gi." +. 1£ he Dp-p distance of LOSTA from Table 3 is scaled. to he canonical LM clistance of kpe. £ becomes 0.75.," If the $D_{\mathrm{P-T}}$ distance of $\,$ 1987A from $\,$ 3 is scaled to the canonical LMC distance of $\,$ kpc, $\xi$ becomes 0.75." + Xnd if the host galaxy NGC3184 of 1990gi with a Dprm distance of Alpe is a member of the same group as 3198 and 3319. for which Freedman οἱ al. (," And if the host galaxy $\,$ 3184 of $\,$ 1999gi with a $D_{\mathrm{P-T}}$ distance of $\,$ Mpc is a member of the same group as $\,$ 3198 and $\,$ 3319, for which Freedman et al. (" +2001) eive a mean Cepheid distance of Mpc. £ becomes 1.2.,"2001) give a mean Cepheid distance of $\,$ Mpc, $\xi$ becomes 1.2." + Eventually additional SNeLIP with large distances.where he influence of peculiar motions are negligible. will better determine the scatter of the Lubble diagram. and. allow a meaningful determination of the actual range of £.," Eventually additional $\,$ IIP with large distances,where the influence of peculiar motions are negligible, will better determine the scatter of the Hubble diagram and allow a meaningful determination of the actual range of $\xi$." +" We have considered three sets of the physical supernova parameters ££. M. and 2: (7) for the Hubble distances Dg with 4/4,=60knms!Mpe+ (pable2. column 3): (7) for the EPM distances Depa, (Lable2. column 4): (77) for the plateau-tail calibrated distances Dyp (Vable3. column 2)."," We have considered three sets of the physical supernova parameters $E$ , $\cal M$, and $R$: $(i)$ for the Hubble distances $D_H$ with $H_0=60\,{\mathrm{km}}\,{\mathrm{s}}^{-1}\,{\mathrm{Mpc}}^{-1}$ $\,$ 2, column 3); $(ii)$ for the EPM distances $D_{\mathrm{EPM}}$ $\,$ 2, column 4); $(iii)$ for the plateau-tail calibrated distances $D_{\mathrm{P-T}}$ $\,$ 3, column 2)." + Although the above parameters derived from the IPM- are not presented.in Table2. the corresponding L and M-values can be read. out of Figs.3 and 4 which compare { and M for sets (7) and (77) with those for set (777) ," Although the above parameters derived from the EPM-distances are not presentedin $\,$ 2, the corresponding $E$ and $\cal M$ -values can be read out of $\,$ \ref{nadezhfg3} and \ref{nadezhfg4} which compare $E$ and $\cal M$ for sets $(i)$ and $(ii)$ with those for set $(iii)$ ." +lor seven SNe ££ and M are rather insensitive to the adopted distances., For seven SNe $E$ and $\cal M$ are rather insensitive to the adopted distances. +However for SNe1986L. and. 199012. labelled: in Fies.3 and 4d. the deviations from the (DP-T)-values are,"However for $\,$ 1986L and 1990E, labelled in $\,$ \ref{nadezhfg3} and \ref{nadezhfg4}, , the deviations from the (P-T)-values are" +during an outburst of the dwarf nova SS Cve have 2 ~ 12. and the DNO periods ( 8 8) place them between. VW Livi and the X-Ray binaries in the two-QPO correlation diagram.,"during an outburst of the dwarf nova SS Cyg have $R$ $\sim$ 12, and the DNO periods $\sim$ 8 s) place them between VW Hyi and the X-Ray binaries in the two-QPO correlation diagram." + This greatly. strengthened the evidence for the existence of a general relation between high and low frequency. OPOs in all of these interacting binaries. irrespective of whether the primary is à black hole. neutron star or white dwarf.," This greatly strengthened the evidence for the existence of a general relation between high and low frequency QPOs in all of these interacting binaries, irrespective of whether the primary is a black hole, neutron star or white dwarf." + In CVs the DNOs are the analogues of the high frequency. X-Ray binary QPOs. and the CVs QPOs are the analogues of the low frequency X-Rav QPOs.," In CVs the DNOs are the analogues of the high frequency X-Ray binary QPOs, and the CV's QPOs are the analogues of the low frequency X-Ray QPOs." + In this paper we will be largely interested in. presenting new observations of DNOs and. QPOs in. CVs. and in reinterpreting previously publishecl observations.," In this paper we will be largely interested in presenting new observations of DNOs and QPOs in CVs, and in reinterpreting previously published observations." + A complication that arises is that. both. DNOs and. QPOs can show frequeney doubling. ancl these can happen independently of cach other (Warner λοιπον in preparation).," A complication that arises is that both DNOs and QPOs can show frequency doubling, and these can happen independently of each other (Warner Woudt, in preparation)." + This may change the measured. value of £2 by a factor of 2 in some cases., This may change the measured value of $R$ by a factor of 2 in some cases. + QPOs are far less coherent and persistent than DNOs., QPOs are far less coherent and persistent than DNOs. + Lt is commonly observed that a train of 5 to 10 moderately coherent QPO excles is clearly. visible. before changing in phase or disappearing altogether.," It is commonly observed that a train of 5 to 10 moderately coherent QPO cycles is clearly visible, before changing in phase or disappearing altogether." + We first indicate some of the theoretical work that appears relevant to understanding the nature of the rapid oscillations in interacting binaries., We first indicate some of the theoretical work that appears relevant to understanding the nature of the rapid oscillations in interacting binaries. + That DNOs are signatures of magnetically controlled aceretion onto the equatorial belt of the white dwarf primaries of CVs was proposed by Paczvnski (1978). made more quantitative by Warner (1995b) and claborated in Paper Hb as the Low Inertia Magnetic Acerctor (LINLA) model.," That DNOs are signatures of magnetically controlled accretion onto the equatorial belt of the white dwarf primaries of CVs was proposed by Paczynski (1978), made more quantitative by Warner (1995b) and elaborated in Paper II as the Low Inertia Magnetic Accretor (LIMA) model." + “Phe last also develops the idea that QPOs may be caused. by prograde travelling waves near the inner edge of the maenctically truncated: aceretion clises., The last also develops the idea that QPOs may be caused by prograde travelling waves near the inner edge of the magnetically truncated accretion discs. +" (X simple excitation mechanism. involving magnetic reconnection. leads to the expectation that 2—Ολο~(1d)1 where QO, is the Ixeplerian. frequeney. in the disc near the corotation radius reo. AG=O,Onus. where O,, is the niaximum angular frequency in the transition zone between reo and the inner edge οἱ the disc. and ως is the ""Tastness parameter. defined by Ghosh Lamb (1979)."," A simple excitation mechanism, involving magnetic reconnection, leads to the expectation that $R \sim {\Omega_{k}}/{\Delta \Omega} \sim +(1 - \omega_{s})^{-1}$, where $\Omega_k$ is the Keplerian frequency in the disc near the corotation radius $r_{co}$, $\Delta \Omega = \Omega_k - \Omega_{\rm max}$, where $\Omega_{\rm max}$ is the maximum angular frequency in the transition zone between $r_{co}$ and the inner edge of the disc, and $\omega_s$ is the `fastness parameter' defined by Ghosh Lamb (1979)." + A somewhat dillerent. physical interpretation is that QPOs are modulations in the rate of mass transfer onto the primary., A somewhat different physical interpretation is that QPOs are modulations in the rate of mass transfer onto the primary. + This concept is used. in QPOs of the luminosities of voung stars. where the QPOs are envisaged as magnetospheric radial oscillations. caused by field. winding and reconnecting. as in the above proposed. mocdoel for CVs.," This concept is used in QPOs of the luminosities of young stars, where the QPOs are envisaged as magnetospheric radial oscillations, caused by field winding and reconnecting, as in the above proposed model for CVs." + The racial oscillations produce quasi-periodic modulation of the mass transfer rate. and a typical model has 2~100/27 (Cioodson Winglee 1999).," The radial oscillations produce quasi-periodic modulation of the mass transfer rate, and a typical model has $R \sim 100/{2 \pi}$ (Goodson Winglee 1999)." + Returning to interacting binaries. in à study. of field winding. inflation and reconnection in the region connecting the inner disc to the primary. Uzdensky. (2002) concludes that. quasi-periodic oscillations should. occur.," Returning to interacting binaries, in a study of field winding, inflation and reconnection in the region connecting the inner disc to the primary, Uzdensky (2002) concludes that quasi-periodic oscillations should occur." + Such QPOs could. cause mass transfer. modulation and/or travelling waves., Such QPOs could cause mass transfer modulation and/or travelling waves. + T'itarchuk Wood (2002) interpret the whole range of the (wo-QPO correlation as evidence for magnetoacoustic oscillations in the transition zone. driven by the adjustment to sub-Ixeplerian Low.," Titarchuk Wood (2002) interpret the whole range of the two-QPO correlation as evidence for magnetoacoustic oscillations in the transition zone, driven by the adjustment to sub-Keplerian flow." + The next two sections of this paper are devoted. to accumulating values of Povo and po and the resulting estimates of A: In Section 2 we examine published papers in order to extract values of A7: in Section 3 we describe new photometric observations of CVs that lead. to further determinations of /?., The next two sections of this paper are devoted to accumulating values of $P_{DNO}$ and $P_{QPO}$ and the resulting estimates of $R$: In Section 2 we examine published papers in order to extract values of $R$; in Section 3 we describe new photometric observations of CVs that lead to further determinations of $R$. + ln Section 4 we draw attention to a new type of DNO that is occasionally seen. which could be confused with the standard DNOs. and in Section 5 we compare the DNOs anc QPOs in CVs with the two-QDPO correlation and other properties of X-Ray binaries.," In Section 4 we draw attention to a new type of DNO that is occasionally seen, which could be confused with the standard DNOs, and in Section 5 we compare the DNOs and QPOs in CVs with the two-QPO correlation and other properties of X-Ray binaries." + Section 6 contains a final discussion ancl assessment., Section 6 contains a final discussion and assessment. + The values of H. their. possible variation for any given star. and their range from star to star. have not. previously been given much attention. but in the light of the newly discovered. possible connection between. CV. anc X-Ray QPOs these ratios are of great interest.," The values of $R$, their possible variation for any given star, and their range from star to star, have not previously been given much attention, but in the light of the newly discovered possible connection between CV and X-Ray QPOs these ratios are of great interest." + In this Section we examine the published studies of CVs with this in mind., In this Section we examine the published studies of CVs with this in mind. + Ideally. we would prefer light curves where both DNOs and QPOs are present simultaneously.," Ideally, we would prefer light curves where both DNOs and QPOs are present simultaneously." + Llowever. largely through the lower interest in QPOs in the past. DNO periods are often the only ones quoted.," However, largely through the lower interest in QPOs in the past, DNO periods are often the only ones quoted." + We can expand the list of useful results by including observations of double DNOs. making use of the conclusion (Papers Land LL) that in at. least some CVs (VW Livi. WZ See) the QPO frequency. is the iference (i.e. beat) frequency of the two DNOs.," We can expand the list of useful results by including observations of `double' DNOs, making use of the conclusion (Papers I and II) that in at least some CVs (VW Hyi, WZ Sge) the QPO frequency is the difference (i.e. beat) frequency of the two DNOs." + The true DNO is the shorter of the two periods: the longer period is 10 result of reprocessing of the DNO by the travelling wave ju ds thought to produce the QPO (Paper HD)., The true DNO is the shorter of the two periods; the longer period is the result of reprocessing of the DNO by the travelling wave that is thought to produce the QPO (Paper II). +" By using re beat frequency. we in ellect generate a ""pseudo. ΟΡΟ: ls mav not be visible directly in the light. curve because 1e travelling wave may happen not to intercept our line of sight. but its presence is indirectly observed by the shielding ancl reprocessing effects it has on the disc. which generate 10 double DNO."," By using the beat frequency we in effect generate a `pseudo' QPO; this may not be visible directly in the light curve because the travelling wave may happen not to intercept our line of sight, but its presence is indirectly observed by the shielding and reprocessing effects it has on the disc, which generate the double DNO." + The €V in which OPOs were first noticed was the dwarf nova hU Peg., The CV in which QPOs were first noticed was the dwarf nova RU Peg. + Patterson et al. (, Patterson et al. ( +1977) found. ~ 50 s oscillations clearly ciseernable in the light curve which. because of their low coherence. were transformed. into a barely significant broad. ancl noisy band. of power in the Fourier. transform (ID).,"1977) found $\sim$ 50 s oscillations clearly discernable in the light curve which, because of their low coherence, were transformed into a barely significant broad and noisy band of power in the Fourier transform (FT)." + Phe QPOs were present during all five nights of the November 1975 outburst., The QPOs were present during all five nights of the November 1975 outburst. + In addition. on four of the nights more stable oscillations. characteristic of DNOs. were seen in the F°Ps at periods near 11.6 s but with unusually small amplitudes 0.6 nimag (millimagnitποος).," In addition, on four of the nights more stable oscillations, characteristic of DNOs, were seen in the FTs at periods near 11.6 s but with unusually small amplitudes $\sim$ 0.6 mmag (millimagnitudes)." + The value of 2? for RU Pee. using the above numbers. is ~ 4.5.," The value of $R$ for RU Peg, using the above numbers, is $\sim$ 4.5." + This is so lar removed from the value ~ 15 that we see in VW Lyi and the X-Ray binaries that it would seem that the QPO ctwpe star itself is highly anomalous., This is so far removed from the value $\sim$ 15 that we see in VW Hyi and the X-Ray binaries that it would seem that the QPO `type star' itself is highly anomalous. + However. the following reasoning leads to a dilferent conclusion.," However, the following reasoning leads to a different conclusion." + The, The +"For p2—1 and e -1$ and $\epsilon \ll \epsilon_{max,T}$ we have $\gamma_{min} \ll \gamma_{max}$." + Since the integrand is then steeper than 5li the above result simplifies to The beaming of the observed radiation is the direct outcome of the electron beaming. and it is characterized by the electron index p.," Since the integrand is then steeper than $\gamma^{-1}$, the above result simplifies to The beaming of the observed radiation is the direct outcome of the electron beaming, and it is characterized by the electron index $p$." +" In the Thomson limit. the resulting spectrum is a simple power law wilh a spectral index a=(p—1)/2 and one can substitute for p in equation (10)) to recover the D!?"" beaming pattern (equation 7 of D95)."," In the Thomson limit, the resulting spectrum is a simple power law with a spectral index $\alpha=(p-1)/2$ and one can substitute for $p$ in equation \ref{thomson}) ) to recover the ${\cal D}^{4+2\alpha}$ beaming pattern (equation 7 of D95)." + The spurious term (1--p).P in the result of D95. which. however. varies only slowly with µ for viewing angles of interest. was introduced by the approximation that the seed photons in the fame of the blob are coming from a direction opposite to the direction of the velocity of the blob.," The spurious term $(1+\mu)^{(\alpha+1)}$ in the result of D95, which, however, varies only slowly with $\mu$ for viewing angles of interest, was introduced by the approximation that the seed photons in the frame of the blob are coming from a direction opposite to the direction of the velocity of the blob." +" In both D95 and here the maximum observed energy 6,,,,5. as well as anv other characteristic energy. scale as xD?. whereas in svnchrotron and SSC they scale as D."," In both D95 and here the maximum observed energy $\epsilon_{max,T}$, as well as any other characteristic energy, scale as $\propto {\cal D}^2$, whereas in synchrotron and SSC they scale as ${\cal D}$." +" If. instead of observing ad a fixed energy. we are interested in the specific luminosity measured at a break or cut-off in the spectrum. then the D? scaling of the break energy introduces an additional D?"" factor. so that the specific luminosity at the break scales as DI."," If, instead of observing at a fixed energy, we are interested in the specific luminosity measured at a break or cut-off in the spectrum, then the ${\cal D}^2$ scaling of the break energy introduces an additional ${\cal D}^{-2\alpha}$ factor, so that the specific luminosity at the break scales as ${\cal D}^4$ ." + The luminosity per logarithmic energy interval of the spectral feature. given by «dL/dedQ. then scales as D. since €xD?.," The luminosity per logarithmic energy interval of the spectral feature, given by $\epsilon \, dL/d\epsilon d\Omega$, then scales as ${\cal D}^6$ , since $\epsilon\propto{\cal D}^2$." +" In the INN case. for energies ejeX6euo Where 1e5542). the lower limit of integration in equation (8)) is [ο by setting c—1 In (his case the integrand is also steeper (hat 51. and fou DEApenxAUT)2Do—6XCima.dyN+ (he integration is dominated by the lowerlimit 5,,5, which is independent of D."," In the KN case, for energies $\epsilon_{min,KN}\leq\epsilon\leq\epsilon_{max,KN}$, where $\epsilon_{min,KN}=4\epsilon_0\gamma_1^2{\cal D}^2/(1+4\epsilon_0\gamma_1{\cal D})$ , the lower limit of integration in equation \ref{eq:sc_int}) ) is found by setting $x=1$ In this case the integrand is also steeper that $\gamma^{-1}$, and for $\gamma_{min} \ll \gamma_2{\cal D} \Rightarrow \epsilon \ll \epsilon_{max,KN}$, the integration is dominated by the lowerlimit $\gamma_{min}$ which is independent of ${\cal D}$." + Therefore. the beaming pattern D? is also valid in the general case of INN scattering.," Therefore, the beaming pattern ${\cal D}^{3+p}$ is also valid in the general case of KN scattering." +" The maximum energv is given by equation (6)). which is reduced (o ej,yΞ55D when the hieh energy tailof the electron energy distribution is well into the NN regime. 5»5DejZ91. a behavior"," The maximum energy is given by equation \ref{eq:gmaxkn}) ), which is reduced to $\epsilon_{max,KN}=\gamma_2{\cal D}$ when the high energy tailof the electron energy distribution is well into the KN regime, $\gamma_2 {\cal D} \epsilon_0 \gg 1$, a behavior" +"rfkpe. ∣My =↽⊲⋅≻ (0G/e23)pyC.pyETE = O0,eλος/.Ry mu (0,35—πο UL JeyἹ ""i01 mEo, = TheyehROS"" redshift fd""EEN dmekun""uuThe I.Maxially The baneC» time function is fjL=0. which means that ↑∐↸∖⋜↧∶↴∙⊾↸∖∪↕⋟↑↕∐∖⋯∐↖↽↸∖↥⋅↴∖↴↸∖↕↴∖↴↑∐↸∖↴∖↴⋜⋯∐∖","where $\ell = r$ /kpc, $M_0 = (4 \pi G /3c^2) \rho_{b} \ell^3$ , $\rho_{b} = \Omega_m \frac{3H_0^2}{8 \pi G}$ , $\Omega_m = 0.25$ , $H_0=72$ km $^{-1}$ $^{-1}$, $x_a= 10^4$ , $M_1 = x_a^{-3} M_2 {\rm e}^{-1.5}$ , $M_2= -7 \times 10^{11}$ kpc, The bang time function is $t_B = 0$, which means that the age of the universe is the same everywhere." +↸∖↖↽↸∖↥⋅⋅↖↽↖↖↽↕∐∖↥⋅↸∖∙↽∕∏∐∖ function & then follows from Eq. (AG))., The function $k$ then follows from Eq. \ref{tbf}) ). +" Aud the functions 5S.DP. and (Q are | is for spropagation from. theuM origin |E'// (δρς107|(j]. and towards the origin ο, r=d(ος107Ο]."," And the functions $S,P,$ and $Q$ are where $+$ is for propagation from the origin ${ E}'/{ E} = 0.78/(5 \times 10^3 + \ell)$ ], and $-$ towards the origin ${ E}'/{ E} = -0.78/(5 \times 10^3 + \ell)$ ]." + As can be seen from Eqs. (A) df ," As can be seen from Eqs. \ref{rho}) \ref{Mm1}) )," +for r. >LOMpe the considered model= becomes the αν Fricdiuaun model. which is iu this particular E. the ACDM model.," for $r>40$ Mpc the considered model becomes the homogeneous Friedmann model, which is in this particular case the $\Lambda$ CDM model." + First light propagates towards the qt center. E>0. aud after passing through the origin. £’ )ocomies negative. and so on.," First light propagates towards the center, $E'>0$, and after passing through the origin, $E'$ becomes negative, and so on." + Because the mbomogeueous docks are matched to the Friecdinzun model the average density is alinost the same as in the ACDAL model The first equalitv is implied bv the dipole not contributing to the average (Bolejko2009)., Because the inhomogeneous blocks are matched to the Friedmann model the average density is almost the same as in the $\Lambda$ CDM model The first equality is implied by the dipole not contributing to the average \cite{KBCMB}. +.. The last approxination is exact when curvature vanishes. althoteh in the considered iiodel k«10 υπο itis quite an accurate approximation.," The last approximation is exact when curvature vanishes, although in the considered model $k < 10^{-5}$, so it is quite an accurate approximation." + Finalv. the junction conditions (matching the Szekeres to Friediamann model) Πρίν that both he total mass and volume of the imhomoeeicous patch are the same as in the homogeneous model.," Finally, the junction conditions (matching the Szekeres to Friedmann model) imply that both the total mass and volume of the inhomogeneous patch are the same as in the homogeneous model." + Thus. the average density of the SzekexSs Swiss-Checse niocl is almost he sale as the backerotud 120cdel the ACDAL model.," Thus, the average density of the Szekeres Swiss-Cheese model is almost the same as the background model – the $\Lambda$ CDM model." + This is also true for theInibble parameter isobtained| for nullgeodesie. equations., This is also true for theHubble parameter Theredshift is obtainedfor null geodesic equations. + (eomM (MacM. uull geodesic (propagation along the axial axis) ds and the redshiftrelation is or equivaleutlv , The axially null geodesic (propagation along the axial axis) is and the redshiftrelation is or equivalently +The mass of individual cloudlets that escape into the ISM lies in the range of some ten solar masses.,The mass of individual cloudlets that escape into the ISM lies in the range of some ten solar masses. + Fig., Fig. + daa shows the evolution of the gravitationally bound cloud mass of the simulations without and with heat conduction., \ref{f4}a a shows the evolution of the gravitationally bound cloud mass of the simulations without and with heat conduction. + For comparison the analytical result of the cloud mass is shown taking mass-loss by evaporation into account (Eq., For comparison the analytical result of the cloud mass is shown taking mass-loss by evaporation into account (Eq. + 6)., 6). + From this figure we see: 1) The pure evaporation effect on a static homogeneous cloud from CM77 is the most destructive because of its shortest timescale. but it overestimates the strength. of heat conduction and its heating effect.," From this figure we see: 1) The pure evaporation effect on a static homogeneous cloud from CM77 is the most destructive because of its shortest timescale, but it overestimates the strength of heat conduction and its heating effect." + 2) The pure dynamical destruction by KH instability happens on a much longer timescale., 2) The pure dynamical destruction by KH instability happens on a much longer timescale. + As in a static. self-gravitating and, As in a static self-gravitating and +redistribute more of the ultimately acquired mass.,redistribute more of the ultimately acquired mass. + Given that less massive halos typically have higher concentrations. we can estimate the magnitude of this effect on the evolution of 5 with Ly.," Given that less massive halos typically have higher concentrations, we can estimate the magnitude of this effect on the evolution of $\slope$ with $\Lp$ ." +" Estimating «Κας~0.1 (where e is the concentration index and we estimate a change ~10 in c changes the inner logarithmic slope at fixed r by ~1). we can determine «ο1οςρω) using Lo,xMpgονMyir (e.g. Marconi Hunt 2003) and ¢=9M./LOM? 2001).. and we find in reasonable agreement with our measured dependence of 5G) in our simulations and only weakly dependent on Ly."," Estimating $dk_{\rho}/dc\sim0.1$ (where $c$ is the concentration index and we estimate a change $\sim10$ in $c$ changes the inner logarithmic slope at fixed $r$ by $\sim1$ ), we can determine $dc/d\log(\Lp)$ using $\Lp\propto M_{\rm BH}\propto M_{\rm vir}$ (e.g., Marconi Hunt 2003) and $c\approx 9 (M_{\rm vir}/10^{13}M_{\sun})^{-0.13}$ \citep{Bullock01}, and we find in reasonable agreement with our measured dependence of $\slope(\Lp)$ in our simulations and only weakly dependent on $\Lp$." +" This actually predicts that the magnitude of difídlogLy4, should be larger at low-Lpea, (7—0.28 at Ly~LON Ly and smaller at high Lica. (~70.16 at 10131.1 which may occur (see Figure 2)). but this is most likely à comeidence. as our modeling of the blowout in scale invariant fashion and the application of a concentration parameter in such chaotic period in evolution of the merger are rough approximations at best."," This actually predicts that the magnitude of $d\slope/d\log{\Lp}$ should be larger at $\Lp$ $\sim-0.28$ at $\Lp\sim10^{11}\,L_{\sun}$ ) and smaller at high $\Lp$, $\sim-0.16$ at $\Lp\sim10^{13}\,L_{\sun}$ ) which may occur (see Figure \ref{fig:slope.v.Lp}) ), but this is most likely a coincidence, as our modeling of the blowout in scale invariant fashion and the application of a concentration parameter in such chaotic period in evolution of the merger are rough approximations at best." + In this model of the quasar blowout phase. however. the approximate values for the rate at which accretion declines are simply determined by a standard Sedov-Taylor solution in a medium with a density gradient.," In this model of the quasar blowout phase, however, the approximate values for the rate at which accretion declines are simply determined by a standard Sedov-Taylor solution in a medium with a density gradient." + The sudden injection of energy as the BH crosses a critical mass/luminosity threshold and the surrounding gas is no longer able to efficiently cool drives a strong outflow and heats the remaining gas. rapidly shutting down aceretion.," The sudden injection of energy as the BH crosses a critical mass/luminosity threshold and the surrounding gas is no longer able to efficiently cool drives a strong outflow and heats the remaining gas, rapidly shutting down accretion." + Incorporating the weak. but not negligible. effects of the change in concentration with mass breaks the scale invariance of this solution. as lower-mass systems have steeper inner density profiles. which flatten the evolution of the accretion rate in time and produce steeper 7.," Incorporating the weak, but not negligible, effects of the change in concentration with mass breaks the scale invariance of this solution, as lower-mass systems have steeper inner density profiles, which flatten the evolution of the accretion rate in time and produce steeper $\slope$." + Of course. many other effects will break the self-similarity of this problem as well — a realistic gravitational potential will imply a characteristic scale length. and the physics of radiative cooling will likewise. define. fundamental physical scales.," Of course, many other effects will break the self-similarity of this problem as well – a realistic gravitational potential will imply a characteristic scale length, and the physics of radiative cooling will likewise define fundamental physical scales." + Even the scale-invariant solution. incorporating radiative energy loss depends on the logarithmic slope of the cooling function ddensity and temperature. but the values of these slopes depend themselves on the characteristic temperature of the blastwaves and change quite significantly over the mass seale of our simulations (heating to virial temperatures ες~02 implies temperatures T~10?— 107K over the mass range shown in Figure 2).," Even the scale-invariant solution incorporating radiative energy loss depends on the logarithmic slope of the cooling function density and temperature, but the values of these slopes depend themselves on the characteristic temperature of the blastwaves and change quite significantly over the mass scale of our simulations (heating to virial temperatures $c_{s}^{2}\sim \sigma^{2}$ implies temperatures $T\sim 10^{5}-10^{7}\,$ K over the mass range shown in Figure \ref{fig:slope.v.Lp}) )." + Although we do not model the chaotic interactions and evolving BH mass of the early merger stages. the more violent torquing associated with more massive mergers can explain the more rapid. peaked BH evolution over a larger range in BH mass. even in early merger stages. generating a flatter quasar lifetime which spans a wider range in luminosity.," Although we do not model the chaotic interactions and evolving BH mass of the early merger stages, the more violent torquing associated with more massive mergers can explain the more rapid, peaked BH evolution over a larger range in BH mass, even in early merger stages, generating a flatter quasar lifetime which spans a wider range in luminosity." + Given these various scalings. it 1s possible that our observed trend of) could change or even reverse at very low Ly. as im Gaya)models of stellar winds in dwarf ellipticals for which lower-mass objects (lower Mpgy) are more easily unbound (e.g.ΜαςLow&Ferrara1999) (although this is more concerned with the large-scale binding of gas. as to evolutionin theinner aceretion regions of interest in our opposedmodeling). but the masses/luminosities where this is likely to become important (MiiSA10M... Lpeak= 1037...) are well below the break luminosity at any redshift. and thus will not affeet our results.," Given these various scalings, it is possible that our observed trend of $\slope(\Lp)$ could change or even reverse at very low $\Lp$, as in models of stellar winds in dwarf ellipticals for which lower-mass objects (lower $\mbh$ ) are more easily unbound \citep[e.g.][]{MLF99} + (although this is more concerned with the large-scale binding of gas, as opposed to evolution in the inner accretion regions of interest in our modeling), but the masses/luminosities where this is likely to become important $M_{\rm gal}\lesssim10^{8}\,M_{\sun}$, $\Lp\lesssim10^{9}\,L_{\sun}$ ) are well below the break luminosity at any redshift, and thus will not affect our results." +" Likewise. this could occur at very large radius r>>e in any Lyoa, system. but again we are not attempting to model the large-scale blastwave but only the evolution relevant to the small accretion regions."," Likewise, this could occur at very large radius $r\gg a$ in any $\Lp$ system, but again we are not attempting to model the large-scale blastwave but only the evolution relevant to the small accretion regions." + The fits and analytical modeling above imply a useful. simple prescription for the quasar light curve as applied in semi-analytical models and other theoretical modeling which cannot resolve the detailed time history of individual objects as we can in our simulations.," The fits and analytical modeling above imply a useful, simple prescription for the quasar light curve as applied in semi-analytical models and other theoretical modeling which cannot resolve the detailed time history of individual objects as we can in our simulations." +" Generally. the quasar light curve is characterized by two ""modes: a ""growing mode.” characterized by high-Eddington ratio. rapid black hole growth. and a “decaying mode.” characterized by the nearly self-similar power-law falloff of the quasar luminosity as nearby gas is heated or expelled."," Generally, the quasar light curve is characterized by two “modes”: a “growing mode,” characterized by high-Eddington ratio, rapid black hole growth, and a “decaying mode,” characterized by the nearly self-similar power-law falloff of the quasar luminosity as nearby gas is heated or expelled." + The “growing mode™ can be most simply parameterized by exponential growth at a constant Eddington ratio i. with an exponential light curve L=Lr2Oexpir/ro]. where tg=rs/m is the e-folding time and f;=4.2«10’ yr is the Salpeter time.," The “growing mode” can be most simply parameterized by exponential growth at a constant Eddington ratio $\dot{m}$, with an exponential light curve $L=L(t=0)\exp{\{t/t_{Q}\}}$, where $t_{Q}=t_{S}/\dot{m}$ is the $e$ -folding time and $t_{S}=4.2\times10^{7}\,$ yr is the Salpeter time." + Such black hole growth is expected in essentially all models of quasar activity. where plentiful fueling easily enables high accretion rates.," Such black hole growth is expected in essentially all models of quasar activity, where plentiful fueling easily enables high accretion rates." +" Once the quasar reaches a eritical luminosity or mass Cin aaccord with the M—0 relation). it begins to heat and expel the surrounding gas. and the accretion rate rapidly falls off — tthe light curve can be roughly parameterized as entering the “decay mode"" described above."," Once the quasar reaches a critical luminosity or mass (in accord with the $M-\sigma$ relation), it begins to heat and expel the surrounding gas, and the accretion rate rapidly falls off – the light curve can be roughly parameterized as entering the “decay mode” described above." +" Our fits to the quasar lightcurves after the “blowout” phase and analytical modeling of this phase of evolution as a driven blastwave suggest a power-law decline in the quasar lighteurve. which can be simple modeled as ∠∣∖↼⋅∣↴⊖∣⊜∣∖⋔⊜∣⊃⊜≏∐∖⇂↴⋂∣⋂⋯⊜⋯∟∣∐⋯⋯⋃∖∐∖↿∐⋋↾∐⋋⋔⊖ quasar enters the""blowout"" phase. and L(r) is the subsequent bolometric luminosity at time 7 after the peak (ZL=Ly at t£— 0)."," Our fits to the quasar lightcurves after the “blowout” phase and analytical modeling of this phase of evolution as a driven blastwave suggest a power-law decline in the quasar lightcurve, which can be simple modeled as $L_{\rm peak}$ here is the peak bolometric luminosity, just as the quasar enters the “blowout” phase, and $L(t)$ is the subsequent bolometric luminosity at time $t$ after the peak $L=L_{\rm peak}$ at $t=0$ )." + It is also not a bad approximation to use this to model both the light curve and accretion rate with ΓΗ)Όρωνστm. because not much total black hole mass is accumulated in this mode.," It is also not a bad approximation to use this to model both the light curve and accretion rate with $L(t)/L_{\rm peak}\approx\dot{m}$, because not much total black hole mass is accumulated in this mode." +" The equation shown assumes 77?«l at peak luminosity. as is true in most of our simulations. but this can easily be renormalized to any assumed constant m in the constant Eddington ratio ""growing mode.”"," The equation shown assumes $\dot{m}\approx1$ at peak luminosity, as is true in most of our simulations, but this can easily be renormalized to any assumed constant $\dot{m}$ in the constant Eddington ratio “growing mode.”" +" The functional form of this equation is chosen such that it joins continuously with the constant Eddington ratio exponential light curve at f=0 (L=Ly. aat the beginning of the ""blowout"" stage). and behaves as our fitted power-laws at times large compared to the duration of the“blowout.”"," The functional form of this equation is chosen such that it joins continuously with the constant Eddington ratio exponential light curve at $t=0$ $L=L_{\rm peak}$, at the beginning of the “blowout” stage), and behaves as our fitted power-laws at times large compared to the duration of the “blowout.”" + The eritical behavior determined from our simulation is this power- decay of the quasar light curve at late times. L(f)x(ffo) lawan," The critical behavior determined from our simulation is this power-law decay of the quasar light curve at late times, $L(t)\propto(t/t_{Q})^{-\beta}$ ." +"dWe have measured ./j directly m our simulations above. estimated its value from simple analytical models of the quasar-driven ""blowout phase."," We have measured $\beta$ directly in our simulations above, and estimated its value from simple analytical models of the quasar-driven “blowout” phase." + Tolowest order. a canonical value of }=2 Is suggested by both our fits to the simulation light curves and the self-similar Sedov-Taylor solution for a quasar-driven blastwave and Bondi accretion.," Tolowest order, a canonical value of $\beta=2$ is suggested by both our fits to the simulation light curves and the self-similar Sedov-Taylor solution for a quasar-driven blastwave and Bondi accretion." + But we have also explicitly determined 3 as a function of peak luminosity. which we inverted to determine 2.54) above.," But we have also explicitly determined $\beta$ as a function of peak luminosity, which we inverted to determine $\gamma(L_{\rm peak})$ above." + Our fits to the simulations yield, Our fits to the simulations yield +"are detected mainly based on the line, which in most of the cases is very faint or not well detected.","are detected mainly based on the line, which in most of the cases is very faint or not well detected." + For this reason no reliable information for the narrow emission lines are included in most of the spectra at higher redshifts., For this reason no reliable information for the narrow emission lines are included in most of the spectra at higher redshifts. + Our selection produced a list of 32 candidates of particular relevance Table , Our selection produced a list of 32 candidates of particular relevance (see Table \ref{tab_candidates}) ). +"For each target, we re-analyzed the SDSS spectrum,(see 1)).modeling it with a power law for the QSO continuum emission, a host galaxy template at the redshift of the NLs and a template of the iron complex, as described in Decarlietal. and DeRosaetal.(2011)."," For each target, we re-analyzed the SDSS spectrum, modeling it with a power law for the QSO continuum emission, a host galaxy template at the redshift of the NLs and a template of the iron complex, as described in \citet{decarli10a} + and \citet{derosa11}." +". We fitted the broad components(2010a) ofMgu,, and with 2 gaussian functions at the same peak."," We fitted the broad components of, and with 2 gaussian functions at the same peak." +" This fitting approach aims to better constrain the peak wavelength, and is not meant to reproduce the line profile in detail."," This fitting approach aims to better constrain the peak wavelength, and is not meant to reproduce the line profile in detail." +" Narrow lines are masked when fitting the broad component; by construction of our sample, there is a velocity offset between BLs and NLs."," Narrow lines are masked when fitting the broad component; by construction of our sample, there is a velocity offset between BLs and NLs." + This simplifies the measurement of the peak wavelengths of the two components., This simplifies the measurement of the peak wavelengths of the two components. + Peak wavelengths are then converted into velocity shifts: Continuum-subtracted velocity plots of all the interesting targets are shown in Figure 2.., Peak wavelengths are then converted into velocity shifts: Continuum-subtracted velocity plots of all the interesting targets are shown in Figure \ref{fig_all}. +" A rough classification scheme was set according to: 1) the magnitude of the velocity shift, in particular when comparing and Balmer lines; the presence of strong asymmetries in the line profiles; 2)3) the occurrence of secondary bumps or peaks; 4) additional information from other emission lines or from the SDSS images."," A rough classification scheme was set according to: 1) the magnitude of the velocity shift, in particular when comparing and Balmer lines; 2) the presence of strong asymmetries in the line profiles; 3) the occurrence of secondary bumps or peaks; 4) additional information from other emission lines or from the SDSS images." +" We define five classes of objects, namely; i) candidates, which are expected to show similar velocity shifts for all the BLs, and a variety of line profiles (e.g.,Shen&Loeb2010).."," We define five classes of objects, namely; $i$ ), which are expected to show similar velocity shifts for all the BLs, and a variety of line profiles \citep[e.g.,][]{shen10b}." +" ii) quasars withprofiles, with small (2000 s-!)) shifts of BL peaks."," $ii$ ) quasars with, with small $\lsim2\,000$ ) shifts of BL peaks." +" These features are observed in some “normal” type-I AGN, and they are possibly related to asymmetries in the BL region (e.g.,Bentzetal.2010)."," These features are observed in some “normal” type-I AGN, and they are possibly related to asymmetries in the BL region \citep[e.g.,][]{bentz10}." +. They may also be associated to a velocity-dependent Balmer decrement of broad lines., They may also be associated to a velocity-dependent Balmer decrement of broad lines. +" ii?) (DPEs), characterized by symmetric features in line profiles (e.g., a secondary peak in the red wing of the line, at the opposite velocity with respect to a blue-shifted peak)."," $iii$ ) (DPEs), characterized by symmetric features in line profiles (e.g., a secondary peak in the red wing of the line, at the opposite velocity with respect to a blue-shifted peak)." + Another property of DPEs is that different lines (in particular low- and high-ionization lines) may show very different shapes and shifts (Halpernetal.1996).., Another property of DPEs is that different lines (in particular low- and high-ionization lines) may show very different shapes and shifts \citep{halpern96}. . + These properties are usually associated to a disk-like structure of the BL region (Eracleous&Halpern1994)., These properties are usually associated to a disk-like structure of the BL region \citep{eracleous1994}. +. iv) (see below)., $iv$ ) (see below). +" v) others, i.e. objects with small shifts or poor signal-to-noise spectra, preventing us from a clear interpretation, or objects with very peculiar properties, not belonging to any of the aforementioned classes."," $v$ ), i.e. objects with small shifts or poor signal-to-noise spectra, preventing us from a clear interpretation, or objects with very peculiar properties, not belonging to any of the aforementioned classes." +" Note that all the BHB candidates with small velocity shifts could also be recoiling BHs, though they are expected to be rarer than binaries (Dottietal.2009;Volonterietal."," Note that all the BHB candidates with small velocity shifts could also be recoiling BHs, though they are expected to be rarer than binaries \citep{dotti09,volonteri10} ." +"2010) In the following, we will not distinguish between 2009)...these two cases, including both in the “BHB candidates"" class."," In the following, we will not distinguish between these two cases, including both in the “BHB candidates” class." +" This classification produced 9 BHB candidates, including the 5 known candidates."," This classification produced 9 BHB candidates, including the 5 known candidates." +" For the new 4 sources, other interpretations are also plausible, including an extremely rare case of quasar-galaxy superposition for one of them."," For the new 4 sources, other interpretations are also plausible, including an extremely rare case of quasar–galaxy superposition for one of them." + Five quasars show very high velocity shifts (=5000 s-1)) and relatively faint lines.," Five quasars show very high velocity shifts $\gsim 5\,000$ ) and relatively faint lines." +" These objects probably represent extreme cases of DPEs (hereafter, they will be referred to as EDPEs)."," These objects probably represent extreme cases of DPEs (hereafter, they will be referred to as EDPEs)." +" In the following, we discuss the properties of each source individually, reporting our interpretation on the nature of the object."," In the following, we discuss the properties of each source individually, reporting our interpretation on the nature of the object." +" The Balmer broad lines of this zy,=0.228 quasar show a peak 1700 blue-shifted with respect to narrow lines."," The Balmer broad lines of this $z_{\rm NL}=0.228$ quasar show a peak $\sim 1\,700$ blue-shifted with respect to narrow lines." + T'he line profile is clearlyasymmetric., The line profile is clearlyasymmetric. +" and have identical profiles, with F(Ha)=2.6 "," and have identical profiles, with $F($ $)=2.6 F($ $)$." +"Balmerlinessuggeststhatthisisastrc peakedemitter(seealsoF(Hp).AbumpintheredwingoStratevaetal.f2003;Shenetal.2010), ,thougl "," A bump in the red wing of Balmer lines suggests that this is a strongly asymmetric double-peaked emitter \citep[see also][]{strateva03,shen10a}, though \citet{shen10b} + showed that the line profile of this source can be ascribed to an unequal mass BHB." +The line of this source shows a small (~1500 red-shift with respect to the narrow lines.," The line of this source shows a small $\sim1\,500$ ) red-shift with respect to the narrow lines." + slight s-1))asymmetry in the line profile is reported., A slight asymmetry in the line profile is reported. +" The asymmetryA is clearer in the profile, which peaks at longer wavelengths (Avzz2200 s-1))."," The asymmetry is clearer in the profile, which peaks at longer wavelengths $\Delta v \approx2\,200$ )." + Shenetal.(2010) reported a blue-shift of ~600 for and ~2300 for Hf.," \citet{shen10a} reported a blue-shift of $\sim600$ for and $\sim2\,300$ for ." + The relatively small velocity shift andthe difference in, The relatively small velocity shift andthe difference in +structured that single ionization zones. or metal abundances be different than solar).,"structured that single ionization zones, or metal abundances be different than solar)." + For simplicity. in the broad band fitting the iron line is modeled with a broad Gaussian.," For simplicity, in the broad band fitting the iron line is modeled with a broad Gaussian." +" No significant changes in the line parameters are found with respect to the hard X-ray band fits described in the previous section,", No significant changes in the line parameters are found with respect to the hard X-ray band fits described in the previous section. + The 0.5-2 (2-10) keV observed flux is 1.53(10.1)* 107) erg em s7!. corresponding to a 0.5-2 (2-10) keV luminosity of 1.17(2.34)x 10? erg s7!. after correction for absorption.," The 0.5-2 (2-10) keV observed flux is $\times$ $^{- 12}$ erg $^{-2}$ $^{-1}$, corresponding to a 0.5-2 (2-10) keV luminosity of $\times$ $^{43}$ erg $^{-1}$, after correction for absorption." + Due to the much weaker absorption and the absence of the Neon emission line. and despite the better statistics. the analysis of the second observation resulted to be easier.," Due to the much weaker absorption and the absence of the Neon emission line, and despite the better statistics, the analysis of the second observation resulted to be easier." + Also in this case. however. the addition of à second zone is definitely required.," Also in this case, however, the addition of a second zone is definitely required." + Inspection of the data/model ratio (see Fig 8)) shows however that some features are still remaining. even if that at about 1.8-2 keV is very likely of instrumental origin.," Inspection of the data/model ratio (see Fig \ref{bestfit_obs2}) ) shows however that some features are still remaining, even if that at about 1.8-2 keV is very likely of instrumental origin." + Particularly prominent ts the feature around | keV. again suggesting a possible problem in the fitting of tron transitions.," Particularly prominent is the feature around 1 keV, again suggesting a possible problem in the fitting of iron transitions." + The addition of a third absorbing zone does not cure this problem., The addition of a third absorbing zone does not cure this problem. + Also for this observation we find similar results with the CLOUDY-based. home-made tables.," Also for this observation we find similar results with the -based, home-made tables." + A significantly worse fit is found. instead. substituting the soft power law either with a disk thermal component or with an ionized reflection model.," A significantly worse fit is found, instead, substituting the soft power law either with a disk thermal component or with an ionized reflection model." + We then fitted the RGS data with the best fit model (all parameters fixed) above described., We then fitted the RGS data with the best fit model (all parameters fixed) above described. + Given the much better statistics with respect to the first observation. spectra were rebinned to have at least 50 counts per bin.," Given the much better statistics with respect to the first observation, spectra were rebinned to have at least 50 counts per ." +. The fit is reasonable (y7/d.o.f.=856.8/679)., The fit is reasonable $\chi^2$ /d.o.f.=856.8/679). + An. improvement (y7/d.0.f.=814.4/672) is found letting the model parameters free to vary., An improvement $\chi^2$ /d.o.f.=814.4/672) is found letting the model parameters free to vary. + The best fit parameters. however. are consistent within the errors with those found in the EPIC-pn analysis.," The best fit parameters, however, are consistent within the errors with those found in the EPIC-pn analysis." + Inspection of the residuals indicates the possible presence of features. but the only significant one (at the confidence level) is an emission line with a centroid energy of 14£0.002 keV - to be possibly identified with Fe XVII L lines - with a flux of 1.80(£0.75)x107 ph/em-/s7!.," Inspection of the residuals indicates the possible presence of features, but the only significant one (at the confidence level) is an emission line with a centroid energy of $\pm$ 0.002 keV - to be possibly identified with Fe XVII L lines - with a flux of $\pm$ $\times10^{-5}$ $^{2}$ $^{-1}$." + However. no such line is found in the EPIC-pn data (upper limit of 3.6x10~° ph/em-/s7!).," However, no such line is found in the EPIC-pn data (upper limit of $\times10^{-6}$ $^{2}$ $^{-1}$ )." + Finally. no significant inflow/outflow velocity is found. with upper limits of a few hundreds km/s (Table 3)).," Finally, no significant inflow/outflow velocity is found, with upper limits of a few hundreds km/s (Table \ref{t_vel}) )." + A significant improvement (Ay7=-49) is found letting the absorbers be partial., A significant improvement $\Delta \chi^2$ =-49) is found letting the absorbers be partial. + Best fit covering factors of 0.56 (but loosely constrained) and 0.38 are found for the colder and warmer ionization zones. respectively (see Table 2)).," Best fit covering factors of 0.56 (but loosely constrained) and 0.38 are found for the colder and warmer ionization zones, respectively (see Table \ref{t_zxipcf}) )." + Both absorbers are now much thicker and slightly less ionized., Both absorbers are now much thicker and slightly less ionized. + The power law indices are much harder; in particular. theD is now 1.18 (even if loosely constrained). a value unusually harc for Seyfert galaxies.," The power law indices are much harder; in particular, the$\Gamma_h$ is now 1.18 (even if loosely constrained), a value unusually hard for Seyfert galaxies." + However. it must be noted that fixing [421.8 a good fit is still obtained (y72243.0/227). with the parameters of the less tonized absorber almost unchangec while the more tonized absorber gets still more tonized anc thicker (Nj. x 107 7. fux~230. covering factor of 0.27).," However, it must be noted that fixing $\Gamma_h$ =1.8 a good fit is still obtained $\chi^2$ =243.0/227), with the parameters of the less ionized absorber almost unchanged while the more ionized absorber gets still more ionized and thicker $N_{H,2}\sim$ $\times$ $^{23}$ $^{-2}$, $\xi_2\sim$ 230, covering factor of 0.27)." + The best fit model and data/model ratio can be found in Fig. 8.., The best fit model and data/model ratio can be found in Fig. \ref{bestfit_obs2}. + In Fig. 9..," In Fig. \ref{contour-2-pc}," + the contour plots (10nization parameter vs. covering factor) are shown., the contour plots (ionization parameter vs. covering factor) are shown. + For the low ionization absorber the two parameters are almost uncorrelated. while for the high ionization absorber they are anticorrelated. indicating a certain degree of degeneracy in the model.," For the low ionization absorber the two parameters are almost uncorrelated, while for the high ionization absorber they are anticorrelated, indicating a certain degree of degeneracy in the model." + The usual check with the RGS is then performed., The usual check with the RGS is then performed. + Fits are better than those obtained with the full absorbers. reflecting the same improvement found ii the EPIC-pn spectrum.," Fits are better than those obtained with the full absorbers, reflecting the same improvement found in the EPIC-pn spectrum." + With all parameters fixed. a y/d.o.f.2821.6/679 is found. while letting the parameters free to vary. a y-/d.o.f.=752.0/670 is found.," With all parameters fixed, a $\chi^2$ /d.o.f.=821.6/679 is found, while letting the parameters free to vary, a $\chi^2$ /d.o.f.=752.0/670 is found." + The best fit parameters are consistent within the errors with those found in the EPIC-pn analysis., The best fit parameters are consistent within the errors with those found in the EPIC-pn analysis. + The spectrum and data/model ratio can be seen in Fig. 10.., The spectrum and data/model ratio can be seen in Fig. \ref{rgsobs2}. + Finally. no significant inflow/outHow velocity is found for the high ionization. absorber (upper limits of a few hundreds km/s). while for the low ionization absorber a marginally significant inflow velocity of 5804340 kni/s is obtained (Table 3)).," Finally, no significant inflow/outflow velocity is found for the high ionization absorber (upper limits of a few hundreds km/s), while for the low ionization absorber a marginally significant inflow velocity of $\pm$ 340 km/s is obtained (Table \ref{t_vel}) )." +" For the second observation. the 0.5-2 (2-10) keV observed flux is 7.62(11.2)x1077. erg em"" s7!. corresponding to a 0.5-2 (2-10) keV luminosity of 2.3442.26)x 10 erg s. after correction for absorption."," For the second observation, the 0.5-2 (2-10) keV observed flux is $\times$ $^{- 12}$ erg $^{- 2}$ $^{-1}$ corresponding to a 0.5-2 (2-10) keV luminosity of $\times$ $^{43}$ erg $^{-1}$, after correction for absorption." + During the revision of the present work. we became aware of a paper by Laha et al. (," During the revision of the present work, we became aware of a paper by Laha et al. (" +2011) dealing with the analysis of the second AM-Newron observation of Mrk 704.,2011) dealing with the analysis of the second $Newton$ observation of Mrk 704. + The results of their analysis are qualitatively similar to ours. the quantitativedifferences probably mostly related to the somewhat different spectral nodel ," The results of their analysis are qualitatively similar to ours, the quantitativedifferences probably mostly related to the somewhat different spectral model ." +The most important qualitative difference is that Laha et al., The most important qualitative difference is that Laha et al. + found the two warm absorbers both outflowing.while in our analysis no significant inflow/outtlow," found the two warm absorbers both outflowing,while in our analysis no significant inflow/outflow" +IRAM 3012 telescope.,IRAM 30m telescope. + This map has already beeu masked we? and so contains ouly positive signal.," This map has already been masked by \citet{NIETEN06} + and so contains only positive signal." + We trace musing the 210m map of ?.. obtained with the Westerbork Svuthesis Radio Telescope (WSRT).," We trace using the 21cm map of \citet{BRINKS84}, obtained with the Westerbork Synthesis Radio Telescope (WSRT)." + ?. preseut.Spitzer naps at 21. 70. and 16072. For M 33. wetake CO data from ?.. which combines DINA (?) and FCRAO data (2)..," \citet{GORDON06} present maps at 24, 70, and $\mu$ m. For M 33, wetake CO data from \citet{ROSOLOWSKY07B}, which combines BIMA \citep{ENGARGIOLA03} and FCRAO data \citep{HEYER04}. ." + We use the WSRT nap by ον We use, We use the WSRT map by \citet{DEUL87}. + Spitzer data reduced following ? and xeseuted bv Ὁ aud ?.., We use data reduced following \citet{GORDON05} and presented by \citet{VERLEY07} and \citet{TABATABAEI07}. + We use the first CO map of the LMC obtained by NANTEN (?).. the Australia Telescope Compact Array (ATCA) | Parkes nunap of ??.. aud IR maps from theSpitzer SAGE legacy program (?7)..," We use the first CO map of the LMC obtained by NANTEN \citep{FUKUI99}, the Australia Telescope Compact Array (ATCA) + Parkes map of \citet{KIM98,KIM03}, and IR maps from the SAGE legacy program \citep{MEIXNER06,BERNARD08}." + We also use the NANTEN CO map of the SAIC (?).. the ATCA | Parkes uuuap bv ?..," We also use the NANTEN CO map of the SMC \citep{MIZUNO01}, the ATCA + Parkes map by \citet{STANIMIROVIC99}." + The SAIC IR maps are a combination of data from the SACE-SAIC legacy program aud the S3MC survey (?)..," The SMC IR maps are a combination of data from the SAGE-SMC legacy program \citet[][and in + prep.]{GORDON09} and the S3MC survey \citep{BOLATTO07}. ." +" For NGC 6822, we use the IRAM 3011. CO map by ?.. the SINGSSpitzer ups presented by ον, and the VEA nunap of ?.."," For NGC 6822, we use the IRAM 30m CO map by \citet{GRATIER10}, the SINGS maps presented by \citet{CANNON06}, and the VLA map of \citet{DEBLOK03}." + 7 mapped the CO 7—5>1 line for this ealaxy. while the rest of our maps are of CO J=1>0.," \citet{GRATIER10} mapped the CO $J=2\rightarrow1$ line for this galaxy, while the rest of our maps are of CO $J=1\rightarrow0$." + We follow ? iu assumune a line ratio of 0.7: we phrase all of our results in terms of CO J=1>0 intensity assunine this ratio., We follow \citet{GRATIER10} in assuming a line ratio of $0.7$ ; we phrase all of our results in terms of CO $J=1\rightarrow0$ intensity assuming this ratio. +" We mask the CO map. keeping ouly cluission above ~39 at the orieiual 15"" resolution."," We mask the CO map, keeping only emission above $\sim 3\sigma$ at the original $\arcsec$ resolution." + For cach galaxy we convolve all data to the resolution of the coarsest data set and align them on a common astrometric erid., For each galaxy we convolve all data to the resolution of the coarsest data set and align them on a common astrometric grid. + In M 31. AD 33. aud NCC 6822 we aro limited by the resolution of theSpitzer 160 pau data and so convolve all data to have a 15” (FWIIMD) Gaussian PSF.," In M 31, M 33, and NGC 6822 we are limited by the resolution of the 160 $\mu$ m data and so convolve all data to have a $45\arcsec$ (FWHM) Gaussian PSF." + Iu the LAIC the NANTEN CO data limit our resolution to >24.6: because sigual-to-noise iu the CO map is also a concern. we convolve all data to [/ resolution.," In the LMC the NANTEN CO data limit our resolution to $> +2\arcmin .6$; because signal-to-noise in the CO map is also a concern, we convolve all data to $4\arcmin$ resolution." + The NANTEN CO data also set the resolution in the SAIC’. where we couvolve all data to 2/.6 resolution.," The NANTEN CO data also set the resolution in the SMC, where we convolve all data to $2\arcmin +.6$ resolution." + Iu the LMC and SAIC we subtract a foreground from the IR maps., In the LMC and SMC we subtract a foreground from the IR maps. + Following ?.. we remove a scaled version of theMilkv Way oover these lines of sight (fortheexactapproachsee?)..," Following \citet{BOT04}, we remove a scaled version of theMilky Way over these lines of sight \citep[for the exact approach + see][]{LEROY09}." + Iu M 33 and M 31 the reduction imposes the coucdition that the intensity is 0 away from the galaxy. making a cimus subtraction uuuecessarv.," In M 33 and M 31 the reduction imposes the condition that the intensity is 0 away from the galaxy, making a cirrus subtraction unnecessary." +" Iu NGC 6822, ο already removed a Galactic foreground."," In NGC 6822, \citet{CANNON06} already removed a Galactic foreground." +" The statistical uncertainty in the CÓ maps is about 0.30 I& lau s| im M 31. 0.35 K lan | in AL 33. 0.30 I gn Fin the LMC. 0.01 I lan + in NGC 6822, and 0.08 I lau s.+ in the SMC (though in each case this varies somewhat with position)."," The statistical uncertainty in the CO maps is about $0.30$ K km $^{-1}$ in M 31, $0.35$ K km $^{-1}$ in M 33, $0.30$ K km $^{-1}$ in the LMC, $0.01$ K km $^{-1}$ in NGC 6822, and $0.08$ K km $^{-1}$ in the SMC (though in each case this varies somewhat with position)." + The statistical noise im the luuaps is vorv roughly M. 2 with the uncertainty dominated by iuperfect knowledge of the oopacitv aud the recoustruction of extended emission., The statistical noise in the maps is very roughly $1$ $3$ $_\odot$ $^{-2}$ with the uncertainty dominated by imperfect knowledge of the opacity and the reconstruction of extended emission. + The noie in the IR maps is ~0.2 My. | at TOpuu and ~0.7 MEE at 160¢an. The zero point iu the TR iaps is uncertain by ~0. δν | at 7Opan aud —0.5 My boat 160;on. Throughout this paper IR intensity has units of ALJy +. color-corrected to the IRAS scale.," The noise in the IR maps is $\sim +0.2$ MJy $^{-1}$ at $\mu$ m and $\sim 0.7$ MJy $^{-1}$ at $\mu$ m. The zero point in the IR maps is uncertain by $\sim +0.1$ MJy $^{-1}$ at $\mu$ m and $\sim 0.5$ MJy $^{-1}$ at $\mu$ m. Throughout this paper IR intensity has units of MJy $^{-1}$, color-corrected to the IRAS scale." + ssurface deusity has units of AL. pe7? aud includes a factor of 1.36 to account for helium., surface density has units of $_\odot$ $^{-2}$ and includes a factor of 1.36 to account for helium. + In the SAIC aud the LMC. includes an opacity correction based on ?..," In the SMC and the LMC, includes an opacity correction based on \citet{DICKEY00}." + Tn M 01. AD 33. and NCC 6822 we have assiuned that the iis optically thin.," In M 31, M 33, and NGC 6822 we have assumed that the is optically thin." + CO 7=1.>0 intensity has units of K laus b andis related to surface density. ii units of M. 7. by a factor aco that includes hei (so that “yo=ocodeo): M 2107 tthen aco=LLAL.," CO $J=1\rightarrow0$ intensity has units of K km $^{-1}$ and is related to surface density, in units of $_\odot$ $^{-2}$, by a factor $\alpha_{\rm CO}$ that includes helium (so that $\Sigma_{\rm H2} = \alpha_{\rm CO} I_{\rm + CO}$ ); if $\xco = 2 \times 10^{20}$ then $\alpha_{\rm CO} += 4.4$." +i Ow goal is to ideutifv regions where both aud ccontribute siguificauth to the interstellar imnediuu (ISMD. use the IR intensity in these regions to estimate the dust ΠΠ and then harness the assumption that eas and dust are linearly related to solve for eco.," Our goal is to identify regions where both and contribute significantly to the interstellar medium (ISM), use the IR intensity in these regions to estimate the dust column, and then harness the assumption that gas and dust are linearly related to solve for $\alpha_{\rm CO}$." + This experuucut leverages our knowledge of ccohuun to infer ace., This experiment leverages our knowledge of column to infer $\alpha_{\rm CO}$. + It thus works best in regions where both aan aare nuportaut to the ISAL mass budeet., It thus works best in regions where both and are important to the ISM mass budget. +If we tarect areas where dadomiuates then oco has little or no impact ou δρ while if we target areas with only tthen oco and cpi are degcucrate.,If we target areas where dominates then $\alpha_{\rm CO}$ has little or no impact on $\delta_{\rm GDR}$ while if we target areas with only then $\alpha_{\rm CO}$ and $\delta_{\rm GDR}$ are degenerate. + For our targets aud resolution. beige dominated by lis not a concern for anv reasonable ace.," For our targets and resolution, being dominated by is not a concern for any reasonable $\alpha_{\rm CO}$." + Ou the other hand each target has large areas where the ISM is overwheluunely., On the other hand each target has large areas where the ISM is overwhelmingly. + Especially in M 231 and M33. much of the jis at Luge radius and appears to have a differcut δρ from the immer galaxy. (?)..," Especially in M 31 and M33, much of the is at large radius and appears to have a different $\delta_{\rm GDR}$ from the inner galaxy \citep[][]{NIETEN06}." + We mostly avoid these Ibouly regions. instead targetius the part of each galaxy near where CO is detected.," We mostly avoid these -only regions, instead targeting the part of each galaxy near where CO is detected." + This gives us a range of total eas surface deusities aud relative contributions bv aand IDL. allowing us to constrain oco aud dcp.," This gives us a range of total gas surface densities and relative contributions by and , allowing us to constrain $\alpha_{\rm CO}$ and $\delta_{\rm GDR}$." +" We define our target region bv à z30 imteusitv cut in the convolved CO map. feo71 K lun + in M 3. AD 33. and the LMC. Zec0.25 K kn ! in the SAIC. and [ουZ20.03 IK lm 3 in NGC 6822,"," We define our target region by a $\approx 3\sigma$ intensity cut in the convolved CO map, $I_{\rm CO} \geq 1$ K km $^{-1}$ in M 31, M 33, and the LMC, $I_{\rm CO} \geq 0.25$ K km $^{-1}$ in the SMC, and $I_{\rm CO} \geq 0.03$ K km $^{-1}$ in NGC 6822." + We reject sinall regions (area Sa resolution clement} as likely noise spikes aud then cousider all area within about l resolutiou element of the remaining cussion., We reject small regions (area $\lesssim$ a resolution element) as likely noise spikes and then consider all area within about $1$ resolution element of the remaining emission. +" Finally. we require a line of sight to have significant IR. cuissiou to be included: this is Πω=5 MJy 1 in NGC 6822, Iu)10 MJy | in all other targets."," Finally, we require a line of sight to have significant IR emission to be included; this is $I_{160} \geq +5$ MJy $^{-1}$ in NGC 6822, $I_{160} \geq 10$ MJy $^{-1}$ in all other targets." + The result reselmhles loosely circling bright CO emission by haud., The result resembles loosely circling bright CO emission by hand. + Figure dl shows the target reeious in coutour ou top of the 160722 may., Figure \ref{fig:sampling} shows the target regions in contour on top of the $\mu$ m map. + Tn M 31. 4033. and the SAIC treating the whole galaxy at once causes problems with our model. which assumes a constantace and ócppg across the area studied.," In M 31, M 33, and the SMC treating the whole galaxy at once causes problems with our model, which assumes a constant$\alpha_{\rm CO}$ and $\delta_{\rm GDR}$ across the area studied." + Previous work arrived at suniblu conclusious., Previous work arrived at similar conclusions. + ?| observed ócpg to be higher iu the iuner part of MN 21 than the 10 Ipc ring coutaining most of the CO., \citet{NIETEN06} observed $\delta_{\rm GDR}$ to be higher in the inner part of M 31 than the 10 kpc ring containing most of the CO. + Tn N32. bright CO exteuds a fair distance out mto the disk. but based ou radial profiles of L. CO. aud E60722 intensity it isΠουμαο] clear that this galaxy. too. has a stroug radial gracdieut in ócppg.," In M 33, bright CO extends a fair distance out into the disk, but based on radial profiles of , CO, and $160\mu$ m intensity it isimmediately clear that this galaxy, too, has a strong radial gradient in $\delta_{\rm GDR}$ ." + Phe SAIC’s COemissiou is clusterediuto thee distinct regions that show evidence forlocal variations iu their depr. Aco. and giant molecular cloud. (ΝΤΟ) properties (2? )..," The SMC's COemission is clusteredinto three distinct regions that show evidence forlocal variations in their $\delta_{\rm GDR}$ , $\alpha_{\rm CO}$ , and giant molecular cloud (GMC) properties \citep{LEROY07,MUELLER10}. ." +"For independent validation of our method and to investigate the impact of the new reduction, we screened the literature for objects for which a similar analysis was performed.","For independent validation of our method and to investigate the impact of the new reduction, we screened the literature for objects for which a similar analysis was performed." +" We chose the three stars6046,,1069,, and with companions found by ?,, ?,, and ??.,, respectively, and exhibiting diverse orbit inclinations and companion masses."," We chose the three stars, and with companions found by \cite{Torres:2007kx}, , \cite{Halbwachs:2000rt}, , and \cite{Zucker:2001ve}, respectively, and exhibiting diverse orbit inclinations and companion masses." +" All these works use the original IAD, whereas we use the new reduction IAD."," All these works use the original IAD, whereas we use the new reduction IAD." +" For all three stars, good agreement is found between our results and the published works, both in terms of value and 1-c uncertainty of semimajor axis and companion mass, as is shown in Table 6.."," For all three stars, good agreement is found between our results and the published works, both in terms of value and $\sigma$ uncertainty of semimajor axis and companion mass, as is shown in Table \ref{tab:compResults}." + Also the orbit significances derived from pseudo-orbits given by ? for two objects match our results., Also the orbit significances derived from pseudo-orbits given by \cite{Zucker:2001ve} for two objects match our results. +" For190228,, we find the same solution as ? and a 2-c significance (see Sect."," For, we find the same solution as \cite{Zucker:2001ve} and a $\sigma$ significance (see Sect." + ?? for further discussion of this object)., \ref{sec:2sresults} for further discussion of this object). +" We confirm the detection of the orbit, caused by a low mass star (??),, and the binary orbit of (?) at better than 3-σ significance."," We confirm the detection of the orbit, caused by a low mass star \citep{Zucker:2001ve, Halbwachs:2000rt}, and the binary orbit of \citep{Torres:2007kx} at better than $\sigma$ significance." +" Especially the case of1069,, that is now analysed by three independent teams finding essentially identical results, attests that our analysis is Both the simulation results and the analysis of a sample of comparison stars confirm that our method for the combined analysis of radial-velocity orbits and Hipparcos astrometry is correct."," Especially the case of, that is now analysed by three independent teams finding essentially identical results, attests that our analysis is Both the simulation results and the analysis of a sample of comparison stars confirm that our method for the combined analysis of radial-velocity orbits and Hipparcos astrometry is correct." + The consideration of the orbit significance ensures that the derived resultisbias-free to reasonable extent., The consideration of the orbit significance ensures that the derived resultisbias-free to reasonable extent. +robust to errors in flux calibration and dust extinction.,robust to errors in flux calibration and dust extinction. +" However, in the case of 55, their use is possibly compromised by the awkward redshifted wavelengths of Ho and the A46550,6585 doublet which fall between the J and H bands, as already explained."," However, in the case of 5, their use is possibly compromised by the awkward redshifted wavelengths of $\alpha$ and the $\lambda \lambda 6550, 6585$ doublet which fall between the $J$ and $H$ bands, as already explained." +" We deduce 12+ from consideration of the ratio N2=log[F(6585)/F(Ho)], and 12+log(O/H)o3n.8.29+0.04 from the ratio O3N2=log[F(5008)/F(H8)]—log[F(6585)/F(H )]|, using in both cases the calibrations of these indices deduced by ?.."," We deduce $12 + +\log{\rm (O/H)}_{\rm N2} = 8.47 \pm 0.07$ from consideration of the ratio $N2 \equiv \log [F(6585)/F(H\alpha)]$, and $12 + \log{\rm + (O/H)}_{\rm O3N2} = 8.29 \pm 0.04$ from the ratio $O3N2 \equiv \log +[F(5008)/F(H\beta)] - \log [F(6585)/F(H\alpha)]$ , using in both cases the calibrations of these indices deduced by \citet{pettini04}." +" Again, the random errors quoted are small compared to the 0.2—0.3 dex systematic uncertainties of the calibrations."," Again, the random errors quoted are small compared to the 0.2–0.3 dex systematic uncertainties of the calibrations." +" We conclude thatthe oxygen abundance in the lensed galaxy in CSWA5S is 12+log(O/H)= 8.3-8.5, or (O/H)cswA52 0.40.65(O/H),."," We conclude thatthe oxygen abundance in the lensed galaxy in 5 is $12+ \log {\rm + (O/H)} = 8.3$ –8.5, or $_{\rm CSWA\,5} \simeq 0.4$ $0.65 \, +{\rm (O/H)}_\odot$." +" In the absence of temperature-sensitive auroral lines, we make use of the method developed by ? to deduce the relative abundances of N and O. These authors used photoionization models to deduce a relationship between the textscii]] temperature and the R23 index; in our case, +1000 KK. Once the textscii]] temperature is known, the N/O ratio can be deduced directly from the ratio of the AA6550,6585 and AA3728,3730 doublets (?),, under the assumption that N*/O* cNN/O which ? argue introduces only a small error."," In the absence of temperature-sensitive auroral lines, we make use of the method developed by \citet{thurston96} to deduce the relative abundances of N and O. These authors used photoionization models to deduce a relationship between the ] temperature and the $R23$ index; in our case, $t_{[N\,\textsc{ii}]} = 11\,000 \pm +1000$ K. Once the ] temperature is known, the N/O ratio can be deduced directly from the ratio of the $\lambda \lambda 6550, 6585$ and $\lambda \lambda 3728, 3730$ doublets \citep{pagel92}, under the assumption that $^+$ $^+ \simeq$ N/O which \citet{thurston96} argue introduces only a small error." +" Following this procedure, we find log(N/O)agya;=—0.95+0.10 or ~80% of the solar value log(N/O),=—0.86 (?).."," Following this procedure, we find $\log {\rm (N/O)}_{\rm CSWA\,5} = +-0.95 \pm 0.10$ or $\sim 80$ of the solar value $\log {\rm + (N/O)}_\odot = -0.86$ \citep{asplund09}." + A slightly subsolar N/O ratio when the abundance of oxygen is ~0.5 solar is in line with the large body of such measurements now available in galaxies at a range of redshifts (e.g. ??)..," A slightly subsolar N/O ratio when the abundance of oxygen is $\sim 0.5$ solar is in line with the large body of such measurements now available in galaxies at a range of redshifts \citep[e.g.][]{izotov06, pettini08b}. ." +" In the low density limit, the ratio Ct?/O*? can be deduced from the measured fluxes of the AA1907,1909 and AA4960,5008 doublets and a knowledge of the relevant"," In the low density limit, the ratio $^{+2}$ $^{+2}$ can be deduced from the measured fluxes of the $\lambda \lambda 1907, 1909$ and $\lambda \lambda 4960, 5008$ doublets and a knowledge of the relevant" +"temperature (kT~ 0.75kkeV) found by Loewenstein (1994) was most likely a result of the large radius (3) aperture used, due to the ASCA point spread function, that extended well beyond the effective radius of NGC 1404.","temperature $kT \sim 0.75$ keV) found by Loewenstein (1994) was most likely a result of the large radius $3'$ ) aperture used, due to the ASCA point spread function, that extended well beyond the effective radius of NGC 1404." +" With the much better ROSAT PSPC resolution, Jones (1997) found an asymmetric surface brightness distribution strongly suggesting that NGC 1404 was undergoing ram pressure stripping."," With the much better ROSAT PSPC resolution, Jones (1997) found an asymmetric surface brightness distribution strongly suggesting that NGC 1404 was undergoing ram pressure stripping." +" Also using ROSAT PSPC data, Paolillo (2002) measured the surface brightness asymmetry between the leading (northwest) sector and trailing (southeast) sector of NGC 1404, showing the steep gradient in the surface brightness in the northwest sector at r~90"" (8kkpc); while O'Sullivan (2003) observed a temperature jump for r>2’, across the leading edge of the galaxy and the surrounding Fornax ICM."," Also using ROSAT PSPC data, Paolillo (2002) measured the surface brightness asymmetry between the leading (northwest) sector and trailing (southeast) sector of NGC 1404, showing the steep gradient in the surface brightness in the northwest sector at $r \sim 90''$ $8$ kpc); while O'Sullivan (2003) observed a temperature jump for $r > 2'$, across the leading edge of the galaxy and the surrounding Fornax ICM." +" In Figure 1 we present the 0.3— 2kkeV coadded image from three Chandra observations, totalling 134.3 kks, (detailed in Section 2)) of NGC 1404 falling into the dominant cluster elliptical NGC 1399 (left panel)."," In Figure \ref{fig:fornax} we present the $0.3-2$ keV coadded image from three Chandra observations, totalling $134.3$ ks, (detailed in Section \ref{sec:obs}) ) of NGC 1404 falling into the dominant cluster elliptical NGC 1399 (left panel)." + For comparison we also show the Digitized Sky Survey optical image matched in WCS coordinates (right panel)., For comparison we also show the Digitized Sky Survey optical image matched in WCS coordinates (right panel). + NGC 1399 is located in the northwest (upper right) corner of each panel; while the bright elliptical NGC 1404 is located ~54 kkpc (9’.8) in the plane of the sky to the southeast (lower left corner)., NGC 1399 is located in the northwest (upper right) corner of each panel; while the bright elliptical NGC 1404 is located $\sim 54$ kpc $9'.8$ ) in the plane of the sky to the southeast (lower left corner). + The X-ray images have been individually background subtracted and corrected for telescope vignetting and spatial efficiency variations by means of exposure maps generated with standard CIAO tools assuming a fixed spectral energy of 0.9kkeV. We clearly see the sharp edge in the surface brightness on the northwest side of NGC 1404 (in the direction of, The X-ray images have been individually background subtracted and corrected for telescope vignetting and spatial efficiency variations by means of exposure maps generated with standard CIAO tools assuming a fixed spectral energy of $0.9$ keV. We clearly see the sharp edge in the surface brightness on the northwest side of NGC 1404 (in the direction of +Sackett et al. (LOOL..,"Sackett et al. \cite{Sackett}," + hereafter SMIID) have fouud that the edeeon spira ealaxy 55907 is surrounded by a faint alo iu the optical R baud., hereafter SMHB) have found that the edge–on spiral galaxy 5907 is surrounded by a faint halo in the optical R band. + The existence of this halo las con confined bv several authors at other wavelengths., The existence of this halo has been confirmed by several authors at other wavelengths. + Lequeux ct al. (1996..," Lequeux et al. \cite{PaperI}," + hereafter Paper I). have observed iis halo iu. two other bands. V and I. aud sugeest that it )ocomies redder at increasing distances from the plane of 16 galaxy.," hereafter Paper I), have observed this halo in two other bands, V and I, and suggest that it becomes redder at increasing distances from the plane of the galaxy." + Rudy et al. (1997)), Rudy et al. \cite{Rudy}) ) + and James Casali (1996)) rave also cletectec the halo iu J aud Is: the combination of reir brightuesses with those of SMIID aud of Paper I gives results difficult to uuderstaud., and James Casali \cite{James}) ) have also detected the halo in J and K; the combination of their brightnesses with those of SMHB and of Paper I gives results difficult to understand. + The halo of 55907 is clearly stellar ium origin mt its nature is still uukuoxu., The halo of 5907 is clearly stellar in origin but its nature is still unknown. + Its relatively ved V-I color implies either a normal. metal-rich. old stellar population. or if the stars are metal-poor an initial mass functiou favoring extremely low masses (see discussion in Paper D.," Its relatively red V-I color implies either a normal, metal-rich, old stellar population, or if the stars are metal-poor an initial mass function favoring extremely low masses (see discussion in Paper I)." + The observatious being verv difficult because of the faintness of the halo. we decided to perform new observations. described in Sect.," The observations being very difficult because of the faintness of the halo, we decided to perform new observations, described in Sect." + 2 aud 3., 2 and 3. + To interpret them. Sect.," To interpret them, Sect." + 1 proposes a scenario in which NGC 5007 las encountered aud cammibalized a snall elliptical ealaxy about 2 Cir ago., 4 proposes a scenario in which NGC 5907 has encountered and cannibalized a small elliptical galaxy about 2 Gyr ago. + Al the observatious have heen obtained with the Canacian-Franuce-Tawaii Telescope., All the observations have been obtained with the Canadian-France-Hawaii Telescope. + The V aud I observations were made in a single photometric night aud used he UII Sk mosaic of CCD at the prime focus., The V and I observations were made in a single photometric night and used the UH 8k mosaic of CCD at the prime focus. + This calucra being insensitive in the blue. the D. observations were performed durius another night with the MOS instrunnent at the Casseerain focus. equiped with the STIS-2 «2018 pixel CCD camera.," This camera being insensitive in the blue, the B observations were performed during another night with the MOS instrument at the Cassegrain focus, equiped with the STIS-2 $\times$ 2048 pixel CCD camera." + The UID Sk mosaic is made of cight 20Lx1096 pixe CCDs arranged o formu a square., The UH 8k mosaic is made of eight 2048x4096 pixel CCDs arranged to form a square. + The scale is 0.206 are second per pixel of 15 jan. but the pixels were binue« so that the final pixels are of 0.112 arc second.," The scale is 0.206 arc second per pixel of 15 $\mu$ m, but the pixels were binned so that the final pixels are of 0.412 arc second." + We use a positionswitch observing mode in order to hit the effects of the changes in the sky background., We used a position–switch observing mode in order to limit the effects of the changes in the sky background. + The image of the ealaxy was ceutered parallel to the longer side of oue of the CCDs ταις half of the exposures. aud ove to the parallel CCD diving the other half.," The image of the galaxy was centered parallel to the longer side of one of the CCDs during half of the exposures, and moved to the parallel CCD during the other half." + Consequently. ouly two of he eight CCDs were used but the field covere by each of them (LIs 7) was sufficient for our purpose.," Consequently, only two of the eight CCDs were used but the field covered by each of them $14\arcmin\times7\arcmin$ ) was sufficient for our purpose." + When the galaxy is unaeged on one CCD. the other CCD is used for defining the flat field used to reduce the images obtained in the alternative situation.," When the galaxy is imaged on one CCD, the other CCD is used for defining the flat field used to reduce the images obtained in the alternative situation." +" We obtained iu eac[um of the V. aud Ie,,5;,; baud 9 frames of [80 s each at one position alternating with 9 similar frames at the other position.", We obtained in each of the V and $_{Cousins}$ band 9 frames of 480 s each at one position alternating with 9 similar frames at the other position. + The frames at a given position were take- with slight shifts with respect to cach other in order te allow clinunation of the spurious eveuts through a mecia- stacking of the nuages., The frames at a given position were taken with slight shifts with respect to each other in order to allow elimination of the spurious events through a median stacking of the images. + The fiat fields obtained im thiρα wav were of excellent quality and we noticed a significant reduction of the largescale backeround ireeularitics 1- the fal inages with respect to the observations of Paper IL This cau be attributed to a partial cancellation of the diffuse light bv our positionswitch technique., The flat fields obtained in this way were of excellent quality and we noticed a significant reduction of the large–scale background irregularities in the final images with respect to the observations of Paper I. This can be attributed to a partial cancellation of the diffuse light by our position–switch technique. + The data were calibrated using reference stars in SA 110 (Laucolt 1992))., The data were calibrated using reference stars in SA 110 (Landolt \cite{Landolt}) ). + The photometric error is of the order of 0.03 magnitude iu each baud., The photometric error is of the order of 0.03 magnitude in each band. + The sky levels measured on Qur framefa were Αν21.13led Alleand 19.22ελ” in V alicaud I respectively. in excelleut agreement with the mean values for photometric nights at Mana Ikea.," The sky levels measured on our frame were 21.43 and 19.22 $^{-2}$ in V and I respectively, in excellent agreement with the mean values for photometric nights at Mauna Kea." +this class of galaxies are now relatively well-established.,this class of galaxies are now relatively well-established. + In particular. interacting processes are widely believed. to play a pivotal role in triggering the LR excess. not only in the local Universe (Sanders Alirabel 1996 ancl references therein) but also at moderately high redshift (Smail 1908).," In particular, interacting processes are widely believed to play a pivotal role in triggering the IR excess, not only in the local Universe (Sanders Mirabel 1996 and references therein) but also at moderately high redshift (Smail 1998)." + While a contribution to the Ilt output. can arisebolh from a dust-enshrouded active galactic nucleus (AGN) and from a (generally. cireumnuclear) starburst. there. is garong evidence from optical or micl-L spectroscopy [or an increasing fraction of objects with ACN-Iike characteristics when progressing toward higher luminosities (e.g.. Lutz 1998: Veilleux. Sanders. Ixim 1999).," While a contribution to the IR output can arise from a dust-enshrouded active galactic nucleus (AGN) and from a (generally circumnuclear) starburst, there is strong evidence from optical or mid-IR spectroscopy for an increasing fraction of objects with AGN-like characteristics when progressing toward higher luminosities (e.g., Lutz 1998; Veilleux, Sanders, Kim 1999)." + Of particular relevance for a better understanding of this important. population are the objects at the upper end of the luminosity distribution (the so-called. hyperluminous infrared galaxies: hereafter H£ their luminosities are starburst-dominated. they are potentially forming the bulk of their stellar population in a single. violent. cpisocle.," Of particular relevance for a better understanding of this important population are the objects at the upper end of the luminosity distribution (the so-called hyperluminous infrared galaxies; hereafter If their luminosities are starburst-dominated, they are potentially forming the bulk of their stellar population in a single, violent episode." + This makes them an interesting sub-population of galaxies. but work so far is severely hampered by inhomogenous and/or AXGN-biased. selection.," This makes them an interesting sub-population of galaxies, but work so far is severely hampered by inhomogenous and/or AGN-biased selection." + Only 13 LIvLIGs are known at present. from far-L or sub-nim surveys. and a further 12 from cross-corrclating fer-LR source Lists with AGN catalogues (Itowan-Itobinson 2000: hereafter RR).," Only 13 HyLIGs are known at present from far-IR or sub-mm surveys, and a further 12 from cross-correlating far-IR source lists with AGN catalogues (Rowan-Robinson 2000; hereafter RR)." + In regard of the exceedingly small space density of IIvbl(s (van der Werf 1999: RR). only major extragalactic LR surveys offer. good prospects to uncover new candidates.," In regard of the exceedingly small space density of HyLIGs (van der Werf 1999; RR), only major extragalactic IR surveys offer good prospects to uncover new candidates." + OF particular interest. in this respect is he European Large Area Survey (191ΛΙ) which was conducted. over = 11 square degrees at 15 and 90 (down to z 3 mJv and zc 100 m.s. respectively) ancl over 6 square degrees at 6.7 (down to z 1 mJy).," Of particular interest in this respect is the European Large Area Survey (ELAIS) which was conducted over $\approx$ 11 square degrees at 15 and 90 (down to $\approx$ 3 mJy and $\approx$ 100 mJy, respectively) and over 6 square degrees at 6.7 (down to $\approx$ 1 mJy)." + We refer rw reader to Oliver (2000: Paper 1) for a complete escription of this project., We refer the reader to Oliver (2000; Paper I) for a complete description of this project. + Details on the technical aspects of 10 CAM and PLOT observations can be found in Serjeant (2000: Paper LL) ancl Efstathiou (20002: Paper LLL). respectively.," Details on the technical aspects of the CAM and PHOT observations can be found in Serjeant (2000; Paper II) and Efstathiou (2000a; Paper III), respectively." + Assuming pure luminosity evolution ofthe orm: (1 | 2)3 (Bovle. Shanks. Peterson 1988: Saunders 1990). we estimate that about 3 IIvLIGs might. be detected in the total area covered by ELALIS.," Assuming pure luminosity evolution of the form: (1 + $^{3.1}$ (Boyle, Shanks, Peterson 1988; Saunders 1990), we estimate that about 3 HyLIGs might be detected in the total area covered by ELAIS." + This estimate is considerably uncertain. as itis strongly dependent on the spectral energy. distribution (SED) and evolutionary. moclel assumed.," This estimate is considerably uncertain, as it is strongly dependent on the spectral energy distribution (SED) and evolutionary model assumed." + As we can safely rule out no-evolution. mocdeLg however. we find that the formal signilicance of detecting one object is very high (zz 3590).," As we can safely rule out no-evolution models, however, we find that the formal significance of detecting one object is very high $\approx$ $\sigma$ )." + We report in this paper on the discovery of such à candidate HvLIG in the ELAIS N2 region., We report in this paper on the discovery of such a candidate HyLIG in the ELAIS N2 region. + This new HsLIG was discovered as part of a study aiming ab studying the Ht colour. properties of ELALS ealaxies (Morel 2001)., This new HyLIG was discovered as part of a study aiming at studying the IR colour properties of ELAIS galaxies (Morel 2001). + Ehe procedure used to isolate galaxies potentially detected. at 6.7. 15. ancl 90 was to cross- the CAM. and. PHOT. source lists using a 35 association radius.," The procedure used to isolate galaxies potentially detected at 6.7, 15, and 90 was to cross-correlate the CAM and PHOT source lists using a $''$ association radius." + Details on the production of the ςΑΔ and PHOT. catalogues can be found. in. Paper LL and Iérraudeau (2001). respectively.," Details on the production of the CAM and PHOT catalogues can be found in Paper II and Hérraudeau (2001), respectively." + Figure 1 shows the PHOT. error circle of the HINLIC 4310502:: hereafter 41)) overlavecl on a deep (down to 7 2 24) optical image., Figure 1 shows the PHOT error circle of the HyLIG ; hereafter ) overlayed on a deep (down to ' $\approx$ 24) optical image. + The CAM error circles are also shown., The CAM error circles are also shown. +" The only obvious optical counterpart to the sources is found to be a point-like object at: à = 1640 10.16"" and 8 = 41°05/22.3” (J2000).", The only obvious optical counterpart to the sources is found to be a point-like object at: $\alpha$ = $^{\rm h}$ $^{\rm m}$ $^{\rm s}$ and $\delta$ = $^{\circ}$ $'$ $''$ (J2000). + This source is. within the uncertainties. spatially coincident with an optically-selected quasar at a quoted ομμ of 1.007 (CCSSS]. 163831.4|411107: Crampton 1988).," This source is, within the uncertainties, spatially coincident with an optically-selected quasar at a quoted redshift of 1.097 ([CCS88] 163831.4+411107; Crampton 1988)." + As can be seen in Fig.l. a bright optical source (as well as à number of much fainter ones) appear to lie in close vicinity. of the quasar.," As can be seen in Fig.1, a bright optical source (as well as a number of much fainter ones) appear to lie in close vicinity of the quasar." + Since no redshifts are available for these objects. it is unclear at this stage whether they are physically associated with the new Εν.," Since no redshifts are available for these objects, it is unclear at this stage whether they are physically associated with the new HyLIG." + We used the quasar {ρα source counts of Wisotzki (2000) to estimate the number of random PLHOT-quasar associations in our sample at B= 17.2 mag (see Table 2). or brighter.," We used the quasar -band source counts of Wisotzki (2000) to estimate the number of random PHOT-quasar associations in our sample at = 17.2 mag (see Table 2), or brighter." + The expected total number of random associations in thesearch radius is only 0.011 for the 285 PLIOT sources., The expected total number of random associations in thesearch radius is only 0.011 for the 285 PHOT sources. +We make an elementary. model of a nearly circular lens(cL... Blandford. Ixovner. LOSS: Schneider. Ehlers Faleo 1992: Blandford Llogg 1996).,"We make an elementary model of a nearly circular lens, Blandford Kovner 1988; Schneider, Ehlers Falco 1992; Blandford Hogg 1996)." + Let the scaled surface potential in the vicinity of the Einstein ring be written where r ids measured in units of the unperturbed Einstein ring radius. so that f/(1)= 1. and g(r) is a perturbation which measures the cllipticity in the potential and its racial variation.," Let the scaled surface potential in the vicinity of the Einstein ring be written where $r$ is measured in units of the unperturbed Einstein ring radius, so that $f'(1)=1$ , and $g(r)$ is a perturbation which measures the ellipticity in the potential and its radial variation." + As f.g depend quite heavily upon the dark matter halo. the cllipticity can only be guessed. though the position angle probably agrees with that of the luminous matter. (," As $f,g$ depend quite heavily upon the dark matter halo, the ellipticity can only be guessed, though the position angle probably agrees with that of the luminous matter. (" +Observed lenses often require external shear to fit their image geometries.),Observed lenses often require external shear to fit their image geometries.) + The time function is given by Images5 at F have sources at 3 located as extrema of f., The time function is given by Images at $\vec r$ have sources at $\vec\beta$ located as extrema of $t$. + llence. where 0=r|1 and all derivatives are evaluated at r—1.," Hence, where $\delta=r-1$ and all derivatives are evaluated at $r=1$." + The Hessian matrix of/ is given by in polar coordinates. (to lowest order). and the scalar magnification. fr. is the reciprocal of its determinant.," The Hessian matrix of $t$ is given by in polar coordinates, (to lowest order), and the scalar magnification, $\mu$, is the reciprocal of its determinant." +" Now. foex when the image lies on the critical curve or equivalently: when the source lies on the caustic If we now clisplace the source perpendicular to the caustic. a pair of images will separate in opposite directions from the critical curve along a line with ar=2gqd)sn2080/(1.—f"") where 66 (assumed to be << 1) is the displacement. of either image from. the critical. curve."," Now, $\mu\rightarrow\infty$ when the image lies on the critical curve or equivalently, when the source lies on the caustic If we now displace the source perpendicular to the caustic, a pair of images will separate in opposite directions from the critical curve along a line with $\delta r=2(g-g')\sin2\phi\delta\phi/(1-f'')$ where $\delta\phi$ (assumed to be $<<1$ ) is the displacement of either image from the critical curve." + Perturbing the Llessian. we find that for each of the neighbouring. bright images.," Perturbing the Hessian, we find that for each of the neighbouring, bright images." + Expancing the time delay to third order. we find that the time delay between the two bright bursts is given hy to leading order.," Expanding the time delay to third order, we find that the time delay between the two bright bursts is given by to leading order." + These expressions must be moclifice near à cusp when |sine.<|pylAt. C," These expressions must be modified near a cusp when $|\sin\phi_2|<|\mu_{2,3}|\Delta t$. (" +ligher order catastrophes are possible. but less probable:e.g... Schneider 199:,"Higher order catastrophes are possible, but less probable:, Schneider 1992.)" + We can also locate the preceding (1) and following (4) bursts in the high-magnification. small-ellipticitv limit at position angles Aleasuring ὧν from the minor axis. we find. without loss of generalitv. that when the merging pair is in the first quadrant. the preceding burst is in the second: quadrant and the following burst is in the fourth quadrant.," We can also locate the preceding (1) and following (4) bursts in the high-magnification, small-ellipticity limit at position angles Measuring $\phi_2$ from the minor axis, we find, without loss of generality, that when the merging pair is in the first quadrant, the preceding burst is in the second quadrant and the following burst is in the fourth quadrant." + The corresponding delays are given by fofy. (fyfa) varies between Sg. (0) and 0. (Sg) as © increases from 0 to z/2.," The corresponding delays are given by $t_2-t_1$, $(t_4-t_2)$ varies between $8g$, (0) and 0, $8g$ ) as $\phi$ increases from 0 to $\pi/2$." + The associated magnifications are eiven by ‘Thus. observation of either burst 2 or 3 allows one to specify completely. the magnifications. time intervals. anc locations of the other three images.," The associated magnifications are given by Thus, observation of either burst 2 or 3 allows one to specify completely the magnifications, time intervals, and locations of the other three images." + These expressions are only valid as long as do<< Land the magnification is large. specifically as long as po2(6(1fq)3.," These expressions are only valid as long as $\delta\phi<<1$ and the magnification is large, specifically as long as $\mu>>(6(1-f'')g)^{-1}$." + When the source is even farther from the caustic. it is possible to create four. similarlv-magnified bursts.," When the source is even farther from the caustic, it is possible to create four, similarly-magnified bursts." + These will be located at the solutions of the quartic In this case. it is necessary to observe two bursts optically in order to solve for the source location. 23.," These will be located at the solutions of the quartic In this case, it is necessary to observe two bursts optically in order to solve for the source location, $\vec\beta$." + The associated magnilications are given by and the arrival times (ignoring a constant) by Note that if LS(4g). then the source is located outside the caustic aad only two bursts will be seen.," The associated magnifications are given by and the arrival times (ignoring a constant) by Note that if $\beta_x^{2/3}+\beta_y^{2/3}>(4g)^{2/3}$, then the source is located outside the caustic and only two bursts will be seen." + Interestingly. if the source is located just outside of the cusp. one of these bursts can be arbitrarily maenified and followed by a single. fainter burst.," Interestingly, if the source is located just outside of the cusp, one of these bursts can be arbitrarily magnified and followed by a single, fainter burst." + However. this is a relatively rare occurence.," However, this is a relatively rare occurence." + [Even less likely is a radial merger geometry. when two. bright bursts. located much closer to the galaxy nucleus. will follow an isolated burst.," Even less likely is a radial merger geometry, when two, bright bursts, located much closer to the galaxy nucleus, will follow an isolated burst." + Finally. if there is no multiple imaging. then the single burst will still be magnified by a factor that depends uponthe detailed mass distribution closer to the nucleus.," Finally, if there is no multiple imaging, then the single burst will still be magnified by a factor that depends uponthe detailed mass distribution closer to the nucleus." + This factor is less than two for an isothermal sphere. as is twpically assumed. anc can only," This factor is less than two for an isothermal sphere, as is typically assumed, and can only" +further the truncation from A. the longer this will take.,"further the truncation from $R$, the longer this will take." + The first analvtic investigation of an ultrarelativistic planar shock wave was perlormec! bv Johnson&Mclxee(1971)., The first analytic investigation of an ultrarelativistic planar shock wave was performed by \cite{johnson71}. +.. The problem they. consider is broadly similar to the one we discuss here. but our work differs in important respects from (heirs.," The problem they consider is broadly similar to the one we discuss here, but our work differs in important respects from theirs." + First. used the method of characteristics in (heir work: (μον analvzed the flow associated with the shock bv tracing the paths of sound waves travelling through the (hud.," First, \cite{johnson71} used the method of characteristics in their work: they analyzed the flow associated with the shock by tracing the paths of sound waves travelling through the fluid." + Our analysis uses (he self-similarity of the flow instead., Our analysis uses the self-similarity of the flow instead. + So while some of their work can be applied to flows moving through fluids with arbitrary decreasing densitv profiles. (heir methods do not eive profiles For the hydrodynamic variables as functions of al a given time.," So while some of their work can be applied to flows moving through fluids with arbitrary decreasing density profiles, their methods do not give profiles for the hydrodynamic variables as functions of $x$ at a given time." + By contrast. our solutions require a power-law density profile inside (he star but eive explicit profiles for the hvdrodynamic. variables.," By contrast, our self-similar solutions require a power-law density profile inside the star but give explicit profiles for the hydrodynamic variables." + Second. the methods used by Johnson&Melee(1971) require initial conditions consisting of a uniform stationary Lot [Iuid about to expand into cold surroundings.," Second, the methods used by \cite{johnson71} require initial conditions consisting of a uniform stationary hot fluid about to expand into cold surroundings." + In our scenario the hot expanding (hud is never uniform or stationary ancl always follows the self-similar profile specilied by our solution., In our scenario the hot expanding fluid is never uniform or stationary and always follows the self-similar profile specified by our solution. + The self-similarity analysis tells us that the solution is Type IH. at least before breakout: this implies that the asymptotic solution is independent of the initial engine.," The self-similarity analysis tells us that the solution is Type II, at least before breakout; this implies that the asymptotic solution is independent of the initial engine." + We can check (hat our asymptotic solution is consistent with the findings of bv looking at the Lorentz factors of individual [hid elements at very late times., We can check that our asymptotic solution is consistent with the findings of \cite{johnson71} by looking at the Lorentz factors of individual fluid elements at very late times. + While in our sell-similar solution the fluid elements formally accelerate forever. each fluid element must in practice stop accelerating when all of its internal energy has been converted (o bulk kinetic energy. or when p/n~affh1.," While in our self-similar solution the fluid elements formally accelerate forever, each fluid element must in practice stop accelerating when all of its internal energy has been converted to bulk kinetic energy, or when $p/n\sim\gamma f/h\sim 1$." + S0 we can estimate the final Lorentz [actor of a given fIuid element [rom Eqs. 36.. 37.. 38..," So we can estimate the final Lorentz factor of a given fluid element from Eqs. \ref{g_outside}, , \ref{f_outside}, \ref{h_outside}." + By taking the acdvective lime derivatives of 5 and of f/f we can write differential equations for their time evolution followinge a singlee fluid element., By taking the advective time derivatives of $\gamma$ and of $f/h$ we can write differential equations for their time evolution following a single fluid element. + These are In the last steps we have taken (he limit of late(mes when the accelerating Πα element approachesthe shock front al 4.= 0., These are In the last steps we have taken the limit of latetimes when the accelerating fluid element approachesthe shock front at $\chi=0$ . + In this limit Eq., In this limit Eq. + 36 implies y4x and, \ref{g_outside} implies $g\rightarrow\infty$ and +space around a phase angle of 4-X or —£.,space around a phase angle of $+\frac{\pi}{2}$ or $-\frac{\pi}{2}$. + A qualitative physical explanation is given to this curious fact., A qualitative physical explanation is given to this curious fact. + We discuss in the final 85. why our model planet rarely fails to jump Chrough the 2:1 resonance despite the tightness of the required conditions to do so.," We discuss in the final \ref{dis.sec} + why our model planet rarely fails to jump through the 2:1 resonance despite the tightness of the required conditions to do so." + We derive the probabilities of capture in spin-orbit resonances Lor both prograde and retrograde evolution of spin rate. aud compare them with the ranges of equilibrium eccentricities.," We derive the probabilities of capture in spin-orbit resonances for both prograde and retrograde evolution of spin rate, and compare them with the ranges of equilibrium eccentricities." + The instantaneous torque acting on a rotating planet is the sum of the triaxial torque. caused by the quadrupole inertial momentum. and the tidal torque. caused by the dynamic deformation of its body.," The instantaneous torque acting on a rotating planet is the sum of the triaxial torque, caused by the quadrupole inertial momentum, and the tidal torque, caused by the dynamic deformation of its body." + In neglect of the obliquity (Danhy1962).. with @ being the sidereal angle of the planet reckoned [rom the axis of ils largest elongation.," In neglect of the obliquity \citep{danb}, with $\theta$ being the sidereal angle of the planet reckoned from the axis of its largest elongation." + All other notations used in this formula and throughout the paper are explained in Table 1l.., All other notations used in this formula and throughout the paper are explained in Table \ref{nota.tab}. + We consiler the specilic. but representative. case when (he obliquity of the planet's equator is small (/ 0) and the planet is not too close to the star (2< 1).," We consider the specific, but representative, case when the obliquity of the planet's equator is small $i\simeq 0$ ) and the planet is not too close to the star $\frac{R}{a}\ll1$ )." + Neglecting the precession and mutation of the planet. the triaxial torque is Peale1966)," Neglecting the precession and nutation of the planet, the triaxial torque is \citep{danb,gold} + )." + Using (he comprehensive development of Ixaula and Darwins harmonic decomposition of the tidal torque by (Elroimsky.&Lainey2007:Efoimsky 201la.b). one can write a simplified equation [for the tidal torque. which we call in the," Using the comprehensive development of Kaula and Darwin's harmonic decomposition of the tidal torque by \citep{efr2,efrw,efr1,efrb}, one can write a simplified equation for the tidal torque, which we call in the" +The finding iu Sect.,The finding in Sect. +" 3.1 that the more massive nelbers of the SAIC Oc/Be population overlaps the LCRDs predicted progenitor area (?).. thanks to theirnasses and (0/0.)zx(s rotation rates. which are today in the second half of their MS evolutionary phase. makes hei designed caucidates for such chemically quasi-ioniogeneonus objects that can evolve towards the WR phase and become LORB progenitors later ? find that the ""De phenomenon” cau be shared by nore numerous stellar populations. favored possibly bv he lower SAIC inetallicitv. than in the MW."," \ref{zrvp} that the more massive members of the SMC Oe/Be population overlaps the LGRBs predicted progenitor area \citep{yoon2006}, thanks to theirmasses and $(\Omega/\Omega_{\rm c})_{\rm ZAMS}$ rotation rates, which are today in the second half of their MS evolutionary phase, makes them designed candidates for such chemically quasi-homogeneous objects that can evolve towards the WR phase and become LGRB progenitors later \citet{martayan2009} find that the “Be phenomenon"" can be shared by more numerous stellar populations, favored possibly by the lower SMC metallicity, than in the MW." +" Since the heoretical predictions show that the lower the metallicity he lower is the stellar mass that can cuter the LCRD oxoesenitor area. if is expected that among the massive stars of the first generations. which are very metal poor. here nueht be a significantly large number of objects that could have undergone the ""De phenomenon."," Since the theoretical predictions show that the lower the metallicity the lower is the stellar mass that can enter the LGRB progenitor area, it is expected that among the massive stars of the first generations, which are very metal poor, there might be a significantly large number of objects that could have undergone the “Be phenomenon""." + These stars could then have had the required plivsical conditions for cine potential LGRD Another test of the ability of the Oe/Be stars in the SAIC to be LGRDs progenitors is based on the estimation of the expected rate of LGRD events that these stars can afford., These stars could then have had the required physical conditions for being potential LGRB Another test of the ability of the Oe/Be stars in the SMC to be LGRBs progenitors is based on the estimation of the expected rate of LGRB events that these stars can afford. + Iu the less favorable case. the predicted frequency must be of the same order of magnitude as the observed ones for this stellaz population be considered a plausible To estimate the LGRD vate from the SAIC Oc/Be stellar population. we need to ideutify the right spectral types to fill the mass requirements of stars entering the theoretically predicted LORB progenitor zoue shown iu Fie. 3.," In the less favorable case, the predicted frequency must be of the same order of magnitude as the observed ones for this stellar population be considered a plausible To estimate the LGRB rate from the SMC Oe/Be stellar population, we need to identify the right spectral types to fill the mass requirements of stars entering the theoretically predicted LGRB progenitor zone shown in Fig. \ref{fig3}." + To this end. and knowing that we are dealing with fast rotators. we used the models of stellar evolution with rotation for stars with SAIC metallicity calculated by 7..," To this end, and knowing that we are dealing with fast rotators, we used the models of stellar evolution with rotation for stars with SMC metallicity calculated by \citet{maeder01}." + We interpolated the evolution paths from the ZAMS o the TANS for the masses M=1541 and AL=33AL.., We interpolated the evolution paths from the ZAMS to the TAMS for the masses $M\!=\!18M_{\odot}$ and $M\!=\!33M_{\odot}$ . +" The (logL/L...Tig) corners thus obtained in the heoretical WR diagram were transformed iuto absolute uaenitude-color pairs AR(WVI), using standard olometyic corrections al the OGLE-ILH coloranaenitude calibrations in current use."," The $(\log L/L_{\odot},T_{\rm eff})$ corners thus obtained in the theoretical HR diagram were transformed into absolute magnitude-color pairs $[M_{\rm V},(V-I)_o]$ using standard bolometric corrections and the OGLE-III color-magnitude calibrations in current use." +" It follows from this that the nain sequence visual absolute magnitudes of SAIC stars with AJ=1sA/.. ranee from My=2.8imaeto dy=LL. while those of 9041, do it from My=3.7 image to Αντ6.3."," It follows from this that the main sequence visual absolute magnitudes of SMC stars with $M\!=\!18M_{\odot}$ range from $M_{\rm V}\!=\!-2.8$ mag to $M_{\rm V}\!=\!-4.4$, while those of $33M_{\odot}$ do it from $M_{\rm V}\!=\!-3.7$ mag to $M_{\rm V}\!=\!-6.3$." + A massespectral type correspondence for stars in the ZAMS has also been receutly obtained by ?.., A mass-spectral type correspondence for stars in the ZAMS has also been recently obtained by \citet{huang2006}. + Iu accordance with the MIN. spectral-types for dw stars in the SAIC calibration agaiust the visual absolute uaenitude AA used iu (2).. the stars cuterine the LGRB xogeuitor zoue in Fig.," In accordance with the MK spectral-types for dwarf stars in the SMC calibration against the visual absolute magnitude $M_{\rm V}$ used in \citep{martayan2009}, , the stars entering the LGRB progenitor zone in Fig." + 3 correspond then to those abeled with B1-OsS spectral types for rest aud oenission-ess stars., \ref{fig3} correspond then to those labeled with B1-O8 spectral types for rest and emission-less stars. + However. according to ? the mass of the LORBs xogenuitors could be as low as LIAL...," However, according to \citet{hunter2008} the mass of the LGRBs progenitors could be as low as $_{\odot}$." + Iu this case. oue should count stars a little cooler than spectral type DI. ie. roni D1.5. up to Os as potential LORBs progenitors with SAIC inetallicitv.," In this case, one should count stars a little cooler than spectral type B1, i.e. from B1.5, up to O8 as potential LGRBs progenitors with SMC metallicity." + Stars from 11 to 33 AL. evolve iu the MS phase. so that their respective absolute magnitudes Afy remain rather constant aud that the (VDy color changes by πο more than ó(1lI)0.0 mag for Ll M. to OWDy~0.07 mae for 33 AL...," Stars from 14 to 33 $M_{\odot}$ evolve in the MS phase, so that their respective absolute magnitudes $M_{\rm V}$ remain rather constant and that the $(V-I)_{0}$ color changes by no more than $\delta(V-I)_{0}\sim0.04$ mag for 14 $M_{\odot}$ to $\delta(V-I)_{0}\sim0.07$ mag for 33 $M_{\odot}$." +" Moreover. in our [AAV Dio] diagram. all counted OD stars are located -ji quite a narrow strip of M as a functiou of (V.I), (sceFie.5in?).. so that there caunot be much confusion reearding the identification of stars bv their masses with 1¢ Cluploved photometric criterion."," Moreover, in our $M_{\rm V},(V-I)_{0}$ ] diagram, all counted OB stars are located in quite a narrow strip of $M_{\rm V}$ as a function of $(V-I)_{0}$ \citep[see Fig. 5 in][]{martayan2009}, so that there cannot be much confusion regarding the identification of stars by their masses with the employed photometric criterion." + The absolute magnitude intervals for 18 and 33M. stars were established from evolutionary models where ie. (logLL..Tug) paraiucters are averaged over the rotationally deformed stellar surfaces.," The absolute magnitude intervals for 18 and $33M_{\odot}$ stars were established from evolutionary models where the $(\log L/L_{\odot},T_{\rm eff})$ parameters are averaged over the rotationally deformed stellar surfaces." + Actual stars show. jiowever apparent hemispherc-dependent spectroscopic and photometric characteristics.," Actual stars show, however apparent hemisphere-dependent spectroscopic and photometric characteristics." + There are then at least WO LTCasolls. rotation- and Be plenomenou-relatecd. for which still cooler spectral types than Bl should cuter he counting: 1) fasterotating stars appear with cooler apparent spectral types than stars with the same mass at rest (27): 2) the argest number of candidate stars are selected using photometric colors in the visible aud near- where both rotation aud the presence of circiuustellar disks male the stars appear stronely reddeued.," There are then at least two reasons, rotation- and Be phenomenon-related, for which still cooler spectral types than B1 should enter the counting: 1) fast-rotating stars appear with cooler apparent spectral types than stars with the same mass at rest \citep{fremat2005, marta2007}; ; 2) the largest number of candidate stars are selected using photometric colors in the visible and near-IR, where both rotation and the presence of circumstellar disks make the stars appear strongly reddened." + We recall that reddeningdue to the circuustellar disks, We recall that reddeningdue to the circumstellar disks +Longinottiοἱal.(2008) placed a limit on the racial distauce to the soft X-ray emitting gas of <0.06 ppc. consistent with a BLR origin.,"\citet{longinotti08} placed a limit on the radial distance to the soft X-ray emitting gas of $<0.06$ pc, consistent with a BLR origin." + A similar claim has been made by (2009).. who detected several broadened soft. N-rav. emission lines with a tvpical EWIIM of ~5000 kkanss.I. [rom a deep NMM-Newton/RGS observation of the narrow lined Sevfert 1. IILOO1707-495.," A similar claim has been made by \citet{blustin09}, who detected several broadened soft X-ray emission lines with a typical FWHM of $\sim 5000$ $^{-1}$, from a deep XMM-Newton/RGS observation of the narrow lined Seyfert 1, 0707-495." + Ixdeed. (here have also been several past claims of broadened soft. X-ray enission lines from grating observations of Sevlert Is. with line widths which appear to be consistent with a BLR origin (e.g. NGC 4051. Ogleetal.2004: NGC 5548. Steenbrugge 2005: Mrk 509. Smithetal.2007: Mrk 279. Costantinietal.2007)).," Indeed there have also been several past claims of broadened soft X-ray emission lines from grating observations of Seyfert 1s, with line widths which appear to be consistent with a BLR origin (e.g. NGC 4051, \citealt{ogle04}; NGC 5548, \citealt{steenbrugge05}; Mrk 509, \citealt{smith07}; Mrk 279, \citealt{cost07}) )." + Thus we may be observing (he same A-ray DLE. emission in the BLRG ος 445., Thus we may be observing the same X-ray BLR emission in the BLRG 3C 445. + As has also been found from previous observations (Sambrunaetal.2007: 2007)). the primary X-ray conünuunm from 4445 is highly. absorbed. with a column densitv exceeding 107* 7.," As has also been found from previous observations \citealt{sambruna07}; \citealt{grandi07}) ), the primary X-ray continuum from 445 is highly absorbed, with a column density exceeding $10^{23}$ $^{-2}$." + Indeed the X-ray column observed towards 4445 [ar exceeds the expected column based on the extinction in the optical band towards of this AGN. of the order £j4~1 (Rudy&Tokunaga1982)..," Indeed the X-ray column observed towards 445 far exceeds the expected column based on the extinction in the optical band towards of this AGN, of the order $E_{B-V} \sim 1$ \citep{rudy82}." + Although the properties of the absorbing gas was unclear from previous shorter (ancl lower spectral resolution) observations. the Chandra LETG shows the absorption can be well modeled with a moderately ionized outflow. with an outflow. velocity of the order 10000 ss.+.," Although the properties of the absorbing gas was unclear from previous shorter (and lower spectral resolution) observations, the Chandra LETG shows the absorption can be well modeled with a moderately ionized outflow, with an outflow velocity of the order $\sim 10000$ $^{-1}$." + As we will discuss here. it appears more plausible that this absorbing gas is associated wilh a disk wind on smaller (sub.parsec) scales rather (han with a putative molecular torus.," As we will discuss here, it appears more plausible that this absorbing gas is associated with a disk wind on smaller (sub–parsec) scales rather than with a putative molecular torus." + We first consider the location of the absorber., We first consider the location of the absorber. +" For a homogeneous radial wind. the observed column density along the line of sieht is equal to: where (2, and A4 are the inner and outer radii along the line of sight through thewind."," For a homogeneous radial wind, the observed column density along the line of sight is equal to:- where $R_{\rm in}$ and $R_{\rm out}$ are the inner and outer radii along the line of sight through thewind." +" In the case where we are looking directly down a homogeneous wind towards an inner radius A. then A,=oe and re-arranging gives Ry,=/f&LionNy."," In the case where we are looking directly down a homogeneous wind towards an inner radius $R_{\rm in}$, then $R_{\rm out}=\infty$ and re-arranging gives $R_{\rm in} = L_{\rm ion} / \xi N_{\rm H}$." +" The best fit model of the absorber 33) gives .Njj=2x107 7 ancl log£= 1.4. thus Ry,=5x10? eem (or e10 ppc)."," The best fit model of the absorber 3) gives $N_{\rm H}=2\times10^{23}$ $^{-2}$ and $\log \xi = 1.4$ , thus $R_{\rm in} = 5\times 10^{19}$ cm (or $\sim 10$ pc)." +" At this radius the density of the absorbing matter is n,e101 oE", At this radius the density of the absorbing matter is $n_{\rm e} \sim 10^{4}$ $^{-3}$ . +individual cluster ages offers the possibility to use M/L values from evolutionary svuthesis models to derive the Mass Function (MF) underline the prescutly observed LF aud this is what we attempt in this Letter.,individual cluster ages offers the possibility to use M/L values from evolutionary synthesis models to derive the Mass Function ) underlying the presently observed LF and this is what we attempt in this Letter. + Since the age distribution of the YSC's is strongly peaked witlin x02.105 vr and the YSC's lave a dncan distance to the ealaxy center of ~5 ρο. YSC ou average cannot have had more than 1 or 2 revolutions.," Since the age distribution of the YSCs is strongly peaked within $\leq 2 \cdot 10^8$ yr and the YSCs have a mean distance to the galaxy center of $\sim 3.5$ kpc, a YSC on average cannot have had more than 1 or 2 revolutions." + We do not expect the AIF therefore to already |)o ο affected by cluster destruction processes., We do not expect the MF therefore to already be significantly affected by cluster destruction processes. + Rather we expect the presentlv derived. AIF to reflect the AIF produced |w the cluster formation process., Rather we expect the presently derived MF to reflect the MF produced by the cluster formation process. + The mass spectra of molecular clouds. iolecular cloud cores. open clusters. and the LF of eiant TTT regions (in non-interacting galaxies) all are power laws with exponents à in the range a~—1.5...La (e.g. Solomon 1987. Lada 1991. I&euuicutt. 1950. see Duris Pudritz 1991 and Ehuecercen Efreinov 1997 for overviews) as is the amass spectrum of open clusters in the Milkv Way aud the LAIC (6.8. van den Berel Lafoutaine 1981. Elsou Fall 1985).," The mass spectra of molecular clouds, molecular cloud cores, open clusters, and the LF of giant HII regions (in non-interacting galaxies) all are power laws with exponents $\alpha$ in the range $\alpha \sim -1.5 \ \dots \ -1.7$ (e.g. Solomon 1987, Lada 1991, Kennicutt 1989, see Harris Pudritz 1994 and Elmegreen Efremov 1997 for overviews) as is the mass spectrum of open clusters in the Milky Way and the LMC (e.g. van den Bergh Lafontaine 1984, Elson Fall 1985)." + Both the LF aud the MIF of old CC svstenus are Caussians with typical parameters (My;~—7.2 imag. 61.9 mae. aud (Log(MMο5.5. 0~0.0. respectively (e.g. Ashinan 1995).," Both the LF and the MF of old GC systems are Gaussians with typical parameters ${\rm \langle M_V \rangle \sim -7.3}$ mag, $\sigma \sim 1.3$ mag, and ${\rm \langle Log~(M/M_{\odot}) \rangle \sim 5.5}$, ${\rm \sigma \sim 0.5}$, respectively (e.g. Ashman 1995)." + The question imunediately arises: Is the transition from a power law molecular cloud mass spectrum to a Cassia old GC lnass spectra performed in the star/cluster formation process or by secular destruction effects witlin a GC system7, The question immediately arises: Is the transition from a power law molecular cloud mass spectrum to a Gaussian old GC mass spectrum performed in the star/cluster formation process or by secular destruction effects within a GC system? + Or. else. is already. the mass spectrum of molecular clouds or molecular cloud cores ciffercut iu strouely interacting and starbursting galaxies from what it is iu normal spirals?," Or, else, is already the mass spectrum of molecular clouds or molecular cloud cores different in strongly interacting and starbursting galaxies from what it is in normal spirals?" + Ou the basis of individual YSC ages woe use our SSP nodels giving M/L iu the passbauds A= UBVRIL as a function of time to derive masses of individual clusters rou their observed Vo Iuniuosities., On the basis of individual YSC ages we use our SSP models giving ${\rm M/L_{\lambda}}$ in the passbands $\lambda = $ UBVRIK as a function of time to derive masses of individual clusters from their observed V – luminosities. + This is done or all the 393 YSCs with ages xL-107 vroand Vo luninositics Irighter than the completeuess 1n My=9.6 nuage., This is done for all the 393 YSCs with ages $\leq 4 \cdot 10^8$ yr and V – luminosities brighter than the completeness limit ${\rm M_V = -9.6}$ mag. + It is stressed that our model M/L - values include the decrease in cluster mass due to stellar uass loss (cf., It is stressed that our model ${\rm M/L}$ - values include the decrease in cluster mass due to stellar mass loss (cf. + Pap., Pap. +D. but iot that due to the evaporation of stars from the cluster.,"I), but not that due to the evaporation of stars from the cluster." + The ME we recover in this wav roni the preseutlv observed LF is prescuted im Fie.1., The MF we recover in this way from the presently observed LF is presented in Fig.1. + A Gaussian with (Log(Mygc/M.=5.6 aud e=0.16. rorimalised to the uuuber of YSCs in the histogram. is overplotted.," A Gaussian with ${\rm \langle Log~(M_{YSC}/M_{\odot}) \rangle = 5.6}$ and ${\rm \sigma = 0.46}$, normalised to the number of YSCs in the histogram, is overplotted." + The intrinsic AIF we obtain for the YSCs xiehter than the completeness iuit iu The Autcnnae clearly looks log-norimal in shape with the maxima at a nean YSC mass of ~1:10?AL..., The intrinsic MF we obtain for the YSCs brighter than the completeness limit in The Antennae clearly looks log-normal in shape with the maximum at a mean YSC mass of ${\rm \sim 4 \cdot 10^5~M_{\odot}}$. + Stellar ass loss within he clusters from the preseut meanage of ~2-105 vr hrough an age of ~12 Carr will lead to a decrease in nass Thus.ofSS15 (fora Sealo IMF (<1054 for Salpeter}., Stellar mass loss within the clusters from the present meanage of $\sim 2 \cdot 10^8$ yr through an age of $\sim 12$ Gyr will lead to a decrease in mass of $\lta 15 ~\%$ for a Scalo – IMF $< 10 \%$ for Salpeter). + without auv destruction or evaporation effects he mean mass of the secondary (GC system in The Auteunae at the age of a ILIubble time would be 93E107MSS," Thus, without any destruction or evaporation effects the mean mass of the secondary GC system in The Antennae at the age of a Hubble time would be ${\rm \sim 3.4 \cdot 10^5 +~M_{\odot}}$." + À cluster with this menu mass would je My=06.9 mae at an age of 12 Cr according to our models., A cluster with this mean mass would have ${\rm M_V = -6.9}$ mag at an age of 12 Gyr according to our models. + This is the position of the maxima of the Gaussian YSC LF we obtain at a lypothetic YSC age of 12 Gar (cf., This is the position of the maximum of the Gaussian YSC LF we obtain at a hypothetic YSC age of 12 Gyr (cf. + Fig., Fig. + Ga in Pap., 6a in Pap. +).,I). + The agreement is no surprise since this is. in fact. the wav how we obtained the parameters for the Gaussian in Fig.l.," The agreement is no surprise since this is, in fact, the way how we obtained the parameters for the Gaussian in Fig.1." + We stress that these parameters are derived from the LF in Pap., We stress that these parameters are derived from the LF in Pap. +T aud are uot the result of aux fit to the cluster MIF in Fig],I and are not the result of any fit to the cluster MF in Fig.1. + Remarkably enough. the parameters of this Gaussian which in Fig.l is secu to reasonably describe the ME of the secondary GC population are quite similar to those given by Ashman (1995) for the Milkv. Way and NI GC systems.," Remarkably enough, the parameters of this Gaussian – which in Fig.1 is seen to reasonably describe the MF of the secondary GC population – are quite similar to those given by Ashman (1995) for the Milky Way and M31 GC systems." + Using evolutionary svutlesis results fron Worthev (1991) for AMI/Ly-. Ashman fiud (Log(MM...)=5.1? aud o=0.50 for the Milky Way aud (Log(CM/MJj=5.53 aud σξ0.13 for M31.," Using evolutionary synthesis results from Worthey (1994) for ${\rm M/L_V}$, Ashman find ${\rm \langle Log~(M/M_{\odot}) \rangle = 5.47}$ and ${\rm \sigma = 0.50}$ for the Milky Way and ${\rm \langle Log~(M/M_{\odot}) \rangle = 5.53}$ and ${\rm \sigma = 0.43}$ for M31." + The AIF in Fie., The MF in Fig. + 1 thus seems compatible with the bulk ofthe YSCs really]cine voune GCs rather than open clusters OY assoclatious. as was alreacky indicated by their small effective radii aud high huuinositics (WS95).," 1 thus seems compatible with the bulk of the YSCs really being young GCs rather than open clusters or associations, as was already indicated by their small effective radii and high luminosities (WS95)." + From the model side. uneertainties in the determination of YSC ages (aud lence masses) on the basis of their (V.I) colours are dominated hy uncertainties iu the YSC metallicities.," From the model side, uncertainties in the determination of YSC ages (and hence masses) on the basis of their ${\rm (V - I)}$ colours are dominated by uncertainties in the YSC metallicities." + Age uncertainties due to metallicity uncertainty (4-Z.SZyso SZ.) are estimated tobe of the order of £15 ., Age uncertainties due to metallicity uncertainty ${\rm \frac{1}{2} \cdot Z_{\odot} \lta Z_{YSC} \lta Z_{\odot}}$ ) are estimated to be of the order of $\pm 15~\%$ . + The uncertainty in AL LatZ=3-Z. due to the age uncertainty is ~8% , The uncertainty in M/L at ${\rm Z = \frac{1}{2} \cdot Z_{\odot}}$ due to the age uncertainty is $\sim 8$ + (Popovetal.2006)., \citep{ptp06}. +. 105.—Lot? (e...Lorimeretal.2006): (c.c.Bildstenctal.1997:Wijnauds&van (e.g.&Bildsten2006) 2104! (whichhistorically (RRATs:MeLaughllinetal.2006):: (Walteretal.1996:Taher]2007).. Sauwal.&Teter2001)..," $10^{8}-10^{13}$ \citep[e.g.,][]{lor06}; \citep[e.g.,][]{bil97,wvdk98} + \citep[e.g.,][]{sb06} $\ga$$10^{14}$ \citep[which historically have been +categorized as +either anomalous X-ray pulsars or soft gamma repeaters; +e.g.,][]{wt06}; \citep[RRATs;][]{mcl06}; \citep{wwn96,hab06}, \citep[][]{cha01,sew03,pst04}." + Understanding the properties of these compact objects and thei birth rates provides important coustraits ou the late-time evolution of massive stars. and on the processes that occur during stellar collapse.," Understanding the properties of these compact objects and their birth rates provides important constraints on the late-time evolution of massive stars, and on the processes that occur during stellar collapse." + The relationships amoue the different classes of compact object could reveal how their magnetic fields decay. aud their interiors cool., The relationships among the different classes of compact object could reveal how their magnetic fields decay and their interiors cool. + Iu this paper. we present a search for magnetars.," In this paper, we present a search for magnetars." + This search is timely for two reasons., This search is timely for two reasons. + First. recent evidence sugeests that maguetars are the products of unusually lnassive progenitors.," First, recent evidence suggests that magnetars are the products of unusually massive progenitors." + Three maguctars have Όσοι fouud to be iu clusters of massive. voune stars (Fuchsotal.1999:Vrbaetal.2000:Eikeuberrv 2001). and the turu-off misses of two of these clusters imply that the progenitors to the ueutron stars were Very nmniassivo. 3010 citepfigüb. niunü6..," Three magnetars have been found to be in clusters of massive, young stars \citep{fuc99,vrb00,eik04}, and the turn-off masses of two of these clusters imply that the progenitors to the neutron stars were very massive, 30–40 \\citep{fig05,mun06}." + fouth maguoetar has been associated with a »bubble of neutral hwdroseu that was probably blownby the wind of a 2230 o»prosenitor (CGacusleretal.2005)., A fourth magnetar has been associated with a bubble of neutral hydrogen that was probably blown by the wind of a $>$ 30 progenitor \citep{gae05}. +. This suggests that nlassive stars may be more likely to produce maguctars. whereas ordinary radio pulsus are ecucrally presumed be left by lower-iass. ὃ20 o»progenitors(o...Ποσοetal.M.2003).," This suggests that massive stars may be more likely to produce magnetars, whereas ordinary radio pulsars are generally presumed to be left by lower-mass, 8–20 progenitors \citep[e.g.,][]{heg03}." +. Ciüven that less nassive stars are much more conuuon (e$.Rroupa 2002).. if massive stars produce maguctars. one would expectthat their birth rates should be πιο] lower thu hose of radio pulsars (Gacusleretal. 2005)..," Given that less massive stars are much more common \citep[e.g.,][]{krou02}, if massive stars produce magnetars, one would expectthat their birth rates should be much lower than those of radio pulsars \citep{gae05}. ." + Secoud. there is siguificant debate about how the," Second, there is significant debate about how the" +relative distance error and which is dominated by the uncertainty in the potential model (Sun&Ian2004).,relative distance error and which is dominated by the uncertainty in the potential model \citep{sun04}. +. From equation (2)). the acceleration of the Solar svstem in any direction can be constrained from each object with a known £4 aud D: where the unit vector n points toward the object Chat we are using.," From equation \ref{pdotprime}) ), the acceleration of the Solar system in any direction can be constrained from each object with a known $\dot{P}_{obs}$ and $\dot{P}_{th}$: where the unit vector $\bf n$ points toward the object that we are using." + If only one object is available. (he acceleration is unconstrained in (he plane perpendicular to the line of sight.," If only one object is available, the acceleration is unconstrained in the plane perpendicular to the line of sight." + Therefore. (he constraint on the acceleration can be improved by combining data on several objects in different parts of the sky.," Therefore, the constraint on the acceleration can be improved by combining data on several objects in different parts of the sky." + In Table 1l we list all the values that enter equation (7)) aud (heir errors [ον the ien pulsars in binary svstems and one DA white dwarl used in our analvsis., In Table 1 we list all the values that enter equation \ref{eq_a_pbdot}) ) and their errors for the ten pulsars in binary systems and one DA white dwarf used in our analysis. + The objects PSR D19124-16 and PSh J17132074T provide the most interesting constraints on the acceleration., The objects PSR B1913+16 and PSR J1713+0747 provide the most interesting constraints on the acceleration. + For PSR 1019-10. the accuracy improved by about an order of magnitude in the last 13 vears (cl.," For PSR B1913+16, the accuracy improved by about an order of magnitude in the last 13 years (cf." + Weisberg&Tavlor2004 and Damour&Tavlor 1991))., \citealt{weis04} and \citealt{damo91}) ). + This object has been timed [or 30 vears and has been used (ο constrain the acceleration of the solar svstem all bv itself. (Thornburg1985)., This object has been timed for 30 years and has been used to constrain the acceleration of the solar system all by itself \citep{thor85}. +. In the object PSR J17134—0747 the orbital period clecay has nol been detected. but the available upper limit on the orbital decay based on 12 vears of observations combined with the long orbital period of this svstem (68 davs) makes it useful for our analvsis.," In the object PSR J1713+0747 the orbital period decay has not been detected, but the available upper limit on the orbital decay based on 12 years of observations combined with the long orbital period of this system (68 days) makes it useful for our analysis." + The best-fit acceleration in (he direction (0.9) from object / is given by where 6; is the angle between (0.9) ancl the direction to the object.," The best-fit acceleration in the direction $(\alpha,\delta)$ from object $i$ is given by $a_{\odot}/c=-(\Delta \dot{P}_i \pm \sigma_{tot, i})/(P_i \cos\theta_i)$ where $\theta_i$ is the angle between $(\alpha,\delta)$ and the direction to the object." + There is no evidence lor a non-zero acceleration al the 26 level for any object., There is no evidence for a non-zero acceleration at the $2\sigma$ level for any object. + In Figure 5. we show the values of accelerations ruled out at a 2o level for each direction on the skv based on the observations of PSR 1010-10 alone., In Figure \ref{pic_a_B1913} we show the values of accelerations ruled out at a $\sigma$ level for each direction on the sky based on the observations of PSR B1913+16 alone. + The least constrained. directions are those perpendicular to the direction to the pulsar., The least constrained directions are those perpendicular to the direction to the pulsar. + The constraints in these regions are significantly improved when we include another five objects from the high-accuracy group. as shown in Figure 6..," The constraints in these regions are significantly improved when we include another five objects from the high-accuracy group, as shown in Figure \ref{pic_a_six}." + In this Figure. lor each position on the skv we calculated the error-weighted mean and (he error-weighted variance of the accelerations obtained using equation (1)) for the six pulsars and plotted (mean + 2 x variance! 7).," In this Figure, for each position on the sky we calculated the error-weighted mean and the error-weighted variance of the accelerations obtained using equation \ref{eq_a_pbdot}) ) for the six pulsars and plotted (mean + 2 $\times$ $^{1/2}$ )." + Adding the remaining five objects from Table 1 has almost no effect on the acceleration constraints., Adding the remaining five objects from Table 1 has almost no effect on the acceleration constraints. + Table 2 and Figure 7 summarize what values of acceleration of the solar svstem can be ruled out bv different methods., Table 2 and Figure \ref{pic_sum} summarize what values of acceleration of the solar system can be ruled out by different methods. + The method described here assumes (hat the peculiar accelerations of each object due to nearby stars aud clouds are negligible compared to their Galactic accelerations relative to the sun., The method described here assumes that the peculiar accelerations of each object due to nearby stars and clouds are negligible compared to their Galactic accelerations relative to the sun. + All objects used in our ealeulation are eitier in the disk of the Galaxy or somewhat above il. rather than in the bulge. and most are within 1 kpc. so the estimate of the peculiar," All objects used in our calculation are either in the disk of the Galaxy or somewhat above it, rather than in the bulge, and most are within 1 kpc, so the estimate of the peculiar" +profile shows significant changes.,profile shows significant changes. +" Then. from Eq.(33)) we can relate the mass Ms. cuclosed with the radius defined by the noulinear density contrast ὃν, to ου. associated with“ith cà.=200.200. byI !"," Then, from \ref{alpha-def}) ) we can relate the mass $M_{\deltas}$, enclosed with the radius defined by the nonlinear density contrast $\deltas$, to $M_{200}$, associated with $\deltas=200$, by = ." +" With the same ouc-to-one ideutificatiou. we can define a reduced variable vs, as CMogod. where Myo{Afoou) is given by the second Eq.(30)) aud Magy is obtaiued as a function of As, through Eq.(3l)). aud the large-mass tail of the halo mass functiou is still een bv s5,CMs,)~€e:l2EET? "," With the same one-to-one identification, we can define a reduced variable $\nu_{\deltas}$ as ) = ), where $\nu_{200}(M_{200})$ is given by the second \ref{fnu-def}) ) and $M_{200}$ is obtained as a function of $M_{\deltas}$ through \ref{Mdelta}) ), and the large-mass tail of the halo mass function is still given by $n_{\deltas}(M_{\deltas}) \sim e^{-\nu_{\deltas}^2/2} = e^{-\nu_{200}^2/2}$." +This one-to-one identification of rare massive halos also implies that their spatial distribution remains the same. iudepeucdently of the choice of 4. so that the largc-mass two-point correlation aud bias are still eiven by Eqs.(21)) aud (21)). Mayo).," This one-to-one identification of rare massive halos also implies that their spatial distribution remains the same, independently of the choice of $\deltas$, so that the large-mass two-point correlation and bias are still given by \ref{xi-M}) ) and \ref{b2-def}) ), ,x) = ,x)." +" Next.. iu. order to describe. typical. halos we again. take advantage of normalizationalizi constraints,constraints."," Next, in order to describe typical halos we again take advantage of normalization constraints." + First. to eusuxeusure that the mass function remains normalized to uuitv as in Eq.(29)). we choose the approximation f(p)) (Ug where the reduced function flv) is still eiven by Eq.(31)) aud the reduced variable v is given by Eq.(35)).," First, to ensure that the mass function remains normalized to unity as in \ref{fnu-norm}) ), we choose the approximation = ) , where the reduced function $f(\nu)$ is still given by \ref{fnu-fit}) ) and the reduced variable $\nu$ is given by \ref{nu-delta}) )." +" Πωο the amass Aog) is still defined bx Eq(41)) but since there is no longer a oue-to-oue ideutification (except at very large mass, as explained below) ου must be seen as an ""effectivemass” rather than the mass within ὃς=200 of the same individualobject."," Here the mass $M_{200}$ is still defined by \ref{Mdelta}) ) but since there is no longer a one-to-one identification (except at very large mass, as explained below) $M_{200}$ must be seen as an “effectivemass” rather than the mass within $\deltas=200$ of the same individualobject." + This prescription automatically provides both the melt large-auass cutoff.," This prescription automatically provides both the right large-mass cutoff," +(Shelvagcta.20073.,\citep{shelyag07}. +. The eranulc-iutererauue transition with positive area alc auuplituce asviuluetries can be explained by ravs crossing the canopy of the flux tubo., The granule-intergranule transition with positive area and amplitude asymmetries can be explained by rays crossing the canopy of the flux tube. + Appareutv. the spectral degradation of the data at full spalal resolution las a relaively small imipact on the spalal disributioi of asvuuuetries. as seen frou a conparisoi of the first and second columus.," Apparently, the spectral degradation of the data at full spatial resolution has a relatively small impact on the spatial distribution of asymmetries, as seen from a comparison of the first and second columns." + The fibuneitary stracture o the asviinetics associated with iutereralar lanes ds maintained. while he xofiles Observer in eraiular regions are lost because 10 8)ectral degradation pushes them below the uQlse threshold.," The filamentary structure of the asymmetries associated with intergranular lanes is maintained, while the profiles observed in granular regions are lost because the spectral degradation pushes them below the noise threshold." + Ilowever. we can see that the spectrally deeraded «ata prescuts lareer (in absoute value) area ak aliujitde asvaunetries thaw the original datasct. beingo 119 ciffereuc especiallv releviui Ol the cores of iutererauular lanes.," However, we can see that the spectrally degraded data presents larger (in absolute value) area and amplitude asymmetries than the original dataset, being this difference especially relevant on the cores of intergranular lanes." + This can be casi vouerstood. beciiSC specral degradation tends to increase relative area and ajlit1cle asviinuerios Solankis]&$cutlo(1986).. alhough the dependeicv on the specific shiaxe of the Stokes V. profile is crucial.," This can be easily understood because spectral degradation tends to increase relative area and amplitude asymmetries \cite{solanki_stenflo86}, although the dependency on the specific shape of the Stokes $V$ profile is crucial." + Spatial degradaion chaices completely t16 scenario., Spatial degradation changes completely the scenario. + The main reason is that spatial suicaring produces two effects: 1) profiles with very different asvnuuuetries are nixed. and 1 l)atecrease on the Stokes V. amplitude. lus pushing the signal iu many pixels below the noise hreshold.," The main reason is that spatial smearing produces two effects: i) profiles with very different asymmetries are mixed, and ii) a decrease on the Stokes $V$ amplitude, thus pushing the signal in many pixels below the noise threshold." + Still. the pixels associated wit1 the strouex‘st signals remain.. and of the pixels for the 30 €. 80 G and L10 Gswapshots. respectively) aud the filamentary 8tructure is somehow lost axd transformed iuto a blobby structure.," Still, the pixels associated with the strongest signals remain, and of the pixels for the 30 G, 80 G and 140 G snapshots, respectively) and the filamentary structure is somehow lost and transformed into a blobby structure." + Typically. asviunetries tei to © organized inside these ους so that zero or very small asviunetries are found in the cores while hey increase iu absolute valuc» towards the borders. where profiles are ost ον the noisc threshokο," Typically, asymmetries tend to be organized inside these blobs so that zero or very small asymmetries are found in the cores while they increase in absolute value towards the borders, where profiles are lost below the noise threshold." +" This behavior Is not exactly he same of what happens at larger spaial resolutioiIs, where the cores of 1itererauular lanes preseut negatiVeo asVIuetres while they conie positive on the eranule-iutereranule trausitio rregion."," This behavior is not exactly the same of what happens at larger spatial resolutions, where the cores of intergranular lanes present negative asymmetries while they become positive on the granule-intergranule transition region." +" From a eeneral perspecve, Wwe can sav that spatia sincaring qauahes the negatiVeo asvnuuetrv of narrow iutereranular alSs appear wihi sunaller absolute values while broadeing the reeio- of positive asviunetrv."," From a general perspective, we can say that spatial smearing makes the negative asymmetry of narrow intergranular lanes appear with smaller absolute values while broadening the region of positive asymmetry." + Tje area and amplitude asvuunevies found in fie spaally deeraded snapsrots tend to be more conipatiie with observaions., The area and amplitude asymmetries found in the spatially degraded snapshots tend to be more compatible with observations. +" On average. asvnunetries tend to IO positive, wit ioa larger absolute value for pliude asviuuetries han for area asviuueties."," On average, asymmetries tend to be positive, with a larger absolute value for amplitude asymmetries than for area asymmetries." + Stokes V. profiCR in iutegrailar lanes have now negative area gasvinduieTICS uot larger thau or even compatible with zero., Stokes $V$ profiles in integranular lanes have now negative area asymmetries not larger than or even compatible with zero. + The oulv exceptiois are isolated patches with strong negaive asviunietres., The only exceptions are isolated patches with strong negative asymmetries. + It is eviceut from Figs., It is evident from Figs. + 2 and 3. that area asvuuuectrics are slieltly OSS affected bv. the spatia] aud specral sinearig tiui amplitude asvuuuetrics.," \ref{fig:amplitude_asymmetry_maps} and \ref{fig:area_asymmetry_maps} + that area asymmetries are slightly less affected by the spatial and spectral smearing than amplitude asymmetries." + It is specially relevant in lie central parts of iuteruetwork lanes. where strong uceative almplitude asvinmictrics show up wen reducing tje spectral resoluion and these are transformed iuto aliost amplitude svuuuetric xofiles when degrading the spatia resolution.," It is specially relevant in the central parts of internetwork lanes, where strong negative amplitude asymmetries show up when reducing the spectral resolution and these are transformed into almost amplitude symmetric profiles when degrading the spatial resolution." + On the contrary. relevant ioegative area asvluluctrics are still ILOSCIL on internetwork lanes in the spajallv aud spectraIv ziueared data.," On the contrary, relevant negative area asymmetries are still present on internetwork lanes in the spatially and spectrally smeared data." + The main point of his work is to verify to what extend axviunietries are recoveore after nage reconstruction techniques., The main point of this work is to verify to what extend asymmetries are recovered after image reconstruction techniques. + The rightmost panes of Fies., The rightmost panels of Figs. + 2 and 3 demonstrate that ani uprovenieut on the spatial ocation of asvnuuetries occurs., \ref{fig:amplitude_asymmetry_maps} and \ref{fig:area_asymmetry_maps} demonstrate that an improvement on the spatial location of asymmetries occurs. +" Obviously. the euliauced noise level and its spatially correlated character prodices that the ver of pixels with detected signals decreases(ον, and of the pixels for the 30 C. 8) C and 110 apshots. respectively)."," Obviously, the enhanced noise level and its spatially correlated character produces that the number of pixels with detected signals decreases, and of the pixels for the 30 G, 80 G and 140 G snapshots, respectively)." + Comparing with Fie. 1..," Comparing with Fig. \ref{fig:continuum_maps}," + ouly INCs associated ο strong maguctic concentrations cau e correctly analyzed., only pixels associated to strong magnetic concentrations can be correctly analyzed. + Consequeutlv. one should be careful when analyzing reconstructed data to take into account his bias.," Consequently, one should be careful when analyzing reconstructed data to take into account this bias." + Several couclusions cau be extracted from the reconstructed images., Several conclusions can be extracted from the reconstructed images. + First. the structures are mich more colmpact than in the degraded case. a cousequence of the cficient reduction of aberrations performed by the pliase-diversity aleorithiun. even with relative errors ou the projections of the wavefrout ou the Zeruike polvuomials.," First, the structures are much more compact than in the degraded case, a consequence of the efficient reduction of aberrations performed by the phase-diversity algorithm, even with relative errors on the projections of the wavefront on the Zernike polynomials." + Secoud. the lareeoO C»eradicut of asviuunetries from the core of imtererauular lanes to the surroundiuss is partially restored.," Second, the large gradient of asymmetries from the core of intergranular lanes to the surroundings is partially restored." + However. the large negative value of }A aud da found iu the verv ceutral cores are not fully recovered.," However, the large negative value of $\delta A$ and $\delta a$ found in the very central cores are not fully recovered." + Generally. in these regions. nuage reconstruction caunot eonerate strong negative asvuunetrics if they were not preseit dn the degraded tages.," Generally, in these regions, image reconstruction cannot generate strong negative asymmetries if they were not present in the degraded images." + Likewise. if they were preseit dn the degraded maps. they will be cuhanced iu the image reconstruction process.," Likewise, if they were present in the degraded maps, they will be enhanced in the image reconstruction process." + Svuthetic Stokes V. profies for the three snapshots considered are shown iu Fie., Synthetic Stokes $V$ profiles for the three snapshots considered are shown in Fig. + { for the cuts indicated iu Figs, \ref{fig:stokes_cuts} for the cuts indicated in Figs. + 2 and 3 in evecn., \ref{fig:amplitude_asymmetry_maps} and \ref{fig:area_asymmetry_maps} in green. + The Stokes profiles are normalized to peak amplitude so one las to take iuto account that spatially and/or spectrally averaged signals possess a sxinaller iiuplitide., The Stokes profiles are normalized to peak amplitude so one has to take into account that spatially and/or spectrally averaged signals possess a smaller amplitude. + The profiles of the full spectral aud spatial resolution are shown oein ercen., The profiles of the full spectral and spatial resolution are shown in green. +" The profiles of the ""ll spatial resoution bit spectra resolution degraded to IMaX are show rin blacx.", The profiles of the full spatial resolution but spectral resolution degraded to IMaX are shown in black. + The fuIv degraded profiles are shown iu red axd the p1άδο-«Iversity recovered ojew are lotted in bhic., The fully degraded profiles are shown in red and the phase-diversity recovered ones are plotted in blue. + The first impression ids that the full spatial and spectral resolution profiles are ταν narrow aud the xesence of several commponcuts (several lobes ou the red obe) along the LOS can be casily witnessed., The first impression is that the full spatial and spectral resolution profiles are very narrow and the presence of several components (several lobes on the red lobe) along the LOS can be easily witnessed. + When the spectral resolution is degraded to 85mA.. the profiles are broadened. with strong modifications of the relative amplitudes of the two lobes.," When the spectral resolution is degraded to 85, the profiles are broadened, with strong modifications of the relative amplitudes of the two lobes." + As a byproduct. the full spatially/spectrally degraded: profiles tend to be inuch more svuuuctric aud only in those cases in which the," As a byproduct, the full spatially/spectrally degraded profiles tend to be much more symmetric and only in those cases in which the" +due to changing sensitivity to diffuse emission. Irecquency-dependent effects. aud uncertainties in component identifieation.,"due to changing sensitivity to diffuse emission, frequency-dependent effects, and uncertainties in component identification." + Apparently due to such effects. our fitting has shown relative position shifts of up to 0.05 mas (occasionally more) lor different. data weighting in the imaging. or between 8 and 15 GlIz fitting of peaks that appeared to be the same component.," Apparently due to such effects, our fitting has shown relative position shifts of up to 0.05 mas (occasionally more) for different data weighting in the imaging, or between 8 and 15 GHz fitting of peaks that appeared to be the same component." + To account for (his additional error source. we add 0.05Hr mas in quadrature to (he error and (he fitting errors for each relative position nieasurenient.," To account for this additional error source, we add 0.05 mas in quadrature to the SNR-determined error and the fitting errors for each relative position measurement." + llere. note (hat we have been forced to add even more nomenclature. since component D3 splits into at least three components al 15 GllIz. which we unimaginativelv call D3a through D3c Crom west to east).," Here, note that we have been forced to add even more nomenclature, since component D3 splits into at least three components at 15 GHz, which we unimaginatively call D3a through D3c (from west to east)." + We measure position shifts relative to D3b. (he most likely identification lor the AGN (see Section 4)).," We measure position shifts relative to D3b, the most likely identification for the AGN (see Section \ref{sec:AGN}) )." + In 1998.42. the 8.4-GIIz separation of D3b and EL was 68.1520.10 mas. where we have used (he beam size in the East-West direction (roughly (he direction of separation) to compute (he error.," In 1998.42, the 8.4-GHz separation of D3b and E1 was $68.15\pm 0.10$ mas, where we have used the beam size in the East-West direction (roughly the direction of separation) to compute the error." + In 2002.37. the 15-GlIz separation between the same (wo components was 68.33+0.06 mas.," In 2002.37, the 15-GHz separation between the same two components was $68.33\pm 0.06$ mas." + Similarly. we can compute the separation on a much smaller scale. between D3b and D3c.," Similarly, we can compute the separation on a much smaller scale, between D3b and D3c." + This changed from 1.1640.20 mas to 1.5620.06 mas over the same d-vr span: the large error in 1998.42 is caused by the cdiffieuliv in separating D3b and D3c at 8.4 GIIz., This changed from $1.16\pm 0.20$ mas to $1.56\pm 0.06$ mas over the same 4-yr span; the large error in 1998.42 is caused by the difficulty in separating D3b and D3c at 8.4 GHz. + On the [ace of it. the above analysis indicates possible detections of motion at slightly ess than a 2e level in components located at 0.16 pe and 6.3 pe from the AGN.," On the face of it, the above analysis indicates possible detections of motion at slightly less than a $2\sigma$ level in components located at 0.16 pc and 6.8 pc from the AGN." + However. since (he possible svstematie and frequency-dependent effects are of somewhat uncertain nagnitude. we would need al least a ὖσ result to be confident of a detection of motion in the radio components.," However, since the possible systematic and frequency-dependent effects are of somewhat uncertain magnitude, we would need at least a $3\sigma$ result to be confident of a detection of motion in the radio components." + Therefore. we quote 30 upper limits for the motion relative to D3b in 4.14 vi: these upper limits are 0.63 mas for component D3c and 0.35 mas for component El. corresponding to respective velocity upper limits of 0.050e and 0.023c..," Therefore, we quote $3\sigma$ upper limits for the motion relative to D3b in 4.14 yr; these upper limits are 0.63 mas for component D3c and 0.35 mas for component E1, corresponding to respective velocity upper limits of $0.050c$ and $0.028c$." + Assuming that the component identification across (wo epochs is correct. this is the lowest speed limit vet measured [or any Sevlert galaxy.," Assuming that the component identification across two epochs is correct, this is the lowest speed limit yet measured for any Seyfert galaxy." + Of course. we must eite (he usual that we cannot distinguish motion (or lack thereof) of the actual radio-emitting material [rom motion (or lack thereof) of some structure such as a shock. which may stay near one position even while material flows through it.," Of course, we must cite the usual that we cannot distinguish motion (or lack thereof) of the actual radio-emitting material from motion (or lack thereof) of some structure such as a shock, which may stay near one position even while material flows through it." + Still. the verv low limit of 215.000 kms ! within 0.16 pe of the AGN is not much larger than the gas velocities within the broad line region. and indicates that the jet in NGC 4151 may be dominated by thermal plasma in its innermost regions.," Still, the very low limit of $~\sim$ 15,000 km $^{-1}$ within 0.16 pc of the AGN is not much larger than the gas velocities within the broad line region, and indicates that the jet in NGC 4151 may be dominated by thermal plasma in its innermost regions." + At radio wavelengths. AGNs are most easily identified by the presence of a compact. flat- or inverted-spectrum core.," At radio wavelengths, AGNs are most easily identified by the presence of a compact, flat- or inverted-spectrum core." + Ulvestadοἱal.(1998) inferred that such a core was most likely to be present in component E. in order (o account for the slightiv flattened raclio," \citet{ulv98} + inferred that such a core was most likely to be present in component E, in order to account for the slightly flattened radio" +'The major limitation of our adopted approach for the calculation of the galaxy angular power spectrum is the computational difficulty.,The major limitation of our adopted approach for the calculation of the galaxy angular power spectrum is the computational difficulty. +" The signal-to-noise of the SDSS DR7 is sufficient to calculate the angular power spectrum to smaller scales than we have here, but doubling the resolution quadruples the number of pixels to n,225,000."," The signal-to-noise of the SDSS DR7 is sufficient to calculate the angular power spectrum to smaller scales than we have here, but doubling the resolution quadruples the number of pixels to $n_p \approx 25,000$." +" Since the matrix muliplication and inversion scales as O(n?), doubling the resolution is a 64-fold increase in computation, which is beyond our current computational resources, though we are looking into the possibility of performing this calculation, perhaps by KL-compressing the data even further."," Since the matrix muliplication and inversion scales as $O(n^3)$, doubling the resolution is a 64-fold increase in computation, which is beyond our current computational resources, though we are looking into the possibility of performing this calculation, perhaps by KL-compressing the data even further." + We have also explored using alternative platforms to accelerate the computation., We have also explored using alternative platforms to accelerate the computation. +" We have implemented this method on Graphics Processing Units (GPUs), which are part of every modern personal computer."," We have implemented this method on Graphics Processing Units (GPUs), which are part of every modern personal computer." +" GPUs are specifically designed to parallelize simple computations across many small multiprocessors, which make it ideal for vector and matrix calculations."," GPUs are specifically designed to parallelize simple computations across many small multiprocessors, which make it ideal for vector and matrix calculations." +" Using an Nvidia 8800 GTX and transferring the matrix operations to the GPU, while the rest of the code ran on the CPU, proved to be very effective at accelerating the quadratic estimation section of this calculation, speeding it up by a factor of 337."," Using an Nvidia 8800 GTX and transferring the matrix operations to the GPU, while the rest of the code ran on the CPU, proved to be very effective at accelerating the quadratic estimation section of this calculation, speeding it up by a factor of 337." +" For this to be effective, however, the matrices had to fit into the relatively small on board memory of the GPU, which in our test system was 768 MB."," For this to be effective, however, the matrices had to fit into the relatively small on board memory of the GPU, which in our test system was 768 MB." +" In comparison, the memory required by the calculation performed in this paper was roughly 75 GB."," In comparison, the memory required by the calculation performed in this paper was roughly 75 GB." +" So while this platform seems very promising in accelerating this computation, the memory available will not be sufficient in the near future to allow us to meet or exceed the calculations that can be performed using current supercomputers."," So while this platform seems very promising in accelerating this computation, the memory available will not be sufficient in the near future to allow us to meet or exceed the calculations that can be performed using current supercomputers." +" While important, this work has merely been the first step."," While important, this work has merely been the first step." +" By applying this method to volume-limited samples, we can constrain the redshift evolution of the galaxy angular power spectrum."," By applying this method to volume-limited samples, we can constrain the redshift evolution of the galaxy angular power spectrum." +" In addition, we can use the photometric galaxy type classification to distinguish differences in the clustering properties of early- and late-type galaxies in different redshift shells."," In addition, we can use the photometric galaxy type classification to distinguish differences in the clustering properties of early- and late-type galaxies in different redshift shells." +" Furthermore, by utilizing a full 3D, nonlinear theoretical power spectrum, we can model our measurements to higher 6 values and make more stringent measurements of cosmological parameters and we plan on taking these steps in a future work."," Furthermore, by utilizing a full 3D, nonlinear theoretical power spectrum, we can model our measurements to higher $\ell$ values and make more stringent measurements of cosmological parameters and we plan on taking these steps in a future work." +" We have used the quadratic estimation method with KL-compression to determine the SDSS DR7 angular power spectrum, first as a means of radical compression of the angular clustering information, and second to match these observed angular power spectra with theoretical angular power spectra to extract the linear bias and cosmological matter density."," We have used the quadratic estimation method with KL-compression to determine the SDSS DR7 angular power spectrum, first as a means of radical compression of the angular clustering information, and second to match these observed angular power spectra with theoretical angular power spectra to extract the linear bias and cosmological matter density." + We masked for observational effects and applied this method to over 18 million SDSS DR7 galaxies and three magnitude subsamples out to <200., We masked for observational effects and applied this method to over 18 million SDSS DR7 galaxies and three magnitude subsamples out to $\ell \le 200$ . + We also measured the angular power spectrum for each individual stripe out to 4<1000 for stripes 9-37., We also measured the angular power spectrum for each individual stripe out to $\ell \le 1000$ for stripes 9--37. +" We have used the photometric redshift distribution of these galaxies to project the 3D power spectrum to two dimensions to obtain theoretical linear angular power spectrum, and used y? minimization to determine the best fit parameters given the observations."," We have used the photometric redshift distribution of these galaxies to project the 3D power spectrum to two dimensions to obtain theoretical linear angular power spectrum, and used $\chi^2$ minimization to determine the best fit parameters given the observations." +" As the linear angular power spectrum approximation is not valid for the entire range of our estimated angular power spectrum, these parameter constraints have a large allowed range of values."," As the linear angular power spectrum approximation is not valid for the entire range of our estimated angular power spectrum, these parameter constraints have a large allowed range of values." +" We found that the linear bias of our samples was b=1.09+0.05 in the 18-19 magnitude range, b=1.03+0.04 for 19-20, and b=0.924-0.04 for 20-21, with an overall bias of b=0.94+0.04 for our combined 18-21 magnitude sample."," We found that the linear bias of our samples was $b = 1.09 \pm 0.05$ in the 18–19 magnitude range, $b = 1.03 \pm 0.04$ for 19–20, and $b = 0.92 \pm 0.04$ for 20–21, with an overall bias of $b = 0.94 \pm 0.04$ for our combined 18–21 magnitude sample." + We have also calculated the cosmological density of matter as Qm—0.31*0:15 from our entire sample., We have also calculated the cosmological density of matter as $\Omega_m = 0.31^{+0.18}_{-0.11}$ from our entire sample. +" The authors would like to thank Adam Myers, Dragan Huterer, Lloyd Knox for their valuable discussion and advice, and the referee for suggestions that have greatly improved the manuscript."," The authors would like to thank Adam Myers, Dragan Huterer, Lloyd Knox for their valuable discussion and advice, and the referee for suggestions that have greatly improved the manuscript." +" This research was supported in part by the National Science Foundation through XSEDE resources provided by Pittsburgh Supercomputing Center's 4,096 core SGI UV 1000 (Blacklight) and 768 core SGI Altix (Pople) as well as the 1,024 processor SGI Altix (Cobalt) and 1,536 processor SGI Altix (Ember) of the National Center for Supercomputing Applications."," This research was supported in part by the National Science Foundation through XSEDE resources provided by Pittsburgh Supercomputing Center's 4,096 core SGI UV 1000 (Blacklight) and 768 core SGI Altix (Pople) as well as the 1,024 processor SGI Altix (Cobalt) and 1,536 processor SGI Altix (Ember) of the National Center for Supercomputing Applications." +" Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England."," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." + The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions., The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. +" The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the"," The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the" +astrophysical objects.,astrophysical objects. + However. dissipation and dark matter are tightly connected (see Eq. (," However, dissipation and dark matter are tightly connected (see Eq. (" +7)). and we necessarily have different values of central dark matter halo densities when we pass from galaxies to clusters scales.,"7)), and we necessarily have different values of central dark matter halo densities when we pass from galaxies to clusters scales." + In fact. if one ignores the dark component. dissipation can be significantly overestimated at cluster scales; hence. our result suggests some influence of pp on the dissipative infall of baryons.," In fact, if one ignores the dark component, dissipation can be significantly overestimated at cluster scales; hence, our result suggests some influence of $\rho_{DM}$ on the dissipative infall of baryons." + At the same time. the infall itself can affect the dark matter component as well.," At the same time, the infall itself can affect the dark matter component as well." + As suggested by ?.. dissipative infall can produce smaller dark core radii and higher dark central densities.," As suggested by \cite{blu86}, dissipative infall can produce smaller dark core radii and higher dark central densities." + This points out the idea of a deep connection between dissipation and the final configuration of both luminous and dark distributions of matter., This points out the idea of a deep connection between dissipation and the final configuration of both luminous and dark distributions of matter. + The virial metaplane with all its features encloses important aspects of galaxy formation., The virial metaplane with all its features encloses important aspects of galaxy formation. + The phenomenology involved is rich and complex., The phenomenology involved is rich and complex. + In this work. we have concentrated our investigation on the 2VT formulation as a function of direct observables and the dissipational features on the fundamental surface defined by the 2VT as a continuation of Paper 1. Our main results are," In this work, we have concentrated our investigation on the 2VT formulation as a function of direct observables and the dissipational features on the fundamental surface defined by the 2VT as a continuation of Paper I. Our main results are" +reside near (=0.90.150. and 270° with a 20° buller zone in either direction to allow Lor possible wander caused by anv reasonable magnetic pitch angles (if present).,"reside near $\ell=0,\,90,\,180$, and $270\degr$ with a $20\degr$ buffer zone in either direction to allow for possible wander caused by any reasonable magnetic pitch angles (if present)." + To measure (his magnetic pilch angle. a sample of Galactic longitudes should be observed at a single Galactic latitude. sav b=15°. similar to the approach of Heiles(1996).," To measure this magnetic pitch angle, a sample of Galactic longitudes should be observed at a single Galactic latitude, say $b=15\degr$, similar to the approach of \citet{H96}." + Predictions for (he polarization of background starlight. based on pliysies-diiven Galactic dvnamo simulations and empirical Galactic dust distributions. are presented.," Predictions for the polarization of background starlight, based on physics-driven Galactic dynamo simulations and empirical Galactic dust distributions, are presented." + A Stokes radiative transfer model was used to predict the observed stellar polarization properties [rom Monte Carlo generated realistic stellar distributions in the Galaxy., A Stokes radiative transfer model was used to predict the observed stellar polarization properties from Monte Carlo generated realistic stellar distributions in the Galaxy. + A range οἱ skv directions are suggested as particularly diagnostic regions for dillerentiating among Galactic magnetic field model geometries., A range of sky directions are suggested as particularly diagnostic regions for differentiating among Galactic magnetic field model geometries. + Samples across many. Galactic longitudes at one Galactic latitude. however. max be more appropriate lor characterizing (he magnetic pilch angle of magnetic field patterns in the Galaxy.," Samples across many Galactic longitudes at one Galactic latitude, however, may be more appropriate for characterizing the magnetic pitch angle of magnetic field patterns in the Galaxy." + The CDF of observed starlight polarizations is proposed as a tool for calibrating these models., The CDF of observed starlight polarizations is proposed as a tool for calibrating these models. + Table 1. presents quartile values. for each model. of the normalized degree of starlight polarization.," Table \ref{model_table} presents quartile values, for each model, of the normalized degree of starlight polarization." + These measures are easily obtained. from observations of starlight polarizations and can be used to determine a scaling coefficient between the predicted degree of polarization and observed degree of polarization., These measures are easily obtained from observations of starlight polarizations and can be used to determine a scaling coefficient between the predicted degree of polarization and observed degree of polarization. + The role of the Galactic magnetic field in interstellar dvnamies and star lormation is only beginning to be understood. but new technical advances will permit probing Chis nmvsterious component of our Galaxy.," The role of the Galactic magnetic field in interstellar dynamics and star formation is only beginning to be understood, but new technical advances will permit probing this mysterious component of our Galaxy." + The study of the Galactic magnetic field has been dominated by Faraday rotation measurements. but new tools. such as NIE. polarization of backeround starlight. complement (hese studies.," The study of the Galactic magnetic field has been dominated by Faraday rotation measurements, but new tools, such as NIR polarization of background starlight, complement these studies." +eelectric currents.,electric currents. +We now presentSpilzer spectra of the 14 mid-IR luminous NLRGs that. ostensibly contain hidden quasar nuclei (Figs.,We now present spectra of the 14 mid-IR luminous NLRGs that ostensibly contain hidden quasar nuclei (Figs. + 2-4)., 2-4). + We also plot the spectral energy. distributions (SEDs) of the sources with published near-IR. photometry (Fig., We also plot the spectral energy distributions (SEDs) of the sources with published near-IR photometry (Fig. + 5)., 5). + The collected photometric data were measured in the J. Il. IX. L/. and M wavelength bands from the ground 2000).," The collected photometric data were measured in the J, H, K, $^\prime$, and M wavelength bands from the ground \citep{ll84,llm85,srl99,sww00}." +". The photometric apertures range in size from 3—11"". with preference eiven to the apertures that most closely match theSpitzer Sb slit width."," The photometric apertures range in size from $3-11\arcsec$, with preference given to the apertures that most closely match the SL slit width." + Where available. the eround-based L' and M-band photometry agrees withSpi/zer spectrophotometry remarkably well.," Where available, the ground-based $^\prime$ and M-band photometry agrees with spectrophotometry remarkably well." + There is no indication of variability over the time span of 20 vr., There is no indication of variability over the time span of 20 yr. +" Four of the low-redshift NLIGs (3C 33. 234. 381. and 452) have broad peaks in their pL, spectra (and SEDs) at 1.5—2.5xLOM Hz (12-20 yan)."," Four of the low-redshift NLRGs (3C 33, 234, 381, and 452) have broad peaks in their $\nu L_\nu$ spectra (and SEDs) at $1.5-2.5\times 10^{13}$ Hz (12-20 $\mu$ m)." + A maxinnumn and spectral curvature near 20 jan are also suggestive of broad peaks in theSpilzer spectra of 3C 55. 244.1. 265. and 330.," A maximum and spectral curvature near 20 $\mu$ m are also suggestive of broad peaks in the spectra of 3C 55, 244.1, 265, and 330." + The large amplitude (~0.5—1.0 dex) of the mid-IB. bump (Fig., The large amplitude $\sim 0.5-1.0$ dex) of the mid-IR bump (Fig. + 5) excludes a large contribution of svnchrotron emission to the mid-IR. continuum of most sources., 5) excludes a large contribution of synchrotron emission to the mid-IR continuum of most sources. + This is nol surprising il (hie equatorial plane of the clusiv torus is roughly. perpendicular to the radio jet. such (hat jet emission is beamed away.," This is not surprising if the equatorial plane of the dusty torus is roughly perpendicular to the radio jet, such that jet emission is beamed away." + The high redshifts of the NLRGs 3C 172. 220.1. 263.1. 268.1. and 280 preclude the identification of a mid-IR bump in the SEDs of these sources.," The high redshifts of the NLRGs 3C 172, 220.1, 263.1, 268.1, and 280 preclude the identification of a mid-IR bump in the SEDs of these sources." + The unusually flat. blue SED of 3€ 433 may indicate a quasar viewed al/oiw inclination (Section 3.2.2).," The unusually flat, blue SED of 3C 433 may indicate a quasar viewed at inclination (Section 3.2.2)." + We attribute (he mil-IR. continuum bump visible in most sources to thermal emission from warm or hot dust., We attribute the mid-IR continuum bump visible in most sources to thermal emission from warm or hot dust. + Fitting the mid-IR peak with a single-temperature blackbody model indicates dust with a temperature of 210—22540.5 W (Fie., Fitting the mid-IR peak with a single-temperature blackbody model indicates dust with a temperature of $210-225\pm 0.5$ K (Fig. + 5)., 5). + While this temperature characterizes the peak of the mid-IR. SED. hotter dust must also be present.," While this temperature characterizes the peak of the mid-IR SED, hotter dust must also be present." + At [requencies grealer than the peak of the SED (2.0—7.5x10! Iz). the continuum emission of most sources can be characterized using a power law with spectral index a=1.1—2.1 (Table 1 Fig.," At frequencies greater than the peak of the SED $2.0-7.5\times 10^{13}$ Hz), the continuum emission of most sources can be characterized using a power law with spectral index $\alpha = 1.1-2.1$ (Table 1 Fig." + 6)., 6). + This emission likelv comes from a continuous distribution of dust temperature., This emission likely comes from a continuous distribution of dust temperature. + We measure the spectral index between 7 and 15 jan. avoiding the 9.7 san and 18 jan silicate absorption troughs.," We measure the spectral index between 7 and 15 $\mu$ m, avoiding the 9.7 $\mu$ m and 18 $\mu$ m silicate absorption troughs." + The most blue and apparently. hottest mid-IB. luminous NLRG is 3C 265. while the most red and coolest are 3C 55 and 3C 268.1 (Fig.," The most blue and apparently hottest mid-IR luminous NLRG is 3C 265, while the most red and coolest are 3C 55 and 3C 268.1 (Fig." + 6)., 6). + In comparison. some mid-IK. weak sources such as 3C 310 and 3C 388 are quite blue (a~—0.1— 470.7). indicating a large contribution of starlight from the host galaxy to the 7 sam continuum.," In comparison, some mid-IR weak sources such as 3C 310 and 3C 388 are quite blue $\alpha \sim -0.1- +0.7$ ), indicating a large contribution of starlight from the host galaxy to the 7 $\mu$ m continuum." + The near-IR continuum shifts into theSpitzer IRS passband [or the highest redshift (2> 0.7) sources., The near-IR continuum shifts into the IRS passband for the highest redshift $z>0.7$ ) sources. + The spectra of the NLRGs 3€ 55 and 3C 265 steepen above 7.5xLOM , The spectra of the NLRGs 3C 55 and 3C 265 steepen above $7.5\times10^{13}$ +Rody colours of our literature sample with those of the Thompson et al. (,$R-K$ colours of our literature sample with those of the Thompson et al. ( +1999) sample.,1999) sample. + For 16:8ἐν<17.8 and IONON«15.5. we found average 2A colours (3.60£0.11 and 3.833:0.09 respectively) which are consistent with those derived by Thompson et al. (," For $16.8\leq K < 17.8$ and $17.8\leq K < 18.8$, we found average $R-K$ colours $3.60\pm0.11$ and $3.83\pm0.09$ respectively) which are consistent with those derived by Thompson et al. (" +1999) in their survey (8.69+0.05 and 3.83+0.04 respectively).,1999) in their survey $3.69\pm0.05$ and $3.83\pm0.04$ respectively). + Figure 4 shows the colour distributions of the galaxies selected [rom the literature field sample and from our ACN fields., Figure 4 shows the colour distributions of the galaxies selected from the literature field sample and from our AGN fields. + Since both distributions contain lower limits on the Rody colours. we used the ASURV. Bev .2 statistical software package (see LaValley. Isobe Feigelson 1992).," Since both distributions contain lower limits on the $R-K$ colours, we used the ASURV Rev 1.2 statistical software package (see LaValley, Isobe Feigelson 1992)." + As already suggested by Figure 4. we found that the ealaxies with A«19.2 selected in AGN fields are reclder han those selected from the general field.," As already suggested by Figure 4, we found that the galaxies with $K<19.2$ selected in AGN fields are redder than those selected from the general field." + In. particular. all he statistical tests available in ASURY show consistently hat the two distributions are dillerent at. 299.994 (2 do) significance level.," In particular, all the statistical tests available in ASURV show consistently that the two distributions are different at $\geq$ $\geq 4 \sigma$ ) significance level." + Such result does not change significantly. if we split our total sample into the RG and he RLQ sub-samples: the RC: sample is redder than the iterature field sample at 2299.99 significance. whereas the (LO sample is redder at 99.0% significance level.," Such result does not change significantly if we split our total sample into the RG and the RLQ sub-samples: the RG sample is redder than the literature field sample at $\geq$ significance, whereas the RLQ sample is redder at $99.0$ significance level." + If we exclude from this analysis the four fields with the üghest densities of EROs (Le. ALRCIOLT-220. NIC1O40-285. MIRCLO4S-272 and PINSIS51-O18). the result. does not change significantly: the galaxies in the AGN fields continue to be redder than the field. galaxies at confidence level (about 3.50).," If we exclude from this analysis the four fields with the highest densities of EROs (i.e. MRC1017-220, MRC1040-285, MRC1048-272 and PKS1351-018), the result does not change significantly: the galaxies in the AGN fields continue to be redder than the field galaxies at confidence level (about $\sigma$ )." + This suggests that τοῦ colour excess: is not due to particularly overdense fields. but to the general population of galaxies in all the AGN fields.," This suggests that red colour excess is not due to particularly overdense fields, but to the general population of galaxies in all the AGN fields." + Such results strengthens the result on the overdensity of EROs with dv>6 discussed in the previous section., Such results strengthens the result on the overdensity of EROs with $R-K>6$ discussed in the previous section. + Finally. we found that the mean 2A colours estimated with the Waplan-Meier estimator. for the literature. (RG|RLQ). IG. and RLQ samples are respectively: 3.717. 4.108. 4.289. and 3.921.," Finally, we found that the mean $R-K$ colours estimated with the Kaplan-Meier estimator for the literature, (RG+RLQ), RG, and RLQ samples are respectively: 3.717, 4.108, 4.289, and 3.921." + Lt is also important to compare the colour distributions of the galaxies in our AGN field sample with other samples of AGN fields taken from the literature., It is also important to compare the colour distributions of the galaxies in our AGN field sample with other samples of AGN fields taken from the literature. + To this purpose. we used the data collected by Hall Green (1998) observing 30 fields containing racio-Ioud quasars: LO at redshifts οκ ld. and 20 at L4«22.0.," To this purpose, we used the data collected by Hall Green (1998) observing 30 fields containing radio-loud quasars: 10 at redshifts $1.02$ are excluded (PKS1351-018 and PKS1556-245). + The results discussed. in section 7.1 show that our RC ancl RLQ sub-samples have dillerent average colours (2 A-4280 vs. FHA —3.921 respectively)., The results discussed in section 7.1 show that our RG and RLQ sub-samples have different average colours $R-K$ =4.289 vs. $R-K$ =3.921 respectively). + Such a cillerence is also confirmed by the comparison of their colour istributions. for which the statistical tests inclicate that re two distributions are dillerent at confidence level.," Such a difference is also confirmed by the comparison of their colour distributions, for which the statistical tests indicate that the two distributions are different at confidence level." + —owever. because of the limited. statistics of our. survey (only 6 It fields vs. S RLQ fields). we have compared rw colour distributions of the RC fields with the colour istribution of large Hall Green (1998) quasar sample (30 jelds at 12< 2).," However, because of the limited statistics of our survey (only 6 RG fields vs. 8 RLQ fields), we have compared the colour distributions of the RG fields with the colour distribution of large Hall Green (1998) quasar sample (30 fields at $11.1rg., We subtracted the background stellar contamination estimated from the star counts in the radial zone $r>1.1~r_t$. + The BS seem to be more concentrated than the corresponding SGB stars only in the inner, The BS seem to be more concentrated than the corresponding SGB stars only in the inner + The BS seem to be more concentrated than the corresponding SGB stars only in the inner, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$ + The BS seem to be more concentrated than the corresponding SGB stars only in the inner2, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$2 + The BS seem to be more concentrated than the corresponding SGB stars only in the inner25, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$25 + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250 + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\ + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\d + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\di + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:3, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div3 + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:30, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div30 + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:300, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300 + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:300, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300\ + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:300, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300\a + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:300, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300\ar + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:300, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300\arc + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:300, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300\arcs + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:300, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300\arcse + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:300, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300\arcsec + The BS seem to be more concentrated than the corresponding SGB stars only in the inner250:3007, The BS seem to be more concentrated than the corresponding SGB stars only in the inner$250\div300\arcsec$ +The high-cucrey ganuua-ray sky will be studied with urecedeuted seusitivity by the Large Area Telescope (LAT). which was launched by NASA onu the mission in June 2008.,"The high-energy gamma-ray sky will be studied with unprecedented sensitivity by the Large Area Telescope (LAT), which was launched by NASA on the mission in June 2008." + The catalog of gamma-ray sources from the previous nuüsson in this euergy range. EGRET on the Compton Caniua-Ray Observatory has approximately 270 sources (7).," The catalog of gamma-ray sources from the previous mission in this energy range, EGRET on the Compton Gamma-Ray Observatory, has approximately 270 sources ." + Por the LAT. several thousand eiuiuuiae-ray sources are expected to be detected. with auch more accurately determined locations. spectra. aud leht curves.," For the LAT, several thousand gamma-ray sources are expected to be detected, with much more accurately determined locations, spectra, and light curves." + We would Like to reliable detect as many celestial sources of euni rays as possible., We would like to reliably detect as many celestial sources of gamma rays as possible. + The question is nof ⋅ ⋅⋅ exposure⋅ ⋅⊟≻↥⋅↻↥⋅↸∖↖↽↕∪∏↴∖↴∐↕∶↴∙⊾∐⊣∖∐↸∖↥⋅∶↴∙≵↖↽∶↴∙⊾⋜⊔⊔⋯⋜⊢↥⋅⋜↧⋅↖↽∐∐↴∖∷∖↴↕∪∐↴∖↴∙↑∐∖ times., The question is not simply one of building up adequate statistics by increasing exposure times. + The majority of the sources that the LAT will detect are likely to be οἱ numerayo blazars (distant galaxies whose gamunaray clussion ds powered * accretion: outo supermassive. black holes). which. are intrinsically⋅⋅⋅ variable.," The majority of the sources that the LAT will detect are likely to be gamma-ray blazars (distant galaxies whose gamma-ray emission is powered by accretion onto supermassive black holes), which are intrinsically variable." +⋅ Thev↴ fare episodically⋅⋅ i ⋅⋝eamunua ravs., They flare episodically in gamma rays. + The time scales of flares. which cau merease the flux ooa factor of LO or more. can be minutes to weeks.," The time scales of flares, which can increase the flux by a factor of 10 or more, can be minutes to weeks." + The duty evcle of faring in eauuna ravs is not well determined vot. but individual blazars cau go mouths or voars between Hares and in ⋅⋝general we will⋅ not know im⋅ advance where ou the sky the sources will. be found.," The duty cycle of flaring in gamma rays is not well determined yet, but individual blazars can go months or years between flares and in general we will not know in advance where on the sky the sources will be found." +". The fluxes of celestial gamuna ravs are low. especially relative to the ~1 iu? effective area of the LAT (by far the lurgest effective collecting area ever in the GeV range),"," The fluxes of celestial gamma rays are low, especially relative to the $\sim$ 1 $^2$ effective area of the LAT (by far the largest effective collecting area ever in the GeV range)." + An additional complicating factor is that diffuse chussion from the Milky Way itself Qvlich originates in cosluic-ray interactions with interstellar gas audradiation) qiakes a relatively intense. structured foreground emission.," An additional complicating factor is that diffuse emission from the Milky Way itself (which originates in cosmic-ray interactions with interstellar gas and radiation) makes a relatively intense, structured foreground emission." + The few verv brightest eammaray sources will provide approximately 1 detected gamuna ray per minute when they are in the field of view of the LAT., The few very brightest gamma-ray sources will provide approximately 1 detected gamma ray per minute when they are in the field of view of the LAT. + The diffuse emission of the Milkv. Way will provide about 2 ganna pays per second. distributed over the ~2 sr field of view.," The diffuse emission of the Milky Way will provide about 2 gamma rays per second, distributed over the $\sim$ 2 sr field of view." + . ↴∖↴∐⊔↻↕⋅↖↽∪∐↸∖∪⊔∏∐↕≼∐∐∶↴∙⊾∏↻⋜⊔∐∖≺∣∏⋜↧↑↸∖↴∖↴↑⋜↧⊓↴∖↴⊓↸⊳↴∖↴↴⋝∙↖⇁↕∐↸⊳↥⋅↸∖⋜↧↴∖↴↕∐∶↴⋁. ⋅⋅ standard imethod of source detection has been model fitting — maxunuiziueg the likelihood function while moving val poiut sources around iu the region of the sky beiug analyzed.," For previous high-energy gamma-ray missions, the standard method of source detection has been model fitting — maximizing the likelihood function while moving trial point sources around in the region of the sky being analyzed." + This approach has been driven by the lanited photon counts auc the relatively. limited⋅⋅ resolution⋅ of. eanmnia-rav telescopes., This approach has been driven by the limited photon counts and the relatively limited resolution of gamma-ray telescopes. + However. at the scusitivity of the LAT. even a relatively “quiet” part of the sky iav wave 10 or more point sources close enough together o need to be modeled simultaneously when maxiuiüziusg he (computationally expensive) likelihood function.," However, at the sensitivity of the LAT, even a relatively ""quiet"" part of the sky may have 10 or more point sources close enough together to need to be modeled simultaneously when maximizing the (computationally expensive) likelihood function." + For lis reason aud because of the need to search im time. ton-paraluetric algoritlaus for detecting sources are beiug investigated.," For this reason and because of the need to search in time, non-parametric algorithms for detecting sources are being investigated." +where d is the the star's distance (to the earth.,where $d$ is the the star's distance to the earth. + Observationallv. one has J-Iconst.," Observationally, one has ^2 = }^2." +—9.5x10? kin?Pin!WyeV⋅ In order to be consistent with observation. (he boundary lavers temperature should be neither too high (not to affect the X-ray spectrum) nor (oo low (to keep theRavleieh—Jeans slope). i.e. (Durwitzetal.2003)..," In order to be consistent with observation, the boundary layer's temperature should be neither too high (not to affect the X-ray spectrum) nor too low (to keep theRayleigh-Jeans slope), i.e. \citep{Burwitz03}, 4 < <33 ." +" From Eqs.(2)). (2.2)). (6)). and (7)). one comes to 17km «(—————)* <49 kan. where only jay, and M ave [ree parameters if (he stars radius (ancl (hus the mass through IE«q.(2.1))) is determined observationallv."," From \ref{B-mum}) ), \ref{rm}) ), \ref{Trm}) ), and \ref{}) ), one comes to 17 < < 49, where only $\mum$ and $\mdot$ are free parameters if the star's radius (and thus the mass through \ref{M-R}) )) is determined observationally." +" These two inequations of Eq.(8)) eive two dashed lines in M-j6, diagram and constrain the allowed region to a small belt. (see Fig. 1)).", These two inequations of \ref{rm2}) ) give two dashed lines in$\mdot$ $\mum$ diagram and constrain the allowed region to a small belt (see Fig. \ref{figct}) ). + To reproduce the observed spectrum in UV-optical bands. the boundary laver should be optically thick.," To reproduce the observed spectrum in UV-optical bands, the boundary layer should be optically thick." + We assume that the accreted mattersradial velocity decreases [rom [ree fall velocity ey to zero al the boundary laver., We assume that the accreted matter's velocity decreases from free fall velocity $v_{\rm ff}$ to zero at the boundary layer. + From mass continuity pe—M/Aziz. the density p should increase inward.," From mass continuity $ +\rho v = {{\mdot}/{4\pi \rmag^2} }, +$ the density $\rho$ should increase inward." + The magnetic pressure at radius ris P(r)=B(r)/(8x)pe/(zr). Let's Consider a cubic mass with border à and density. p near the boundary laver of the mass flow.," The magnetic pressure at radius $r$ is $ \mathcal{P}(r) = {B(r)^2 +/(8\pi)} = \mu^2/(2\pi r^6).$ Let's Consider a cubic mass with border $a$ and density $\rho$ near the boundary layer of the mass flow." + The eube would feel a force by the magnetic field Fw UP, The cube would feel a force by the magnetic field F a^3. + The pressure gradient OP/Orxrq is proximately a constant if the the laver is thin.," The pressure gradient ${\partial \mathcal{P}}/{\partial r}\propto +r_{\rm m}^{-7}$ is proximately a constant if the the layer is thin." + With the conservation of radial momentum. —£d= de). and the definition of differential displacement. die=—ved/. we have Fdr~medee?pede.," With the conservation of radial momentum, $-F{\rm d}t={\rm +d}(mv)$ , and the definition of differential displacement, ${\rm +d}x=-v{\rm d}t$, we have $F{\rm d}x \sim mv{\rm d}v\sim a^3\rho v +{\rm d}v$." + One could then estimate the w-value of the laver Ge220 at the bottom where e220and p—py) tobe. ure xr.," One could then estimate the $x$ -value of the layer $x\simeq 0$ at the bottom where $v\simeq 0$and $\rho=\rho_{\rm +max}$) tobe, x v v ." +Making (hese assumptions. we can compute a=a/itp. lor each known exoplanet planet whose semimajor axes @ has been measured.,"Making these assumptions, we can compute $\alpha=a/R_E,$ for each known exoplanet planet whose semimajor axes $a$ has been measured." + Figure 1 shows (he results lor all planets for which we have estimates of a.AL.My.Dj. and the orbital period. 7. We have delined q=Αμαν. The two dashed lines in each panel enclose the region 0.5 Ly) from the center of mass.," In the next section we will study the geometry of the isomagnification contours of close-orbit planetary systems, and will find that there is a small region exhibiting deviations from the point-lens form at large distances $u>1\, R_E$ ) from the center of mass." + This region rotates around the center of mass al the orbital period., This region rotates around the center of mass at the orbital period. + The region of deviation can therefore rotate into the path οἱ the source track. increasing the probability of detection.," The region of deviation can therefore rotate into the path of the source track, increasing the probability of detection." + If eis the relative transverse motion. the proper motion is The Einstein angle is Define τι lo be the time taken for the source-lens separation to change by an angle equal to the Einstein angle.," If $v$ is the relative transverse motion, the proper motion is The Einstein angle is Define $\tau_{E,1}$ to be the time taken for the source-lens separation to change by an angle equal to the Einstein angle." + For nearby lenses. te72:05/4. and ils value can be comparable to the value of 2. when α is small.," For nearby lenses, $\tau_{E,1}\approx \theta_E/\mu$, and its value can be comparable to the value of $P,$ when $\alpha$ is small." + For. example. a solar mass lens at 125 pe will have TeyCNN days if e—20 kms |. If the detection limit is 2. the event may be detectable during the time taken to cross through 6/25. For a range of lens masses and distances. several orbits may occur during a lensing event.," For, example, a solar mass lens at $125$ pc will have $\tau_{E,1}\approx 88$ days if $v=20$ km $^{-1}.$ If the detection limit is $2\%$, the event may be detectable during the time taken to cross through $6\, R_E.$ For a range of lens masses and distances, several orbits may occur during a lensing event." + When the projected distance between planet and star is significantly smaller (han, When the projected distance between planet and star is significantly smaller than +1) Highly accreting stars are seen to be less active with respect to low accretion counterparts. possibly because of (a) different rotational properties. (b) disk/accretion induced modifications of the coronal magnetic field geometry. or (c) anomalous interstellar X-ray. absorption due to the presence of circtumstelar materiL,"4) Highly accreting stars are seen to be less active with respect to low accretion counterparts, possibly because of (a) different rotational properties, (b) disk/accretion induced modifications of the coronal magnetic field geometry, or (c) anomalous interstellar X-ray absorption due to the presence of circumstellar material." + Additional deep X-ray. aud LR observations are needed to advance our understanding and euable us to identify which scenario(s) Nature prefers., Additional deep X-ray and IR observations are needed to advance our understanding and enable us to identify which scenario(s) Nature prefers. + The authors would like to thauk L. Hartiuan for useful discussion., The authors would like to thank L. Hartman for useful discussion. + This work was partially supported at the CfA by NASA contracts NASS-38218 and aud by NASA erant NASS-1967., This work was partially supported at the CfA by NASA contracts NAS8-38248 and NAS8-39073 and by NASA grant NAS5-4967. + F.D.. ELF. CLNL. aud ο. wish to acknowledge support from the Italian Space Agency (ASL) and MURST.," F.D., E.F., G.M., and S.S. wish to acknowledge support from the Italian Space Agency (ASI) and MURST." + ELF. would like to thank the CLA for its hospitality curing his Fellow visits., E.F. would like to thank the CfA for its hospitality during his Fellow visits. + Here we describe a “composite” source metlioc we employed to study the mean X-ray. properties oL groups of ONC inembers. some or all of which were individually undetected in our HRC cata.," Here we describe a “composite” source method we employed to study the mean X-ray properties of groups of ONC members, some or all of which were individually undetected in our HRC data." + The method was applied iu 2.2 to undetected low mass stars. auc in 82.3.. to objects of substellar mass.," The method was applied in \ref{sect:LxvsMass} to undetected low mass stars, and in \ref{sect:bd}, to objects of substellar mass." +" The basic steps of our methocl are to: 1) defiue a suitable sample of stellar or substellar objects: 2) determine the number of pliotons detected in a circular region at the X-ray position correspouciug to eachoplical object: 3) correct the photon uumbers for backgrouud coutributious aud the Lact that a (predictable) fraction of the photons from a poinut-like source will fall outside the extraction circle: 1) stun the contributions of siugle objects aud derive a signal-to-noise ratio (SNR) for the ""composite"" source: 5) divide the “composite” source net counts (or upper limit. for SNRs below a set threshold) by the cumulative exposure time to obtain a mean couut rate for objects in the sample: aud finally. 6) convert the mean count rate (or upper limit) to a ""composite"" Ly value."," The basic steps of our method are to: 1) define a suitable sample of stellar or substellar objects; 2) determine the number of photons detected in a circular region at the X-ray position corresponding to each object; 3) correct the photon numbers for background contributions and the fact that a (predictable) fraction of the photons from a point-like source will fall outside the extraction circle; 4) sum the contributions of single objects and derive a signal-to-noise ratio (SNR) for the “composite” source; 5) divide the “composite” source net counts (or upper limit, for SNRs below a set threshold) by the cumulative exposure time to obtain a mean count rate for objects in the sample; and finally, 6) convert the mean count rate (or upper limit) to a “composite” $L_X$ value." + The critical points iu these six steps for estimating Ly values for tle composite sources are as follows: The selection of composite source samples was based on stellar (or substellar) mass as given by ourseinple., The critical points in these six steps for estimating $L_X$ values for the composite sources are as follows: The selection of composite source samples was based on stellar (or substellar) mass as given by our. + We also added three more requirements: a) that the objects lay in the inner 5' of the HRC field of view. b) that the closest detected X-ray source (other than the object in question. if detected) was farther away than 5” and e) that the measured optical extinction Ay was," We also added three more requirements: a) that the objects lay in the inner $^{\prime}$ of the HRC field of view, b) that the closest detected X-ray source (other than the object in question, if detected) was farther away than $^{\prime\prime}$ and c) that the measured optical extinction $A_V$ was" +heat large5 columns of molecular 5gas while experiencing5 very little extinction.,heat large columns of molecular gas while experiencing very little extinction. + The effect. of X-aavs on the Jeans mass of dense cores and the IMIF has been recently proposed for a powerful distant QSO (Bradford et al., The effect of X-rays on the Jeans mass of dense cores and the IMF has been recently proposed for a powerful distant QSO (Bradford et al. + 2009) and it mav represent a neglected but important AGN [eedback factor on its cireumnuclear star formation., 2009) and it may represent a neglected but important AGN feedback factor on its circumnuclear star formation. + The molecular line diagnostics of starburst-inducecd CRDRs and AGN-originating NDRs can be to a large degree degenerate when galaxies host both power sources., The molecular line diagnostics of starburst-induced CRDRs and AGN-originating XDRs can be to a large degree degenerate when galaxies host both power sources. +" This has been noticed in earlier comparative studies of NDRs and regions with higher Ve, values (thoug[un onlv up to 100xVer cay) found that only carefully chosen line ratios can distinguish between (hem (Meijerink. Spaans. Israel 2006)."," This has been noticed in earlier comparative studies of XDRs and regions with higher $\rm U_{CR}$ values (though only up to $\times $$\rm U_{CR,Gal}$ ) found that only carefully chosen line ratios can distinguish between them (Meijerink, Spaans, Israel 2006)." + The still larger CIR energy. densiües expected in CRDRs of ULIBGs will further compound (hese difficulties., The still larger CR energy densities expected in CRDRs of ULIRGs will further compound these difficulties. + Provided that a powerful X-ray huninous AGN heating up the bulk of the molecular eas in ils host galaxy. can be somehow exeluded (e.g. via hard. X-ray. observations). anv set of molecular lines and ratios (hat can strongly constrain (he temperature of the dense gas UV-shielded phase (n(Ils)710cem 7?) in ULIRGs will be valuable.," Provided that a powerful X-ray luminous AGN heating up the bulk of the molecular gas in its host galaxy can be somehow excluded (e.g. via hard X-ray observations), any set of molecular lines and ratios that can strongly constrain the temperature of the dense gas UV-shielded phase $\rm n(H_2)$$>$ $^4$ $^{-3}$ ) in ULIRGs will be valuable." + Indeed. given that in the hierachical structures of typical molecular clouds the dense gas regions: a) lie well inside nuch larger ones that strongly attenuate far-UV light and b) cool strongly via molecular ine emission because of their high densities. (hen any evidence for high temperatures for the dense gas phase would be a indicator of strong Cli-heating.," Indeed, given that in the hierachical structures of typical molecular clouds the dense gas regions: a) lie well inside much larger ones that strongly attenuate far-UV light and b) cool strongly via molecular line emission because of their high densities, then any evidence for high temperatures for the dense gas phase would be a indicator of strong CR-heating." + In that regaud observations of ügh-J CO lines such as J=65 andits CO isotopologue have already been proven excellent in revealing Cli-heated rather (han UV/photoelectricallv-heated molecular gas in galactic iiclei (Hailev-Dunsheath οἱ al., In that regard observations of high-J CO lines such as J=6–5 its $^{13}$ CO isotopologue have already been proven excellent in revealing CR-heated rather than UV/photoelectrically-heated molecular gas in galactic nuclei (Hailey-Dunsheath et al. + 2008)., 2008). +" respective of the particular set of rotational lines used as à “thermometer” of the dense gas. tliree general requirements must be met: a) all lines mist ave high critical densities (Neg >lOhcem 7). b) have widely separated Ey4,/kpy factors. and c) the J-corresponding lines of al least one rare isotopologue must also be observed (e.g. PCOand POCO. or CPSand CS. ete)."," Irrespective of the particular set of rotational lines used as a “thermometer” of the dense gas, three general requirements must be met: a) all lines must have high critical densities $\rm n_{crit}$$>$ $^{4}$ $^{-3}$ ), b) have widely separated $\rm E_{J+1,J}/k_B$ factors, and c) the J-corresponding lines of at least one rare isotopologue must also be observed (e.g. $^{12}$ CO $^{13}$ CO, or $^{32}$ S $^{34}$ S, etc)." + The first two ensure probing of the dense eas phase while maintaining good Tj-sensitivitv. and the last one is necessary [or reducing well-known degeneracies when modeling only transitions of the most abundant isotopologue which often have significant optical depths.," The first two ensure probing of the dense gas phase while maintaining good $\rm T_k$ -sensitivity, and the last one is necessary for reducing well-known degeneracies when modeling only transitions of the most abundant isotopologue which often have significant optical depths." +" Molecular lines with n4 210"" * (e.g. HCN. CS rotational transitions) are particularly valuable since. aside [rom emanating Iron eas well within (vpical pre-stellar cores. they (race a phase whose kinematic state is either dictated by selleravily (e.& Goldsmith 2001). or has fully dissipated to thermal motions."," Molecular lines with $\rm n_{crit}$$\ga $ $^5$ $^{-3}$ (e.g. HCN, CS rotational transitions) are particularly valuable since, aside from emanating from gas well within typical pre-stellar cores, they trace a phase whose kinematic state is either dictated by self-gravity (e.g Goldsmith 2001), or has fully dissipated to thermal motions." + This constrains the line formation mechanism (and can be used to remove degeneracies of radiative transfer, This constrains the line formation mechanism (and can be used to remove degeneracies of radiative transfer + By construction. the transition is first. order. and (he resulting temperature dependence is shown in re[24 b. At T... the energy density increases abruptly by the latent heat of decontinement. Ae.,"and = 37 T^4 + B. By construction, the transition is first order, and the resulting temperature dependence is shown in \\ref{2_3}$ $~\!$ b. At $T_c$, the energy density increases abruptly by the latent heat of deconfinement, $\Delta \e$." + Using ((2)). ils value is found to be =e -e 2 ADD. so (hat itis determined completely by the bag pressure measuring the level difference between physical and colored vacua.," Using \ref{Tc}) ), its value is found to be = - = 4 B, so that it is determined completely by the bag pressure measuring the level difference between physical and colored vacua." + For an ideal gas of massless constituents. the trace e—32? of the energv-momentum tensor «quite generally vanishes.," For an ideal gas of massless constituents, the trace $\e-3P$ of the energy-momentum tensor quite generally vanishes." + Nevertheless. in our model of the ideal plasma of massless quarks and egluons. we have for T'>T; ce—3P—A BB. again specified by the bag pressure ancl not zero.," Nevertheless, in our model of the ideal plasma of massless quarks and gluons, we have for $T\geq T_c$ - 3P = 4 B, again specified by the bag pressure and not zero." + This is related to tlie so-called trace anomaly and indicates the dvnamical generation of a dimensional seale: we shall return to it in the next section. where we will find (hat (his scale is set by the vacuum expectation value of the eluon condensate.," This is related to the so-called trace anomaly and indicates the dynamical generation of a dimensional scale; we shall return to it in the next section, where we will find that this scale is set by the vacuum expectation value of the gluon condensate." + We now want to show that the conceptual considerations of the last section indeed follow from strong interaction (ΠοιοςπαΙός as based on QCD as the input. dvnanics., We now want to show that the conceptual considerations of the last section indeed follow from strong interaction thermodynamics as based on QCD as the input dynamics. + QCD is defined by the Lagrangian C= a - CU + ni —g, QCD is defined by the Lagrangian = _a - (i + m_f -g + QCD is defined by the Lagrangian C= a - CU + ni —g, QCD is defined by the Lagrangian = _a - (i + m_f -g +" QCD is defined by the Lagrangian C= a - CU + ni —g,", QCD is defined by the Lagrangian = _a - (i + m_f -g +"centre to the surface of the cloud (which occurs at 0— 90?), divided by the minimum optical depth from the centre to the surface of the cloud (which occurs at 0—0? and 0— 180?).","centre to the surface of the cloud (which occurs at $\theta = +90\degr$ ), divided by the minimum optical depth from the centre to the surface of the cloud (which occurs at $\theta = 0\degr$ and $\theta = 180\degr$ )." +" The parameter p determines how rapidly the optical depth from the centre to the surface rises with increasing 6, i.e. going from the north pole at 0—0? to the equator at 0=90°."," The parameter $p$ determines how rapidly the optical depth from the centre to the surface rises with increasing $\theta$, i.e. going from the north pole at $\theta += 0\degr$ to the equator at $\theta = 90\degr$." +" In this model we assume e=1.03, i.e. a slightly flattened cloud, and p—4."," In this model we assume $e=1.03$, i.e. a slightly flattened cloud, and $p=4$." + This geometry may be more realistic than the spherical cloud presented in the previous section., This geometry may be more realistic than the spherical cloud presented in the previous section. + The mass of the cloud is 510 (see Table 1)., The mass of the cloud is 510 $_{\sun}$ (see Table 1). + Figure 3 shows that the temperature Meprofile in the cloud is similar to the case of the spherical cloud; the temperature drops from 18 K at the edge to 5 K in the centre of the cloud., Figure 3 shows that the temperature profile in the cloud is similar to the case of the spherical cloud; the temperature drops from 18 K at the edge to 5 K in the centre of the cloud. +" However, due to the flattened cloud geometry the cloud ‘equator’ is colder than the cloud ‘poles’."," However, due to the flattened cloud geometry the cloud `equator' is colder than the cloud `poles'." + Figure 4 shows that the SED of the cloud is also similar to that of the spherical cloud., Figure 4 shows that the SED of the cloud is also similar to that of the spherical cloud. + There is no dependence on the viewing angle despite the fact that the optical depth to the centre of the cloud becomes Tejoug~1 at ~200jum., There is no dependence on the viewing angle despite the fact that the optical depth to the centre of the cloud becomes $\tau_{\rm cloud}\sim 1$ at $\sim 200~\micron$. +" 'This is because the temperature varies with the direction in the cloud only in the outer region of the cloud, which is optically thin even at wavelengths up to ~200um."," This is because the temperature varies with the direction in the cloud only in the outer region of the cloud, which is optically thin even at wavelengths up to $\sim 200~\micron$." +" We finally examine a more realistic cloud geometry, i.e. a turbulent cloud."," We finally examine a more realistic cloud geometry, i.e. a turbulent cloud." +" To produce this cloud we start off with a spherical cloud having a density profile where nc. is the density at the centre of the cloud, and ro is the extent of the region in which the density is approximately uniform."," To produce this cloud we start off with a spherical cloud having a density profile where $n_{\rm c}$ is the density at the centre of the cloud, and $r_0$ is the extent of the region in which the density is approximately uniform." +" Note that this profile is less steep than the profile used for the spherical IRDC, hence the higher mass of this cloud."," Note that this profile is less steep than the profile used for the spherical IRDC, hence the higher mass of this cloud." + The values of the parameters are again given in Table 1., The values of the parameters are again given in Table 1. + The mass of the cloud is 27200 Mo., The mass of the cloud is 27200 $_{\sun}$. + A large turbulent velocity field (a= 0.5) is imposed to the cloud (e.g. Goodwin et al., A large turbulent velocity field $\alpha=0.5$ ) is imposed to the cloud (e.g. Goodwin et al. +" 2004), and the cloud is evolved using the SPH code DRAGON, for enough time to produce substructure, i.e. until cores form in the cloud (e.g. Stamatellos et al."," 2004), and the cloud is evolved using the SPH code DRAGON, for enough time to produce substructure, i.e. until cores form in the cloud (e.g. Stamatellos et al." + 2007)., 2007). + DRAGON is a gravitational hydrodynamics code which invokes a large number of particles to represent a physical system., DRAGON is a gravitational hydrodynamics code which invokes a large number of particles to represent a physical system. +" It uses an octal tree (to compute gravity and find neighbours), adaptive smoothing lengths, multiple particle timesteps, and a second-order Runge-Kutta integration scheme."," It uses an octal tree (to compute gravity and find neighbours), adaptive smoothing lengths, multiple particle timesteps, and a second-order Runge-Kutta integration scheme." +" The resulting cloud is shown in Figure 5, in which we plot its density on 3 planes (y=—0.2 pc, left, y=0 pc, centre and y—4-0.2 pc, right)."," The resulting cloud is shown in Figure 5, in which we plot its density on 3 planes $y=-0.2$ pc, left, $y=0$ pc, centre and $y=+0.2$ pc, right)." + We perform a radiative transfer simulation for this cloud using the method of Stamatellos Whitworth (2005)., We perform a radiative transfer simulation for this cloud using the method of Stamatellos Whitworth (2005). + The calculated dust temperature is presented in Figure 6., The calculated dust temperature is presented in Figure 6. + The dust temperature is similar to the temperature calculated in the previous cases., The dust temperature is similar to the temperature calculated in the previous cases. +" However, the temperature distribution at a particular distance from the centre of the cloud is broader due to the clumpiness of the cloud."," However, the temperature distribution at a particular distance from the centre of the cloud is broader due to the clumpiness of the cloud." +" Figure 7 shows that the SED of the cloud peaks at longer wavelengths than in the previous two cases, as the cloud is more massive and consequently it is cooler."," Figure 7 shows that the SED of the cloud peaks at longer wavelengths than in the previous two cases, as the cloud is more massive and consequently it is cooler." +" Simulated observations of the modelled IRDCs are performed, to assess the impact of instrument systematics."," Simulated observations of the modelled IRDCs are performed, to assess the impact of instrument systematics." +" The simulations are produced using V2.31b of the SPIRE photometer simulator (Sibthorpe, Chanial and Griffin 2009)."," The simulations are produced using V2.31b of the SPIRE photometer simulator (Sibthorpe, Chanial and Griffin 2009)." +" This software simulates both the SPIRE instrument, and theHerschel observing modes."," This software simulates both the SPIRE instrument, and the observing modes." + The simulations are performed in a configuration which matches the Hi-GAL observations., The simulations are performed in a configuration which matches the Hi-GAL observations. +" The fast scanning speed (60""per second) option is used (see the SPIRE Observers’ Manua??)), and the observations are made in the SPIRE parallel mode, to match the Hi-GAL mapping mode."," The fast scanning speed per second) option is used (see the SPIRE Observers' ), and the observations are made in the SPIRE parallel mode, to match the Hi-GAL mapping mode." + These observations are performed by continuously scanning the telescope backwards and forwards in a raster pattern while the instruments continuously take data., These observations are performed by continuously scanning the telescope backwards and forwards in a raster pattern while the instruments continuously take data. +" For Hi-GAL two maps are obtained by scanning first along one axis of the instrument array, and then scanning along the perpendicular axis of the array."," For Hi-GAL two maps are obtained by scanning first along one axis of the instrument array, and then scanning along the perpendicular axis of the array." +" This provides redundancy in the data, allowing for the use of maximum likelihood techniques to be used in the subsequent data reduction (Sibthorpe et al."," This provides redundancy in the data, allowing for the use of maximum likelihood techniques to be used in the subsequent data reduction (Sibthorpe et al." + 2008)., 2008). + Realistic noise with a spectrum is simulated with each of the SPIRE bolometers using independent noise parameters based on pre-flight test data., Realistic noise with a spectrum is simulated with each of the SPIRE bolometers using independent noise parameters based on pre-flight test data. + Thermal drifts are not included in these simulations as the information is not available to model these accurately., Thermal drifts are not included in these simulations as the information is not available to model these accurately. +" However, the Herschel/SPIRE pipeline will automatically remove"," However, the /SPIRE pipeline will automatically remove" +The nearby Vireo cluster. is a perfect laboratory to investigate the evolution of galaxies in a dense environment.,The nearby Virgo cluster is a perfect laboratory to investigate the evolution of galaxies in a dense environment. + Recently. observations of a large sample of galaxies suggested that the properties of nuclei. either quiescent or active. in Vireo galaxies are strongly. mass-dependent.," Recently, observations of a large sample of galaxies suggested that the properties of nuclei, either quiescent or active, in Virgo galaxies are strongly mass-dependent." +" This latter fincling is in very good agreement with the general trend found also in the SDSS. where very few AGN are found in galaxies with stellar mass AM, 10^{10.5}\msun$ the AGN fraction is unity." + As a central black hole is a necessary condition for AGN activity. we conclude that the black hole occupation fraction (BILOP) must be unity as well. Coteetal. (2006).," As a central black hole is a necessary condition for AGN activity, we conclude that the black hole occupation fraction (BHOF) must be unity as well. \cite{Cote2006}," +.. Webner Larris (2006) ancl Ferrarese et al. (, Wehner Harris (2006) and Ferrarese et al. ( +"2006) find that. below Al,~LOM Virgo galaxies exhibit nuclear star clusters. whose mass AL...scales with Al, in the same fashion as those of the massive black holes detected in brighter galaxies (Alagorrianetal.1998:Marconi&Lunt2003:LavineRix 2004).","2006) find that, below $M_*\sim 10^{10}\msun$, Virgo galaxies exhibit nuclear star clusters, whose mass scales with $M_*$ in the same fashion as those of the massive black holes detected in brighter galaxies \citep{Magorrian1998, MarconiHunt2003, Haring2004}." +. Although the existence of a nuclear star cluster does not rule out a small. hidden ALDLL. it is suggestive that Ferrarese et al. (," Although the existence of a nuclear star cluster does not rule out a small, hidden MBH, it is suggestive that Ferrarese et al. (" +2006) conclude that “bright galaxies often. and perhaps always. contain supermassive black holes but not stellar nuclei;,"2006) conclude that “bright galaxies often, and perhaps always, contain supermassive black holes but not stellar nuclei." + As one moves to fainter galaxies. nuclei become the dominant feature while AIBIIs might become less common and. perhaps clisappcar entirely at the faint end.," As one moves to fainter galaxies, nuclei become the dominant feature while MBHs might become less common and perhaps disappear entirely at the faint end.""" + There are. three interlaced sides of the intriguing story which appears to link stellar nuclei ancl ALBIS: 1) unclerstanel if (and why) MDIIS. populate preferentially: wright galaxies: 2) understand why stellar nuclei populate xeferentially faint galaxies and 3) understand why the ratio of nuclear to galaxy mass is identical to the ratio of ALBIL o galaxy mass., There are three interlaced sides of the intriguing story which appears to link stellar nuclei and MBHs: 1) understand if (and why) MBHs populate preferentially bright galaxies; 2) understand why stellar nuclei populate preferentially faint galaxies and 3) understand why the ratio of nuclear to galaxy mass is identical to the ratio of MBH to galaxy mass. + In this paper we address the first. issue., In this paper we address the first issue. + A »xossible hint to explain the predominance of star clusters in small galaxies may come from comparing the dynamical time scale and the fragmentation time scale of the infalling σας., A possible hint to explain the predominance of star clusters in small galaxies may come from comparing the dynamical time scale and the fragmentation time scale of the infalling gas. + Detailed calculations are necessary to test this hypothesis. out it can be argued that in shallow potentials gas could ragment before reaching the center of the galaxy.," Detailed calculations are necessary to test this hypothesis, but it can be argued that in shallow potentials gas could fragment before reaching the center of the galaxy." + This is even more suggestive in the case of merger-induced: gaseous infall., This is even more suggestive in the case of merger-induced gaseous infall. + Reearcing the third. issue. Emsellem&vandeVen(2007) for instance show that if galaxies have Sersic profiles. radial compressive forces trigger the collapse of gas in the central regions. and the mass of the nuclear cluster that orms is about of the mass of the host galaxy.," Regarding the third issue, \cite{Emsellem2007} for instance show that if galaxies have Sersic profiles, radial compressive forces trigger the collapse of gas in the central regions, and the mass of the nuclear cluster that forms is about of the mass of the host galaxy." + So. nuclear cluster formation ancl SIBLE feedback might produce he same scaling relation with galaxy mass. but it is unclear whether this is à coincidence or the result of a single. unexplored process.," So, nuclear cluster formation and MBH feedback might produce the same scaling relation with galaxy mass, but it is unclear whether this is a coincidence or the result of a single, unexplored process." +- some but not all have a shell surrounding the star which is detected by the presence of narrow circiustcllar colmpouncuts of Ca IT IS line (okveger aud Reutzsch-ITohu 1995) and of metal liues (Παπος ct al 1995 aud 1998: Andrillat et al 1995): - sole but no all show he UW broad absorption eature centered on ALGOO (Baschek et al 1981: Farageiana85 et al 1900: Tlolweeer et al 1991).,- some but not all have a shell surrounding the star which is detected by the presence of narrow circumstellar components of Ca II K line (Holweger and Rentzsch-Holm 1995) and of metal lines (Hauck et al 1995 and 1998; Andrillat et al 1995); - some but not all show the UV broad absorption feature centered on $\lambda$ 1600 (Baschek et al 1984; Faraggiana et al 1990; Holweger et al 1994). + We recall ji the com#ines cffect of the stellar fux drop aud 1e lowering IUE scusitivity is responsible for the mostly uiderexposed IUE spectra of the middle aud late A-type y.ars. so that the AJ600 could be searched only among 1ο hottest candidates: - for three of t1011 ad abiidance pattern similar to vat of the ISAL has been derived (Venn Lambert On the basis of the few aliudance coherent analvses avalable. several hypotheses have been made ou the aeaep of these stars: 1) very voung stars which have not reached the main sequence (Wacrs et al 1992: Gerbaldi et al 1993: Tolweecr Roentzsch-IIohu 1995)," We recall that the combined effect of the stellar flux drop and the lowering IUE sensitivity is responsible for the mostly underexposed IUE spectra of the middle and late A-type stars, so that the $\lambda$ 1600 could be searched only among the hottest candidates; - for three of them an abundance pattern similar to that of the ISM has been derived (Venn Lambert On the basis of the few abundance coherent analyses available, several hypotheses have been made on the age of these stars: i) very young stars which have not reached the main sequence (Waters et al 1992; Gerbaldi et al 1993; Holweger Rentzsch-Holm 1995)." +" ii) cvarfs in the middle of thei life on the main sequence, wit ran age of 10-10? years (Hiev Barzova. 1995): ii) quite old ojects represcuting a merger of binaries of W UMa tve (Ancievsky The ouly pro)rtv conuuon to all A Boo sirs of Table Lois the weakness of most metal lines. wuch ds also coufixiued by the negative Aa values (a photometric index measuring he blauketiug iu the region A52X0 A3) liensred by Maizen Pavlovski (1989a aud 19895) for he stars they observed."," ii) dwarfs in the middle of their life on the main sequence, with an age of $^7$ $^9$ years (Iliev Barzova, 1995); iii) quite old objects representing a merger of binaries of W UMa type (Andrievsky The only property common to all $\lambda$ Boo stars of Table 1 is the weakness of most metal lines, which is also confirmed by the negative $\Delta$ a values (a photometric index measuring the blanketing in the region $\lambda$ 5200 ) measured by Maitzen Pavlovski (1989a and 1989b) for the stars they observed." + Taking this conunon characteristic of the exot pasa starting point. we| mspoect the possible causes that max odice a weak-Imed spectrum.," Taking this common characteristic of the group as a starting point, we inspect the possible causes that may produce a weak-lined spectrum." + T1ο classical explanatio1 of metal inderaluudauces. Orosars belonging to Population L is related to the existence of simele stars with peculiar atmospheres iu which some eleiueuts are deeted by different aniounts.," The classical explanation of metal underabundances, for stars belonging to Population I, is related to the existence of single stars with peculiar atmospheres in which some elements are depleted by different amounts." + Disturbing is that the abundance pattern is not the same in the A Doo candidates analyzed up to now: one particular clement shows dierent abundance peculiarities in different stars. so that it is citiicult. at present. to establish the average chemical composition of stars and thus to elaborate a theory explaining the phenomenon.," Disturbing is that the abundance pattern is not the same in the $\lambda$ Boo candidates analyzed up to now; one particular element shows different abundance peculiarities in different stars, so that it is difficult, at present, to establish the average chemical composition of stars and thus to elaborate a theory explaining the phenomenon." +" Venn Lambert (]90) formulated the hpothesis hat the phenomenon could IC he result of accretion of gas mt not of dust from circ""nustellar or iuterstellar material.", Venn Lambert (1990) formulated the hypothesis that the phenomenon could be the result of accretion of gas but not of dust from circumstellar or interstellar material. + The only moderm aux detailed analyses available at oeseut are the two pavers by Venji Lambert (1990) aud by St93., The only modern and detailed analyses available at present are the two papers by Venn Lambert (1990) and by St93. + We compared the etal abundances derived for the A Boo stars by these authors wit1 those of the ISM as eiven by Savage Sembach (1996)., We compared the metal abundances derived for the $\lambda$ Boo stars by these authors with those of the ISM as given by Savage Sembach (1996). + This conarison shows that the similarity is ouly mareiual: in the first place there is a laree difference from star to star in the abundance of any eiven clement. uulike what happens in the ISML iu the second place the highest underabundauces in the ISAL are those of Ca aud Ti while inmost A Boo candidates it is that of Alone possible explanations of he phenomenon oue should also take into account the )ossibilitv tiat these stars indeed belong to a metalweals »opulation.," This comparison shows that the similarity is only marginal; in the first place there is a large difference from star to star in the abundance of any given element, unlike what happens in the ISM, in the second place the highest underabundances in the ISM are those of Ca and Ti while in most $\lambda$ Boo candidates it is that of Among possible explanations of the phenomenon one should also take into account the possibility that these stars indeed belong to a metal-weak population." + The kinematic data imiplv that stars »lous to he disk population. which has indeed a uctal-poor population in the range -0.5«|Fe/TI| --1.0 and possibly the thick disk has a uectalaweaς tail at much ower ictalicities (Beors Sonuucr-Larseu. L995).," The kinematic data imply that stars belong to the disk population, which has indeed a metal-poor population in the range $<$ $<$ -1.0 and possibly the thick disk has a metal-weak tail at much lower metallicities (Beers Sommer-Larsen 1995)." + We nust exaiui1ο the two possible cases that stars are either Aain Sequence (MS) aud therefore relatively VOlne. or on the IHorizoutal Brauch aud therefore old.," We must examine the two possible cases that stars are either Main Sequence (MS) and therefore relatively young, or on the Horizontal Branch and therefore old." + The main aremuent to reject the hwpothesis that stars are metal-poor AIS stars is that while in stars Me. 8i. Ca aud Ti are among the most nuderabundant elements. iu metal-poor stars the even-Z ight clemeuts. svuthesized by a capture processes. show au dcrcasing Chahancement over won with decreasing 11οallicity. reaching a 0.4 - 0.5 dex cuhancement at TI|-1.0.," The main argument to reject the hypothesis that stars are metal-poor MS stars is that while in stars Mg, Si, Ca and Ti are among the most underabundant elements, in metal-poor stars the even-Z light elements, synthesized by $\alpha$ capture processes, show an increasing enhancement over iron with decreasing metallicity, reaching a 0.4 - 0.5 dex enhancement at $=-1.0$." + To distinguish. Dlue Horizoutal Branch (BIB) stars youn A Doo stars on the basis of spectroscopic properties alone. is not trivial.," To distinguish Blue Horizontal Branch (BHB) stars from $\lambda$ Boo stars on the basis of spectroscopic properties alone, is not trivial." + However. the BIB population iu he solar neighbourhood wotId be uncoimfortablv large if HOS belonged to this class.," However, the BHB population in the solar neighbourhood would be uncomfortably large if most belonged to this class." + A further argument aeuiist. the BUB hwpothesis is that most stars aro characterized bw mean o high projected rotational volcities. while BIB stars are all slow rotaors.," A further argument against the BHB hypothesis is that most stars are characterized by mean to high projected rotational velocities, while BHB stars are all slow rotators." + All fast rotetors nav be thus rejected as DIIB stars., All fast rotators may be thus rejected as BHB stars. + Although the oossibilitv could be stil considered open for slowly roteving stars (e.g. HD 61191 auk UD ΙΣΤΟ (Diinzen παν (1997) aud a few οhers proposed. by AM). their nunber is very small.," Although the possibility could be still considered open for slowly rotating stars (e.g. HD 64491 and HD 74873 (Paunzen Gray (1997) and a few others proposed by AM), their number is very small." + We recall that low vsui stars may be either intrinsicallv slow roators or fast rotaors seen at high inclination., We recall that low $\sin i$ stars may be either intrinsically slow rotators or fast rotators seen at high inclination. + From the foregoing discussion we reject the lypothesis of ΠΟΙΟΥΣ) of the class to a metal-poor pomulation aud do not discuss it any further., From the foregoing discussion we reject the hypothesis of membership of the class to a metal-poor population and do not discuss it any further. + A completely different origin of weak metal lines is that xoduced by stellar duplicitv., A completely different origin of weak metal lines is that produced by stellar duplicity. + Examples of how a composite spectrum which is the average of two actual coniponents of not very dissimilar spectral type. can be Classified. as Ae-woeak is given by Corbally (1987) for IID 27657 and ΠΟ 53921.," Examples of how a composite spectrum, which is the average of two actual components of not very dissimilar spectral type, can be classified as Mg-weak is given by Corbally (1987) for HD 27657 and HD 53921." + Corbally remarks also that the AB spectrun of TID 11628 “is close to imitating a A Boo star. but the Ad Balmer line class is a compromise betweeu," Corbally remarks also that the AB spectrum of HD 41628 ""is close to imitating a $\lambda$ Boo star, but the A5 Balmer line class is a compromise between" +VB is grateful to Y. Lu. S. Ixaspi aud T. Boller for valuable suggestious.,"VB is grateful to Y. Lu, S. Kaspi and T. Boller for valuable suggestions." + SC is grateful to S. 'Temporiu for having supported this work with useful This research was partially based on data from the ING —u this work we have used the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion. Laboratory. Caliloruia. Tustitute of Techuology. uuder contract. with the National Aeronautics aud Space This research has mace use of the TARTARUS database. which is supported by Jane Turner and Wirpal Naudra under NASA grants NAC5-7385 and NAC5-7067.," SC is grateful to S. Temporin for having supported this work with useful This research was partially based on data from the ING In this work we have used 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 This research has made use of the TARTARUS database, which is supported by Jane Turner and Kirpal Nandra under NASA grants NAG5-7385 and NAG5-7067." +today in relsec:Comp..,today in \\ref{sec:Comp}. + Finally. a discussion of (he limitations of this model and what impact that will have on the results is eiven in re[sec:C'óne..," Finally, a discussion of the limitations of this model and what impact that will have on the results is given in \\ref{sec:Conc}." + A cdwarl galaxy with an eecentric orbit will experience a wide range of extremes as ib (ravels along ils orbit. lrom a low velocity through sparse gas al its apogalacticon to a large velocity through dense eas wilh a strong external radiation field al its perigalacticon.," A dwarf galaxy with an eccentric orbit will experience a wide range of extremes as it travels along its orbit, from a low velocity through sparse gas at its apogalacticon to a large velocity through dense gas with a strong external radiation field at its perigalacticon." + All these environments must be modelled., All these environments must be modelled. + We describe this wide range of environments by considering four scenarios: (he orbital path of the dwarf around the host galaxy. cliscussed in relssec:orbit:: (he heating aud cooling of the gas present. discussed in relssec:healine:: how tidal or rami pressure stripping removes eas from the dwarl in PS: and how (his stripping can be influenced by stellar formation aud feedback. detailed in re[ssecistarform..," We describe this wide range of environments by considering four scenarios: the orbital path of the dwarf around the host galaxy, discussed in \\ref{ssec:orbit}; the heating and cooling of the gas present, discussed in \\ref{ssec:heating}; how tidal or ram pressure stripping removes gas from the dwarf in \\ref{ssec:RPS}; and how this stripping can be influenced by stellar formation and feedback, detailed in \\ref{ssec:starform}." + All four. to varving degrees. will be influenced by how much gas the dwarl ealaxv has al the beginning of its orbit aud the properties of the dark matter halo that envelopes the cdwart.," All four, to varying degrees, will be influenced by how much gas the dwarf galaxy has at the beginning of its orbit and the properties of the dark matter halo that envelopes the dwarf." + The profile of the dwarf galaxy clark-matter halo is not a simple choice. with no solid consensus on which profile most accurately describes the low-mass subhalos present in cdisvaif ealaxies.," The profile of the dwarf galaxy dark-matter halo is not a simple choice, with no solid consensus on which profile most accurately describes the low-mass subhalos present in dwarf galaxies." + Observationallv. (he dark-matter profile of cdwarls cannot be distinguished between a cuspvy profile aad that of a cored. constant-densityv profile (Walkeretal.2009).," Observationally, the dark-matter profile of dwarfs cannot be distinguished between a cuspy profile and that of a cored, constant-density profile \citep{Walker2009}." +. Both of these profiles also arise through simulations with the cuspy Einasto profile arising (through large N-body. dark-matter only. simulations (Springeletal.2008).," Both of these profiles also arise through simulations with the cuspy Einasto profile arising through large -body, dark-matter only, simulations \citep{Springel2008}." +. With the addition of barvons. it has been argued (hat an even sleeper central corethrough (he. process of barvonic contraction|can be present (han predicted by the dissipationless V-body simulations (BhimentPopolo2009:Napolitanoetal. 2010).," With the addition of baryons, it has been argued that an even steeper central core—through the process of baryonic contraction—can be present than predicted by the dissipationless $N$ -body simulations \citep{Blumenthal1986,DelPopolo2009,Napolitano2010}." +. ILowever. bv coupling (he barvons with the dark matter. and allowing dvnamical and angular momentum transfer (ο occur. constant density cores wilh Burkert like profiles (Burkert1995) ave able to develop in simulation DelPopolo 2009).," However, by coupling the baryons with the dark matter, and allowing dynamical and angular momentum transfer to occur, constant density cores with Burkert like profiles \citep{Burkert1995} are able to develop in simulation \citep{El-Zant2001,DelPopolo2009}." +. Since our major locus is on dark matter-halos with low eas fraction. whereby both barvondark-matter coupling and barvonic contraction will have a smaller impact. we ignore (hese competing factors aud use the Einasto profile.," Since our major focus is on dark matter-halos with low gas fraction, whereby both baryon–dark-matter coupling and baryonic contraction will have a smaller impact, we ignore these competing factors and use the Einasto profile." +The In]galaxy NGC 7339.). due to the small extent of. the kinematical data and 1the value of its dark mass. shows a degeneracy between the predicted: Burkert and. NEW halo rotation curves.,"The galaxy NGC 7339, due to the small extent of the kinematical data and the value of its dark mass, shows a degeneracy between the predicted Burkert and NFW halo rotation curves." + As can be seen in Fig., As can be seen in Fig. + 13. and in Table 4.. th models provide equally good fits to the rotation curve.," \ref{7339} and in Table \ref{tab-param}, both models provide equally good fits to the rotation curve." + This is not due to the fitting procedure but it derives from he fact that both models have similar predictions., This is not due to the fitting procedure but it derives from the fact that both models have similar predictions. + We treat in detail this case to show that ACDAL haloes. for certain virial masses and in certain ranges of radii has a racial profile hat meets that of the Universal Rotation Curve (see PSS).," We treat in detail this case to show that $\Lambda$ CDM haloes, for certain virial masses and in certain ranges of radii has a radial profile that meets that of the Universal Rotation Curve (see PSS)." + First. let us notice that from Table 1 that the rotation curve of this galaxy has a small spatial extent. ic. about 5 kpe.," First, let us notice that from Table \ref{physical} that the rotation curve of this galaxy has a small spatial extent, i.e. about 5 kpc." + Then in Fig., Then in Fig. + Al (left panel) we show the NEW halo rotation curve. very dillerent in general from the derived actual haloes (Salucci&Burkert 20002). for objects having a number of virial masses. ranging [rom 1.107 M. to 3.1077 A...," \ref{halos} (left panel) we show the NFW halo rotation curve, very different in general from the derived actual haloes \citealt{SB:00}) ), for objects having a number of virial masses, ranging from $1 \times 10^{11}$ $_{\odot}$ to $3 \times 10^{12}$ $_{\odot}$ ." + However. as shown in the right panel of Fig. AI..," However, as shown in the right panel of Fig. \ref{halos}," + for virial masses close to about 11077 M. and. for radii up to 5 kpe. the NEW and Burkert halo rotation curves almost coincide: this similarity. combined. with the uncertainty on This the reason for the equal quality of the two fits.," for virial masses close to about $1 \times 10^{12}$ $_{\odot}$, and for radii up to 5 kpc, the NFW and Burkert halo rotation curves almost coincide; this similarity, combined with the uncertainty on $\Upsilon_{*}^{\rm I}$, is the reason for the equal quality of the two fits." + With the data used here we cannot probe the regions of NGC 7339 where the dilference is noticeable., With the data used here we cannot probe the regions of NGC 7339 where the difference is noticeable. +" Pherclore. for galaxies having Vορ) approximately in the range 190170 km 5 and for the radial range 1«r/r,4. in order to distinguish between the two cases. we need. kinematical information at larger radii."," Therefore, for galaxies having $V(r_{opt})$ approximately in the range $120 - 170$ km $^{-1}$ and for the radial range $1 < r/r_d < 4$, in order to distinguish between the two cases, we need kinematical information at larger radii." + At smaller ancl larger V(ru) the two profiles are intrinsically much. more dilferent. and the comparison is easier (seePSS)., At smaller and larger $V(r_{opt})$ the two profiles are intrinsically much more different and the comparison is easier (seePSS). +et al.,et al. + 2001)., 2001). + Han et al. (, Han et al. ( +2006) claimed that many magnetic field reversals can be recognized in the Milky Way.,2006) claimed that many magnetic field reversals can be recognized in the Milky Way. +" However, the existence of multiple reversals is not statistically well established (Men et al."," However, the existence of multiple reversals is not statistically well established (Men et al." + 2008)., 2008). + The global field structure of the Milky Way it is not known yet., The global field structure of the Milky Way it is not known yet. + Standard galactic dynamo models which start from a very week seed field give usually a final magnetic field configuration without reversals., Standard galactic dynamo models which start from a very week seed field give usually a final magnetic field configuration without reversals. + Traditional mean-field dynamo theory has considered reversals as long-lived transients (Vasil'yeva et al., Traditional mean-field dynamo theory has considered reversals as long-lived transients (Vasil'yeva et al. +" 1994, Moss et al."," 1994, Moss et al." +" 1998, 2000, Petrov et al.,"," 1998, 2000, Petrov et al.," +" 2001, 2002) which occur if the initial field is strong enough and has a suitable configuration."," 2001, 2002) which occur if the initial field is strong enough and has a suitable configuration." + These traditional 1D models are however obviously too oversimplified to be fully convincing because they assume that the galactic magnetic field is purely axisymmetric., These traditional 1D models are however obviously too oversimplified to be fully convincing because they assume that the galactic magnetic field is purely axisymmetric. + Here we consider a 2D model where the magnetic field can have an arbitrary configuration., Here we consider a 2D model where the magnetic field can have an arbitrary configuration. + We consider the results obtained in this paper to be sufficiently, We consider the results obtained in this paper to be sufficiently +OC's (with a mass range and in different ονοιτς) that are undergoing this carly phase.,OCs (with a mass range and in different environments) that are undergoing this early phase. + In the present paper πο derive astroplivsical paramcters aud investigate the nature of the voung OCs 1197 and 992., In the present paper we derive astrophysical parameters and investigate the nature of the young OCs 197 and 92. + Their location in the 377 Galactic quadrant minimises contamination by field stars., Their location in the $3^{rd}$ Galactic quadrant minimises contamination by field stars. + We work with field-stay decontaminated 2MLASS photometry (vith errors Z50 πας). which enhances CALID evolutionary sequences and stellar RDPs. vielding more constrained fundamental and structural parameters.," We work with field-star decontaminated 2MASS photometry (with errors $\la0.1$ mag), which enhances CMD evolutionary sequences and stellar RDPs, yielding more constrained fundamental and structural parameters." + The decoutanünated CMDs are characterised by siuilar properties. an under-populated aud developing MS. a dominant fraction (2 75%) of PAIS stars. aud sole differeufial reddening.," The decontaminated CMDs are characterised by similar properties, an under-populated and developing MS, a dominant fraction $\ga75\%$ ) of PMS stars, and some differential reddening." + Iu both cases. the AIS and PAIS CMD inorphlologies consistently imply a time-spread of LOAD in the star formation.," In both cases, the MS and PMS CMD morphologies consistently imply a time-spread of $\sim10$ Myr in the star formation." + Thus. we set the age of Crl1197 and vdB992 as coustrained within 5c ΕΛΙΑ," Thus, we set the age of 197 and 92 as constrained within $5\pm4$ Myr." +", Their | PAIS stellar masses are zz660EDeM. L197) aud zm750!1AM. 992)."," Their $+$ PMS stellar masses are $\approx660^{+102}_{-59}\,\ms$ 197) and $\approx750^{+101}_{-51}\,\ms$ 92)." + By mcans of the proper motion of the member MS aud PAIS stars. we estimate their velocity dispersious to be in the range xlans 5toc?2Lkms1," By means of the proper motion of the member MS and PMS stars, we estimate their velocity dispersions to be in the range $\approx15\,\kms$ to $\approx22\,\kms$." + Compared to a set ofclussical bound OC's. both Crll97 and 992 appear to have core aud cluster radi abnormally huge. with Roz1.5. LOppc aud ReppRE~12. Sppe. respectively for 1197 and 992.," Compared to a set of bound OCs, both 197 and 92 appear to have core and cluster radii abnormally large, with $\rc\approx1.5,~1.9$ pc and $\rl\approx12,~8$ pc, respectively for 197 and 92." + Structurally. the stellar RDPs follow a cluster-like profile for most of the radial range. except in the central region. where they have a pronounced cusp.," Structurally, the stellar RDPs follow a cluster-like profile for most of the radial range, except in the central region, where they have a pronounced cusp." + A less than about Myr. this cusp is xobablyv related o the star formation and/or molecular cloud fragmentation. aud not the product of dynamical evolution.," At less than about Myr, this cusp is probably related to the star formation and/or molecular cloud fragmentation, and not the product of dynamical evolution." + A possible conchision is that Cr1197 aud vdB992 deviate critically from dynamical equilibrin. and similarly to the equally voune 222tL aud. Bochum1l. (of comparable mass). aud Pisais55 and L931 (of significantly lower mass). they are heading owards dissolution.," A possible conclusion is that 197 and 92 deviate critically from dynamical equilibrium, and similarly to the equally young 2244 and 1 (of comparable mass), and 5 and 1931 (of significantly lower mass), they are heading towards dissolution." + This interpretation is also consistent with the super-viral state of both clusters (as well as the dissolving OC 22211). which have velocity dispersions auch higher than the σιzclkmis expecte for nearly virialised clusters of simular luüass and size as Crl1197 and 3992.," This interpretation is also consistent with the super-virial state of both clusters (as well as the dissolving OC 2244), which have velocity dispersions much higher than the $\sigma_v\approx1\,\kms$ expected for nearly virialised clusters of similar mass and size as 197 and 92." + Iu this context. CrllO7 and vdB992 may be taken as a link between clubedded clusters and voung stellar associations.," In this context, 197 and 92 may be taken as a link between embedded clusters and young stellar associations." + We provide evidence that carlystar cluster dissolutiou nay ο detected. for instance. by neans of important and systematic ireenlaritics iu the stellar radial density profile of clusters as massive as several 10?AL...," We provide evidence that early star cluster dissolution may be detected, for instance, by means of important and systematic irregularities in the stellar radial density profile of clusters as massive as several $10^2\,\ms$." + Studies like the resent oue are important ‘or a better understanding of he crucial carly evolution of embedded star clusters - aud he dependence ou mass and environment - that rarely result ina bound OC or. more frequently. lead to heir dissolution into the field.," Studies like the present one are important for a better understanding of the crucial early evolution of embedded star clusters - and the dependence on mass and environment - that rarely result in a bound OC or, more frequently, lead to their dissolution into the field." + We thank the referee. Simon Goodwin. for interesting collents and suggestions.," We thank the referee, Simon Goodwin, for interesting comments and suggestions." + We acknowledge support fron the Brazilian Institution CNPq., We acknowledge support from the Brazilian Institution CNPq. + This publication makes use of data products from the Two Micron. All Sky Survey. which is a joiut project of the Universitv of Massachusetts and the Infrared Processing and Analvsis Centre/California Institute of Technology. fuuded by the National Acronautics and Space Adiministration and the National Science Foundation.," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Centre/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation." + This research has mace use of the WEBDA «database. operated at the Tustitute for Astronomy of the University of Viena.," This research has made use of the WEBDA database, operated at the Institute for Astronomy of the University of Vienna." +about till the end of 2000. while the scatter increases in 2001 (Fig.,"about till the end of 2000, while the scatter increases in 2001 (Fig." + 6bb)., \ref{plot_mojave99}b b). + The jet Hux density has more moderate variability than the core., The jet flux density has more moderate variability than the core. + Despite the lack of simultaneous multifrequeney observations. we can confirm a steep overall spectral index for the jet (a—0.5 - 0.7) between 8.4 and 15 Cllz.," Despite the lack of simultaneous multifrequency observations, we can confirm a steep overall spectral index for the jet $\alpha =$ 0.5 - 0.7) between 8.4 and 15 GHz." + On the other hand a characteristic value of the spectral index of the core could. not. be determined. due to its strong and irregular variability associated with changes in the opacity., On the other hand a characteristic value of the spectral index of the core could not be determined due to its strong and irregular variability associated with changes in the opacity. + A realistic value for the core spectral index could. be derived. only for the observations carried. out. on January 1999 when simultaneous observations at. S.4 and 22 (111 are available. providing a Lat spectral index. (Fig. 3))," A realistic value for the core spectral index could be derived only for the observations carried out on January 1999 when simultaneous observations at 8.4 and 22 GHz are available, providing a flat spectral index (Fig. \ref{spix})" +. The polarization properties of both core (Fig., The polarization properties of both core (Fig. + Gee.c) and jet (Fig.," \ref{plot_mojave99}c c,e) and jet (Fig." + 6dd.f) components are quite dilferent.," \ref{plot_mojave99}d d,f) components are quite different." + In the three observing epochs at 8.4 Gllz we find that both the core and the jet are polarized with a fractional polarization varving between 1.6 and. S.6 per cent in the core region. and about 2.9 and 6.3 per cent in the jet (Table 2.. bottom Οἱ of Fig. 2..," In the three observing epochs at 8.4 GHz we find that both the core and the jet are polarized with a fractional polarization varying between 1.6 and 8.6 per cent in the core region, and about 2.9 and 6.3 per cent in the jet (Table \ref{vlba_table}, bottom panel of Fig. \ref{vlba_images}," + and Fig., and Fig. + 6ec.d).," \ref{plot_mojave99}c c,d)." + At 15 GllIz the polarization »ereentage of the core is very variable. between 1.6 and 5.5 per cent (Fig.," At 15 GHz the polarization percentage of the core is very variable, between 1.6 and 5.5 per cent (Fig." + Gee). and shows no evident. correlation with the total intensity. flux density.," \ref{plot_mojave99}c c), and shows no evident correlation with the total intensity flux density." + On the other hand. he polarization percentage of the jet at 15 Cllz (Fig.," On the other hand, the polarization percentage of the jet at 15 GHz (Fig." + Gael) is roughly. constant around 4.5 per cent., \ref{plot_mojave99}d d) is roughly constant around 4.5 per cent. + In the core component the position angle of the electric vector E (ΕΝΑ) at SA Cllz is 140 and 110 curing the first. two epochs. then it changes abruptly in Alay 2001. when it is 167.," In the core component the position angle of the electric vector $\vec{E}$ (EVPA) at 8.4 GHz is $^{\circ}$ and $^{\circ}$ during the first two epochs, then it changes abruptly in May 2001, when it is $^{\circ}$." + A similar behaviour is found at 15 Cllz. where the EVDPA is between 168 ancl 130 degrees from. 1999 to 2000. i.c. roughly parallel to the jet axis. while in June 2001 it is 32 degrees (Fig.," A similar behaviour is found at 15 GHz, where the EVPA is between 168 and 130 degrees from 1999 to 2000, i.e. roughly parallel to the jet axis, while in June 2001 it is 32 degrees (Fig." + Gee). becoming perpendicular to the jet direction.," \ref{plot_mojave99}e e), becoming perpendicular to the jet direction." + On the other hand. the jet ΙΟΟΛΑ does not show such a large variation. being between SO and. LOO degrees. with the exception of September 2000. when it turned out to be 120 degrees.," On the other hand, the jet EVPA does not show such a large variation, being between 80 and 100 degrees, with the exception of September 2000 when it turned out to be 120 degrees." + We note that only the integrated rotation measure (RAL) is available for this source (-1541 rad 7. Simard-Normandin et al.," We note that only the integrated rotation measure (RM) is available for this source $\pm$ 1 rad $^{-2}$, Simard-Normandin et al." + 1984)., 1984). + The corrections to the observed EVPA to obtain the intrinsic orientation are therefore The multi-epoch analysis of the pe-seale morphology. of L1510-089 shows a considerable evolution of the source structure: jet components emerge from the core at cillerent times and their changes can be followed by comparing observations carried out after short time intervals., The corrections to the observed EVPA to obtain the intrinsic orientation are therefore The multi-epoch analysis of the pc-scale morphology of 1510-089 shows a considerable evolution of the source structure: jet components emerge from the core at different times and their changes can be followed by comparing observations carried out after short time intervals. + With the aim of characterizing variations in the source structure we mocelfitted the visibility data at each. epoch (see Section 2.3)., With the aim of characterizing variations in the source structure we modelfitted the visibility data at each epoch (see Section 2.3). + Direct comparison of models obtained. inclepencently at each epoch is not the best approach to detect. small changes (Conwayctal.1992)., Direct comparison of models obtained independently at each epoch is not the best approach to detect small changes \citep{conway92}. + For this reason. we produced a zero-order model consisting of 3. elliptical. Gaussian components. which was used as the initial model in modelfitting the visibility data of cach observing epoch.," For this reason, we produced a zero-order model consisting of 3 elliptical Gaussian components, which was used as the initial model in modelfitting the visibility data of each observing epoch." + Errors Ar associated with the component position were estimated by means where @ is the component deconvolved major axis. ορ is its peak Hux density and rms is the La noise level measured on the image plane (Polatidis&Conway2003).," Errors $\Delta r$ associated with the component position were estimated by means where $a$ is the component deconvolved major axis, $S_{\rm p}$ is its peak flux density and rms is the $\sigma$ noise level measured on the image plane \citep{polatidis03}." +. In. the case the errors estimated by Eq., In the case the errors estimated by Eq. + 1. are unreliably small. we assume a more conservative value for Ar that is of the beam.," \ref{eq_rms} are unreliably small, we assume a more conservative value for $\Delta r$ that is of the beam." + The data points are then fitted by a linear mocel that minimizes the chi-square error statistic., The data points are then fitted by a linear model that minimizes the chi-square error statistic. + The Linear fit on the three epochs of S.4-Cillz data (Table 1 and Fig. 2)), The linear fit on the three epochs of 8.4-GHz data (Table \ref{vlba_obs} and Fig. \ref{vlba_images}) ) + provides an angular separation rate of 0.990+0.040 mas/vr that corresponds to 53)=16.2d-0.7., provides an angular separation rate of $\pm$ 0.040 mas/yr that corresponds to $\beta_{\rm J}=16.2\pm0.7$. + From the linear back extrapolation fit. ancl considering the uncertainties on the fit. parameters. we estimate the time of zero separation Z5 between the jet component ane the core. that results to be σι —1997.1240.12.," From the linear back extrapolation fit, and considering the uncertainties on the fit parameters, we estimate the time of zero separation $T_{0}$ between the jet component and the core, that results to be $T_{\rm 0,J}=$ $\pm$ 0.12." + Phe accuracy of the fit has been tested also by comparing the component separation derived by modcllitting the visibility of the two epochs 4.8-Gllz Space-VLBI data and the three epochs ab 15 CGllz available from. the MOJAVIZ. project in the same time interval (left panel in Fig. 7)).," The accuracy of the fit has been tested also by comparing the component separation derived by modelfitting the visibility of the two epochs 4.8-GHz Space-VLBI data and the three epochs at 15 GHz available from the MOJAVE project in the same time interval (left panel in Fig. \ref{fit_vsop}) )," + all with a similar resolution., all with a similar resolution. + To extend the analysis of the knot. separation. speed till the end. of 2010. we ποσοτος the data at 15 Cillz from the ALOJAVE programme.," To extend the analysis of the knot separation speed till the end of 2010, we modelfitted the data at 15 GHz from the MOJAVE programme." + Results from the analysis of data between 1905 ancl 2008 were already published in previous works by Lomanetal.(2001) anc, Results from the analysis of data between 1995 and 2008 were already published in previous works by \citet{homan01} and +unaffected by the spectral distortion introduced by the οποιον dependent PSF aud depends only weakly onthe the adopted continui model.,unaffected by the spectral distortion introduced by the energy dependent PSF and depends only weakly on the the adopted continuum model. + Thus it can be used to derive an iudependent aud robust estimate of the temperature profile., Thus it can be used to derive an independent and robust estimate of the temperature profile. + Considering the limited wuuber of counts available in the line we have performed the analysis ou 2 anuuuli with bounding radii. 0-8 aud 8-16’.," Considering the limited number of counts available in the line we have performed the analysis on 2 annuli with bounding radii, $^{\prime}$ $^{\prime}$ and $^{\prime}$ $^{\prime}$." + We have fitted cach spectrum with a brenmsstralluug model plus a line. both at a redshift of z=0.055 (ZBREMSS and ZGAUSS models in NSPEC). absorbed by the ealactic Nyy.," We have fitted each spectrum with a bremsstrahlung model plus a line, both at a redshift of z=0.055 (ZBREMSS and ZGAUSS models in XSPEC), absorbed by the galactic $N_H$." + A svstematic uceative shift of LO eV has been included im the ceutroid cherey to account for a slelt miusscalibration of the energv pulscheight-chanuel relationship near the Fe line., A systematic negative shift of 40 eV has been included in the centroid energy to account for a slight misscalibration of the energy pulseheight-channel relationship near the Fe line. + To convert the energy ceutroid iuto a temperature we lave derived an euergv centroid vs. temperature relationship., To convert the energy centroid into a temperature we have derived an energy centroid vs. temperature relationship. + This has been done by simulating thermal spectra. using he MEIRAL aodel and the MECS response matrix. and fitting them with the same model. which has beeu used to fit the real data.," This has been done by simulating thermal spectra, using the MEKAL model and the MECS response matrix, and fitting them with the same model, which has been used to fit the real data." + In figure 2 we have overlaid he temperatures derived frou the centroid analysis ou hose previously obtained through the thermal continua fitting., In figure 2 we have overlaid the temperatures derived from the centroid analysis on those previously obtained through the thermal continuum fitting. + The two measurements of the temperature profile are in aereciuent with cach other., The two measurements of the temperature profile are in agreement with each other. + Uufortunatelv. the uodest statistics available iu the line does not allow us ο sav iuuch more than that.," Unfortunately, the modest statistics available in the line does not allow us to say much more than that." + We have divided A3266 iuto [| sectors: NW. SW. SE aud NE.," We have divided A3266 into 4 sectors: NW, SW, SE and NE." +" Eac rsector has hee1 divided iuto 3 aunuli with )onuding racui. 2-[/. Vee’:ud 8-16""."," Each sector has been divided into 3 annuli with bounding radii, $^{\prime}$ $^{\prime}$, $^{\prime}$ $^{\prime}$ and $^{\prime}$ $^{\prime}$." + The oricutation of the sectors has been chosen so that the North-South division rougilv coincides wit ithe apparent major axis of he N-rav isoNotes., The orientation of the sectors has been chosen so that the North-South division roughly coincides with the apparent major axis of the X-ray isophotes. + In figure 3 we show the MECS image with the sectors overlaid., In figure 3 we show the MECS image with the sectors overlaid. + A correction for the absorption caused by the strougback supvorting the detector window its been applied for the secors belonging to the s’-16/ annulus., A correction for the absorption caused by the strongback supporting the detector window has been applied for the sectors belonging to the $^{\prime}$ $^{\prime}$ annulus. + For the sectors in the 2/1 aud Ó'-S/ auunli. we used the 2-10 keV. energy rauge for spectral fittine. while or the S'-16' auuulus we adopted the 2-8 keV range.," For the sectors in the $^{\prime}$ $^{\prime}$ and $^{\prime}$ $^{\prime}$ annuli, we used the 2-10 keV energy range for spectral fitting, while for the $^{\prime}$ $^{\prime}$ annulus we adopted the 2-8 keV range." + We ave fitted each spectrum with a MERAL model absorbed x the ealactic Vy., We have fitted each spectrum with a MEKAL model absorbed by the galactic $N_H$. + Iu fleure Lowe show the temperature profiles obtained roni the spectral fits for each of the 1 sectors., In figure 4 we show the temperature profiles obtained from the spectral fits for each of the 4 sectors. + Note that iu all the profiles we have included the temperature nieasure obtained for the ceutral circular region with radius 2’., Note that in all the profiles we have included the temperature measure obtained for the central circular region with radius $^{\prime}$. + Fitting cach radial profile with a constant temperature we derive the following average sector teniperatures: 8.80.5 keV for the NW. sector. 9.60.5 keV for the SW sector. S.1£0.5 keV for the SE sector and 8.20.1 keV for the NE sector.," Fitting each radial profile with a constant temperature we derive the following average sector temperatures: $\pm$ 0.5 keV for the NW sector, $\pm$ 0.5 keV for the SW sector, $\pm$ 0.5 keV for the SE sector and $\pm$ 0.4 keV for the NE sector." + For all sectors we fiud a statistically siguificaut teiiperature decrease with increasing radius., For all sectors we find a statistically significant temperature decrease with increasing radius. + Frou the \? statistics we find 47=21.1 for 3 d.o.f., From the $\chi^2$ statistics we find $\chi^2 =21.4$ for 3 d.o.f. + (Prob.9«10 7) for the NW sector. 4?=9.2 for 3 do-t.," $= 9\times 10^{-5}$ ) for the NW sector, $\chi^2 =9.2$ for 3 d.o.f." + (Prob.22.6«10 7) for the SW sector. u=2[.0 for 3 of.," $= 2.6\times 10^{-2}$ ) for the SW sector, $\chi^2 +=24.0$ for 3 d.o.f." + (Prob.2.5«10. 75) for the SE sector and 4?=10.5 for 3 d.o.f., $= 2.5\times 10^{-5}$ ) for the SE sector and $\chi^2 =10.5$ for 3 d.o.f. + (Prob.21.5«10. 2) for the NE sector., $= 1.5\times 10^{-2}$ ) for the NE sector. + In the SE and NE sectors the temperature decreases continously as the distance from the cluster ceuter increases., In the SE and NE sectors the temperature decreases continuously as the distance from the cluster center increases. + Ta the NW and SW sectors the temperature first increases. reaching a niaxinuuin in either the second (NW sector) or third (SW sector) annulus. and then decreases.," In the NW and SW sectors the temperature first increases, reaching a maximum in either the second (NW sector) or third (SW sector) annulus, and then decreases." + Iuterestiugly. a fit to the temperatures of the Lt sectors in the third annulus (bounding radi ls’) with a constaut. vields ye=8.5 for 3 dio.£.," Interestingly, a fit to the temperatures of the 4 sectors in the third annulus (bounding radii $^\prime$ $^\prime$ ) with a constant, yields $\chi^2=8.45$ for 3 d.o.f.," + with an associated probability for the temperature to be coustant of 0.03. indicating that an azinuthal temperature eracdicut may be prescut near the core of the cluster.," with an associated probability for the temperature to be constant of 0.03, indicating that an azimuthal temperature gradient may be present near the core of the cluster." + More specifically the caster side of the cluster appears to be somewhat cooler than the western side., More specifically the eastern side of the cluster appears to be somewhat cooler than the western side. + From the analysis of the abundance map we fiud that all sector averaged abundances are consistent with the average abundance for A3266 derived in the previous subsection The 47 values derived frou the fits indicate that all abundance profiles are consistent with being constant., From the analysis of the abundance map we find that all sector averaged abundances are consistent with the average abundance for A3266 derived in the previous subsection The $\chi^2$ values derived from the fits indicate that all abundance profiles are consistent with being constant. + Previous imeasurenieuts of the temperature structure of À3266 have been performed by Alarkevitch οἳ al. (, Previous measurements of the temperature structure of A3266 have been performed by Markevitch et al. ( +"1998). using ASCA data. and by πα, Bregman Evrard (1999). using ROSAT PSPC data.","1998), using ASCA data, and by Irwin, Bregman Evrard (1999), using ROSAT PSPC data." + Markevitch et al. (, Markevitch et al. ( +1998) find a decreasing racial temperature profile.,1998) find a decreasing radial temperature profile. + Iu feure 2 we have overlaid the temperature profile obtained w Markevitch et al. (, In figure 2 we have overlaid the temperature profile obtained by Markevitch et al. ( +1998) using ASCA data. to our own BeppoSAX profile.,"1998) using ASCA data, to our own BeppoSAX profile." + The aerecment between the two independent measurements is clearly very good., The agreement between the two independent measurements is clearly very good. + A lincar xofle of the type. kT =a | b zr. where kT is in keV and r in arcnimnutes. which provides an acceptable ft to he ASCA profile νο=5«10% for 1 d.o.f.)," A linear profile of the type, kT = a $ + $ b r, where kT is in keV and r in arcminutes, which provides an acceptable fit to the ASCA profile $\chi^2 =5\times 10^{-5}$ for 1 d.o.f.)" + vields vost fitting values: a =10.7EOS keV. b=0.39+Lll keV arcmin+.," yields best fitting values: a $= 10.7 \pm 0.8$ keV, $= - 0.39 \pm 0.11$ keV $^{-1}$." + These values aro in good aereenmenut with those derived frou the BeppoSAX data., These values are in good agreement with those derived from the BeppoSAX data. + Recently Irwin. Bregman Evrard (1999) have used ROSAT PSPC madness ratios to measure temperature eradieuts for a sample of nearby galaxy clusters. which includes A3266.," Recently Irwin, Bregman Evrard (1999) have used ROSAT PSPC hardness ratios to measure temperature gradients for a sample of nearby galaxy clusters, which includes A3266." + Iu their analysis they find evidence of a radial decrease in one of the two harcuess ratios sensitive to teniperature variations., In their analysis they find evidence of a radial decrease in one of the two hardness ratios sensitive to temperature variations. + The authors do not attribute this variation to a eniperature decrement. because a similar variation is also seen in an another harduess ratio. which is not scusitive o temperature eradieuts.," The authors do not attribute this variation to a temperature decrement, because a similar variation is also seen in an another hardness ratio, which is not sensitive to temperature gradients." + Optical studies by various authors (e.g. QRW. Teague ( al.," Optical studies by various authors (e.g., QRW, Teague et al." + 1990). have shown that A3266 is characterized bv a aree velocity dispersion. 1000 kins *.," 1990), have shown that A3266 is characterized by a large velocity dispersion, $\sim$ 1000 km $^{-1}$ ." + Moreover both QRW and Cdvardi et al. (, Moreover both QRW and Girardi et al. ( +1997) find evidence of a decrease of the velocity dispersion with increasing distance from he cluster core.,1997) find evidence of a decrease of the velocity dispersion with increasing distance from the cluster core. + QRW ineasure a velocity dispersion of ~ 1600 kii | within 200 kpe from the core of the cluster and a velocity dispersion of ~ 1000 kins + at a radial distance of Ls’ (1.5 AIpe)., QRW measure a velocity dispersion of $\sim$ 1600 km $^{-1}$ within 200 kpc from the core of the cluster and a velocity dispersion of $\sim$ 1000 km $^{-1}$ at a radial distance of $^\prime$ (1.5 Mpc). + Thus. it would seems that th. the hot X-ray cutting eas aud the ealaxics visible i optical wavelengths are characterized by a decrease in heir specific kinetic energv with increasing radius.," Thus, it would seems that both the hot X-ray emitting gas and the galaxies visible at optical wavelengths are characterized by a decrease in their specific kinetic energy with increasing radius." +" From he velocity dispersion profile produced by QRW aud our own temperature profile. we lave computed the radial xofile of the so-called A, parameter (Sarazin 1955). which is deftued as An—jnuyo2kT. where p is the nean molecular weight in aut nay is the proto inass aud σι is the velocity dispersion."," From the velocity dispersion profile produced by QRW and our own temperature profile, we have computed the radial profile of the so-called $\beta_{\rm spec}$ parameter (Sarazin 1988), which is defined as: $\rm {\beta_{\rm spec} +\equiv \mu m_p\sigma_r^2/kT}$, where $\mu$ is the mean molecular weight in amu, $_{\rm p}$ is the proton mass and $\sigma_{\rm r}$ is the velocity dispersion." + The derived ρου profile is consistent with being fiat. with an average value of Άμος=1.5+0.2. indicating that. although the specific kinetic eunergv of the galaxies is ereater than that of the hot gas. the rate at which it decreases. with increasing radius. is the same for the galaxies and the hot eas.," The derived $\beta_{\rm spec}$ profile is consistent with being flat, with an average value of $\beta_{\rm spec} = 1.5 \pm 0.2$, indicating that, although the specific kinetic energy of the galaxies is greater than that of the hot gas, the rate at which it decreases, with increasing radius, is the same for the galaxies and the hot gas." + QRW have proposed that the velocity dispersion eradieut aud the preseuce of a distorted central dumb-bell ealaxy iav have resulted from a recent merger betweentwo clusters., QRW have proposed that the velocity dispersion gradient and the presence of a distorted central dumb-bell galaxy may have resulted from a recent merger betweentwo clusters. + Evidence of a merger event can also be found from the, Evidence of a merger event can also be found from the +In our analvses the magnetic field has been assumed to be weak and the effect of instabilities of the disk plasma and (he magnetic field has been ignored.,In our analyses the magnetic field has been assumed to be weak and the effect of instabilities of the disk plasma and the magnetic field has been ignored. +" The situation with a strong magnetic field may be significantly different. [rom that has been discussed in this paper. al least the inner part of (he disk will not be Keplerian any more and quasi-steady state solutions may not exist: accretion may be stopped and a state similar to the ""propeller"" phase for pulsars (Schwartzman1971:HlarionovandSunvaev1975:Lipunov1992) max be produced. or even the accretion [low is reversed (Blandford1999)."," The situation with a strong magnetic field may be significantly different from that has been discussed in this paper, at least the inner part of the disk will not be Keplerian any more and quasi-steady state solutions may not exist: accretion may be stopped and a state similar to the “propeller” phase for pulsars \citep{sch71,ill75,lip92} may be produced, or even the accretion flow is reversed \citep{bla99}." +. The instabilities of the disk plasma and (the magnetic field may seriously affect the dvnamics aud enereelics of the disk. which will make the situation much more complicated than that considered in this paper.," The instabilities of the disk plasma and the magnetic field may seriously affect the dynamics and energetics of the disk, which will make the situation much more complicated than that considered in this paper." + The effect of photon capture caused by the black hole and Che disk has also been ignored. which is expected to modify both the radiation flux aud the total power of the cisk.," The effect of photon capture caused by the black hole and the disk has also been ignored, which is expected to modify both the radiation flux and the total power of the disk." + All these issues will be addressed in future., All these issues will be addressed in future. + Tam very grateful to Bohdan Paczvisski and Jeremy Goodman for stimulating discussions and valuable comments., I am very grateful to Bohdan Paczyńsski and Jeremy Goodman for stimulating discussions and valuable comments. + This work was supported by the NASA grant. NAG5-T016 and a Harold W. Docdds Fellowship of Princeton University., This work was supported by the NASA grant NAG5-7016 and a Harold W. Dodds Fellowship of Princeton University. +sample have the same median redshift). a mecian of 2.15 for he objects with spectroscopic redshifts from Chapman οἱ al. (,"sample have the same median redshift), a median of 2.15 for the objects with spectroscopic redshifts from Chapman et al. (" +2005) ancl a median redshift of 1.52 for the Lockman Llole SILXDES sources (Dye et al..,"2005) and a median redshift of 1.52 for the Lockman Hole SHADES sources (Dye et al.," + 2007)., 2007). + Once account is aken for the elfects of the spectroscopic redshift desert. at around z~ 1.5. the median redshift from Chapman et al.," Once account is taken for the effects of the spectroscopic redshift desert at around $\sim$ 1.5, the median redshift from Chapman et al." + falls ο z2., falls to $\sim 2$. + There thus appears to be a lack of high redshift sources in our sample compared to Chapman et al., There thus appears to be a lack of high redshift sources in our sample compared to Chapman et al. + and Pope ct al., and Pope et al. + hough we are in reasonable agreement with Dve et al. The radio Hux limit of our identifications is as deep as all but two of the Chapman fields (Lockman ancl SSA-13) which are a actor of ~2 deeper. but which account for only 13 of their 76 redshifts.," though we are in reasonable agreement with Dye et al.. The radio flux limit of our identifications is as deep as all but two of the Chapman fields (Lockman and SSA-13) which are a factor of $\sim$ 2 deeper, but which account for only 13 of their 76 redshifts." + Phe redshfts measured in these two fields are somewhat higher than the rest of the sample., The redshfts measured in these two fields are somewhat higher than the rest of the sample. + Phe C:OODS- field. has a comparable depth to the deepest Chapman iclels. ie. La~Syed," The GOODS-N field has a comparable depth to the deepest Chapman fields, ie. $\sigma \sim 5\mu Jy$," + so this could account for the dillerence oetween the current y.paper and the Pope et al. (, so this could account for the difference between the current paper and the Pope et al. ( +2006) recshilt clistribution.,2006) redshift distribution. + The seven raclio-iclentified sources in our sample without SWIRLoptical counterparts are potentially at high redshift or might be very heavily obscured., The seven radio-identified sources in our sample without SWIRE/optical counterparts are potentially at high redshift or might be very heavily obscured. + Lowe combine the redshift estimates for these sources from their racio-submuam-[zr-II. properties from. Arctxaga ct al. (, If we combine the redshift estimates for these sources from their radio-submm-far-IR properties from Aretxaga et al. ( +2007). using their MC2 value. then the median redshift for our sample rises to 1.9.,"2007), using their $z_{phot}^{MC}$ value, then the median redshift for our sample rises to 1.9." +" However. there are large uncertainties in the LAL""phe estimates. with confidence intervals typically covering the range 2<2<3. and sometimes much larger."," However, there are large uncertainties in the $z_{phot}^{MC}$ estimates, with confidence intervals typically covering the range $\le$ $\le$ 3, and sometimes much larger." + The radio non-cetected sources may lie at still higher redshift., The radio non-detected sources may lie at still higher redshift. + The racio non-detected subsample in GOODS-N has a median z= 2.4. for example (Pope ct al..," The radio non-detected subsample in GOODS-N has a median z = 2.3, for example (Pope et al.," + 2005)., 2005). + The GOODS-N Spitzer data is signilicanthy deeper than the SWIRE data. with. for example. 245/m fluxes reaching a 5e sensitivity of 24yJy compared to the SWIRE limit of 1067:Jy. allowing their Spitzer identifications to reach higher redshilts.," The GOODS-N Spitzer data is significantly deeper than the SWIRE data, with, for example, $\mu$ m fluxes reaching a $\sigma$ sensitivity of $\mu$ Jy compared to the SWIRE limit of $\mu$ Jy, allowing their Spitzer identifications to reach higher redshifts." + A comparison between our redshift estimates. based on oplical-to-submim fluxes. with those derived. [rom the racio-to-lar-LR. Fluxes by Aretxaga et al. (," A comparison between our redshift estimates, based on optical-to-submm fluxes, with those derived from the radio-to-far-IR fluxes by Aretxaga et al. (" +2007) is shown in ligure 2.,2007) is shown in Figure 2. + As can be seen there is broad agreement between the two results. but there are a small number of sources where things may have gone wrong.," As can be seen there is broad agreement between the two results, but there are a small number of sources where things may have gone wrong." + Examining this in detail we find that there are six sources (SWIRE-SXDE 1. 3. 12. 30. 74 and 119) whose optical-subnin photonietric redshilt [ies outside the confidence interval given. for he racio-Far-H1t. derived: redshift from Arctxaga et al.," Examining this in detail we find that there are six sources (SWIRE-SXDF 1, 3, 12, 30, 74 and 119) whose optical-submm photometric redshift lies outside the confidence interval given for the radio-far-IR derived redshift from Aretxaga et al." + For our sample size we would expect 3 sources to be outside his confidence interval., For our sample size we would expect 3 sources to be outside this confidence interval. + On examining the SED Lits [or hese cliscordant objects we find that 4 of them (1. 3. 74 and 119) have cirrus-type. cust SED fits.," On examining the SED fits for these discordant objects we find that 4 of them (1, 3, 74 and 119) have cirrus-type dust SED fits." + These sources iive cooler dust (—201l) than is normally expected. for zw-Hi-Iuminous objects and it is likely this factor which is leading the racio-far-L method to place them at a ueher redshift than the method. we have used., These sources have cooler dust $\sim$ 20K) than is normally expected for far-IR-luminous objects and it is likely this factor which is leading the radio-far-IR method to place them at a higher redshift than the method we have used. + These sources fully account for the apparent disagreement between our and Aretxaga’s redshift estimates., These sources fully account for the apparent disagreement between our and Aretxaga's redshift estimates. + Lt is also worth noting that the identification for source 74 is potentially. unreliable. though there are no indications of this from the photo-z or SED fit.," It is also worth noting that the identification for source 74 is potentially unreliable, though there are no indications of this from the photo-z or SED fit." + Disagreements at. higher redshift may well result. form higher luminosity objects having a higher temperature than the ensemble average used. by Aretxaga et al (2007). though these disagreements are largely within the acknowledged statistical uncertainties.," Disagreements at higher redshift may well result form higher luminosity objects having a higher temperature than the ensemble average used by Aretxaga et al (2007), though these disagreements are largely within the acknowledged statistical uncertainties." + 1n conclusion. the recdshift. distribution we recover [ου the SANDE region of SILADISS. is consistent. with previous work. eiven the advantages and limitations of the techniques we are using. with the bulk of submm galaxies Lving at z71.5 2.5.," In conclusion, the redshift distribution we recover for the SXDF region of SHADES, is consistent with previous work, given the advantages and limitations of the techniques we are using, with the bulk of submm galaxies lying at $\sim$ 1.5 – 2.5." + Furthermore. Aretxaga et al. (," Furthermore, Aretxaga et al. (" +2007). using racdio-submm-far-H1t. techniques. conclude that the SXDE SLILADISS field. has a somewhat lower redshift peak than the Lockman SILADIZS field. (2.2 compared. to 2.6).,"2007), using radio-submm-far-IR techniques, conclude that the SXDF SHADES field has a somewhat lower redshift peak than the Lockman SHADES field (2.2 compared to 2.6)." + The results we derive for the radio/SWLIE identified sources are Consistent. with this conclusion., The results we derive for the radio/SWIRE identified sources are consistent with this conclusion. + As well as estimating redshifts. the photo-z/SED fitting system gives an optical and far-LR SED class that has been fit to the sources.," As well as estimating redshifts, the photo-z/SED fitting system gives an optical and far-IR SED class that has been fit to the sources." + We find that the fitted optical templates are mostly star-forming classes. as would be expected if these sources are high redshift. starbursts.," We find that the fitted optical templates are mostly star-forming classes, as would be expected if these sources are high redshift starbursts." + Two of the sources. rather surprisingly. are best fitted by an Elliptical or proto-elliptical template in the optical (SILADIZS-SNDE 3 and 5202).," Two of the sources, rather surprisingly, are best fitted by an Elliptical or proto-elliptical template in the optical (SHADES-SXDF 3 and 5202)." + The first of these is a low redshift source (ρω = 0.41) with a cirrus-type far-LR SED., The first of these is a low redshift source $_{phot}$ = 0.41) with a cirrus-type far-IR SED. + The second. E-type source is 5202 which has an Arp220 tvpe far-LR SED on top of an elliptical optical SED at à photometric redshift of 2.08. making it an interesting object for further study.," The second E-type source is 5202 which has an Arp220 type far-IR SED on top of an elliptical optical SED at a photometric redshift of 2.98, making it an interesting object for further study." + At this high a redshift the E-type template is that of a proto- from Maraston (2005)., At this high a redshift the E-type template is that of a proto-elliptical from Maraston (2005). + Lt is very faint in the optical. with red optical-to-3.6//m colours (Davoodi et al.," It is very faint in the optical, with red $\mu$ m colours (Davoodi et al.," + 2006). and," 2006), and" +it was detected in 2005-08.,it was detected in 2005-08. + The average width is 4200 km s!. consistent with the width observed in 1984.," The average width is 4200 km $^{-1}$, consistent with the width observed in 1984." + Due to the weakness of the broad emission lines we are unable to study the connection between continuum and line luminosity or between the BLR velocity field and the proposed periastron. of the secondary black hole in 2005-07., Due to the weakness of the broad emission lines we are unable to study the connection between continuum and line luminosity or between the BLR velocity field and the proposed periastron of the secondary black hole in 2005-07. +"the 4 degrees of freedom: the Lamiltonian is now H=Huiri.giisposανrunsfo.ip). We also adel constant. precessions of the perihelion anc the node. respectively «σται=0.2712831860533198.10! rad/y and d£2,/di=O.2189047296429404-103 rad/y from the VSOP planctary theory (FiengaandSimon2005).","the 4 degrees of freedom: the Hamiltonian is now $\mathcal H=\mathcal H(l_o,x_1,y_1,x_2,y_2,\xi_1,\eta_1,\xi_2,\eta_2)$ We also add constant precessions of the perihelion and the node, respectively $d\varpi_o/dt=0.2772831860533198\times10^{-4}$ $rad/y$ and $d\ascnode_o/dt=-0.2189047296429404\times10^{-4}$ $rad/y$ from the VSOP planetary theory \citep{fs05}." +. These precessions. through the introduction of the resonant angle e». will result in forced libration in latitucle.," These precessions, through the introduction of the resonant angle $\sigma_2$, will result in forced libration in latitude." +" To compute the equilibria of the Hamiltonian. we first average the Llamiltonian over the fast angular variable (the mean anomaly £,)."," To compute the equilibria of the Hamiltonian, we first average the Hamiltonian over the fast angular variable (the mean anomaly $l_o$ )." + Assumine that Mercury lies at the Cassini equilibrium and that there is no wobble motion (for the whole body and the core). we have wry2are=&)yp&—gp0.," Assuming that Mercury lies at the Cassini equilibrium and that there is no wobble motion (for the whole body and the core), we have $x_1=x_2=\xi_1=\eta_1=\xi_2=\eta_2=0$." +" Putting that into the Llamiltonian. we compute the equilibria of μι and ye using Lamilton’s equations and an iterative process and we find yy=1.56.317«10.' and yi=0.1502. resulting in an ecliptic obliquity of A""=71873arcmin. After a translation to this equilibrium. our quadratic averaged. Hamiltonian looks like this: We notice that the degrees of freedom related to the librations in longitude rj.714) and Iatitude (Cro.jo). and those related to the wobbles of the planet (έν.η} and the core (£5.79) are coupled two by two. the coupling being much weaker in the first case than in the second ‘To compute the fundamental periods of this Hamiltonian. we must first disentangle the coupled degrees of freedom."," Putting that into the Hamiltonian, we compute the equilibria of $y_1$ and $y_2$ using Hamilton's equations and an iterative process and we find $y_1^\star=1.5-6.117\times 10^{-7}$ and $y_2^\star=0.1502$, resulting in an ecliptic obliquity of $K^\star=7^\circ 1.873 \text{ arcmin}$ After a translation to this equilibrium, our quadratic averaged Hamiltonian looks like this: We notice that the degrees of freedom related to the librations in longitude $(x_1,y_1)$ and latitude $(x_2,y_2)$, and those related to the wobbles of the planet $(\xi_1,\eta_1)$ and the core $(\xi_2,\eta_2)$ are coupled two by two, the coupling being much weaker in the first case than in the second To compute the fundamental periods of this Hamiltonian, we must first disentangle the coupled degrees of freedom." + To do this we use an untaneling transformation (LHenrardandLemaitre2005). twice. and after changes of variables to action-angle variables: we have the following quadratic Llaniltonian: With rae. mo. na the free frequencies corresponding respectively to the libration in longitude. the libration in latitude. the wobble of the planet and the wobble of the These frequencies (especially a.) actually depend on the shape of the core.," To do this we use an untangling transformation \citep{hl05} twice, and after changes of variables to action-angle variables: we have the following quadratic Hamiltonian: with $n_u$, $n_v$, $n_w$, $n_z$ the free frequencies corresponding respectively to the libration in longitude, the libration in latitude, the wobble of the planet and the wobble of the These frequencies (especially $n_v$ ) actually depend on the shape of the core." +" For the parameters given in Table 1. and 3—€, and εἰ=cs. the corresponding funcamental periods are To compute the evolution of the dillerent variables. we use a perturbation theory by. Lie transforms (see e.g. Deprit (1960)))."," For the parameters given in Table \ref{tab:values} and $\epsilon_3=\epsilon_1$ and $\epsilon_4=\epsilon_2$, the corresponding fundamental periods are To compute the evolution of the different variables, we use a perturbation theory by Lie transforms (see e.g. \citet{d69}) )." + Our main Hamiltonian is the quadratic Hamiltonian described in the previous section and the perturbation contains all the other terms that we neglected to compute the Fundamental frequencies (and to which we applied the same transformations)., Our main Hamiltonian is the quadratic Hamiltonian described in the previous section and the perturbation contains all the other terms that we neglected to compute the fundamental frequencies (and to which we applied the same transformations). + Llere is a quick reminder on how this, Here is a quick reminder on how this +magnetic confinement may also play a role in setting ignition latitude.,magnetic confinement may also play a role in setting ignition latitude. + Our simulations can be very easily. extended. to neutron stars with cdillerent rotation rates: spreading speed is inversely proportional to rotation rate. so a more slowly rotating star will have a higher ον than à star with more rapid rotation. all other factors being identical.," Our simulations can be very easily extended to neutron stars with different rotation rates: spreading speed is inversely proportional to rotation rate, so a more slowly rotating star will have a higher $v_p$ than a star with more rapid rotation, all other factors being identical." + The change in oblateness has a very small effect on convexity ancl rise time., The change in oblateness has a very small effect on convexity and rise time. + We need to. be somewhat cautious in comparing different sources. as burst properties will. clilfer.," We need to be somewhat cautious in comparing different sources, as burst properties will differ." +" ""οσο differences will vellect variations in the composition of accreted material. deep crustal heating. ancl accretion history."," These differences will reflect variations in the composition of accreted material, deep crustal heating, and accretion history." + The F diagram for one source max be olfset from the I diagram for another. or different regions of the diagram may be populated. depending on the source.," The F diagram for one source may be offset from the F diagram for another, or different regions of the diagram may be populated, depending on the source." + A star with an II-poor donor. for example. would not trace out the lower portions of the F diagram.," A star with an H-poor donor, for example, would not trace out the lower portions of the F diagram." + However. if our model is correct. then there should be two transitional accretion rates for each source. for which ignition occurs at the pole rather than the equator.," However, if our model is correct, then there should be two transitional accretion rates for each source, for which ignition occurs at the pole rather than the equator." + As our simulations show. not all polar ignition will result in negative convexity bursts.," As our simulations show, not all polar ignition will result in negative convexity bursts." + However. all negative convexity bursts should indicate polar ignition.," However, all negative convexity bursts should indicate polar ignition." + We therefore expect to fined negative convexity bursts on the horizontal strokes of the F diagram., We therefore expect to find negative convexity bursts on the horizontal strokes of the F diagram. + In Figure 14. we plot EF diagrams for the other sources examined. marking those bursts with negative convexity.," In Figure \ref{othersources} we plot F diagrams for the other sources examined, marking those bursts with negative convexity." + As [or 4U. 1636-536 we excluded: both the faintest bursts and those with kinked or multi-peaked. rises., As for 4U 1636-536 we excluded both the faintest bursts and those with kinked or multi-peaked rises. + For. the accreting millisecond pulsar NTE J1814-338. the IEEddington luminosity has not been measured so we show unscaled persistent [ux rather than 5.," For the accreting millisecond pulsar XTE J1814-338, the Eddington luminosity has not been measured so we show unscaled persistent flux rather than $\gamma$." + The properties of the sources examined are summarized in Table 3.., The properties of the sources examined are summarized in Table \ref{osrc}. + Inclination is for most sources unconstrained (although it is expected to be «70 due to the absence ofdips or eclipses)., Inclination is for most sources unconstrained (although it is expected to be $< 70^\circ$ due to the absence of dips or eclipses). + Phe exception is EXO 0748-676. which is a high inclination eclipsing svstem.," The exception is EXO 0748-676, which is a high inclination eclipsing system." + We expect the range of accretion rates for which polar ignition is important to be larger for the more rapidly rotating sources (although whether or not we see negative convexity bursts would of course depend on the inclination)., We expect the range of accretion rates for which polar ignition is important to be larger for the more rapidly rotating sources (although whether or not we see negative convexity bursts would of course depend on the inclination). + The picture that emerges is certainly not clear-cut., The picture that emerges is certainly not clear-cut. + AL but one of the sources (4U. 1702-429) show some negative convexity bursts. and many of these sit on what we might interpret as the lower horizontal stroke of the E diagram.," All but one of the sources (4U 1702-429) show some negative convexity bursts, and many of these sit on what we might interpret as the lower horizontal stroke of the F diagram." + 4U 1746-37 is interesting in that it secms to trace out the entire upper portion of the F diagram. with two negative convexity bursts at high aceretion rates that might be polar ignition bursts trigecred by Hoe burning.," 4U 1746-37 is interesting in that it seems to trace out the entire upper portion of the F diagram, with two negative convexity bursts at high accretion rates that might be polar ignition bursts triggered by He burning." + There are however a ew negative convexity bursts at intermediate accretion rates (as there were for 4U 1636-536)., There are however a few negative convexity bursts at intermediate accretion rates (as there were for 4U 1636-536). + EXO 0748-676 has a large »ercentage of negative convexity bursts: if these are caused » polar ignition then this may seem. a Little surprising. since this source is thought to have a much slower spin rate.," EXO 0748-676 has a large percentage of negative convexity bursts: if these are caused by polar ignition then this may seem a little surprising, since this source is thought to have a much slower spin rate." + This source does span a very narrow of accretion rates. i0wever. and as à high inclination svstem we also expect he south pole ignition bursts to have negative convexities.," This source does span a very narrow of accretion rates, however, and as a high inclination system we also expect the south pole ignition bursts to have negative convexities." + llowever. i£ the accretion rate is not extremely finebv-tuned. hen there may be some other factor (such a strong magnetic ield) that is controlling fuel deposition and hence ignition atitude.," However, if the accretion rate is not extremely finely-tuned, then there may be some other factor (such a strong magnetic field) that is controlling fuel deposition and hence ignition latitude." + The relatively slow spin inferred. for this source suggests that magnetic field. cllects might. be. important., The relatively slow spin inferred for this source suggests that magnetic field effects might be important. + In this respect the results from the pulsar (NPE J1814-338) are also extremely interesting., In this respect the results from the pulsar (XTE J1814-338) are also extremely interesting. + This source too shows a large number of negative convexity bursts. as one might expect if ignition were occurring oll-equator at the magnetic pole.," This source too shows a large number of negative convexity bursts, as one might expect if ignition were occurring off-equator at the magnetic pole." + The phase-locking of persistent pulsations ancl burst oscillations in this source also suggests that this may be the case (Strohmaveretal.2003)., The phase-locking of persistent pulsations and burst oscillations in this source also suggests that this may be the case \citep{SMSI}. +. We have shown. using parameterized simulations. that burst rise shape can be a valuable diagnostic of the burning process.," We have shown, using parameterized simulations, that burst rise shape can be a valuable diagnostic of the burning process." + Changes in ignition latitude. in particular. can have a major impact on burst morphology. ancl such changes may explain the variation in burst rise shape seen in the well-stucdied: source εἰ 1636-536.," Changes in ignition latitude, in particular, can have a major impact on burst morphology, and such changes may explain the variation in burst rise shape seen in the well-studied source 4U 1636-536." + We have argued. that a change from oll-equatorial to equatorial ignition might be the hallmark of the transition from LE triggered mixed bursts to He triggered bursts at low accretion rates., We have argued that a change from off-equatorial to equatorial ignition might be the hallmark of the transition from H triggered mixed bursts to He triggered bursts at low accretion rates. + Such a moclel can also plausibly explain variations in the detectability of burst. oscillations., Such a model can also plausibly explain variations in the detectability of burst oscillations. + Phere are also areas. however. where aclelitional physics is clearly. required.," There are also areas, however, where additional physics is clearly required." + Our spreading: and »irning models. were not. for example. able to. generate multi-peakecl or kinkecl burst rises.," Our spreading and burning models were not, for example, able to generate multi-peaked or kinked burst rises." + Our goal with this work was to develop a simple whenomenological model to study the interactions between he various processes operating during the burst rise. and heir influence on lighteurve shape.," Our goal with this work was to develop a simple phenomenological model to study the interactions between the various processes operating during the burst rise, and their influence on lightcurve shape." + What we have done is clearly simplistic: the various elements of the model will be more closely connected than we have considered here. and we jwe made a number of assumptions that may not be valid.," What we have done is clearly simplistic: the various elements of the model will be more closely connected than we have considered here, and we have made a number of assumptions that may not be valid." + The parameter space that we have considered. however. is extremely wide. giving us confidence in our conclusions.," The parameter space that we have considered, however, is extremely wide, giving us confidence in our conclusions." + What we have done also demonstrates the power of simple measures of the burst shape: if our model is valid: we have been able to identifv ignition latitude and rule out. latitucle-independent Dame spreading speeds. for example (see also DBhattacharvya&Strohmaver. (200722).," What we have done also demonstrates the power of simple measures of the burst shape: if our model is valid we have been able to identify ignition latitude and rule out latitude-independent flame spreading speeds, for example (see also \citet{BSd}) )." + This type of study could ancl should. be repeated. as more detailed models. of the nuclear burning. spreading and emission process become available.," This type of study could and should be repeated as more detailed models of the nuclear burning, spreading and emission process become available." + We would like to thank Edward: Brown. IHandall Cooper. Andrew Cumming. Fane Peng. Alike Revnivisey. Lenk Spruit ancl Rashid Sunvaey and the anonymous. referee for helpful comments.," We would like to thank Edward Brown, Randall Cooper, Andrew Cumming, Fang Peng, Mike Revnivtsev, Henk Spruit and Rashid Sunyaev and the anonymous referee for helpful comments." + This research has made use of data obtained from the Ligh Enerey Astrophysics Science Archive Research Centre (LIEZASAIC) provided by NASA's Goddard Space Flight Centre., This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Centre (HEASARC) provided by NASA's Goddard Space Flight Centre. +5ον LBGs is still very small.,$z \sim 5$ LBGs is still very small. + In addition. (he spectroscopic studies have so lar been relving on the Lvo emission. and (he features seen in the continuum are still not clear except for rare bright objects such as gravitationallylensed LDGs (Fryeetal.2002:Swinbank2007).," In addition, the spectroscopic studies have so far been relying on the $\alpha$ emission, and the features seen in the continuum are still not clear except for rare bright objects such as gravitationallylensed LBGs \citep{fry02,swi07}." +. Thus a larger deep spectroscopic sample of LBGs at 2Z5 is required to reveal spectroscopic properties of LBGs., Thus a larger deep spectroscopic sample of LBGs at $z \gtrsim 5$ is required to reveal spectroscopic properties of LBGs. + We have constructed a large sample of LBGs at z~5 based on Subaru/Suprime-Cam observations (Iwataetal.2003.2007).. and we are conducting spectroscopic observations of selected targets [rom the photometric sample.," We have constructed a large sample of LBGs at $z \sim 5$ based on Subaru/Suprime-Cam observations \citep{iwa03,iwa07}, and we are conducting spectroscopic observations of selected targets from the photometric sample." + The target fields are the region including the GOODS-N and the J0053--1234 region., The target fields are the region including the GOODS-N and the J0053+1234 region. + The total area of the survev fields is 1290 arcmin? and 228 objects are obtained with z/<25.0 mag ie. L>L* in the UVLF of z~5 LBCs (Iwataοἱal.2007)., The total area of the survey fields is 1290 $^2$ and 228 objects are obtained with $z'<25.0$ mag i.e. $L > L^*$ in the UVLF of $z \sim 5$ LBGs \citep{iwa07}. +. Results of our follow-up spectroscopy. with Faint Object Camera And Spectrograph (FOCAS) on Subaru Telescope were reported by Andoetal.(2004.2007).. and the number of bright (z<25.0 mag) 2~5 LBCs with spectroscopic identilication was nine and that of faint (z>25.0 mag) LDGs was two.," Results of our follow-up spectroscopy with Faint Object Camera And Spectrograph (FOCAS) on Subaru Telescope were reported by \citet{and04,and07}, and the number of bright $z'<25.0$ mag) $z \sim 5$ LBGs with spectroscopic identification was nine and that of faint $z'\geq 25.0$ mag) LBGs was two." + Combining the data with those from literature. Andoοἱal.(2006). claimed the deficiency of bright LDGs with large EWs ol Lya emissions al ze5 and 2~6.," Combining the data with those from literature, \citet{and06} claimed the deficiency of bright LBGs with large EWs of $\alpha$ emissions at $z \sim 5$ and $z \sim 6$." + Hlowever. the sample size of our spectroscopically confirmed LDBGs at 2~5 was still verv small.," However, the sample size of our spectroscopically confirmed LBGs at $z \sim 5$ was still very small." + Thus we intended to increase the size of the speclroscopie sample., Thus we intended to increase the size of the spectroscopic sample. + In this paper we present the results of spectroscopic observations ol z5 LDBGs in the region including the GOODS-N and the J0053+1234 region with Gemini Multi-Object Spectrograph North (GMOS-N) ancl South (GMOS-5). respectively.," In this paper we present the results of spectroscopic observations of $z \sim 5$ LBGs in the region including the GOODS-N and the J0053+1234 region with Gemini Multi-Object Spectrograph North (GMOS-N) and South (GMOS-S), respectively." + Gemini/GAIOS spectrographs have nocd-and-shulfle capability. which enables us to subtract sky eniission more clearly ancl helps the detection of conünuum features.," Gemini/GMOS spectrographs have nod-and-shuffle capability, which enables us to subtract sky emission more clearly and helps the detection of continuum features." + In section 2.. we describe our sample selection. observations. and data reduction.," In section \ref{observation}, , we describe our sample selection, observations, and data reduction." + The results aud obtained spectra are presented in section 3.., The results and obtained spectra are presented in section \ref{results}. + In section 4.. we discuss distributions of redshifts and colors. an implication to the UVLF of LDGs at z~ 5. aud rest-Draame EWs of να emission. combining present results with previous data by Andoetal.(2004.2007) and bv others.," In section \ref{discussion}, we discuss distributions of redshifts and colors, an implication to the UVLF of LBGs at $z \sim 5$ , and rest-frame EWs of $\alpha$ emission, combining present results with previous data by \citet{and04,and07} and by others." +" Throughout (his paper. we used a flat A cosmology: O4,=0.3. O4=0.7. and Ly=10 kin ! +."," Throughout this paper, we used a flat $\Lambda$ cosmology; $\Omega_{\mathrm{M}} = 0.3$, $\Omega_\Lambda=0.7$, and $H_0 = 70$ km $^{-1}$ $^{-1}$ ." + All magnitudes are given in the AB svstem (Oke&Gunn 1983).., All magnitudes are given in the AB system \citep{oke83}. . + The photometric sample of LBGs at z5 was obtained in the region including the GOODS-N and the J0053--1234 region. based on V-. Zc-. and z'-band imagestakenwith Subaru/Suprime-Cam (Iwataetal.2003.2007).. The color criteria for z~5 LBGs are," The photometric sample of LBGs at $z \sim 5$ was obtained in the region including the GOODS-N and the J0053+1234 region, based on $V$-, $I_{\mathrm{C}}$ -, and $z'$ -band imagestakenwith Subaru/Suprime-Cam \citep{iwa03,iwa07}.. The color criteria for $z \sim 5$ LBGs are" +of the X-ray luminosity is uncertain.,of the X-ray luminosity is uncertain. + We therefore dare not estimate an orbital period on the basis of the magnitude of our caucdidato., We therefore dare not estimate an orbital period on the basis of the magnitude of our candidate. + The core of 66110 coutaius 20 (Lyne et 11996)., The core of 6440 contains $-$ 20 (Lyne et 1996). + The totaeuer loss E=190) for the pulsar is about (6.6«LO?orονwhere J£ ds the moment of inertia of the neutron star. OQ its rotation frequency aud © the time derivative of Q.," The total energy loss $\dot E\equiv I\Omega\dot\Omega$ for the pulsar is about $6.6\times 10^{32}\ergs$, where $I$ is the moment of inertia of the neutron star, $\Omega$ its rotation frequency and $\dot\Omega$ the time derivative of $\Omega$." + Typical X-ray Iuniünosities for radio pulsars are of order Ly~10.2709 LL in Verbuut et We coucluce that it is very iulikelv that the pulsar is responsible for the observed ταν fiux of Xl or N2., Typical X-ray luminosities for radio pulsars are of order $L_{\rm x}\sim 10^{-3}I\Omega\dot\Omega$ 4 in Verbunt et We conclude that it is very unlikely that the pulsar is responsible for the observed X-ray flux of X1 or X2. +systems.,systems. +" In this paper we use Very Large Array radio data for two additional systems, B1450+333 and B18344-620, which have been the subjects of detailed studies previously (?;; ?))."," In this paper we use Very Large Array radio data for two additional systems, B1450+333 and B1834+620, which have been the subjects of detailed studies previously \citealt{ksj06}; ; \citealt{sbrl00}) )." +" We summarise previous results from the literature in the remainder of Section 1, we present the VLA observations in Section 2, the resulting total intensity, spectral index and polarisation images in Sections 3 and 4 for B1450+333 and B1834+620 respectively and then use the results as inputs for the model in Sections 5-7."," We summarise previous results from the literature in the remainder of Section 1, we present the VLA observations in Section 2, the resulting total intensity, spectral index and polarisation images in Sections 3 and 4 for B1450+333 and B1834+620 respectively and then use the results as inputs for the model in Sections 5–7." +" We note that the modelling sections assume a WMAP cosmology, with 71kms~*Mpc~', Qm=0.27, Q4=0.73 (?))."," We note that the modelling sections assume a WMAP cosmology, with $H_0=71\mbox{km\,s}^{-1}\mbox{Mpc}^{-1}$ , $\Omega_{\mbox{m}}=0.27$, $\Omega_{\Lambda}=0.73$ \citealt{s03}) )." +" B1450+333 (=J1453+3308) was identified as a DDRG by ? using data from Faint Images of the Radio Sky at 20- (FIRST: ?)), the NRAO VLA Sky Survey (NVSS: ?)) and the Westerbork Northern Sky Survey (WENSS: ?))."," B1450+333 (=J1453+3308) was identified as a DDRG by \citet{sbrlk00} using data from Faint Images of the Radio Sky at 20-cm (FIRST: \citealt{bwh95}) ), the NRAO VLA Sky Survey (NVSS: \citealt{ccg98}) ) and the Westerbork Northern Sky Survey (WENSS: \citealt{rtb97}) )." +" It consists of four radio lobes distributed about a central core and only the southern, outer lobe shows tentative evidence for a weak hotspot."," It consists of four radio lobes distributed about a central core and only the southern, outer lobe shows tentative evidence for a weak hotspot." +" The southern lobes are weaker and more extended than the northern lobes and the outer lobes display an extended morphology perpendicular to, as well as along, the jet axis."," The southern lobes are weaker and more extended than the northern lobes and the outer lobes display an extended morphology perpendicular to, as well as along, the jet axis." +" ? studied this object further, using a wide range of observing frequencies and resolutions."," \citet{ksj06} studied this object further, using a wide range of observing frequencies and resolutions." +" They modeled the spectra of the lobes and determined spectral ages for the northern and southern outer lobes of ~47 and 58 Myr respectively, implying a mean separation velocity of 0.036c; the synchrotron age of the inner lobes was ~2 Myr, implying a velocity of 0.1c."," They modeled the spectra of the lobes and determined spectral ages for the northern and southern outer lobes of $\sim 47$ and 58 Myr respectively, implying a mean separation velocity of $0.036c$; the synchrotron age of the inner lobes was $\sim 2$ Myr, implying a velocity of $\sim 0.1c$." + B1450+333 lies at a redshift of 0.249 (?))., B1450+333 lies at a redshift of 0.249 \citealt{sbrlk00}) ). + B1834+620 was similarly identified as a DDRG by ?? using data from the WENSS and NVSS.," B1834+620 was similarly identified as a DDRG by \citet{sbrlk00, sbrl00} using data from the WENSS and NVSS." +" It too consists of four radio lobes about a central core, with hotspots present at the leading edges of the northern outer and southern inner lobes."," It too consists of four radio lobes about a central core, with hotspots present at the leading edges of the northern outer and southern inner lobes." +" 'The authors used the presence of these hotspots to argue in favour of the inner lobes having rapid advance velocities in a low-density environment; such a conclusion was supported by the discrepancy between the large optical emission line luminosity of the host galaxy and the relatively low radio power of the inner lobes, as well as by the model of ?.."," The authors used the presence of these hotspots to argue in favour of the inner lobes having rapid advance velocities in a low-density environment; such a conclusion was supported by the discrepancy between the large optical emission line luminosity of the host galaxy and the relatively low radio power of the inner lobes, as well as by the model of \cite{ksr00}." + B18344-620 lies at a redshift of 0.519 (?))., B1834+620 lies at a redshift of 0.519 \citealt{sbrl00}) ). +" Radio observations of B1450+333 and B1834+620 were obtained using the VLA on 2000 October 20—21, when the array was in the highest resolution A-configuration, and 2001 April 2, when the array was in the B-configuration."," Radio observations of B1450+333 and B1834+620 were obtained using the VLA on 2000 October 20–21, when the array was in the highest resolution A-configuration, and 2001 April 2, when the array was in the B-configuration." +" Data were obtained at three frequencies — 1.40-GHz (L-band), 4.86-GHz (C-band) and 8.46-GHz (X-band) - in each array,as for our previous observing campaign for B09254-420 (?)); IFs at two adjacent frequencies were used"," Data were obtained at three frequencies – 1.40-GHz (L-band), 4.86-GHz (C-band) and 8.46-GHz (X-band) – in each array,as for our previous observing campaign for B0925+420 \cite{bks07}) ); IFs at two adjacent frequencies were used" +NGC 4258 is a bright. barred-spiral galaxy at a distance of7.2Alpe (Llerrnsteinetal.1999).,"NGC 4258 is a bright barred-spiral galaxy at a distance of$7.2\,\rm +Mpc$ \citep{H99}." +.. Lt is in Sevfert's first catalogue of active galaxies (Sevfert1943)., It is in Seyfert's first catalogue of active galaxies \citep{S43}. +.. It has anomalous spiralarms of Ho. emission (Courtes&Cruvellier1961). in the inner regions which are symmetric with respect to the nucleus., It has anomalous spiralarms of $\rm H\alpha$ emission \citep{CC61} in the inner regions which are symmetric with respect to the nucleus. + This emission is probably from shocks formed where the matter ejected. from the nucleus meets the interstellar medium (vanderIxruit.Oort&Alathewson1972:Fordοἱal. 1986).," This emission is probably from shocks formed where the matter ejected from the nucleus meets the interstellar medium \citep{K72, F86}." +. Alasers are the microwave equivalent of lasers., Masers are the microwave equivalent of lasers. + Water vapour maser emission at a wavelength of 1.35em. provides information about the accretion. discs. around highly compact objects in the centres of active galaxies.," Water vapour maser emission at a wavelength of $1.35\,\rm cm$ provides information about the accretion discs around highly compact objects in the centres of active galaxies." + Masers are bright where there is no gradient in the bulk linc-of-sight velocity (Grinin&CGrigorev1983:WatsonΑνα2000).," Masers are bright where there is no gradient in the bulk line-of-sight velocity \citep{GG83,WW00}." +. In à nearly eclge-on Weplerian accretion disc the strongest features occur along the line to the disc centre where the disc is moving perpendicular to the line of sight. these are the systemic masers.," In a nearly edge-on Keplerian accretion disc the strongest features occur along the line to the disc centre where the disc is moving perpendicular to the line of sight, these are the systemic masers." + We also see masers where the plane of the sky intersects the disc. these are the high-velocity mascrs.," We also see masers where the plane of the sky intersects the disc, these are the high-velocity masers." + Alasers were first detected in the galaxy NGC 4258 by Claussen.Heiligman&Lo(1984). and Henkeletal.(1984)., Masers were first detected in the galaxy NGC 4258 by \cite{CHL84} and \cite{H84}. +. The structure and dynamics of these clises can be accurately probed. with very long bascline interferometry because the emission lines are strong and intrinsically narrow., The structure and dynamics of these discs can be accurately probed with very long baseline interferometry because the emission lines are strong and intrinsically narrow. + NGC 4258 has a set of masers that might trace out a warped accretion disc which is seen nearly edge on (Alivoshictal.1995:Ler-rnsteinοἱal. 2005).," NGC 4258 has a set of masers that might trace out a warped accretion disc which is seen nearly edge on \citep{M95,H05}." +.. Radio interferometry has shown that their rotation is Weplerian (Nakai.Inoue&Mivoshi1993) and that the dise extends from 2.8mas to 8.2mas from the nucleus.," Radio interferometry has shown that their rotation is Keplerian \citep{NIM93} and that the disc extends from $2.8\,\rm mas$ to $8.2\,\rm mas$ from the nucleus." + At its distance of 7.2Mpe. in the plane of the sky. we have the scaling mas=L07710+em0.0349 pe.," At its distance of $7.2\,\rm Mpc$, in the plane of the sky we have the scaling $1\,\rm mas=1.077\times 10^{17}\,\rm cm=0.0349\,\rm pc$ ." +" ""Ehe Ixeplerian rotation of the high velocity masers implies an enclosed mass of 3.78«LOOM. within 2.8mas of the nucleus (Llerrnstein.Greenhill&Moran.1996)."," The Keplerian rotation of the high velocity masers implies an enclosed mass of $3.78 \times 10^7\,\rm M_\odot$ within $2.8\,\rm mas$ of the nucleus \citep{HGM96}." +.. This is consistent with a central supermassive black hole., This is consistent with a central supermassive black hole. + On à scale of milliarcseconds the central core breaks up into à jet oriented. along the axis of the water maser disc (Llerrnsteinetal.1997.1998).," On a scale of milliarcseconds the central core breaks up into a jet oriented along the axis of the water maser disc \citep{H97,H98}." +. The northern jet has a Dux of 3mJyv and its mean location is about O1mas north (in he plane of the skv) of the implied position of the black hole which is the centre of the rotation of the masers.," The northern jet has a flux of $3\,\rm mJy$ and its mean location is about $0.4\,\rm mas$ north (in the plane of the sky) of the implied position of the black hole which is the centre of the rotation of the masers." + However he jet position varies in time., However the jet position varies in time. + The southern jjet has not varied in lux or position and is located about 1.0mas south of the black hole position.," The southern jet has not varied in flux or position and is located about $1.0\,\rm mas$ south of the black hole position." + lt has a flux of 0.5mJy.," It has a flux of $0.5\,\rm mJy$." +ut The ree-Lree absorption in the masing disc causes the dillerence in brightness between the jets (Hlerrnstein.ctal.1997)., The free-free absorption in the masing disc causes the difference in brightness between the jets \citep{H97}. + The position angles of the jets are poorly determined., The position angles of the jets are poorly determined. + We estimate the northern jet is at a position angle of 5°x15° measured. from Llerrnsteinetal.(1998)., We estimate the northern jet is at a position angle of $5^\circ \pm 15^\circ$ measured from \cite{H98}. +.. Phe jets do not appear to be verv well aligned with cach other and the southern jet is at a position angle of about 173., The jets do not appear to be very well aligned with each other and the southern jet is at a position angle of about $173^\circ$. + On larger scales the jet appears to be orientated north-south (C'eciletal. 2000)., On larger scales the jet appears to be orientated north-south \citep{C00}. +. The systemic masers are about 0.57mas below the cise centre as indicated by the high velocity masers (Herrnsteinetal.2005). and at a disc radius of 3.9mas.," The systemic masers are about $0.57\,\rm mas$ below the disc centre as indicated by the high velocity masers \citep{H05} and at a disc radius of $3.9\,\rm mas$." + Hence. the masers at the inner edge of the disc suggest that it is inclined at an angle of ὦμ=sin1(0.57/3.9)S4° to the plane of the sky.," Hence, the masers at the inner edge of the disc suggest that it is inclined at an angle of $\zeta_{\rm + in}=\sin^{-1}(0.57/3.9)\approx 8.4^\circ$ to the plane of the sky." + There appears to be no structure to the vertical positions of the masers in the disc and so the dise is probably un (Mivoshictal. 1995).., There appears to be no structure to the vertical positions of the masers in the disc and so the disc is probably thin \citep{M95}. . + Alasers operate when the temperature of the surlace lavers in the disc is greater than 300Ix but less than 1000Ix. (Moranetal. 1995)...," Masers operate when the temperature of the surface layers in the disc is greater than $300\,\rm K$ but less than $1000\,\rm K$ \citep{Mo95}. ." + Phe outer edge of thedisc is where the molecular to atomic transition occurs. just outside the outer," The outer edge of thedisc is where the molecular to atomic transition occurs, just outside the outer" +For GW Lib itsell. we are still dependent on a number of assumptions in order to solve ils svsleni parameters.,"For GW Lib itself, we are still dependent on a number of assumptions in order to solve its system parameters." + To properly alien all methods. we need to revisit the mass from asteroseismologv taking into account the effects of rotation and see if à. WD moclel with a mass of OSA. at the latest distance can be fitted to the UV data with reasonable temperatures.," To properly align all methods, we need to revisit the mass from asteroseismology taking into account the effects of rotation and see if a WD model with a mass of $0.84 M_\odot$ at the latest distance can be fitted to the UV data with reasonable temperatures." + To be able to calculate a direct mass ratio. a determination of A4 from the Ale should be possible through hieh S/N phase-resolved spectroscopy.," To be able to calculate a direct mass ratio, a determination of $K_1$ from the Mg should be possible through high S/N phase-resolved spectroscopy." + If furthermore malched wilh an solid ephemeris using the emission from the donor star (giving A» and 5). a fully consistent and accurate WD mass for this prototvpical accreting WD pulsator is entirelv feasible.," If furthermore matched with an solid ephemeris using the emission from the donor star (giving $K_2$ and $\gamma$ ), a fully consistent and accurate WD mass for this prototypical accreting WD pulsator is entirely feasible." + DS acknowledges an STFC Advanced Fellowship., DS acknowledges an STFC Advanced Fellowship. + TRAI was supported by an STFC Rolling Grant., TRM was supported by an STFC Rolling Grant. + Based on observations made with ESO Telescopes at (he Paranal Observatory under programme ID 69.D-0591, Based on observations made with ESO Telescopes at the Paranal Observatory under programme ID 69.D-0591 +wavelengths/frequencies required.,wavelengths/frequencies required. +" Each time a photon packet scatters, a photon packet is peeled-off, and each time a photon packet is absorbed, it is terminated."," Each time a photon packet scatters, a photon packet is peeled-off, and each time a photon packet is absorbed, it is terminated." +" Thus, there is no immediate re-emission following an absorption."," Thus, there is no immediate re-emission following an absorption." + The next step is to compute the scattered dust emission., The next step is to compute the scattered dust emission. + The specific energy absorption rate is used to compute the emissivity at the fixed wavelengths/frequencies inside each cell., The specific energy absorption rate is used to compute the emissivity at the fixed wavelengths/frequencies inside each cell. +" To emit a photon packet, a random cell is selected in the grid, and the photon packet is emitted randomly within the cell, carrying an amount of energy proportional to the local emissivity."," To emit a photon packet, a random cell is selected in the grid, and the photon packet is emitted randomly within the cell, carrying an amount of energy proportional to the local emissivity." +" The photon packet is then propagated, and a photon packet is peeled-off at each scattering."," The photon packet is then propagated, and a photon packet is peeled-off at each scattering." +" As before, the photon packet is terminated once it is absorbed."," As before, the photon packet is terminated once it is absorbed." + This algorithm ensures conservation of the total scattered light contribution., This algorithm ensures conservation of the total scattered light contribution. +" When computing SEDs and images, allows the user to compute uncertainties, which uses the scatter in the photon packet flux values to derive errors in the flux at each wavelength/frequency and in each aperture or pixel."," When computing SEDs and images, allows the user to compute uncertainties, which uses the scatter in the photon packet flux values to derive errors in the flux at each wavelength/frequency and in each aperture or pixel." +" The fact that a given SED or image can be constructed using a combination of techniques, such as peeling-off and raytracing — which can produce very different signal-to-noise — is properly taken into account by computing the uncertainties for the contribution from each technique to the final SEDs or images separately and then combining them."," The fact that a given SED or image can be constructed using a combination of techniques, such as peeling-off and raytracing – which can produce very different signal-to-noise – is properly taken into account by computing the uncertainties for the contribution from each technique to the final SEDs or images separately and then combining them." + offers the option for the user to track the origin of each photon packet to split SEDs and images into different components., offers the option for the user to track the origin of each photon packet to split SEDs and images into different components. +" A basic mode allows SEDs and images to be split into contributions from sources and from dust, while a more detailed mode allows the flux to be split into individual sources and dust types."," A basic mode allows SEDs and images to be split into contributions from sources and from dust, while a more detailed mode allows the flux to be split into individual sources and dust types." +" In both cases, the flux can be split further into photon packets reaching the observer directly, and photon packets having been scattered since the last emission/re-emission and before reaching the observer."," In both cases, the flux can be split further into photon packets reaching the observer directly, and photon packets having been scattered since the last emission/re-emission and before reaching the observer." +" Users have the option to specify a dust sublimation specific energy absorption rate for each dust type, and three different dust sublimation modes are possible: As mentioned in Section 1,, forced first scattering (e.g.??) can be used to improve the signal-to-noise of scattered radiation in optically thin dust."," Users have the option to specify a dust sublimation specific energy absorption rate for each dust type, and three different dust sublimation modes are possible: As mentioned in Section \ref{sec:introduction}, forced first scattering \citep[e.g.][]{mattila:70:53, wood:99:799} can be used to improve the signal-to-noise of scattered radiation in optically thin dust." + includes an implementation of this algorithm., includes an implementation of this algorithm. +" 'The reason for not using the ? immediate temperature correction method in is that each time a photon gets absorbed and re-emitted, the specific energy absorption rate grid has to be updated."," The reason for not using the \citet{bjorkman:01:615} immediate temperature correction method in is that each time a photon gets absorbed and re-emitted, the specific energy absorption rate grid has to be updated." +" Thus, it is not possible to compute the propagation of multiple photons simultaneously and to then combine the results, and codes using this method can therefore not easily be parallelized."," Thus, it is not possible to compute the propagation of multiple photons simultaneously and to then combine the results, and codes using this method can therefore not easily be parallelized." +" By simply using an iterative approach to computing the specific energy absorption rate using the ? continuous absorption method, one has the advantage that within an iteration, the problem is “embarrassingly parallel""."," By simply using an iterative approach to computing the specific energy absorption rate using the \citet{Lucy:99:282} continuous absorption method, one has the advantage that within an iteration, the problem is “embarrassingly parallel”." +" Each process can propagate photon packets independently, and at the end of the iteration, the energy absorbed in each cell is synchronized over processes."," Each process can propagate photon packets independently, and at the end of the iteration, the energy absorbed in each cell is synchronized over processes." +" Similarly, when SEDs, images, or polarization maps are computed, these can be computed by separate processes, and combined at the end of the calculation."," Similarly, when SEDs, images, or polarization maps are computed, these can be computed by separate processes, and combined at the end of the calculation." + The code has been parallelized using the Message Passing Interface (MPI)., The code has been parallelized using the Message Passing Interface (MPI). +" Since different cores or nodes can have inhomogeneous performance, rather than dividing the total number of photon packets equally between processes, the task is divided into chunks of photon packets that are small enough that there are many more chunks than total number of processes, but large enough that the processes do not communicate too often."," Since different cores or nodes can have inhomogeneous performance, rather than dividing the total number of photon packets equally between processes, the task is divided into chunks of photon packets that are small enough that there are many more chunks than total number of processes, but large enough that the processes do not communicate too often." +" Each process then computes one batch of photon packets, and reports back to the main process to find out whether to process another batch or whether to stop."," Each process then computes one batch of photon packets, and reports back to the main process to find out whether to process another batch or whether to stop." +" This incurs a very small overhead, since the request consists essentially of a single number both ways."," This incurs a very small overhead, since the request consists essentially of a single number both ways." +" Only at the end of the iteration, once all processes have received the signal to stop, are the results combined."," Only at the end of the iteration, once all processes have received the signal to stop, are the results combined." +" This last step incurs an overhead, which scales with the number of processes and the grid, image, or SED resolution."," This last step incurs an overhead, which scales with the number of processes and the grid, image, or SED resolution." +" However, in most cases, the overhead is negligible compared to the main computation."," However, in most cases, the overhead is negligible compared to the main computation." +corresponding to specilic eigenvalues of specific solutions.,corresponding to specific eigenvalues of specific solutions. + The Agus. Aree: and ος components. corresponding to the second-order change in the variance for each of the eigenvalues of the two anisotropic solutions. are given in Table 3..," The $\Lambda_{uuuu}$ , $\Lambda_{vvvv}$ and $\Lambda_{wwww}$ components, corresponding to the second-order change in the variance for each of the eigenvalues of the two anisotropic solutions, are given in Table \ref{tensor}." + We continue with the F-ratio test as a wav of interpreting these components., We continue with the F-ratio test as a way of interpreting these components. + Recall that a change in the ratio of variance by a certain amount corresponds (o a certain probability that one solution is significantly different from another., Recall that a change in the ratio of variance by a certain amount corresponds to a certain probability that one solution is significantly different from another. + For the number of degrees of [reedonm in the 35-galaxy sample. for instance. a ratio of 1.3 means a probability that the smaller variance corresponds to the better solution.," For the number of degrees of freedom in the 35-galaxy sample, for instance, a ratio of 1.8 means a probability that the smaller variance corresponds to the better solution." + The allowable change in the eigenvalue to remain within this window is thus The results of this kind of ealeulation are shown in Table 4.., The allowable change in the eigenvalue to remain within this window is thus The results of this kind of calculation are shown in Table \ref{error}. + From the table. the uncertainty in the out-of-plane tensor components is rather large.," From the table, the uncertainty in the out-of-plane tensor components is rather large." +" If confidence is recquired. for instance. the 77,4, eigenvalues in each solution are still only known with a error."," If confidence is required, for instance, the $H_{ww}$ eigenvalues in each solution are still only known with a error." +" The effect of these uncertainties on the whole solution may be illustrated by the 35-galaxy. £7,, eigenvalue.", The effect of these uncertainties on the whole solution may be illustrated by the 35-galaxy $H_{uu}$ eigenvalue. + At confidence it may vary by a fraction of 0.44. which means it could have à value of 61 km + 5 smaller indeed than the middle eigenvalue.," At confidence it may vary by a fraction of 0.44, which means it could have a value of 61 km $^{-1}$ $^{-1}$, smaller indeed than the middle eigenvalue." + In (hat case its direction ceases to be an eigenvector., In that case its direction ceases to be an eigenvector. + As suggested by the great differences in direction and magnitude among the models. the details of anisotropic flow are quite uncertain.," As suggested by the great differences in direction and magnitude among the models, the details of anisotropic flow are quite uncertain." + An exactly similar derivation gives the error tensor corresponding to solar reflex motion: and in the same wav (using the F-ratio test) it can be turned. into uncertainties of components of the reflex motion vector., An exactly similar derivation gives the error tensor corresponding to solar reflex motion: and in the same way (using the F-ratio test) it can be turned into uncertainties of components of the reflex motion vector. + To allow comparison with the entries in Table 2.. the --confidence limits of each component (corresponding to about one-sigma error bars’ were combined into limits on the magnitude and direction and listed in Table 5..," To allow comparison with the entries in Table \ref{solar}, the -confidence limits of each component (corresponding to about one-sigma error bars) were combined into limits on the magnitude and direction and listed in Table \ref{vectorprop}." + Some of the uncertaintv comes from distance errors. which translate into correlated errors in the components: most is uncorrelated.," Some of the uncertainty comes from distance errors, which translate into correlated errors in the components; most is uncorrelated." + Figures are given [for both extremes. with the actua situation being closer to the uncorrelated ideal.," Figures are given for both extremes, with the actual situation being closer to the uncorrelated ideal." + For large values of angle uncertainties (about 15* or over) the limits become strongly asvimetrical: thefigures listed are averages., For large values of angle uncertainties (about $15\arcdeg$ or over) the limits become strongly asymetrical; thefigures listed are averages. + For comparison. karachentsev&Makarov(2001) give their uncertainties (stancare," For comparison, \citet{KM01} give their uncertainties (standard" + For comparison. karachentsev&Makarov(2001) give their uncertainties (stancarel," For comparison, \citet{KM01} give their uncertainties (standard" +"are sog=2250""36.977.520)1577315427 (which is within ON” of the A-ray position).","are $\alpha_{2000}=22^{h} 50^{m} 36.97^{s}, +\delta_{2000}=+57^{\circ} 31^{'} 54.2^{''}$ (which is within $^{''}$ of the X-ray position)." + We searched the LPLLAS catalogue (Drew ct al 2005) which surveved the northern galactic plane in r./.tla filters to determine if the optical counterpart of was detected in this survey.," We searched the IPHAS catalogue (Drew et al 2005) which surveyed the northern galactic plane in $r,i,$ $\alpha$ filters to determine if the optical counterpart of was detected in this survey." + We find that IPLLAS gives 20.32£0.05.7=20.130.2.Ha19.69+0.09 for31.," We find that IPHAS gives $r=20.32\pm0.05, i=20.1\pm0.2, H\alpha=19.69\pm0.09$ for." + All sources within a 0 radius of the X-ray position were extracted., All sources within a $^{''}$ radius of the X-ray position were extracted. + is at the extreme blue end in the Gr7) distribution and consistent with the location of the CVs found in IPLLAS data in the (er2).Ho) colour-colour plane (ef Πο] of Corradi et al 2008).," is at the extreme blue end in the $(r-i)$ distribution and consistent with the location of the CVs found in IPHAS data in the $(r-i), (r-H\alpha)$ colour-colour plane (cf fig1 of Corradi et al 2008)." + We also obtained C.g.H2 images of using the Wide Field Camera on the Isaac Newton Telescope on 6th Nov 2008: Figure 4. shows the g band image of the immediate field.," We also obtained $U, g, R$ images of using the Wide Field Camera on the Isaac Newton Telescope on 6th Nov 2008: Figure \ref{finding} shows the $g$ band image of the immediate field." + Using standard star observations taken immediately before these observations we find that (6=51 TSAO. g=21.1640.05 and i= 21.53-40.05.," Using standard star observations taken immediately before these observations we find that $U=21.75\pm$ 0.11, $g=21.16\pm0.05$ and $r=21.53\pm$ 0.05." + Compared to other stars in the field. it is clearky blue and appears to be more than 1 mag fainter than found at the epoch of the IPLLAS pointings.," Compared to other stars in the field, it is clearly blue and appears to be more than 1 mag fainter than found at the epoch of the IPHAS pointings." + This is not unexpected. since polars are known to show cdilferent accretion states., This is not unexpected since polars are known to show different accretion states. + We obtained spectra of using the 4.2m William Llersehel Telescope and the Intermediate dispersion Spectrograph ancl Imaging System. (ISIS) on La Palma on 6th. Oct 2008., We obtained spectra of using the 4.2m William Herschel Telescope and the Intermediate dispersion Spectrograph and Imaging System (ISIS) on La Palma on 6th Oct 2008. + We used the 300D. and. RSS gratings giving a spectral resolution of 72.5. and 5A. respectively., We used the R300B and R158R gratings giving a spectral resolution of $\sim$ and $\sim$ respectively. + The seeing was O0.8 and the slit was set to match the seeing., The seeing was $\sim0.8^{''}$ and the slit was set to match the seeing. + We took 16 spectra in both the red and blue arms., We took 16 spectra in both the red and blue arms. + With an out of eclipse brightness of 7—21. each individual spectrum was of low signal to noise.," With an out of eclipse brightness of $r\sim$ 21, each individual spectrum was of low signal to noise." + Moreover. in the blue arm. there was electronic noise in the images. the pattern of which varied from image o image.," Moreover, in the blue arm, there was electronic noise in the images, the pattern of which varied from image to image." + This coupled with the low signal to noise of the spectra prevented: us from extracting anv useful information from the blue arm., This coupled with the low signal to noise of the spectra prevented us from extracting any useful information from the blue arm. + In the red arm. we were able to exract a spectrum [rom each image.," In the red arm, we were able to extract a spectrum from each image." + For 9 sequential spectra we were able to detect lea in emission., For 9 sequential spectra we were able to detect $\alpha$ in emission. + We show the mean of these spectra. in ligure 5.., We show the mean of these spectra in Figure \ref{red-spec}. + For the remaining 7 spectra for which we cid not detect Ho in emission we attribute this to the fact that the observations occurred. during the phase interval of the pre-eclipse absorption dip or that the accretion stream was presenting a small surface area at those phase intervals. (, For the remaining 7 spectra for which we did not detect $\alpha$ in emission we attribute this to the fact that the observations occurred during the phase interval of the pre-eclipse absorption dip or that the accretion stream was presenting a small surface area at those phase intervals. ( +Given the error on the orbital period. 83. the phasing of the NIIT spectra using the NOT photometric observations as à marker of the phasing is uncertain by approximately one orbital evele).,"Given the error on the orbital period, 3, the phasing of the WHT spectra using the NOT photometric observations as a marker of the phasing is uncertain by approximately one orbital cycle)." + In polars. it is thought that the magnetic axis of the white chwarl is tiltecl towards the secondary star. but shifted a few 10's of degrees ahead in azimuth (as the binary rotates) of the line of center joining the two stars (eg Cropper LOSS).," In polars, it is thought that the magnetic axis of the white dwarf is tilted towards the secondary star, but shifted a few 10's of degrees ahead in azimuth (as the binary rotates) of the line of center joining the two stars (eg Cropper 1988)." + Lt is therefore the accretion region in the upper hemisphere, It is therefore the accretion region in the upper hemisphere +haloes.,haloes. + The origin of the power-law-like form of the pseudo phase-space density. profile and the effects of major mergers are discussed in Section ??.., The origin of the power-law-like form of the pseudo phase-space density profile and the effects of major mergers are discussed in Section \ref{mm}. +" Our results are summarised in Section οοι,", Our results are summarised in Section \ref{summ}. + A package with the numerical codes used in the present paper is publicly available (romwww., A package with the numerical codes used in the present paper is publicly available from. +am.ub.es/--cosmo/haloes&peaks.tgz. There are in the literature several wavs to characterise the shape of a triaxial svstem with semiaxes ez5&e: the axial ratios. the ellipticity and prolateness (e.g. BBINS) and thetriaxialitv parameter (e.g. Fransetal.1991)). among others.," There are in the literature several ways to characterise the shape of a triaxial system with semiaxes $a\ge b\ge c$: the axial ratios, the ellipticity and prolateness (e.g. BBKS) and thetriaxiality parameter (e.g. \citealt{Fea91}) ), among others." + In the present paper. we use the primary and secondary eccentricities. respectively defined as," In the present paper, we use the primary and secondary eccentricities, respectively defined as." + As the eccentricities vary. in general. over the svstem (we assume from now on that the centre of svmmetry remains the same at all scales). we will deal with the eccentricity profiles ορ) and ος). being r the radius of a sphere associated with each ellipsoid (see details below).," As the eccentricities vary, in general, over the system (we assume from now on that the centre of symmetry remains the same at all scales), we will deal with the eccentricity profiles $\ep(r)$ and $\es(r)$, being $r$ the radius of a sphere associated with each ellipsoid (see details below)." + Numerical stucies of virialised halocs usually work with spherically averaged. profiles., Numerical studies of virialised haloes usually work with spherically averaged profiles. +" Of course. triaxial svstems show non-null departures op(r.0.,) and δν0.5) of the local density ptr8.45) and gravitational potential (r.8.45) from their respective spherical averages £pi(e) and. C437)."," Of course, triaxial systems show non-null departures $\delta\rho\sphc$ and $\delta\Phi\sphc$ of the local density $\rho\sphc$ and gravitational potential $\Phi\sphc$ from their respective spherical averages $\srho(r)$ and $\spot(r)$ ." + Hence. the (scaled) mean squared or erossed density ancl potential Huctuation proliles. ((8p/i£py(ie). οςο and (9pας(0)(7). also give a measure of the triaxial shape ofthose svstenis.," Hence, the (scaled) mean squared or crossed density and potential fluctuation profiles, $\lav (\delta\rho/\srho)^2\rav(r)$, $\lav +(\delta\Phi/\spot)^2\rav(r)$ and $\lav (\delta\rho/\srho) +(\delta\Phi/\spot)\rav(r)$, also give a measure of the triaxial shape of those systems." + 3clow. we relate these profiles to the cecentricity profiles definedabove.," Below, we relate these profiles to the eccentricity profiles definedabove." +" ‘Take the Cartesian axis z aligned along with the major axis of the ellipsoidal isodensitv contour o""(r). labelled by the radius"," Take the Cartesian axis $z$ aligned along with the major axis of the ellipsoidal isodensity contour $\rho\el(r)$, labelled by the radius." +" The local density at the point (6.42) then takes the form ] ].. where ej, stands for one of the two eccentricities and e for the other one*."," The local density at the point $\sphc$ then takes the form ] , where $\eps$ stands for one of the two eccentricities and $\esp$ for the other ." +. Phe spherically averaged density at ris then equal to Gr) where we have defined the function ]e," The spherically averaged density at $r$ is then equal to ]G(r), where we have defined the function ]." +"«0)|— Dividing equation (5)) by £p(r) and replacing p""(r) by its value given in equation (6)). we obtain "," Dividing equation \ref{ellips}) ) by $\srho(r)$ and replacing $\rho\el(r)$ by its value given in equation \ref{norm})), we obtain ." +The mean squared. densityHuctuation over the sphere with radius r.," The mean squared densityfluctuation over the sphere with radius$r$ ," +FURST Radio SurveyBecker! R.L A ite? The cohereut image distortions induced by weak gravitational lensing can be used to measure the power spectrmu of density inhomoecueities in the universe (see [0]. for a review. and 10 for a bibliography).,"IRST Radio Survey, R. L. $^{5}$ } The coherent image distortions induced by weak gravitational lensing can be used to measure the power spectrum of density inhomogeneities in the universe (see \cite{nar96} for a review, and \cite{ref98a} for a bibliography)." + While most scarches for this effect are couducted in the optical band. we are eugaged in au effort to detect this effect with the FIRST radio survey.," While most searches for this effect are conducted in the optical band, we are engaged in an effort to detect this effect with the FIRST radio survey." +" The main advantages of our experiment are the high redshitt of the sources (6:5~ 1). the wide solid angle covered by the FIRST survey (currently L200 σσ), and the reproducibility of the svstematic effects."," The main advantages of our experiment are the high redshift of the sources $\langle z \rangle \sim 1$ ), the wide solid angle covered by the FIRST survey (currently 4,200 $^{2}$ ), and the reproducibility of the systematic effects." + While a detailed account of our study will appear in ref., While a detailed account of our study will appear in ref. + [O} (see also |0])). its theoretical framework aud the study of one of the systematic effects are presented in refs.," \cite{ref98c} (see also \cite{ref98a}) ), its theoretical framework and the study of one of the systematic effects are presented in refs." + [3] ancl [0]., \cite{kam98} and \cite{ref98b}. . +by interstellar dust in the optical is for GRO 165540. adopting the extinction upper limit of shy<4.0 ClFable 2).,"by interstellar dust in the optical is for GRO J1655--40, adopting the extinction upper limit of $A_{\rm V} < 4.0$ (Table 2)." + In the A-band. cig~O.Liiv. so LPRX12% much lower than is observed.," In the $K$ -band, $A_{\rm K }\sim 0.1 A_{\rm V}$, so $_{\rm K}\leq 1.2$ – much lower than is observed." + In addition Dubus&Chaty(2006) measured LP 0$ are the same constants as employed by CG00, and $a_b$ is the semi-major axis of the ring boundary that is nearest a given wire at $a$." + According to (3)). the velocity dispersion decreases from either ring boundary. lowards the ring interior over a lenethscale i..," According to \ref{collprescrip}) ), the velocity dispersion decreases from either ring boundary towards the ring interior over a lengthscale $w_r$." +" The physics underlving the enhancement of velocity. dispersion near ring boundaries is elucidated by Borcleries. Goldreich. Tremaine (1982) and estimates [or οι. ον. aud iv, are derived by CGOO."," The physics underlying the enhancement of velocity dispersion near ring boundaries is elucidated by Borderies, Goldreich, Tremaine (1982) and estimates for $c_i$ , $c_b$, and $w_r$ are derived by CG00." + The actual values we employ. are contained in Table 2.., The actual values we employ are contained in Table \ref{param2}. + The function is a soltening parameter that we impose because the (rue acceleration due to particle collisions near a ring boundary is likely overestimated by (he usual hydrodinanmic expression for the acceleration due to pressure gradients [X! V(Xc?)]., The function is a softening parameter that we impose because the true acceleration due to particle collisions near a ring boundary is likely overestimated by the usual hydrodynamic expression for the acceleration due to pressure gradients $-\Sigma^{-1} \nabla (\Sigma c^2)$ ]. + Within a few mean free paths. ~A. of the ring edge. the hydrodynamie approximation breaks down ancl particles behave more ballistically with less regard for large-scale eracients in the surface density.," Within a few mean free paths, $\sim$$\lambda$, of the ring edge, the hydrodynamic approximation breaks down and particles behave more ballistically with less regard for large-scale gradients in the surface density." + The parameter 5 quickly grows Irom €.7 to unity as we recede [rom (he ring edge towards (he ring midline., The parameter $S$ quickly grows from $e^{-2}$ to unity as we recede from the ring edge towards the ring midline. + The collisional acceleration. C. is inserted into Gausss equation for a given ring particle's apsidal precession rate. di/df. and averaged over (rue anomaly {ο vield. for a given. wire. (dic/ dle.," The collisional acceleration, $\mathbf{C}$, is inserted into Gauss's equation for a given ring particle's apsidal precession rate, $d\pomega/dt$, and averaged over true anomaly to yield, for a given wire, $\langle d\pomega/dt \rangle_C$ ." + This collisional contribution to the wire's precession rate adds to other contributions due to planetary oblateness and inter-wire gravity., This collisional contribution to the wire's precession rate adds to other contributions due to planetary oblateness and inter-wire gravity. + Expressions for the latter (wo contributions, Expressions for the latter two contributions + In order to present the results in a clearer and more concise way. the partial derivatives ol the relative age with Y and CNONa. with different iron contents. have been calculated.," In order to present the results in a clearer and more concise way, the partial derivatives of the relative age with Y and CNONa, with different iron contents, have been calculated." + The partial derivatives lyeyora/OY have been computed using the mass chauge in Ile. that is Y20.25. 0.30. 0.35 and 0.40.," The partial derivatives $\delta Age_{NORM} / \delta Y$ have been computed using the mass change in He, that is Y=0.25, 0.30, 0.35 and 0.40." + For this purpose. and for each value of input age ancl iron content. a least squares fit has been performed to derive the slope of the Ageyopay as a [function of Y. Finally. results for dilferent input ages have been averaged to derive the final OAdgexopgu/0Y as a function of [Fe/H].," For this purpose, and for each value of input age and iron content, a least squares fit has been performed to derive the slope of the $Age_{NORM}$ as a function of Y. Finally, results for different input ages have been averaged to derive the final $\delta Age_{NORM} / \delta Y$ as a function of $[Fe/H]$." + Concerning the CNONa. a similar procedure has been followed. but in this case. since the CNONa extreme mixture has a sum (C+N+O+Na) that is a factor of 2 (about 0.3 dex) lareer than im the reference case. 0-1geopu/0CΝΟΝα has been computed by accounting for a dCNONa = 0.3.," Concerning the CNONa, a similar procedure has been followed, but in this case, since the CNONa extreme mixture has a sum (C+N+O+Na) that is a factor of 2 (about 0.3 dex) larger than in the reference case, $\delta Age_{NORM} / \delta CNONa$ has been computed by accounting for a $\delta CNONa$ = 0.3." +D The results ave shown in Figure8. where (he partial derivatives of the relative age with Y (left panel) and with CNONa (right panel) are plotted for the horizontal (ved squares). vertical (blue circles) ancl YMSE (black triangles) methods.," The results are shown in Figure, where the partial derivatives of the relative age with Y (left panel) and with CNONa (right panel) are plotted for the horizontal (red squares), vertical (blue circles) and rMSF (black triangles) methods." + The left panel clearly shows (hat the vertical method is strongly dependent on Y for all metallicities. while the horizontal method is very sensitive toY oiv for metallicities higher that [Fe/II]—1.3.," The left panel clearly shows that the vertical method is strongly dependent on Y for all metallicities, while the horizontal method is very sensitive toY only for metallicities higher that $>-1.3$." + The rMSE method. on the other hand. is euite insensitive to Y for the whole metallicity interval except. mavbe. for very hieh iron content.," The rMSF method, on the other hand, is quite insensitive to Y for the whole metallicity interval except, maybe, for very high iron content." + The right panel shows that the three methods are nol very sensitive to CNONa. rMSE nethod having the relative advantage of showing a CNONa dependence (hat is metallicity independent.," The right panel shows that the three methods are not very sensitive to CNONa, rMSF method having the relative advantage of showing a CNONa dependence that is metallicity independent." + In conclusion. it is evident that both the horizontal and the vertical methocs are significantly affected by undetected differences in both the initial Ile content and/or heavy element clistribution between the stellar svstens under scrutiny.," In conclusion, it is evident that both the horizontal and the vertical methods are significantly affected by undetected differences in both the initial He content and/or heavy element distribution between the stellar systems under scrutiny." + Between the two methods. the worst one in this context is clearly the vertical method.," Between the two methods, the worst one in this context is clearly the vertical method." +" With regard to the rMSE relative age technique. this is almost unallected by anm"" variation in the helium content. and affected bv a chanee in the metal distribution (in particular in the CNO element abundance) as the sade level of the horizontal and vertical method."," With regard to the rMSF relative age technique, this is almost unaffected by any variation in the helium content, and affected by a change in the metal distribution (in particular in the CNO element abundance) as the same level of the horizontal and vertical method." + On the basis of present analysis. and taking into account the advantages discussed bv(2009). we consider the r\ISF method much more suitable than other techniques lor retrieving relative GGC's ages.," On the basis of present analysis, and taking into account the advantages discussed by, we consider the rMSF method much more suitable than other techniques for retrieving relative GGCs ages." +Protostellar disks require sufficiently strong turbulence to enhance the efficiency of angular momentum transport.,Protostellar disks require sufficiently strong turbulence to enhance the efficiency of angular momentum transport. + The origin of turbulence is often attributed to hydrodynamic and hydromagnetic instabilities that can arise in. differentially-rotating. stratified gaseous disks.," The origin of turbulence is often attributed to hydrodynamic and hydromagnetic instabilities that can arise in differentially-rotating, stratified gaseous disks." + One of the candidates is magnetorotational instability (MRI). which can operate in a conductive flow if the angular velocity decreases with the cylindrical radius and the magnetic field is not strong (Velikhov 1959).," One of the candidates is magnetorotational instability (MRI), which can operate in a conductive flow if the angular velocity decreases with the cylindrical radius and the magnetic field is not strong (Velikhov 1959)." + The MRI has been studied in depth in the case of stellar and accretion disk conditions (see. e.g.. Fricke 1969: Safronov 1969: Acheson 1978. 1979; Balbus Hawley 1991: Kaisig et al.," The MRI has been studied in depth in the case of stellar and accretion disk conditions (see, e.g., Fricke 1969; Safronov 1969; Acheson 1978, 1979; Balbus Hawley 1991; Kaisig et al." + 1992; Kumar et al., 1992; Kumar et al. + 1994; Zhang et al., 1994; Zhang et al. + 1994)., 1994). + Simulations of the MRI in disks (Hawley et al., Simulations of the MRI in disks (Hawley et al. + 1995. Matsumoto Tajima 1995. Brandenburg et al.," 1995, Matsumoto Tajima 1995, Brandenburg et al." + 1995. Torkelsson et al.," 1995, Torkelsson et al." + 1996. Arlt Rüddiger 2001) show the turbulence generated can significantly enhance the angular momentum transport.," 1996, Arlt Rüddiger 2001) show the turbulence generated can significantly enhance the angular momentum transport." + Most likely. however. the number of instabilities that can arise in astrophysical disks is quite large.," Most likely, however, the number of instabilities that can arise in astrophysical disks is quite large." + An analysis of MHD modes in stratified accretion disks demonstrates a wide variety of instabilities even im the case of simple magnetic geometry (Keppens. Casse Goedbloed 2002).," An analysis of MHD modes in stratified accretion disks demonstrates a wide variety of instabilities even in the case of simple magnetic geometry (Keppens, Casse Goedbloed 2002)." + Therefore. the current point of view on the origin of turbulence in disks ts likely highly simplified.," Therefore, the current point of view on the origin of turbulence in disks is likely highly simplified." + Even pure. hydrodynamic origin of turbulence cannot be excluded (see Urpin 2003. Arlt Urpin 2004. Dubrulle et al.," Even pure, hydrodynamic origin of turbulence cannot be excluded (see Urpin 2003, Arlt Urpin 2004, Dubrulle et al." + 2005) despite the most efficient local linear hydrodynamie instabilities advocated to date are not sufficiently efficient., 2005) despite the most efficient local linear hydrodynamic instabilities advocated to date are not sufficiently efficient. + Global instabilities. such as the barochinie-like instability of Klahr Bodenheimer (2003). are sensitive to boundary conditions. (Johnson. and Gammie 2006) and. therefore. are unlikely to drive turbulence in. disks.," Global instabilities, such as the baroclinic-like instability of Klahr Bodenheimer (2003), are sensitive to boundary conditions (Johnson and Gammie 2006) and, therefore, are unlikely to drive turbulence in disks." + Astrophysical disks are stratified and stratification can change stability properties of shear flows. providing either a stabilizing or destabilizing effect. depending on details of the disk structure.," Astrophysical disks are stratified and stratification can change stability properties of shear flows, providing either a stabilizing or destabilizing effect, depending on details of the disk structure." + Recently. Dubrulle et al. (," Recently, Dubrulle et al. (" +"2005) have considered one of the possible ""strato-rotational"" instabilities arising in the presence of both differential rotation and stable stratification.",2005) have considered one of the possible “strato-rotational” instabilities arising in the presence of both differential rotation and stable stratification. + However. Brandenburg Rüddiger (2005) demonstrated that the growth rate of this instability decreases with an increasing Reynolds number. rendering the instability less relevant for astrophysical applications.," However, Brandenburg Rüddiger (2005) demonstrated that the growth rate of this instability decreases with an increasing Reynolds number, rendering the instability less relevant for astrophysical applications." + Note also that convection can drive turbulence in disks with unstable stratification. but 1t induces inward turbulent transport of the angular momentum instead of the required outward one (see. e.g.. Stone Balbus 1996).," Note also that convection can drive turbulence in disks with unstable stratification, but it induces inward turbulent transport of the angular momentum instead of the required outward one (see, e.g., Stone Balbus 1996)." + As it has been argued by Lesur Longaretti (2005). nonlinear hydrodynamic instability that often occurs. in linearly-stable flows at sufficiently large Reynolds numbers is likely inefficient in disks even for the most optimistic extrapolations of numerical data.," As it has been argued by Lesur Longaretti (2005), nonlinear hydrodynamic instability that often occurs in linearly-stable flows at sufficiently large Reynolds numbers is likely inefficient in disks even for the most optimistic extrapolations of numerical data." + At least. the suberitical transition to hydrodynamic turbulence cannot occur in quasi-keplerian flows at Reynolds numbers up to ~10° (Ji et al.," At least, the subcritical transition to hydrodynamic turbulence cannot occur in quasi-keplerian flows at Reynolds numbers up to $\sim 10^6$ (Ji et al." + 2006)., 2006). + Of course. Reynolds numbers are much higher in real disks: nevertheless it seems that there is little room for onlinear instability.," Of course, Reynolds numbers are much higher in real disks; nevertheless it seems that there is little room for nonlinear instability." +" The stability properties of protostellar disks are much ""Sifferent from those of accretion disks.", The stability properties of protostellar disks are much different from those of accretion disks. +" The magnetic Reynolds umber is likely not very large in cold- and dense-protostellar disks because of a low electrical conductivity. and so the field cannot be treated as ""frozen"" into the gas (Gammie 1996)."," The magnetic Reynolds number is likely not very large in cold- and dense-protostellar disks because of a low electrical conductivity, and so the field cannot be treated as ""frozen"" into the gas (Gammie 1996)." + The effect of Ohmie dissipation on the MRI has been considered in the linear (Jin. 1996) and nonlinear regimes (Sano. Inutsuka Miyama 1998; Drecker. Rüddiger Hollerbach 2000).," The effect of Ohmic dissipation on the MRI has been considered in the linear (Jin 1996) and nonlinear regimes (Sano, Inutsuka Miyama 1998; Drecker, Rüddiger Hollerbach 2000)." + Fleming Stone (2003) and Turner et al. (, Fleming Stone (2003) and Turner et al. ( +2006) treated turbulent mixing caused by the MRI in. protostellar disks. taking into account magnetic diffusivity.,"2006) treated turbulent mixing caused by the MRI in protostellar disks, taking into account magnetic diffusivity." + They found that the midplane is shielded from cosmic rays. and that MRI does not occur even under the most favorable conditions.," They found that the midplane is shielded from cosmic rays, and that MRI does not occur even under the most favorable conditions." + Nevertheless. turbulence can mix a fraction of the weakly-conducting surface material into the interior. providing some coupling of the midplane gas to the magnetic field.," Nevertheless, turbulence can mix a fraction of the weakly-conducting surface material into the interior, providing some coupling of the midplane gas to the magnetic field." + As a result. weak stresses can appear in the disk midplane.," As a result, weak stresses can appear in the disk midplane." + As first pointed out by Wardle (1999). poorly conducting protostellar disks can be strongly magnetized if electrons are the main charge carriers.," As first pointed out by Wardle (1999), poorly conducting protostellar disks can be strongly magnetized if electrons are the main charge carriers." + Therefore. transport must be anisotropic with substantially different properties along and across the magnetic field.," Therefore, transport must be anisotropic with substantially different properties along and across the magnetic field." + In strongly magnetized gas the Hall component provides the main contribution to the resistivity, In strongly magnetized gas the Hall component provides the main contribution to the resistivity +From the compilation of Sandquist(200L).. we have selected all single-star probale members ol M67 with adjusted. aud reddeuiug-corrected. (8—Vy above 0.75.,"From the compilation of \citet{sa04}, we have selected all single-star probable members of M67 with adjusted and reddening-corrected $(B-V)_0$ above 0.75." + From 38 stars. giving all iudividual moduli equal weight. the average apparent 1uocdulus [or 167 is (in—M = 9.807 + 0.011I (seam).," From 38 stars, giving all individual moduli equal weight, the average apparent modulus for M67 is $(m-M)$ = 9.807 $\pm$ 0.014 (s.e.m)." + With welghtiug based upon the inverse square of the uucertainty in V.1 iclucling the effects of the color errors. the apparent modulus rises slightly to 9.520 with the uncerainty cut iu half.," With weighting based upon the inverse square of the uncertainty in $V$, including the effects of the color errors, the apparent modulus rises slightly to 9.820 with the uncertainty cut in half." +" ID we were to fit the M67 malu sequence directly to field stars of comparable ineallicity. i.e.. stars between [Fe/H] = —0.05 aud 0.05 adjusted in AM, to an acopted value of [Fe/H] = 0.00. the moduli would be increased by 0.033 mae. or (in—M) = 9.81 or the unweighted average."," If we were to fit the M67 main sequence directly to field stars of comparable metallicity, i.e., stars between [Fe/H] = $-0.05$ and 0.05 adjusted in $M_V$ to an adopted value of [Fe/H] = 0.00, the moduli would be increased by 0.033 mag, or $(m-M)$ = 9.84 for the unweighted average." + With Ay = XIEGB—V). this becomes ΕΕ = 9.71 x 0.02 (se.u.).," With $A_V$ = $(B-V)$, this becomes $(m-M)_0$ = 9.71 $\pm$ 0.02 (s.e.m.)," + taking the uncertainty in the reddeuiug into account., taking the uncertainty in the reddening into account. + Is the offset between the current value for the modulus aid those of Anetal.(2007). or Pasquinietal.(2008) siguilicant?, Is the offset between the current value for the modulus and those of \citet{an07} or \citet{pa08} significant? + The errors quoted above are the internal errors defined by the scatter within the photometry., The errors quoted above are the internal errors defined by the scatter within the photometry. + Because the comparisons are nuae uuder the same assuimnptious Lor the reclclening aucl metallicity. at a systemaic level. the domiuaut source of uucertaiuty remaius the size aud applicajlity of tie color adjustiuent to transfer the 8—Vosystem of Sandquist(2001). to theTycho-2 system that defines the Ποιά sars and the Hyacdes.," Because the comparisons are made under the same assumptions for the reddening and metallicity, at a systematic level, the dominant source of uncertainty remains the size and applicability of the color adjustment to transfer the $B-V$ system of \citet{sa04} to the system that defines the field stars and the Hyades." + I we adopt £0.009 as a plausible estimate for the uncertainty in the differential color correction. this aloue leads to an uncertainty in (n—AL) ot £0.0LO.," If we adopt $\pm$ 0.009 as a plausible estimate for the uncertainty in the differential color correction, this alone leads to an uncertainty in $(m-M)$ of $\mp$ 0.040." + There is one potential source of a systematic offset between he distauce scale of aud ours., There is one potential source of a systematic offset between the distance scale of \citet{an07} and ours. + The main sequences used to fit the cluster sequences are tied to theoretical isochrones empirically mo«ilied to iuach the Hyacles at an adopted [Fe/H] = +0.13 and (ar—ALjy = 3.33: the Hyades mean ‘elation trausferred to the Tycho-2 system is an excellent match to field stars of comparable metallicity in our database., The main sequences used to fit the cluster sequences are tied to theoretical isochrones empirically modified to match the Hyades at an adopted [Fe/H] = +0.13 and $(m-M)_0$ = 3.33; the Hyades mean relation transferred to the system is an excellent match to field stars of comparable metallicity in our database. + When sified in Aly at agSos ἰνοι 5—V usiug AAI /A[Fe/HJ=0.98. the Hyades relation overshoots the field sar solar sample by a mexest amount. Le.. it is too faiut compared to the field stars. 1iplying that our slope over this short distance is too large.," When shifted in $M_V$ at a given $B-V$ using $\Delta M_V/\Delta$ $ = 0.98$, the Hyades relation overshoots the field star solar sample by a modest amount, i.e., it is too faint compared to the field stars, implying that our slope over this short distance is too large." +" However. as discussed previously. the isochroues emplovecd by predict AAA, /A[Fe/HJ=1.E. though the trends with metallicity for individual clusters in inclicate values between 1.2 and Lot."," However, as discussed previously, the isochrones employed by \citet{an07} predict $\Delta M_V/\Delta$ $ = 1.4$, though the trends with metallicity for individual clusters in \citet{an07} indicate values between 1.2 and 1.4." +" If the isochrone sequences delinine he main sequence relations predict too great a change in Afy with [Fe/H] relaive to the Hyades. fora shift in [Fe/H] of —0.13 dex aud AA‘, /.A[Fe/H]—1.25. the main sequence matched to M67 will be systematically too faint by 0.035 mag relative to our system aud 0.065 mae too faint compared to the field stars."," If the isochrone sequences defining the main sequence relations predict too great a change in $M_V$ with [Fe/H] relative to the Hyades, for a shift in [Fe/H] of $-0.13$ dex and $\Delta M_V/\Delta$ $ = 1.25$, the main sequence matched to M67 will be systematically too faint by 0.035 mag relative to our system and 0.065 mag too faint compared to the field stars." + While the old open cluster. NGC 6791. isut the primary focus of this investigation. it does have a valuable role to play as a test of the more extreme limits of the field star main sequeuce calibration.," While the old open cluster, NGC 6791, isn't the primary focus of this investigation, it does have a valuable role to play as a test of the more extreme limits of the field star main sequence calibration." + NOT aud the Hyacles are both well-placed among the richly populated metallicity distribution aud differentially separated byonly a modest shift in [Fe/H]., M67 and the Hyades are both well-placed among the richly populated metallicity distribution and differentially separated byonly a modest shift in [Fe/H]. + By contrast. current metallicity estimates [rom photometric aud spectroscopic techniques," By contrast, current metallicity estimates from photometric and spectroscopic techniques" +ew timesΙΟΝΙΟ. perhaps even 10!ML.,"few times$10^3 +\msun$, perhaps even $10^4 \msun$." + Significantly. there is currently no trace of even a remnant gaseous disc near ((Cuadra et al.," Significantly, there is currently no trace of even a remnant gaseous disc near (Cuadra et al." + 2003. Paumare et al.," 2003, Paumard et al." + 2004)., 2004). + This) led ravakshin Cuacra (2005) to question whether failed to become a quasar because this recent star formation event consumed nearly all the available eas in the central xuwsec of the Milky Way., This led Nayakshin Cuadra (2005) to question whether failed to become a quasar because this recent star formation event consumed nearly all the available gas in the central parsec of the Milky Way. + They noted that this could. be constrained with future observations: “a past bright CIN yhase shoulel also leave a hot buovant racio bubble in the Milky Way halo”., They noted that this could be constrained with future observations: “a past bright AGN phase should also leave a hot buoyant radio bubble in the Milky Way halo”. + The recent. LAV observations by Su et al. (, The recent –LAT observations by Su et al. ( +2010) show that the Milky Way has a pair of gammaray lobes. svmmoetrical about its dynamical centre A*)) and about the Galactic plane.,"2010) show that the Milky Way has a pair of gamma–ray lobes, symmetrical about its dynamical centre ) and about the Galactic plane." + The lobes extend ~5 kpe from the plane. but have a narrow (d~LOO pe) waist along it.," The lobes extend $\sim + 5$ kpc from the plane, but have a narrow $d \sim 100$ pc) waist along it." + The limbs of the lobes coincide with the extended. structure seen in mediumenergv X.ravs by ROSAT (Snowden et al., The limbs of the lobes coincide with the extended structure seen in medium–energy X–rays by ROSAT (Snowden et al. + 1997)., 1997). + The lobes have gamma.ray luminosity L.c4107eres and their total energy content is at least ~10777 org.," The lobes have gamma–ray luminosity $L_{\gamma} \simeq 4\times 10^{37}~{\rm erg\, s}^{-1}$, and their total energy content is at least $\sim 10^{54 - 55}$ erg." + Su et al. (, Su et al. ( +"2010) considered numerous physical processes that could give rise to the bubble structure and. provided a constraint that if they are older than a few 10"". vr. the gamma-ray emission must be powered. by ions rather than electrons due to a short cooling time of the latter.","2010) considered numerous physical processes that could give rise to the bubble structure and provided a constraint that if they are older than a few $\times 10^6$ yr, the gamma-ray emission must be powered by ions rather than electrons due to a short cooling time of the latter." + Crocker et al. , Crocker et al. ( +0011) and Crocker Abaronian (2011) detailed these arguments further anc suggested that the emission is powered by Cosmic Ray (CR) protons rather than electrons.,2011) and Crocker Aharonian (2011) detailed these arguments further and suggested that the emission is powered by Cosmic Ray (CR) protons rather than electrons. + They. further consider a quasisteady state model in which the CR protons are continuously injected by supernova explosions., They further consider a quasi–steady state model in which the CR protons are continuously injected by supernova explosions. + CR. protons and heavier tons are then trapped inside the bubbles for approximately the age of the Galaxy., CR protons and heavier ions are then trapped inside the bubbles for approximately the age of the Galaxy. + Alternatively. the LAXE lobes could be a more recent feature.," Alternatively, the –LAT lobes could be a more recent feature." + For example. \lertsch Sarkar (2011) argue that the spectral and morphological details of the emission are incompatible with hacdronic radiation. leaving electrons as the main energy source.," For example, Mertsch Sarkar (2011) argue that the spectral and morphological details of the emission are incompatible with hadronic radiation, leaving electrons as the main energy source." + In that case. the mechanism of inllating the bubbles is then unlikely to be of star formation origin.," In that case, the mechanism of inflating the bubbles is then unlikely to be of star formation origin." + One would require ~LO” recent Type HL supernovae to provide the energy content of the bubbles. which is far higher than can be realistically expected. from the inner 100 pc.," One would require $\sim 10^5$ recent Type II supernovae to provide the energy content of the bubbles, which is far higher than can be realistically expected from the inner $\sim 100$ pc." + Cheng et al. (, Cheng et al. ( +2011) thus argued that the bubbles are inllated by episodic aactivity caused. by tidal clisruptions of stars passing too close toA.,2011) thus argued that the bubbles are inflated by episodic activity caused by tidal disruptions of stars passing too close to. +.. Guo Alathews (2011) performed. hyclrodvnamical numerical simulations of jets launched by aand showed. that the LAT observations are qualitatively consistent with their simulations if the jets were launched ~1.2 Alwes ago., Guo Mathews (2011) performed hydrodynamical numerical simulations of jets launched by and showed that the –LAT observations are qualitatively consistent with their simulations if the jets were launched $\sim 1-2$ Myrs ago. + In this paper we shall argue that lis à very natural candidate for the source of the energy that inllated the gamma-ray lobes., In this paper we shall argue that is a very natural candidate for the source of the energy that inflated the gamma-ray lobes. + As noted above. the Galactic Centre underwent a peculiar star formation event localised to the inner 0.03. 0.5 pe about 6 Myr ago (Paumarel et al.," As noted above, the Galactic Centre underwent a peculiar star formation event localised to the inner 0.03 – 0.5 pc about 6 Myr ago (Paumard et al." + 2006)., 2006). + “Phus. a plausible scenario is that not all of the gas deposited into the central pe of the Alilky Way went into making the voung stars. and a fraction of it was accreted by.. as found in realistic simulations of the process (e.g.. Bonnell Rice 2008. Llobbs Navakshin 2009).," Thus, a plausible scenario is that not all of the gas deposited into the central pc of the Milky Way went into making the young stars, and a fraction of it was accreted by, as found in realistic simulations of the process (e.g., Bonnell Rice 2008, Hobbs Nayakshin 2009)." + Fhus iis likely to have had a short but. very. bright quasar phase concurrent with the star formation event 6 million vears ago., Thus is likely to have had a short but very bright quasar phase concurrent with the star formation event $\sim 6$ million years ago. + We further argue that the observed highly symmetrical lobes are unlikely to have originated from a jet outflow., We further argue that the observed highly symmetrical lobes are unlikely to have originated from a jet outflow. + To obtain the qualitative agreement with the observed. shape of the lobes. Guo Mathews. (2011) directed. their jets perpenclicular to the plane of the Galaxy.," To obtain the qualitative agreement with the observed shape of the lobes, Guo Mathews (2011) directed their jets perpendicular to the plane of the Galaxy." + We believe this would be unlikely., We believe this would be unlikely. + Itadio surveys show that jet. directions are completely uncorrelated with the largescale structure of the host galaxies (Ixinnev. 2000: Nagar Wilson. 1999).," Radio surveys show that jet directions are completely uncorrelated with the large–scale structure of the host galaxies (Kinney, 2000; Nagar Wilson, 1999)." + Furthemore. the observed orientations of the stellar disces in the central pe of the Galaxy (see απατά ct al.," Furthemore, the observed orientations of the stellar discs in the central pc of the Galaxy (see Paumard et al." + 2006) are inclined at very large angles to the Galactic plane., 2006) are inclined at very large angles to the Galactic plane. + Phe jets are likely to be fed by σας disces oriented. similarly to the stellar cises., The jets are likely to be fed by gas discs oriented similarly to the stellar discs. + We would therefore expect that accretion of eas onto 6 million vears ago would. result in jets directed at. very large angles to the svmunetry axis of the lobes. contraclicting observations.," We would therefore expect that accretion of gas onto $\sim 6$ million years ago would result in jets directed at very large angles to the symmetry axis of the lobes, contradicting observations." + In contrast. a svmmetrical pair of lobes with a narrow waist along the galaxy plane is natural if an isotropic outllow from near the black hole encounters higher gas densities along this plane than perpendicular to it.," In contrast, a symmetrical pair of lobes with a narrow waist along the galaxy plane is natural if an isotropic outflow from near the black hole encounters higher gas densities along this plane than perpendicular to it." + spherical outllows like this are a clirect consequence of superI5ddington dise accretion (Shakura Sunvaev 1973: Wine Pounds 2003) and offer a plausible explanation for the AL 0 relation (Silk Rees 1998: Ixing 2003. 2005).," Near--spherical outflows like this are a direct consequence of super--Eddington disc accretion (Shakura Sunyaev 1973; King Pounds 2003) and offer a plausible explanation for the $M$ $\sigma$ relation (Silk Rees 1998; King 2003, 2005)." + The paper is structured as follows., The paper is structured as follows. + We first discuss the simpler and better understood quasi-pherical AGN outllows in £2. and then we consider the more complicated case of the present clay Milky Way nucleus in 83.," We first discuss the simpler and better understood quasi-spherical AGN outflows in 2, and then we consider the more complicated case of the present day Milky Way nucleus in 3." + The implications of the quasar outburst for the observed. ganima-ray lobes are elucidated in δε while δρ spells out ramifications for the poorly uncerstood problem of star formation versus gas accretion in the central parsecs of AGN.," The implications of the quasar outburst for the observed gamma-ray lobes are elucidated in 4, while 5 spells out ramifications for the poorly understood problem of star formation versus gas accretion in the central parsecs of AGN." + We note that our approach here is to try to reproduce the main energeties of the lobes and their morphology. rather than to produce detailed spectral models., We note that our approach here is to try to reproduce the main energetics of the lobes and their morphology rather than to produce detailed spectral models. + We assume that ooutflow either carries with it CL protons created near the black hole. or that the C1. protons are accelerated on shock fronts where the outflow runs into the interstellar medium.," We assume that outflow either carries with it CR protons created near the black hole, or that the CR protons are accelerated on shock fronts where the outflow runs into the interstellar medium." + In regions close to the black hole. the AGN outllows are revealed. through blueshifted: absorption lines in Nrav emission (Pounds et al.," In regions close to the black hole, the AGN outflows are revealed through blueshifted absorption lines in X–ray emission (Pounds et al." + 2003a. b: Ixing 2010a).," 2003a, b; King 2010a)." + Tombesi et al. (, Tombesi et al. ( +2010a. b) show that they are present in more than 35 percent of a sample of over 50 local AGN. and. deduce that their solid angles are large (certainly >0.6« 2z. and probably greater).,"2010a, b) show that they are present in more than 35 percent of a sample of over 50 local AGN, and deduce that their solid angles are large (certainly $> 0.6 \times 2\pi$ , and probably greater)." + Ehe observed absorption columns imply that in many cases the outllows are quite recent (Lew vears)," The observed absorption columns imply that in many cases the outflows are quite recent (few years)," +ancl clusters are reliable out to 20.6.,and clusters are reliable out to $z \sim 0.6$. + The discrepancies ovond this range may be owing to the small number of eroups and clusters detected at higher redshifts., The discrepancies beyond this range may be owing to the small number of groups and clusters detected at higher redshifts. + Also. there may be some contamination ellects in the histograms fron he photometric redshift errors in the SDSS data.," Also, there may be some contamination effects in the histograms from the photometric redshift errors in the SDSS data." + We produce mass estimates for our catalogue using the cluster velocity dispersions according to equation. 19..., We produce mass estimates for our catalogue using the cluster velocity dispersions according to equation \ref{eq:sigmavir}. + We ested the reliability of this approach by comparing mass estimates for clusters found in the 28LACO mock with the ruc masses of the mock haloes to which they are matched., We tested the reliability of this approach by comparing mass estimates for clusters found in the 2SLAQ mock with the true masses of the mock haloes to which they are matched. + We find that the mass estimates of our mock catalogue eroups and clusters are for the most part a good fit to he true halo masses. however with large error bars.," We find that the mass estimates of our mock catalogue groups and clusters are for the most part a good fit to the true halo masses, however with large error bars." + The deviations seen are the result of contaminating galaxies in he richness estimates and the small number of high mass clusters detected., The deviations seen are the result of contaminating galaxies in the richness estimates and the small number of high mass clusters detected. + In general we see that the range of cluster masses is à good match to known masses of massive clusters., In general we see that the range of cluster masses is a good match to known masses of massive clusters. + We analysed optical SDSS and i-band colour images of a selection. of the our. clusters. which span cilferent. redshifts.," We analysed optical SDSS and -band colour images of a selection of the our clusters, which span different redshifts." + We observe that the galaxy members are distributed in a small region of space. on the sky and in redshift.," We observe that the galaxy members are distributed in a small region of space, on the sky and in redshift." + We also see an overdensity of red. galaxies around the cluster centres., We also see an overdensity of red galaxies around the cluster centres. + This is strong evidence that the clusters are genuine., This is strong evidence that the clusters are genuine. + The distribution of LRGs in the clusters varies from spherical to elongated. filamentary structures., The distribution of LRGs in the clusters varies from spherical to elongated filamentary structures. + “Phis highlights an advantage of the percolation method in that it makes no prior assumptions about the cluster shapes. which allows us to detect some structures that other methods may not.," This highlights an advantage of the percolation method in that it makes no prior assumptions about the cluster shapes, which allows us to detect some structures that other methods may not." + We test. different clipping procedures on the 25LAQ mock group and cluster sizes., We test different clipping procedures on the 2SLAQ mock group and cluster sizes. + This analysis indicated that the majority of the contamination in the cluster catalogue was attributed to groups with 3 or 4 members., This analysis indicated that the majority of the contamination in the cluster catalogue was attributed to groups with 3 or 4 members. +" We found that by clipping out clusters with Ly, 0.11 Alpe fh for Niven = 3 and Rugο 0.49 Alpe fh+ for Noa) = 4 improves the purity from52% to 88%. while reducing the completeness by only 4%. in the 28LACO mock catalogue."," We found that by clipping out clusters with $_{clt} >$ 0.11 Mpc $h^{-1}$ for $_{mem}$ = 3 and $_{clt} >$ 0.49 Mpc $h^{-1}$ for $_{mem}$ = 4 improves the purity from$\%$ to $\%$, while reducing the completeness by only $\%$, in the 2SLAQ mock catalogue." +" By applying this procedure to the real 2SLAQ group ancl cluster catalogue. we separated the clusters into ""gold! and ‘silver’ samples."," By applying this procedure to the real 2SLAQ group and cluster catalogue, we separated the clusters into `gold' and `silver' samples." + Where the gold. samples consists of clusters that passed the clipping procedure and are therefore the most reliable and the silver sample consists of clusters that failed the clipping procedure ancl may still be genuine. however less reliable.," Where the gold samples consists of clusters that passed the clipping procedure and are therefore the most reliable and the silver sample consists of clusters that failed the clipping procedure and may still be genuine, however less reliable." + Out of the 313 total 28LAO groups and clusters. 70 are gold and the remaining 243 are silver.," Out of the 313 total 2SLAQ groups and clusters, 70 are gold and the remaining 243 are silver." + Finally. we test the two-point correlation function of our cluster catalogue.," Finally, we test the two-point correlation function of our cluster catalogue." + We find a best-fitting power law model. fr)=(rfro)?. with parameters ry=2444 Alpe fh.| and 5;=21+022.," We find a best-fitting power law model, $\xi(r)=(r/r_0)^{\gamma}$, with parameters $r_0=24 \pm 4$ Mpc $h^{-1}$ and $\gamma=-2.1 \pm 0.2$." + The value of the reduced: chi-sequared. is Vea=094., The value of the reduced chi-squared is $\chi_{red}^2 = 0.94$. + These values are consistent with those of the mock halo catalogue and are in good agreement with those in literature (?).., These values are consistent with those of the mock halo catalogue and are in good agreement with those in literature \citep{Nichol:01}. + Future surveys such as the Dark Energy Survey (DIES). Euched and Planck will images millions of galaxies across the whole sky.," Future surveys such as the Dark Energy Survey (DES), Euclid and Planck will images millions of galaxies across the whole sky." + An abundance of photometric cata will be obtained for cach of these objects. however it will not be possible to obtain spectroscopic data for all of them.," An abundance of photometric data will be obtained for each of these objects, however it will not be possible to obtain spectroscopic data for all of them." + Therefore. it is important to develop reliable cluster finding techniques that utilise the photometric data that will be available.," Therefore, it is important to develop reliable cluster finding techniques that utilise the photometric data that will be available." + Photometric redshifts. for example. provide a useful way to probe the properties of galaxies along the line of sight when spectroscopic data is not. present.," Photometric redshifts, for example, provide a useful way to probe the properties of galaxies along the line of sight when spectroscopic data is not present." + All of the results presented in the paper will be compared. to those found in Farrens et al. (, All of the results presented in the paper will be compared to those found in Farrens et al. ( +in prep). which will examine galaxy clusters in the 28LAC catalogue using photometric redshilts.,"in prep), which will examine galaxy clusters in the 2SLAQ catalogue using photometric redshifts." + This comparison will test the reliability of the Dok code to detect structures using photometric data., This comparison will test the reliability of the DFoF code to detect structures using photometric data. + The authors would. like to thank Nice Ross for data and assistance with 25LAQ. correlation functions. Prof. Ofer Lahav for his advice and support. Ignacio berreras ancl Ablucus Viniccius Costa Duarte for. help regarding k-corrections. the DES clusters working group for discussions. John Deacon. Fabrizio Sidoli and. Dugan Witherick [or technical support. and. Magda Vasta for helpful suggestions and tips.," The authors would like to thank Nic Ross for data and assistance with 2SLAQ correlation functions, Prof. Ofer Lahav for his advice and support, Ignacio Ferreras and Marcus Viníccius Costa Duarte for help regarding k-corrections, the DES clusters working group for discussions, John Deacon, Fabrizio Sidoli and Dugan Witherick for technical support, and Magda Vasta for helpful suggestions and tips." + The authors also acknowledge the use of the CCL Legion Ligh Performance Computing Facility. ane associated support services. in the completion of this work.," The authors also acknowledge the use of the UCL Legion High Performance Computing Facility, and associated support services, in the completion of this work." + SE and COs acknowledge support received from the Science ancl Technology. Facilities Council anc FBA acknowledges support received from the oval Society via URE., SF and CGS acknowledge support received from the Science and Technology Facilities Council and FBA acknowledges support received from the Royal Society via URF. + The catalogue contains 313 clusters. with the following properties: identifier. number of galaxy members (or richness) right ascension. declination. redshift. velocity dispersion (in Ly padial size (in Alpe fhly estimated mass (in logis M.) and sample to which it belongs (Ci: gold S: silver).," The catalogue contains 313 clusters with the following properties: identifier, number of galaxy members (or richness), right ascension, declination, redshift, velocity dispersion (in $^{-1}$ ), radial size (in Mpc $h^{-1}$ ), estimated mass (in $_{10}$ $_{\odot}$ ) and sample to which it belongs (G: gold ; S: silver)." + A sample of the first. LO clusters is shown in table-AT.., A sample of the first 10 clusters is shown in \ref{tab:catalogue}. . +evidence for this additional fiux causing a shoulder inthe xofile.,evidence for this additional flux causing a `shoulder' in the profile. + No ceutral or outer peaks are seen iu the £= 5 nean profiles. or indeed in any of the profiles for types ater than this.," No central or outer peaks are seen in the $T=$ 5 mean profiles, or indeed in any of the profiles for types later than this." + Thus we have identified a clear effect of bars ou the ρατοσα of SF as a function of radius within galaxy disks. which results in strongly eublauced eenission. and moderately chhauced R-baud emission. ia voth the central regions aud at 0.5 754.," Thus we have identified a clear effect of bars on the pattern of SF as a function of radius within galaxy disks, which results in strongly enhanced emission, and moderately enhanced $R$ -band emission, in both the central regions and at 0.5 $r_{24}$." + This effect sects o apply nost stronely to those galaxies classified as SBb or SBhe (T= 1). where the overall distributions of SF are profoundly different from their wubarrecd counterparts.," This effect seems to apply most strongly to those galaxies classified as SBb or SBbc $T=$ 3, 4), where the overall distributions of SF are profoundly different from their unbarred counterparts." + It should be recalled that the mean profiles we show here are constructed such that areas under the profiles are directly proportional to fractious of total flux., It should be recalled that the mean profiles we show here are constructed such that areas under the profiles are directly proportional to fractions of total flux. + Thus inspection of the SDb mean pprofile shows that a significant fraction of the total comission fromthescqalavicsisassociatedwiththeouterpoak featur, Thus inspection of the SBb mean profile shows that a significant fraction of the total $+$ emission from these galaxies is associated with the outer peak feature. + The ereater streneth of the bii-induced features iu the mnuueau profiles thanin the Παπά profiles is inportant. since this confirms that the bars are inducing SF that would not otherwise be happening. aud are not merely redistributing pre-existing stellar populations.," The greater strength of the bar-induced features in the mean profiles than in the $R$ -band profiles is important, since this confirms that the bars are inducing SF that would not otherwise be happening, and are not merely redistributing pre-existing stellar populations." + If the latter were the case. the amplitude of the effect would be the same in ας helt aud ((see ?/ for a sinuülar argument applied to the trigecrine οἳ SF by spiral arms).," If the latter were the case, the amplitude of the effect would be the same in $R$ -band light and (see \citet{seig02} for a similar argument applied to the triggering of SF by spiral arms)." +theoretical [üxes is somewhat facilitated.,theoretical fluxes is somewhat facilitated. + The test is only completely fair for the Sun. as this is the only star in this eroup with parameters that are truly independent from model atmospheres (ancl have negligible errors). but the others are included as they may help to confirm the conclusions found from the of examinationthe solar case.," The test is only completely fair for the Sun, as this is the only star in this group with parameters that are truly independent from model atmospheres (and have negligible errors), but the others are included as they may help to confirm the conclusions found from the examination of the solar case." + Lig., Fig. + GE compares the predicted. spectral energy distributions. obtained by linear interpolation in a) our purely theoretical grid. of model spectra (red. line in left-hand. panels). and b) our empirically calibrated ericl (red line in right-hand panels).," 6Ê compares the predicted spectral energy distributions, obtained by linear interpolation in a) our purely theoretical grid of model spectra (red line in left-hand panels), and b) our empirically calibrated grid (red line in right-hand panels)." + The interpolatecl spectra have also been smoothed to approximate the lower resolution of the LIST spectrophotomoetry. with a EWLAL resolving power A/OA~1000.," The interpolated spectra have also been smoothed to approximate the lower resolution of the HST spectrophotometry, with a FWHM resolving power $\lambda/\delta\lambda \sim 1000$." + Overall. the calibrated. grid. performs slightly better than the purely theoretical eric in some regions. but the opposite is true in others.," Overall, the calibrated grid performs slightly better than the purely theoretical grid in some regions, but the opposite is true in others." + ‘This result suggests that there may be some systematic differences between the Εαν. seale adopted for LST calibration and that of the MILES. library. ancl the corrections derived. from AILLES may not. be widely applicable.," This result suggests that there may be some systematic differences between the flux scale adopted for HST calibration and that of the MILES library, and the corrections derived from MILES may not be widely applicable." + To keep a perspective. we note that systematic and random: errors in the MILES Iuxes were estimated to be about 2 and 3'A. respectively. from the comparison with photometry (2 1j) [rom the Lausanne cata base (Mermilliod. et al.," To keep a perspective, we note that systematic and random errors in the MILES fluxes were estimated to be about 2 and 3, respectively, from the comparison with photometry $B-V$ ) from the Lausanne data base (Mermilliod et al." +.. 1997)., 1997). + X. reduction. in effective temperature for the solar model by 150 Ix. which is a typical error in this quantity to be expected. for most stars (not the Sun) would be enough to bridge the gap in the, A reduction in effective temperature for the solar model by 150 K – which is a typical error in this quantity to be expected for most stars (not the Sun)– would be enough to bridge the gap in the +due to velocity dispersion.,due to velocity dispersion. + This will highlight the scale at which non-linear velocity divergence terms alfect the matter power spectrum in redshift space and cause it to depart [rom the linear theory. prediction., This will highlight the scale at which non-linear velocity divergence terms affect the matter power spectrum in redshift space and cause it to depart from the linear theory prediction. +" If we rewrite dofdz as edtalftQ4,01).5)0. where 9 is the matter perturbation and 7 is the conformal time. a(r)dr. then the linear continuity equation becomes Throughout this paper we normalise the velocity divergence as βία)all(a)f(Quia).s)]. so 80. in the lincar regime."," If we rewrite $\rm{d}\delta/\rm{d}\tau$ as $a H(a) f(\Omega_{\rm m}(a), \gamma)\, \delta$ , where $\delta$ is the matter perturbation and $\tau$ is the conformal time, $\rm{d}t = a(\tau)\rm{d}\tau $ , then the linear continuity equation becomes Throughout this paper we normalise the velocity divergence as $\theta(k,a) /[-a H(a) f(\Omega_{\rm m}(a),\gamma)]$, so $ \theta = \delta$ in the linear regime." + Phe volume weighted velocity divergence »ower spectrum is calculated from the simulations according o the prescription given in ?7.., The volume weighted velocity divergence power spectrum is calculated from the simulations according to the prescription given in \citet{Scoccimarro:2004tg}. + We interpolate the velocites and the densities onto a grid of 350° points and then measure he ratio of the interpolated momentum to the interpolated density field., We interpolate the velocites and the densities onto a grid of $350^3$ points and then measure the ratio of the interpolated momentum to the interpolated density field. + In this way. we avoid having to correct for he CIC assignment scheme.," In this way, we avoid having to correct for the CIC assignment scheme." + A larger grid dimension could result in empty cells where 0+0., A larger grid dimension could result in empty cells where $\delta \rightarrow 0$. + A EET grid of 350° was used to ensure all erid points had non-zero density. and rence a well defined⋅ velocity. at each point., A FFT grid of $350^3$ was used to ensure all grid points had non-zero density and hence a well defined velocity at each point. +. We] only plot the velocity power spectra in each of the figures up to halfthe quist [requeney. for our default choice of Ανν= 3507.," We only plot the velocity power spectra in each of the figures up to halfthe Nyquist frequency for our default choice of $N_{\mbox{\tiny {FFT}}} = 350^3$ ," +somewhat smaller than the values found in our simulations.,somewhat smaller than the values found in our simulations. + lxav ct al. (, Kay et al. ( +2002) implemented. a feedback. mechanism in their simulations. which accounts for the rate of both type la and type LL SN.,"2002) implemented a feedback mechanism in their simulations, which accounts for the rate of both type Ia and type II SN." + By assuming an energetics twice as large as that provided by standard supernova computations. they were able to reproduce the observed No ray scaling properties. while obtaining only 3 per cent of the gas to be converted into stars.," By assuming an energetics twice as large as that provided by standard supernova computations, they were able to reproduce the observed $X$ –ray scaling properties, while obtaining only 3 per cent of the gas to be converted into stars." + The main limitation of this type of simulations is that one is restricted. to relatively poor numerical resolution in order to limit the computational cost., The main limitation of this type of simulations is that one is restricted to relatively poor numerical resolution in order to limit the computational cost. + For instance. the simulations by Aluanwone οἱ al. (," For instance, the simulations by Muanwong et al. (" +"2002) have a mass resolution which is about one order of magnitude worse than that of our ""Virgo"" runs and almost two orders of magnitude worse than that of our group runs.",2002) have a mass resolution which is about one order of magnitude worse than that of our “Virgo” runs and almost two orders of magnitude worse than that of our group runs. + A better mass resolution within a smaller box was used by Ίαν et al. (, A better mass resolution within a smaller box was used by Kay et al. ( +2002). for which the mass of gas particles are a factor 2.8 and 22 smaller than for our Virgo and. Croup runs. respectively.,"2002), for which the mass of gas particles are a factor 2.8 and 22 smaller than for our Virgo and Group runs, respectively." + The results that we presented in Section 3 demonstrate that the cooling elliciencv is quite sensitive. to. mass resolution., The results that we presented in Section 3 demonstrate that the cooling efficiency is quite sensitive to mass resolution. + For this reason. one has to be careful in crawing conclusions about overcooling ancl how it is suppressed bv extra heating. in the presence of limited numerical resolution.," For this reason, one has to be careful in drawing conclusions about overcooling and how it is suppressed by extra heating, in the presence of limited numerical resolution." + In fact. our simulations demonstrate that. the two main problems caused by the introduction of radiative cooling. namely the overproduction of stars and the steeply increasing temperature profiles in central cluster regions. may not be easily solved by the. introduction. of noneravitational heating.," In fact, our simulations demonstrate that the two main problems caused by the introduction of radiative cooling, namely the overproduction of stars and the steeply increasing temperature profiles in central cluster regions, may not be easily solved by the introduction of non--gravitational heating." + Does this imply that none of our heating schemes is a realistic approximation to what happens in real clusters?, Does this imply that none of our heating schemes is a realistic approximation to what happens in real clusters? + The energy release in all these schemes misses. although to different degrees. to faithfully follow the simulated. rate of star production.," The energy release in all these schemes misses, although to different degrees, to faithfully follow the simulated rate of star production." + A realistic scheme for SN feedback should dump thermal energy with a rate that accurately follows the star formation rate. properly accounting for the typical lifetimes of dilferent stellar populations.," A realistic scheme for SN feedback should dump thermal energy with a rate that accurately follows the star formation rate, properly accounting for the typical life–times of different stellar populations." + Furthermore. our schemes for energy release demonstrate that for feedback to have a sizeable effect on the ICM thermodvnamies. it has to act in a nonlocal way. so as to assign most of the energy on gas particles which have a sullicientlv long cooling time.," Furthermore, our schemes for energy release demonstrate that for feedback to have a sizeable effect on the ICM thermodynamics, it has to act in a non–local way, so as to assign most of the energy on gas particles which have a sufficiently long cooling time." + Such nonlocal feedback mechanisms may arise from AGN activity. cosmic ravs or galactic winds. for example.," Such non–local feedback mechanisms may arise from AGN activity, cosmic rays or galactic winds, for example." + While further work is clearly needed to. study such feedback mechanisms self-consistentlv. in simulations. a better understanding is also required às. to whether optical/.NX rav data really implies a stellar fraction as small as το10 per cent within clusters ancl eroups.," While further work is clearly needed to study such feedback mechanisms self-consistently in simulations, a better understanding is also required as to whether $X$ –ray data really implies a stellar fraction as small as $\mincir 10$ per cent within clusters and groups." + Balogh et al. (, Balogh et al. ( +2001) used the 2ALASS results on the Ix.band. luminosity function by Cole et al. (,2001) used the 2MASS results on the K–band luminosity function by Cole et al. ( +2001) to estimate the cosmic fraction of barvons converted into stars.,2001) to estimate the cosmic fraction of baryons converted into stars. +" After assuming a Ixennicutt IME. (Ixennicutt 1983). they find f;20.05 for our choice of ,, and h. and argued that no much evidence exists for fs to increase inside clusters. or to depend on the cluster mass (cf."," After assuming a Kennicutt IMF (Kennicutt 1983), they find $f_*\simeq 0.05$ for our choice of $\Omega_m$ and $h$, and argued that no much evidence exists for $f_\ast$ to increase inside clusters, or to depend on the cluster mass (cf." + also Bryan 2000)., also Bryan 2000). + However. this estimate of the cosmic value of f; increases by about a factor 2 if a Salpeter ALP (Salpeter 1955) were used instead.," However, this estimate of the cosmic value of $f_\ast$ increases by about a factor 2 if a Salpeter IMF (Salpeter 1955) were used instead." + Furthermore. it is worth reminding that the estimate inside clusters relies to some degree of extrapolation.," Furthermore, it is worth reminding that the estimate inside clusters relies to some degree of extrapolation." + For instance. Balogh ct a. (2001) obtained the stellar mass in clusters from the Boband luminosity data by Roussel et al. (," For instance, Balogh et a. (2001) obtained the stellar mass in clusters from the B–band luminosity data by Roussel et al. (" +2000). using M/Lg=4.5. and. correcting for undetected galaxies by extrapolating the luminosity function to the faint end. slope.,"2000), using $M/L_B=4.5$, and correcting for undetected galaxies by extrapolating the luminosity function to the faint end slope." + Ht is clear that a more robust determination of f£. in clusters should rather rely on Ix or HI:band luminosity. which is more cirectly related to stellar mass (c.g... Gavazzi et al.," It is clear that a more robust determination of $f_\ast$ in clusters should rather rely on K– or H–band luminosity, which is more directly related to stellar mass (e.g., Gavazzi et al." + 1996). rather than to Bband luminosity whose conversion to stellar mass is quite sensitive to galaxy morphology.," 1996), rather than to B–band luminosity whose conversion to stellar mass is quite sensitive to galaxy morphology." + More recently. Huang et al. (," More recently, Huang et al. (" +2002) used the LELawaii-AAO Ix-band. redshift survey to estimate the WK-bancl luminosity function in the local Universe.,2002) used the Hawaii-AAO K-band redshift survey to estimate the K-band luminosity function in the local Universe. + They found that the Ix.band. luminosity density is twice as large as that from 2\LASS. thus implying a twice as large f. value.," They found that the K–band luminosity density is twice as large as that from 2MASS, thus implying a twice as large $f_\ast$ value." + In light of this discussion. a. f; value somewhat larger than 10 per cent. possibly as large as 20 per cent. may still be viable at present. which would. tend to alleviate the problem of ICM overcooling.," In light of this discussion, a $f_*$ value somewhat larger than 10 per cent, possibly as large as 20 per cent, may still be viable at present, which would tend to alleviate the problem of ICM overcooling." + As for the temperature profile. our results. indicate that the discrepaney. between observations and simulations is unlikely to be. solved. by the inclusion o£. feedback mechanisms that are similar to the ones explored here.," As for the temperature profile, our results indicate that the discrepancy between observations and simulations is unlikely to be solved by the inclusion of feedback mechanisms that are similar to the ones explored here." + Lt his is the case. it would. demonstrate that our simulations are nussing some basic physical mechanisms.," If this is the case, it would demonstrate that our simulations are missing some basic physical mechanisms." + For instance. as we discussed. thermal conduction has been proposed. to be an important elect in clusters.," For instance, as we discussed, thermal conduction has been proposed to be an important effect in clusters." + Another piece of physics which is currently missing from most simulation work is the elfect of magnetic fields (ο... Dolag. Dartelmann Lesch 2002).," Another piece of physics which is currently missing from most simulation work is the effect of magnetic fields (e.g., Dolag, Bartelmann Lesch 2002)." + Their introduction might eive rise to nontrivial structures in the gas distribution if they can locally suppress thermal conduction. or it they provide a nonthernial contribution to the gas pressure.," Their introduction might give rise to non–trivial structures in the gas distribution if they can locally suppress thermal conduction, or it they provide a non–thermal contribution to the gas pressure." + There is little doubt that including such more complex physics. will represent a significant. non-trivial challenge for cluster simulations of the next generation.," There is little doubt that including such more complex physics will represent a significant, non-trivial challenge for cluster simulations of the next generation." + Most. of the processes involved require both. a rather sophisticated numerical method. and a treatment of sub-grid. physics.," Most of the processes involved require both, a rather sophisticated numerical method, and a treatment of sub-grid physics." + Still. the inclusion of more physics in numerical codes. is mandatory if the reliability. anc the predictive power of cluster simulations want to keep pace with the increasing quality of observational clata.," Still, the inclusion of more physics in numerical codes is mandatory if the reliability and the predictive power of cluster simulations want to keep pace with the increasing quality of observational data." + Simulations were run at the CINECA Supercomputing Center. with CPU time provided by a grant of the National Institute for Astrophysics (NAB). at. the Computing Center of the Astronomical Observatory of Catania and at the Computing Center of the University of Trieste.," Simulations were run at the CINECA Supercomputing Center, with CPU time provided by a grant of the National Institute for Astrophysics (INAF), at the Computing Center of the Astronomical Observatory of Catania and at the Computing Center of the University of Trieste." + We wish to thank Lans Boóhhringer. Alexis Finoguenov. Fabio Governato. Paolo Tozzi and NianPing Wu for enlightening CLISCUSSLOLIS.," We wish to thank Hans Böhhringer, Alexis Finoguenov, Fabio Governato, Paolo Tozzi and Xian–Ping Wu for enlightening discussions." +The SSHIVOVYS wave brought a clear. self-cousisteut picture about statistical properties of sources flat constitite about of the CNB in the broad enerev baud of 0.710 keV. Fietre 3 smuarizes the 210 keV oobtaiue from the ssurvevs together with the results from previous nuissions.,"The surveys have brought a clear, self-consistent picture about statistical properties of sources that constitute about of the CXB in the broad energy band of 0.7–10 keV. Figure 3 summarizes the 2–10 keV obtained from the surveys together with the results from previous missions." +" The direct source counts from combined results of the LSS (Ueda 119995) aud the AMSS (Veda 11999c: these contain the data used by Caguoui. Della Ceca. Alaccacaro 1998) eive the tightest constraints so far over a wide flux ranec fron 10H to —τνοHi 7: N(ο) = 168412 statistical error). 13252.L. 3.7640. 12. 1084017. aud 0.3340.09 2, at ο — 7.1«101. 1.0«10 21,20«1015, L0«10P. and La.10.127. respectively."," The direct source counts from combined results of the LSS (Ueda 1999b) and the AMSS (Ueda 1999c; these contain the data used by Cagnoni, Della Ceca, Maccacaro 1998) give the tightest constraints so far over a wide flux range from $\sim 10^{-11}$ to $\sim 7\times10^{-14}$ : $N(>S)$ = $\pm$ 7.2 statistical error), $\pm$ 2.4, $\pm$ 0.42, $\pm$ 0.17, and $\pm$ 0.09 $^{-2}$, at $S$ = $7.4\times10^{-14}$, $1.0\times10^{-13}$, $2.0\times10^{-13}$, $4.0\times10^{-13}$, and $1.0\times10^{-12}$, respectively." + The DSS vives a direct source counts at the faintest fux. 3.8&«101! *(Ovasaka 11995). whereas the fluctuation analysis of deep SIS fields coustraims the aat fluxes down to 1.5«1011 (Cendrean. Barcous. Fabian 1998).," The DSS gives a direct source counts at the faintest flux, $3.8\times10^{-14}$ (Ogasaka 1998), whereas the fluctuation analysis of deep SIS fields constrains the at fluxes down to $1.5\times10^{-14}$ (Gendreau, Barcons, Fabian 1998)." + As seen from the figure. the dadirect source counts smoothly connect 10 two regions constrained by the aand ‘fluctuation analysis.," As seen from the figure, the direct source counts smoothly connect the two regions constrained by the and fluctuation analysis." + The AMSS/LSS results demonstrate iat the average spectrum of X-ray sources vecolcs harder toward fainter fluxes: the apparent photon iudex in the 0.7.10 keV range changes from 2.1 at the flux of ~| to LG at ~10. ((210 keV).," The AMSS/LSS results demonstrate that the average spectrum of X-ray sources becomes harder toward fainter fluxes: the apparent photon index in the 0.7–10 keV range changes from 2.1 at the flux of $\sim +10^{-11}$ to 1.6 at $\sim 10^{-13}$ (2–10 keV)." +" This fact can be explained x the rapid cimerecuce of population with jud energy spectra. as is clearly iudicat ‘din Figure 210),"," This fact can be explained by the rapid emergence of population with hard energy spectra, as is clearly indicated in Figure 2(b)." + The evolution of properties of sources solves the puzze of discrepancy discrepancy of the source counts between the soft (EMSS) and the hard band aud ZZ, The evolution of broad-band properties of sources solves the puzzle of discrepancy discrepancy of the source counts between the soft (EMSS) and the hard band and ). +EAO01) If sve compare the s (ncludiug Galactic objects) between above and below 2 keV. the hard baud source counts at S~10ores ((210 keV) matches the soft band one when we assume a photon inex of 1.6 for fix conversion. whereas at brighter level of S=1.«10.15~1? ((210 keV). we have to use a photon iudex of about 1.9 to make hem match.," If we compare the s (including Galactic objects) between above and below 2 keV, the hard band source counts at $S\sim 10^{-13}$ (2–10 keV) matches the soft band one when we assume a photon index of 1.6 for flux conversion, whereas at brighter level of $S = 4\times 10^{-13} \sim 10^{-12}$ (2–10 keV), we have to use a photon index of about 1.9 to make them match." +" The latter fact is consistent with the average 0.7.10 keV. specfun af the same flux evels. aud cau be connected the the ""soft spectrum of the fiuctuation observed withGinga. which shows a photon index of 1.54 EO.liuthe210 keV raise (Butcher 11997)."," The latter fact is consistent with the average 0.7–10 keV spectrum at the same flux levels, and can be connected the the “soft” spectrum of the fluctuation observed with, which shows a photon index of $\pm0.1$ in the 2–10 keV range (Butcher 1997)." + The optical identification revealedthat the major populalon at fluxes of 1013 aare AGNs., The optical identification revealedthat the major population at fluxes of $10^{-13}$ are AGNs. + The population of hard sources. which are most responsible for making," The population of hard sources, which are most responsible for making" +continuously in the ealaxv for the last 250\Iwr.,continuously in the galaxy for the last 250Myr. + Our asstuuption about the age of the galaxies is iu agreement with the estimate of Taccoui et al. (, Our assumption about the age of the galaxies is in agreement with the estimate of Tacconi et al. ( +2008).,2008). + We further assuuethat the stars that formed im the last 5bMyr ave still eiibedaded in the molecular clouds in which they formect., We further assume that the stars that formed in the last 5Myr are still embedded in the molecular clouds in which they formed. +" Using Druzual Charlot (1995) models with a star formation rate of 1000ML, ""vr we find hat the bolometric Iunüuositv of the SMiyr old starburst is 3.2«41072L. whereas the ""uninositv of the rest of the stars; which are between 5 - 250Myr old. is 3.5ΡΟ t"," Using Bruzual Charlot (1993) models with a star formation rate of $1000\ \rm{M}_\odot$ /yr we find that the bolometric luminosity of the 5Myr old starburst is $3.2 \times +10^{12} \ \rm{L}_\odot$ whereas the luminosity of the rest of the stars, which are between 5 - 250Myr old, is $3.5 \times 10^{12} \ \rm{L}_\odot$." +"hat the optical/UV radiation emitted bv the 5-250Mvis old stellar population is obscured by dust with an ly of linag. aud that all the euergyC» absorbe in the optical/UV ix re-radiated[m] at a teniperature of 28K. his eives a cold dust luminosity o£ 2.5«1072Των,"," Assuming that the optical/UV radiation emitted by the 5-250Myrs old stellar population is obscured by dust with an $A_V$ of 1mag, and that all the energy absorbed in the optical/UV is re-radiated at a temperature of 28K, this gives a cold dust luminosity of $2.5 \times 10^{12} \ +\rm{L}_\odot$." + So this explains the fact hat the derived luminosities of the starburst and cirus conrponeuts are comparable., So this explains the fact that the derived luminosities of the starburst and cirrus components are comparable. + The median of the log of i1uninosities of the cirrus component of the 12 galaxies (iu solar wits) is 12.1 for the evolutionary models aud 12.6 or the ho spot models., The median of the log of luminosities of the cirrus component of the 12 galaxies (in solar units) is 12.4 for the evolutionary models and 12.6 for the hot spot models. + The star formation rate for the vpical galaxw is therefore ~10001600NL. /vr which is in good agrecinent with the estimates of Ivison ct al. (, The star formation rate for the typical galaxy is therefore $\sim 1000-1600 \ \rm{M}_\odot$ /yr which is in good agreement with the estimates of Ivison et al. ( +2002).,2002). + It is interesting to note that the timescale we infer or thecloud phase of star formation is similar o the value found by Cranato et al. (, It is interesting to note that the timescale we infer for the phase of star formation is similar to the value found by Granato et al. ( +2000) aud Efstathiou Rowan-Robinsou (2003) for uormal quiesceutlv star-ornnes galaxies.,2000) and Efstathiou Rowan-Robinson (2003) for normal quiescently star-forming galaxies. + The analysis presented in. this paper is clearly inuted bv the lack of data in the rest-frame far-infrared where both the starburst aud cirtus compoucuts veal., The analysis presented in this paper is clearly limited by the lack of data in the rest-frame far-infrared where both the starburst and cirrus components peak. + Measurements withHerschel whose launch is now iuuinenut. will allow us to test the model outlined above.," Measurements with, whose launch is now imminent, will allow us to test the model outlined above." + They will allow us in particular to put a stronger constraint on the iuteusitv of starlight in the case of the cibrus Component and possibly differcutiate between the two starburst models considered iu this paper., They will allow us in particular to put a stronger constraint on the intensity of starlight in the case of the cirrus component and possibly differentiate between the two starburst models considered in this paper. + We thank Wartun Meuéuudez-Dehuestre and Elisabeta Valiaute for providing the spectra of the SMCs iu electronic form. Andreas Seifalnrt for introduction to SWARP aud Uchuut Dauuerbaucr for his conuneuts on an eurer draft of this work.," We thank Karínn Menénndez-Delmestre and Elisabeta Valiante for providing the spectra of the SMGs in electronic form, Andreas Seifahrt for introduction to SWARP and Helmut Dannerbauer for his comments on an earlier draft of this work." + , +Whilst this scheme is very ellective. Ἡ is also important to note that the classifications of up to a third of sources contracict in cülferent bands (?)..,"Whilst this scheme is very effective, it is also important to note that the classifications of up to a third of sources contradict in different bands \citep{Yasuda_etal:2001}." +" The Stripe S2 data are significantly. deeper than the UIXIDSS. LAS (in the sense that all but. the. reelclest sources are detected with a greater signaltonoise ratio in Stripe S2 than in the LAS. and an average UINIDSS- source has a,ο Olay)."," The Stripe 82 data are significantly deeper than the UKIDSS LAS (in the sense that all but the reddest sources are detected with a greater signal–to–noise ratio in Stripe 82 than in the LAS, and an average UKIDSS-selected source has $\sigma_r \simeq 0.1\, \sigma_Y$ )." + Even though the SDSS optical imagine has a significantly larger seeing (~172) than the UIKIDSS. NIR data (~005). the SDSS Stripe S2 data of the morphologically ambiguous sources near the LAS detection. limit is able to separate point ancl extended sources reliably.," Even though the SDSS optical imaging has a significantly larger seeing $\sim1\,\farcs2$ ) than the UKIDSS NIR data $\sim0\,\farcs8$ ), the SDSS Stripe 82 data of the morphologically ambiguous sources near the LAS detection limit is able to separate point and extended sources reliably." + This is illustrated by1.. 2 and 3..," This is illustrated by, \ref{figure:1DslicesSDSS} and \ref{figure:1DslicesUKIDSS}." + shows SDSS ραπ concentration plotted against. UINIDSS Y -bandClassStat., shows SDSS $r$ -band concentration plotted against UKIDSS $Y$ -band. +. For the faintest. two magnitude bins (Y=19 and Yc 20) it is impossible to identify two dillerent. populations of sources along the horizontal (ClassStat)) axis. whereas this is still possible along the vertical (concentration) axis.," For the faintest two magnitude bins $Y\simeq19$ and $Y\simeq20$ ) it is impossible to identify two different populations of sources along the horizontal ) axis, whereas this is still possible along the vertical (concentration) axis." + This is confirmed bv the one-dimensional histograms of both classification statistics (concentration) and 3. (ClassStat))]., This is confirmed by the one-dimensional histograms of both classification statistics (concentration) and \ref{figure:1DslicesUKIDSS} )]. + For Yzc19. in3.. the two populations of sources have almost. completely merged. even though the histogram is still bi-mocdal and for Y2:20 the two populations of sources cannot be distinguished at all.," For $Y\simeq19$, in, the two populations of sources have almost completely merged, even though the histogram is still bi-modal and for $Y\simeq20$ the two populations of sources cannot be distinguished at all." + However the corresponding histograms for SDSS concentration clearly show two distinct populations ofsources., However the corresponding histograms for SDSS concentration clearly show two distinct populations of. +. In particular. for Yc20. the SDSS r-band. class labels misclassifv only ~4% of sources (this number is obtained by fitting a Gaussian distribution to the star population and a logenormal to the galaxy population for the SDSS concentration data).," In particular, for $Y\simeq20$, the SDSS $r$ -band class labels misclassify only $\sim4\%$ of sources (this number is obtained by fitting a Gaussian distribution to the star population and a log-normal to the galaxy population for the SDSS concentration data)." + This is a very good result when compared to the UINLDSS ddata which. at this faintness regime. no longer allow a separation into two populations of sources 3)).," This is a very good result when compared to the UKIDSS data which, at this faintness regime, no longer allow a separation into two populations of sources )." + Ilence. for the purpose of sseparation. we treat the SDSS Stripe N2 data as definitive classifications against which our Bavesian LAS classifications can be tested.," Hence, for the purpose of separation, we treat the SDSS Stripe 82 data as definitive classifications against which our Bayesian LAS classifications can be tested." +Our starting point is a sample of 121902 UINIDSS sources ina 14.4deg? area defined by right ascensions of eithor à:60deg or az300deg ancl declinations of Jo)<0.1.,"Our starting point is a sample of $121\,902$ UKIDSS sources in a $14.4 \unit{deg}^2$ area defined by right ascensions of either $\alpha \leq 60 \unit{deg}$ or $\alpha \geq 300 \unit{deg}$ and declinations of $|\delta| \leq 0.1$." + This area is entirely within the SDSS Stripe 82 region. and has been covered by UIXIDSS in the Y. J. ff and dy bands.," This area is entirely within the SDSS Stripe 82 region, and has been covered by UKIDSS in the $Y$, $J$, $H$ and $K$ bands." + Our main aimi is to classify these sources and compare the results to the SDSS Stripe 82 classifications., Our main aim is to classify these sources and compare the results to the SDSS Stripe 82 classifications. + But to clo so requires the preliminary task of generating the magnitucde-dependent prior distributions ofClassStat.. along with the star and galaxy number counts.," But to do so requires the preliminary task of generating the magnitude-dependent prior distributions of, along with the star and galaxy number counts." + Fhis is not part of the actual classification process(i.c... it is independent. of any single source). and so is considered separately from the results.," This is not part of the actual classification process, it is independent of any single source), and so is considered separately from the results." + The number counts of stars ancl galaxies provide the prior that will be used to classify sources for which the image data are ambiguous., The number counts of stars and galaxies provide the prior that will be used to classify sources for which the image data are ambiguous. + Ehe counts could be obtained [rom deeper surveys (although none exist in all the UINIDSS LAS bancs) or from physical models of the source populations (although this would be unnecessarily complicated)., The counts could be obtained from deeper surveys (although none exist in all the UKIDSS LAS bands) or from physical models of the source populations (although this would be unnecessarily complicated). + For the restrictec problem of sseparation. however. it is more direct to fit the star anc galaxy counts to the target sample itself.," For the restricted problem of separation, however, it is more direct to fit the star and galaxy counts to the target sample itself." + At the bright. enc the numbers are given directly by the data: at the faint en it is also necessary to assume some weak prior information (essentially that a smooth extrapolation from the brigh counts is reasonable)., At the bright end the numbers are given directly by the data; at the faint end it is also necessary to assume some weak prior information (essentially that a smooth extrapolation from the bright counts is reasonable). + For the UIXIDSS. LAS we have chosen the Y barn as the reference., For the UKIDSS LAS we have chosen the $Y$ band as the reference. +baud... Phe observed Y band. counts of stars ancl galaxies (identified here by using our model with number counts obtained by binning the data by magnitude ancl interpolating the parameters) from the test. sample described in are shown in4., The observed $Y$ band counts of stars and galaxies (identified here by using our model with number counts obtained by binning the data by magnitude and interpolating the parameters) from the test sample described in are shown in. +. Both exhibit exponential counts down to Y219. bevond. which the survey incompleteness dominates. (as expected. given the average UIKIDSS LAS limit of Yc20.2).," Both exhibit exponential counts down to $Y \simeq 19$ beyond which the survey incompleteness dominates (as expected, given the average UKIDSS LAS limit of $Y \simeq 20.2$ )." +" For both stars and galaxies the intrinsic number counts are taken to be of the form where jV, is the number of sources (optionally per unit solid angle. although this detail is unimportant as long as the same normalising convention is used for stars and. galaxies) of tvpe / brighter than the reference magnitude Yo. and o, is he tvpe-depencent logarithmic slope."," For both stars and galaxies the intrinsic number counts are taken to be of the form where $N_\pop$ is the number of sources (optionally per unit solid angle, although this detail is unimportant as long as the same normalising convention is used for stars and galaxies) of type $\pop$ brighter than the reference magnitude $Y_0$, and $\alpha_\pop$ is the type-dependent logarithmic slope." +" Even though Y, and Ny are degenerate it is convenient to set Yo to the Y-band magnitude limit. in which case IN; is approximately equal to he number of objects of type / in the sample."," Even though $Y_0$ and $N_\pop$ are degenerate it is convenient to set $Y_0$ to the $Y$ -band magnitude limit, in which case $N_\pop$ is approximately equal to the number of objects of type $\pop$ in the sample." + In order to fit these parameters. however. it is necessary o account for the incompleteness in each band. denoted rere as Pr(det|Y). which was introduced in(7).," In order to fit these parameters, however, it is necessary to account for the incompleteness in each band, denoted here as $\prob(\detected | Y)$, which was introduced in." +". The magnitude limit ng.» ancl incompleteness range Anz, are it in the Y. J. df and A bands for both stars ancl galaxics."," The magnitude limit $m_{\rmn{lim},\band}$ and incompleteness range $\Delta m_{\band}$ are fit in the $Y$, $J$, $H$ and $K$ bands for both stars and galaxies." +" Fitting dA,/dYPr(det|Y) to the observed. UINIDSS counts vields the fits shown in4."," Fitting ${\diff N_\pop}/{\diff Y} \, \prob(\detected | Y)$ to the observed UKIDSS counts yields the fits shown in." +. Although there are some discrepancies. the key. point is that the relative nunibers of stars and galaxies at a given magnitude will give far more accurate prior probabilities than. sav. an uninformative prior dens Pr(s)=Pr(g)0.5 for all sources].," Although there are some discrepancies, the key point is that the relative numbers of stars and galaxies at a given magnitude will give far more accurate prior probabilities than, say, an uninformative prior , $\prob(s) = \prob(g) = 0.5$ for all sources]." + iis constructed so that. on average.e=0 for stars and e>0 for extended sources.," is constructed so that, on average,$\stat=0$ for stars and $\stat>0$ for extended sources." + We observe ὁ however. the distribution of which. for isolated stars should be normal (with zero mean and unit variance). again by construction.," We observe $\hat{\stat}$ however, the distribution of which, for isolated stars should be normal (with zero mean and unit variance), again by construction." + However, However +Table 6..,Table \ref{table_sizes}. + As one would expect [rom a disk-like structure showing a decrease in temperature wilh radius the semimajor axes of the ellipses increase wilh wavelength., As one would expect from a disk-like structure showing a decrease in temperature with radius the semimajor axes of the ellipses increase with wavelength. + However. due to the increasing visibility of the UT3-UT4 baseline the semiminor axis and also the total area. of the ellipse are slightly smaller at 12.55 Chan at 11.05an. An inclination angle for an assumed circular disk can be derived by computing the arecos of the ratio of the semiminor and semimajor axis.," However, due to the increasing visibility of the UT3-UT4 baseline the semiminor axis and also the total area of the ellipse are slightly smaller at $\mu$ m than at $\mu$ m. An inclination angle for an assumed circular disk can be derived by computing the $arccos$ of the ratio of the semiminor and semimajor axis." + The resulting angles agree very well (55.47 22.47) and are also in good agreement to what was found for FU Ori disk models based on NIR observations (Malbetetal.2005)., The resulting angles agree very well $^\circ\pm$ $^\circ$ ) and are also in good agreement to what was found for FU Ori disk models based on NIR observations \citep{malbet}. +. By combining the derived inclination angle wilh rotational velocity measurements in the optical spectral region it is possible to estimate the central mass., By combining the derived inclination angle with rotational velocity measurements in the optical spectral region it is possible to estimate the central mass. + Basecl on Ixenvon.Hartmann&IHewett(1988) we derive for FU Ori M/AL. 820.36 which is reasonably consistent with typical values lor low-mass pre-main sequence stars.," Based on \citet{kenyon1988} we derive for FU Ori $M/M_{\sun}\approx\,$ 0.36 which is reasonably consistent with typical values for low-mass pre-main sequence stars." + In addition to the inclination (he fitted ellipses provide also information on the position angle of the disk., In addition to the inclination the fitted ellipses provide also information on the position angle of the disk. + The posiüon angles (measured from north eastwards) we find for the semimajor axes at different wavelengths show a larger scatter (109.1711.67) than the inclinations and differ significantly from the NIB. findings of Malbetetal.(2005). (see also section 1)., The position angles (measured from north eastwards) we find for the semimajor axes at different wavelengths show a larger scatter $^\circ\pm$ $^\circ$ ) than the inclinations and differ significantly from the NIR findings of \citet{malbet} (see also section 7). + It seems as if the position angle becomes smaller for longer wavelengths. although one has to keep in mind that. again. al least for the UT3-UT4 baseline the increasing visibility is the main reason for the observed rotation.," It seems as if the position angle becomes smaller for longer wavelengths, although one has to keep in mind that, again, at least for the UT3-UT4 baseline the increasing visibility is the main reason for the observed rotation." + At this point we leave it to future investigations to derive a 3-D disk model based on a more complex dust distribution possibly able to confirm the apparent changes in the position angle for different wavelength regimes., At this point we leave it to future investigations to derive a 3-D disk model based on a more complex dust distribution possibly able to confirm the apparent changes in the position angle for different wavelength regimes. + The correlated [αν is directly linked (o the total flix (i.e. the flux from a single UT telescope) via the visibility: Figure 6 depicts the results lor the correlated flux lor the three different baselines., The correlated flux is directly linked to the total flux (i.e. the flux from a single UT telescope) via the visibility: Figure \ref{correlflux} depicts the results for the correlated flux for the three different baselines. + The total spectrum is plotted for comparison., The total spectrum is plotted for comparison. + Taking into account the spatial resolution of (he tree baselines it is possible to estimate from where the correlated 8-135. flux. originates., Taking into account the spatial resolution of the three baselines it is possible to estimate from where the correlated $\mu$ m flux originates. + Our UT2-UT3 baseline has a spatial resolution of #25 AU at the distance of FU Ori. and if we assume an average visibility of 0.95 we hence know that of the Sjim-13jn flux must come from within this 25 AU.," Our UT2-UT3 baseline has a spatial resolution of $\approx$ 25 AU at the distance of FU Ori, and if we assume an average visibility of 0.95 we hence know that of the $\mu$ $\mu$ m flux must come from within this 25 AU." +of finite volume. the observed Fourier amplitudes are convolved with the survey window [function I The beat coupling contribution arises because neighboring Fourier modes 9(k)0(—k—€) are coupled bv nonlinear growth to the beat mode d(e).,"of finite volume, the observed Fourier amplitudes are convolved with the survey window function $W_s$: The beat coupling contribution arises because neighboring Fourier modes $\delta({\bf k}) \delta(-{\bf k} - {\bf \epsilon})$ are coupled by nonlinear growth to the beat mode $\delta({\bf \epsilon})$." +" When the DC mode of (he survey is positive. all modes are anipliliecl, when it is negative. all modes are suppressed."," When the DC mode of the survey is positive, all modes are amplified; when it is negative, all modes are suppressed." + This term can be large since (he linear power spectrum drops so sharply with A., This term can be large since the linear power spectrum drops so sharply with $k$. + ?. emphasize that this term does not contribute to the covariance of power measured [rom ensembles of traditional periodic box simulations. where the band power 7; is averaged over .N; complex modes by IIlere. the beat mode is k;;-=0. the DC mode.," \citet{hamilton/rimes/scoccimarro:2006} emphasize that this term does not contribute to the covariance of power measured from ensembles of traditional periodic box simulations, where the band power $k_i$ is averaged over $N_i$ complex modes by Here, the beat mode is ${\bf k}_{ij} - {\bf k}_{ij} = 0$, the DC mode." + However. since our simulations allow ihe DC mode to vary. (?2).. we will capture this term.," However, since our simulations allow the DC mode to vary \citep{sirko:2005}, we will capture this term." +" We therefore model our covariance matrix as the sum of the usual diagonal Gaussian and shot noise contributions and the beat-coupling contribution: lere 05 is the Kronecker delta. and 05,.(2)=Pr0.20)/VausxD(:)/D(z0) is the variance of the. DC mode linearly evolved. to redshift z in the simulation volume Vau=L* (?).."," We therefore model our covariance matrix as the sum of the usual diagonal Gaussian and shot noise contributions and the beat-coupling contribution: Here $\delta^{K}_{ij}$ is the Kronecker delta, and $\delta_{DC}^2(z) = P_{L}(k=0,z=0)/V_{sim} \times D^2(z)/D^2(z=0)$ is the variance of the DC mode linearly evolved to redshift $z$ in the simulation volume $V_{sim} = L^3$ \citep{sirko:2005}." +" In perturbation theory 72,22.62 (2)..", In perturbation theory $R_{\alpha} \approx 2.62$ \citep{hamilton/rimes/scoccimarro:2006}. +" We introduce 0,4, and jy; to allow [or excess shot noise and variation in the amplitude of the beat coupling term. though we expect both parameters to be ~1."," We introduce $\alpha_{shot}$ and $\beta_{beat}$ to allow for excess shot noise and variation in the amplitude of the beat coupling term, though we expect both parameters to be $\sim 1$." + We show in G (hat Eqn., We show in \ref{results} that Eqn. + 13. provides a good model for both the dark matter and LRG covariance matrices., \ref{cijmodel} provides a good model for both the dark matter and LRG covariance matrices. + For the dark matter. the shot noise contribution is ? showed that Poisson fluctuations about the mean halo mass funcüon introduce variance in (he aunplitude of the one-halo contribution to the dark matter power spectrum that can dominate the covariance matrix in the nonlinear regime.," For the dark matter, the shot noise contribution is \citet{neyrinck/szapudi/rimes:2006} showed that Poisson fluctuations about the mean halo mass function introduce variance in the amplitude of the one-halo contribution to the dark matter power spectrum that can dominate the covariance matrix in the nonlinear regime." + Since our reconstruction of the halo density field seeks to eliminate the one-halo contribution [rom galaxies. we expect the covariance to be smaller [or the reconstructed halo density field than for the original ealaxy," Since our reconstruction of the halo density field seeks to eliminate the one-halo contribution from galaxies, we expect the covariance to be smaller for the reconstructed halo density field than for the original galaxy" +shorteitebesOGa.. the jetinduced star formation mechanism can also account directly for the evolution of the opticalUV morphology with radio size: the mass of stars required to produce the excess opticalUV. emission is only a. [ew TOTAL. (2:2)... well below of the stellar mass of the galaxy. and since the starburst’ luminosity crops rapiclly with age they become indistinguishable from the evolved star population over a timescale of a [ον 105 vears.,", the jet–induced star formation mechanism can also account directly for the evolution of the optical--UV morphology with radio size: the mass of stars required to produce the excess optical–UV emission is only a few $\times 10^8 +M_{\odot}$ \cite{lil84a,dun89a}, well below of the stellar mass of the galaxy, and since the starburst luminosity drops rapidly with age they become indistinguishable from the evolved star population over a timescale of a few $\times 10^7$ years." + On the negative side. no direct evidence for voung stars in these racio galaxies was found in our spectra (cf.," On the negative side, no direct evidence for young stars in these radio galaxies was found in our spectra (cf." + 4621.17 at higher redshift. 2=3.8: Dev ).. although the clearest features of voune stellar populations Fall outside the observed wavelength ranges.," 4C41.17 at higher redshift, $z=3.8$; Dey \nocite{dey97}, although the clearest features of young stellar populations fall outside the observed wavelength ranges." + Another important Continuum alignment model is scattering of lightfrom a hidden quasar nucleus by electrons (?) or dust (e.g Tadhunter 119892. di Serego Alighieri 11989).," Another important continuum alignment model is scattering of lightfrom a hidden quasar nucleus by electrons \cite{fab89a} or dust (e.g Tadhunter 1989a, di Serego Alighieri \nocite{tad89a,dis89}." + Strong support for this model comes from the observation that the optical emission of some clistant racio galaxies is polarised at the ~10 level with the electric vector oriented. perpendicular to the radio axis (e.g. Cimatti 11996 and references and the detection of broad »ermitted. lines in polarised light) (7:τι2): clearly some fraction of the excess opticalUV. emission. must oe associated. with this mechanism.," Strong support for this model comes from the observation that the optical emission of some distant radio galaxies is polarised at the $\sim +10$ level with the electric vector oriented perpendicular to the radio axis (e.g. Cimatti 1996 and references \nocite{cim96}, , and the detection of broad permitted lines in polarised light \cite{dey96,cim96,tra98}: clearly some fraction of the excess optical–UV emission must be associated with this mechanism." + However. the lack of »olarised. emission. [rom some sources (e.g. 3€$368. van Dreugel 1996: see also Tacdhbunter dictates that this is not universal: even for ὃς2394 where the polarisation percentage is high. only a fraction LI3050% of the opticalUV. emission is associated. with the scattered. component. (?).. X.," However, the lack of polarised emission from some sources (e.g. 3C368, van Breugel 1996; see also Tadhunter \nocite{bre96c,tad97} dictates that this is not universal; even for 3C324 where the polarisation percentage is high, only a fraction $\lta 30-50$ of the optical–UV emission is associated with the scattered component \cite{cim96}." + problem for scattering mioclels is that. in the simplest. picture. a biconical emission region is expected. for the scattered. light. rather than the knotty strings of emission observed to lie along the radio jet.," A problem for scattering models is that, in the simplest picture, a biconical emission region is expected for the scattered light, rather than the knotty strings of emission observed to lie along the radio jet." + However. in light of jetshock models. this could. be explained by extra scattering particles being mace available along the radio jet axis. either as dust grains being produced in jetinduced star forming regions. or by radio source shocks clisrupting optically thick clouds along the radio jet direction and exposing previously hidden dust grains (?)..," However, in light of jet–shock models, this could be explained by extra scattering particles being made available along the radio jet axis, either as dust grains being produced in jet–induced star forming regions, or by radio source shocks disrupting optically thick clouds along the radio jet direction and exposing previously hidden dust grains \cite{bre96b}." + In conclusion. radio source shocks will play a key role in producing the observed morphology ancl radio size evolution of the continuum alignment. οσο.," In conclusion, radio source shocks will play a key role in producing the observed morphology and radio size evolution of the continuum alignment effect." + Nebular continuum. emission will be enhanced in small racio sources. some gas clouds may be induced to collapse ancl form stars. and extra scattering particles associated either with any star formation or the disruption of gas clouds could enhance the scattered component.," Nebular continuum emission will be enhanced in small radio sources, some gas clouds may be induced to collapse and form stars, and extra scattering particles associated either with any star formation or the disruption of gas clouds could enhance the scattered component." + Phe main conclusions of this work can be summarised. as follows: The William Lersehel Telescope is operated on the island of La Palma by the Isaac. Newton Group in the Spanish Observatorio del Roches de los Muchachos of the Instituto de Astrofisica de Canarias., The main conclusions of this work can be summarised as follows: The William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roches de los Muchachos of the Instituto de Astrofisica de Canarias. + This work was supported in xut bv the Formation and. Evolution of Galaxies network set up by the European Commission under contract ERB JFMIN. οτοῦ086 of its PAIR programme., This work was supported in part by the Formation and Evolution of Galaxies network set up by the European Commission under contract ERB FMRX– CT96–086 of its TMR programme. + We are grateful o Mark Allen for supplying the output of the NLAPPINCS LL photoionisation models in digitised form. and Hx Spinrad or providing the Neon line ratios for 3€217 and 3C340.," We are grateful to Mark Allen for supplying the output of the MAPPINGS II photoionisation models in digitised form, and Hy Spinrad for providing the Neon line ratios for 3C217 and 3C340." + We thank Matt Lehnert. Arno Schoenmakers and Christian Ixaiser for useful discussions. and the referee. Mike Dopita. or his careful consideration of the original manuscript and a number of useful suggestions.," We thank Matt Lehnert, Arno Schoenmakers and Christian Kaiser for useful discussions, and the referee, Mike Dopita, for his careful consideration of the original manuscript and a number of useful suggestions." +" Consider a spherical cloud of emission line gas with number density n, and radius ro travelling at velocity e; through gas of number density à, ancl velocity es.", Consider a spherical cloud of emission line gas with number density $n_{\rm c}$ and radius $r_{\rm c}$ travelling at velocity $v_{\rm c}$ through gas of number density $n_{\rm g}$ and velocity $v_{\rm g}$. + In a time d/ à mass of gas of approximately siZp4mptes—0s)di. where my is the proton mass. is displaced bv the cloud. and accelerated [rom velocity ος to velocity eo.," In a time ${\rm d}t$ a mass of gas of approximately $\pi +r_{\rm c}^2 n_{\rm g} m_p (v_{\rm c}-v_{\rm g}) {\rm d}t$, where $m_p$ is the proton mass, is displaced by the cloud and accelerated from velocity $v_{\rm g}$ to velocity $v_{\rm c}$ ." + The momentum ofthe cloud is corresponcingly decreased:, The momentum ofthe cloud is correspondingly decreased: +the occurrence of the apsidal resonance.,the occurrence of the apsidal resonance. + In Section 5 we investigate the scenario in which the Jupiter-like planet is substituted by a eas giant. with a smaller mass., In Section 5 we investigate the scenario in which the Jupiter-like planet is substituted by a gas giant with a smaller mass. + Finally. we summarize and ciscuss our findings in Section 6.," Finally, we summarize and discuss our findings in Section 6." + We have performed numerical simulations of a svsten containing two interacting planets and a gaseous protoplanctary disc with which the planets. /—interact., We have performed numerical simulations of a system containing two interacting planets and a gaseous protoplanetary disc with which the planets interact. + One of the planets is a Super-Earth and the other is a eas giant., One of the planets is a Super-Earth and the other is a gas giant. +" They are considered as point masses orbiting around the central star with mass Al,=M..", They are considered as point masses orbiting around the central star with mass $M_*=M_\odot$. + The disc undergoes near-Keplerian rotation and its vertical semi-thickness Hf is small in comparison with the distance x from the central star., The disc undergoes near-Keplerian rotation and its vertical semi-thickness $H$ is small in comparison with the distance $r$ from the central star. + We assume a constant aspect ratio fh=fr. so that the temperature profile of the disc is Yooxr," We assume a constant aspect ratio $h=H/r$, so that the temperature profile of the disc is $T +\propto r^{-1}$." + The best choice of coordinates for this problem is that of evlindrical coordinates (ry. z) with the origin located at the position of the central star.," The best choice of coordinates for this problem is that of cylindrical coordinates $r$, $\varphi$, $z$ ) with the origin located at the position of the central star." + The equations of motion can be vertically averaged., The equations of motion can be vertically averaged. + In this wav the problem is reduced to two dimensions. given. by the radial and. azimuthal directions.," In this way the problem is reduced to two dimensions, given by the radial and azimuthal directions." + The evolution of the gaseous disc in our system. is eoverned by the continuity equation and two equations of motion (for the full formulation. see Nelsonetal. (2000))).," The evolution of the gaseous disc in our system is governed by the continuity equation and two equations of motion (for the full formulation, see \citet{nelson2000}) )." + We are not solving the full energy. equation because of the ugh computational cost., We are not solving the full energy equation because of the high computational cost. + “Phe locally isothermal equation of state of the gas in the dise is adopted instead., The locally isothermal equation of state of the gas in the disc is adopted instead. + Llowever. it has been noticed that solving the energy. equation could iive dramatic elfects on the migration. of the low-mass λαοί (Paardekooper&Alcllema2006).," However, it has been noticed that solving the energy equation could have dramatic effects on the migration of the low-mass planet \citep{paarmel06}." +.. Namely. in non-isothermal disces the migration can be directed outward.," Namely, in non-isothermal discs the migration can be directed outward." + We rave used the same Eulerian hydrodynamic code NIRVANA (Ziceloer1998) as in our previous paper (Pocllewska&Szuszkiewicz 2008)., We have used the same Eulerian hydrodynamic code NIRVANA \citep{ziegler} as in our previous paper \citep{paperI}. +. The details of the numerical scheme can be found in Nelsonetal.(2000)., The details of the numerical scheme can be found in \citet{nelson2000}. +".. We have checked hat the results obtained with our version of the NIRVANA code are in very good agreement with those obtained. in he framework of the project ""Ehe. Origin of Planetary Systems” (DeVal-Dorroetal.2006)."," We have checked that the results obtained with our version of the NIRVANA code are in very good agreement with those obtained in the framework of the project ""The Origin of Planetary Systems"" \citep{devalborro}." +. Following a common oractice. in order to assess the robustness of our results we rave repeated part of our investigation with a second code. which in our case was FARGO (Alasset2000).," Following a common practice, in order to assess the robustness of our results we have repeated part of our investigation with a second code, which in our case was FARGO \citep{masset2000}." +.. The initial surface density profile of the cise X(r) is taken to be flat at he planet location., The initial surface density profile of the disc $\Sigma(r)$ is taken to be flat at the planet location. + Its overall shape shown in (Fig. 1)), Its overall shape shown in (Fig. \ref{fig1}) ) + has »een constructed for computational convenience. namely to avoid an unwanted behaviour of the disce at the boundaries of the computational domain.," has been constructed for computational convenience, namely to avoid an unwanted behaviour of the disc at the boundaries of the computational domain." +" sEhe surface⋅ density. value X,.=ο10‘(seM. of the Hat. part of this profile corresponds to the minimum mass solar nebula (XMMSN) which consists of a gas weighing two Jupiter masses spread out within a circular area of radius equal to the mean distance of Jupiter from the Sun."," The surface density value $\Sigma_0=6\times10^{-4} +\left(\frac{M_\odot}{(5.2AU)^2}\right)$ of the flat part of this profile corresponds to the minimum mass solar nebula (MMSN) which consists of a gas weighing two Jupiter masses spread out within a circular area of radius equal to the mean distance of Jupiter from the Sun." + The adopted unit of length corresponds to 5.224€., The adopted unit of length corresponds to $5.2 AU$. +" The uni of ⋅⋠time is uugiven by (CALfry"")""enm (C. is. the gravitationa⋠⋠ constant. M; denotes the mass of the star andr, the initia racial position of the inner planet)."," The unit of time is given by $(GM_*/{r_p}^3)^{-1/2}$ $G$ is the gravitational constant, $M_*$ denotes the mass of the star and $r_p$ the initial radial position of the inner planet)." + This quantity amounts to (1/22) times the orbital period of the initial orbit of the inner planet and it will be called just an “orbit” throughou he whole paper.," This quantity amounts to $1/2\pi$ ) times the orbital period of the initial orbit of the inner planet and it will be called just an ""orbit"" throughout the whole paper." + The initial locations of the planets and heir masses are given in Table 1.., The initial locations of the planets and their masses are given in Table \ref{tab1}. + At the beginning of all runs we have put both planets on circular. orbits in the lat part of the surface density profile., At the beginning of all runs we have put both planets on circular orbits in the flat part of the surface density profile. + The computational domain extends between train=0.33 and tree.=4.15 in he racial direction as it is shown in Fig. L.., The computational domain extends between $r_{min}=0.33$ and $r_{max}=4.15$ in the radial direction as it is shown in Fig. \ref{fig1}. . + We have also xvíormed one run with rye.=5 in order to check the evolution for a larger initial separation of the planets., We have also performed one run with $r_{max}=5$ in order to check the evolution for a larger initial separation of the planets. + The azimuthal angle 42 takes its values in the interval (0.2," The azimuthal angle $\varphi$ takes its values in the interval $[0,2\pi]$." + The disc is divided into 400512 grid. cells in the racial ancl azimuthal directions respectively., The disc is divided into $400\times 512$ grid cells in the radial and azimuthal directions respectively. + For the model with Mae=5 we increased. the resolution in such a way that he size of cach single erid cell remains unchanged., For the model with $r_{max}=5$ we increased the resolution in such a way that the size of each single grid cell remains unchanged. + We have also run one simulation with a higher number of grid cells (516 986) and we have found no significant dillerence in he mügration« rate and the cecentricity evolution. so we assume that our standard. resolution is appropriate for our experiments.," We have also run one simulation with a higher number of grid cells $576\times 986$ ) and we have found no significant difference in the migration rate and the eccentricity evolution, so we assume that our standard resolution is appropriate for our experiments." + The radial boundary. conditions were taken o be open. so that the material in the disc can outflow hrough the boundaries of the computational domain.," The radial boundary conditions were taken to be open, so that the material in the disc can outflow through the boundaries of the computational domain." + In his case the profile of the dise changes with time., In this case the profile of the disc changes with time. + In order ο avoid unrealistic cllects due to gas depletion. we have run our simulations for no longer than LO! orbits.," In order to avoid unrealistic effects due to gas depletion, we have run our simulations for no longer than $10^4$ orbits." + The potential is softened. with softening parameter ¢=0.8/4., The potential is softened with softening parameter $\varepsilon=0.8H$. + Some of he simulations have been run also with s=0.6/7 and =L34 in order to check the influence of the softening ength on the evolution of the planets., Some of the simulations have been run also with $\varepsilon=0.6H$ and $\varepsilon=1.3H$ in order to check the influence of the softening length on the evolution of the planets. + In the calculation of the gravitational potential of the planets we do not exclude the matter contained in the planet Hill sphere., In the calculation of the gravitational potential of the planets we do not exclude the matter contained in the planet Hill sphere. + The selferavitv of the disc is not taken into account., The selfgravity of the disc is not taken into account. + In. order to get the convergent migration of the planets when the eas giant is on the internal orbit and the Super-Exuth on the external one. we have performed. a series of numerical simulations using cilferent clise parameters.," In order to get the convergent migration of the planets when the gas giant is on the internal orbit and the Super-Earth on the external one, we have performed a series of numerical simulations using different disc parameters." + ALL simulations are summarized in Table 1.., All simulations are summarized in Table \ref{tab1}. +" We have run our experiments with constant aspect ratio ranging from 0.08 to 0.05 and constant kinematic viscosity 7=2-10""[E in cimensionless units (this corresponds to the à. parameter being equal to 22.10? forhb=0.03 and 8:10.+ for f=0.05 ).", We have run our experiments with constant aspect ratio $h$ ranging from $0.03$ to $0.05$ and constant kinematic viscosity $\nu=2 \cdot 10^{-6}$ in dimensionless units (this corresponds to the $\alpha$ parameter being equal to $2.2 \cdot 10^{-3}$ for$h=0.03$ and $8 \cdot 10^{-4}$ for $h=0.05$ ). + In one case. a higher viscosity value (vy=5-10 °) has been used in order to obtain that the eap opened by the gas giant is," In one case, a higher viscosity value $\nu=5 \cdot 10^{-6}$ ) has been used in order to obtain that the gap opened by the gas giant is" +The companion is (he most massive known around a fully recycled pulsar.,The companion is the most massive known around a fully recycled pulsar. + If (his is a double neutron star svstem. it is only the second known in GC's. the first being Απ (??)..," If this is a double neutron star system, it is only the second known in GCs, the first being M15C \citep{agk+90,jcj+06}." + It is likely Chat the pulsar was recvcled by a different companion. which was then ejected in an exchauge interaction.," It is likely that the pulsar was recycled by a different companion, which was then ejected in an exchange interaction." + Deep Hubble Space Telescope images of the cluster may be able to detect a white dwarf companion. while a non-detection of the companion would strengthen the case lor a double neutron star svstem.," Deep Hubble Space Telescope images of the cluster may be able to detect a white dwarf companion, while a non-detection of the companion would strengthen the case for a double neutron star system." + We have measured three PIX parameters (co. ¢. and fs).," We have measured three PK parameters $\dot{\omega}$, $\varsigma$, and $h_3$ )." +" Assuming GR is correct. all three agree on the same region of the MM, plane."," Assuming GR is correct, all three agree on the same region of the $M\rmsub{c}$ $M\rmsub{p}$ plane." + As such. GR passes this test. albeit at relatively low precision.," As such, GR passes this test, albeit at relatively low precision." + Our current best measurement of a fourth. PIX parameter. the gravitational redshift. is ο=0.026(14)s.," Our current best measurement of a fourth PK parameter, the gravitational redshift, is $\gamma = +0.026(14)\; \s$." + Thisis consistent with the GR prediction of 0.014s., Thisis consistent with the GR prediction of $0.014\; \s$. + We plan to continue monitoring this svstem long-term. and in a few vears expect to have a more precise nmieasurement of that will allow for a second test of GR.," We plan to continue monitoring this system long-term, and in a few years expect to have a more precise measurement of $\gamma$ that will allow for a second test of GR." + PSR JIS23—3021C (NGC 6624C) has P=0.406s. unusually slow among globular cluster pulsars bul. surprisingly. (he second such slow pulsar in NGC 6624.," PSR $-$ 3021C (NGC 6624C) has $P = 0.406\; \s$, unusually slow among globular cluster pulsars but, surprisingly, the second such slow pulsar in NGC 6624." + It was discovered by ?: we have now measured. for the first time. P=2.2510!ss4.," It was discovered by \citet{cha03}; ; we have now measured, for the first time, $\dot{P} = 2.25 \times +10^{-16}\; \s\: \ps$." + Using Eq. 2..," Using Eq. \ref{eqn:amax}," + we find PooLTx10Pss Hover an order of magnitude smaller than the measured P.," we find $\dot{P}\rmsub{c,max} = 1.7 \times 10^{-17}\; \s\: \ps$, over an order of magnitude smaller than the measured $\dot{P}$." + The contributions from the Galaxy. and (the Shklovskii effect are even smaller still. so it is clear that the observed P is due almost entirely to the intrinsic pulsar spin-down.," The contributions from the Galaxy and the Shklovskii effect are even smaller still, so it is clear that the observed $\dot{P}$ is due almost entirely to the intrinsic pulsar spin-down." + The implied characteristic age and surface magnetic field is 7.~2.8x10*vr and 3.1xLOMG., The implied characteristic age and surface magnetic field is $\tau\rmsub{c} \sim 2.8\times 10^7\; \yr$ and $3.1 \times 10^{11}\; \gauss$. + This makes NGC 6624C. like NGC 6624D. similar to the “normal”. non-recycled pulsars (ΗΝ) usuallv seen in the Galactic disk.," This makes NGC 6624C, like NGC 6624B, similar to the “normal”, non-recycled pulsars (NRPs) usually seen in the Galactic disk." + As explained in relsecintro.. NRPs are tvpically assumed to form in core collapse supernova. which require massive stars that have not existed in GC's for billions of vears.," As explained in \\ref{sec:intro}, NRPs are typically assumed to form in core collapse supernova, which require massive stars that have not existed in GCs for billions of years." + Since NRPs have lifetimes <10?vr. core collapse supernovae cannot explain the presence of NGC 6624C and pulsars like it.," Since NRPs have lifetimes $\ll 10^{9}\; \yr$, core collapse supernovae cannot explain the presence of NGC 6624C and pulsars like it." + The leading alternative explanation is electron capture supernovae (EC'S)., The leading alternative explanation is electron capture supernovae (ECS). + The kick velocities (οκ) (at pulsars receive when they form via ECS are not well known. though there is evidence that Όμωςc10kms| (2???7)..," The kick velocities $v\rmsub{kick}$ ) that pulsars receive when they form via ECS are not well known, though there is evidence that $v\rmsub{kick} \sim 10\; \km\: \ps$ \citep{prp+02,kjh06,dbo+06,mtp09,wwk10}." + The escape velocity [rom the center of NGC 6624 is ~35kms. which effectively places an upper bound on (he Όμως that NGC 6624C received.," The escape velocity from the center of NGC 6624 is $\sim 35\; \km\: \s$, which effectively places an upper bound on the $v\rmsub{kick}$ that NGC 6624C received." + This supports the notion that ECS kicks are much smaller than those induced by core collapse supernovae., This supports the notion that ECS kicks are much smaller than those induced by core collapse supernovae. + GC NRPs can also enable useful statistical constraints on the properties of ECS (?7)..," GC NRPs can also enable useful statistical constraints on the properties of ECS \citep{blt+11,ldr+11}. ." + NGC 6624C is one of only four GC NRPs known. making it an important additionto this rare family of pulsars.," NGC 6624C is one of only four GC NRPs known, making it an important additionto this rare family of pulsars." +Studics of substellar populations in clusters have the advantage over those in the field that the objects have a common age. Inctallicitv and origi aud occupy a well defined region iu the sla.,"Studies of substellar populations in clusters have the advantage over those in the field that the objects have a common age, metallicity and origin and occupy a well defined region in the sky." + These parameters are specially Huportaut for the study of the mass functiou iu the substellar regine. where the liminosity fiction depends drastically ou the age.," These parameters are specially important for the study of the mass function in the substellar regime, where the luminosity function depends drastically on the age." + The very vouug σ Orionis cluster. located around the star of the same nune. has been known since the carly studies ofCarrison(1967) aud Lynea(1981. 1983).," The very young $\sigma$ Orionis cluster, located around the star of the same name, has been known since the early studies of\cite{garr67} and \cite{lynga81,lynga83}." + The o Oriouis multiple star. whose brightest component is au Q9.5V. belongs to the OBLb association iu the Orion complex popularly known as Oriou's Belt.," The $\sigma$ Orionis multiple star, whose brightest component is an O9.5V, belongs to the OB1b association in the Orion complex popularly known as Orion's Belt." + satellite obscrvatious of this association led to the discovery of a very vouug stellar population around σ Orionis (Walteretal.1997:Wolk 2000).," satellite observations of this association led to the discovery of a very young stellar population around $\sigma$ Orionis \citep{walter97,wolk00}." +.. Previous photometric searches in the cluster (Béjarctal. 1999.. hereafter. BZOR: Béjaral. 2001.. hereafter DMZO: Béjaretal.20012: etal. 200k: IXeuvonetal. 2005: Caballerooetαἱ. 2007: Caballero 2008::: Lodieuetal. 2009)) have fouud a laree stellar aud substellar population.," Previous photometric searches in the cluster \citealt{bejar99}, , hereafter BZOR; \citealt{bejar01}, hereafter BMZO; \citealt{bejar04a}; \citealt{sherry04}; \citealt{kenyon05}; \citealt{cab07a}; \citealt{cab08a}; \citealt{lodieu09}) ) have found a large stellar and substellar population." + Follow-up specroscopic studies have allowed us to characterize the PAoectral sequence of substellar imenibers between M6 and T5.5 (BZOR: ZapateroOsorioctal.1999a..2000. 2002a.b: DarradoyNavascuésetal.2001.2002a. 2003: Magztinetal. 2001: Ieuvonetal. 2005:: Buruineghametal. 20053).," Follow-up spectroscopic studies have allowed us to characterize the spectral sequence of substellar members between M6 and T5.5 (BZOR; \citealt{osorio99a,osorio00,osorio02a,osorio02b}; \citealt{barrado01,barrado02a,barrado03}; \citealt{martin01}; \citealt{kenyon05}; \citealt{burn05}) )." + Studies of the depletion of lithiui in the atmosphere of NGMB8.5 spectral type low mass nienibers of the cluster impose an upper age limit of 8 Aly and sugeest a inost likely age for the cluster in the interval 21 Myr (ZapateroOsorioetal.20025)., Studies of the depletion of lithium in the atmosphere of K6–M8.5 spectral type low mass members of the cluster impose an upper age limit of 8 Myr and suggest a most likely age for the cluster in the interval 2–4 Myr \citep{osorio02b}. +.. This is in good agreement with previous age determinations based on more Inassive stars iu the Orion association (Dluunv1961.1991:Warren&Iesser1978:Brownctal. 1991).," This is in good agreement with previous age determinations based on more massive stars in the Orion association \citep{blaauw64,blaauw91,warren78,brown94}. ." +. Other studies. based on jsochroue fts to photometric sequences. have determined simular ages of the cluster (see Wolk&Walter2000: DZOR: Oliveiraetal.2002. 2001: Sherryctal. 20013).," Other studies, based on isochrone fits to photometric sequences, have determined similar ages of the cluster (see \citealt{wolk00}; BZOR; \citealt{oliveira02, oliveira04}; \citealt{sherry04}) )." + The satellite provides a distance of 352! ape (Perrvinanetal.1997) for the central star 6. AAD., The satellite provides a distance of $^{+166}_{-85}$ pc \citep{perryman97} for the central star $\sigma$ AB. + This distance agrees with previous works on the Orion OBL) association. which determine a distance between 360 and ppc (Blaauw1961.1991:Warren&Iesser1978:Brownetal.1991). aud with recent estimates based ou nian sequence fitting and the dynaiuical parallax of σ AAD. wwhichi eive distances of LLL + ppc. ppc. Hid 331/125o yespectively(Sherryetal.2008:Mane&Navlor2008:Caballero 2008€).," This distance agrees with previous works on the Orion OB1b association, which determine a distance between 360 and pc \citep{blaauw64,blaauw91,warren78,brown94} and with recent estimates based on main sequence fitting and the dynamical parallax of $\sigma$ AB, which give distances of 444 $\pm$ pc, pc, and $^{+25}_{-22}$ respectively \citep{sherry08,mayne08,cab08c}." +.. This star is affected oa low extinction of E(5VP) = 005nunas1968).. aud the associated cluster also exhibits very little reddening. with a typical visual extinction ly < μιας (see BAIZO: Oliveiraetal.2002:: Déjaretal.2001).," This star is affected by a low extinction of $E(B-V)$ = mag, and the associated cluster also exhibits very little reddening, with a typical visual extinction $A_{V}$ $<$ mag (see BMZO; \citealt{oliveira02}; \citealt{bejar04a}) )." + Iu addition. the average metallicity of the σ Orionis cluster is determined to be 0.0240.0940.13 (vandom and systematic errors).[Fe/II]|2. which is cousisteut with solar values (Couzalez-Ternanucdezetal.," In addition, the average metallicity of the $\sigma$ Orionis cluster is determined to be $\pm$ $\pm$ 0.13 (random and systematic errors), which is consistent with solar values \citep{jonay08}." +2008).. The σ Orionis star cluster is one of the best sites in which to define the substellar initial mass function because of its ligh nmuuber of the cluster members. which leads to good statistics m a relatively πια] area and a knowledge of the cluster sequence for a wide range of masses from 25 AL. to 0.003 AL.: its low extinction. which allows us to assign directly masses from magnitudes in comparison with theoretical isochrones: and the absence of differential reddening. which would otherwise obscure some of its members.," The $\sigma$ Orionis star cluster is one of the best sites in which to define the substellar initial mass function because of its high number of the cluster members, which leads to good statistics in a relatively small area and a knowledge of the cluster sequence for a wide range of masses from 25 $M_{\odot}$ to 0.003 $M_{\odot}$; its low extinction, which allows us to assign directly masses from magnitudes in comparison with theoretical isochrones; and the absence of differential reddening, which would otherwise obscure some of its members." + In spite of these unique characteristics. σ Orionis has a very voung age. which means that no dvnamical evolution is expected. aud that the mass fiction is verv close to the initial lass function.," In spite of these unique characteristics, $\sigma$ Orionis has a very young age, which means that no dynamical evolution is expected, and that the mass function is very close to the initial mass function." + Several studies have dealt with the cluster mass function both iu the stellar aud substelar domaiu Cal(BAIZO: Couzalez-Garciaetal.2006:2009:Caballero2007:20093).," Several studies have dealt with the cluster mass function both in the stellar and substellar domain (BMZO; \citealt{gon06,cab07,cab07a,lodieu09,bihain09}) )." + In addition. a lot of effort has been expeuded ou this site to investigate the formation process ofubstellar objects. and in particular. the study of accretion disks and/or outflows (Barradovsensotal.2002a.2003:Ienvouetal.2005:Cahaloveal 2006). aud the existence of infrared excesses possibly related with the presence of disks. both in the ucar-infrared (Oliveira2001a) aud iu the mid-infrared --(Javawardlana&Javawardhana2008:Lulinanetal. 2008).," In addition, a lot of effort has been expended on this site to investigate the formation process of substellar objects, and in particular, the study of accretion disks and/or outflows \citep{barrado02a,barrado03,osorio02a,osorio02b,muzerolle03,kenyon05,cab06}, and the existence of infrared excesses possibly related with the presence of disks, both in the near-infrared \citep{oliveira02,barrado03,bejar04a} and in the mid-infrared \citep{jaya03,oliveira04,oliveira06,hernandez07,cab07a,osorio07,scholz08,luhman08}." +. Iu this paper we present a deep £Z(.7) survey covering an area of 1.12 dee? around the star & Oviouis., In this paper we present a deep $IZ(J)$ survey covering an area of 1.12 $^2$ around the star $\sigma$ Orionis. + We zin to detect and characterize very low-1uass stars iud substellar objects with completeness iu the whole brown dwart domain im a significaut area of the cluster., We aim to detect and characterize very low-mass stars and substellar objects with completeness in the whole brown dwarf domain in a significant area of the cluster. + Details of the observations are indicated iu Section 2., Details of the observations are indicated in Section 2. + In Section ) woe explain the criteria for sclecting member candidates., In Section 3 we explain the criteria for selecting member candidates. + Section Lis devoted to study the spatial distribution of candidates iu the cluster., Section 4 is devoted to study the spatial distribution of candidates in the cluster. + Iu section 5 we study their infrared excesses usine the available Two Micron All Sky Survey (2MASS). UKIRT Deep Infrared Sky Survey (UKIDSS) audSpitzer photometry. and in Section 6 we estimate the substellarmass spectrum of the cluster.," In section 5 we study their infrared excesses using the available Two Micron All Sky Survey (2MASS), UKIRT Deep Infrared Sky Survey (UKIDSS) and photometry, and in Section 6 we estimate the substellarmass spectrum of the cluster." + Concluxious are given in Section 7., Conclusions are given in Section 7. + Part of the data on which the present paper is based were used iu previous survers bv ZapateroOsorioetal.(2000) and DMZO. covering an area of aarciniiz.," Part of the data on which the present paper is based were used in previous surveys by \cite{osorio00} and BMZO, covering an area of $^2$ ." + Preliminary results of the cluster substellar spatial distributionwere preseuted by Béjaretal.(200 LD)., Preliminary results of the cluster substellar spatial distributionwere presented by \cite{bejar04b}. . + We obtained ZZ inaages with the Wide Field Camera (WFC) amounted on the Cassegrain focus of the Isaac, We obtained $IZ$ images with the Wide Field Camera (WFC) mounted on the Cassegrain focus of the Isaac +"Since the errors in the estimation of both the forced eccentricity e, and the secular frequency e do not come from the limitations in the adopted disturbing function. their origin. must He in the construction of the averaged solution itself.","Since the errors in the estimation of both the forced eccentricity $e_f$ and the secular frequency $g$ do not come from the limitations in the adopted disturbing function, their origin must lie in the construction of the averaged solution itself." + As mentioned previously. Heppenheimer’s (1978) expressions are a first-order model with respect to the perturbing mass.," As mentioned previously, Heppenheimer's (1978) expressions are a first-order model with respect to the perturbing mass." + Here. we extend the calculations to the second order.," Here, we extend the calculations to the second order." + One of the most widely used perturbation. techniques is the so-called. Hort’s averaging process (Hort 1966. see also Perraz-Mello 2007). which employs Lie-type canonical transformations to eliminate the dependence of the Hamiltonian with respect to a given set of variables.," One of the most widely used perturbation techniques is the so-called Hori's averaging process (Hori 1966, see also Ferraz-Mello 2007), which employs Lie-type canonical transformations to eliminate the dependence of the Hamiltonian with respect to a given set of variables." + The new Hamiltonian function is given by a power series in the small parameter (e.g. perturbing mass)., The new Hamiltonian function is given by a power series in the small parameter (e.g. perturbing mass). + Since we adopt a Hamiltonian formulation. we first need to introduce canonical variables.," Since we adopt a Hamiltonian formulation, we first need to introduce canonical variables." + We have chosen the modified Delaunay variables (L.A.G—Lot.lg.τσ). where the canonical momenta are given in terms of the orbital elements. by L=| G-L=L(vl-e-1) and A is the canonical conjugate of the mean longitude of the perturbing mass (1.9. tg).," We have chosen the modified Delaunay variables $(L,\Lambda,G-L,\lambda,\lambda_B,\varpi)$, where the canonical momenta are given in terms of the orbital elements, by L =; G-L = L - 1) and $\Lambda$ is the canonical conjugate of the mean longitude of the perturbing mass (i.e. $\lambda_B$ )." + This third degree of freedom appears when passing to the extended phase space to eliminate the non-autonomous character of the perturbation., This third degree of freedom appears when passing to the extended phase space to eliminate the non-autonomous character of the perturbation. + The full Hamiltonian function governing the dynamies of the planetesimal 7 is given by ..where 75 is the mean-motionD of the perturbing mass 7/5 and R the disturbing function., The full Hamiltonian function governing the dynamics of the planetesimal $m$ is given by ) = + n_B - Rwhere $n_B$ is the mean-motion of the perturbing mass $m_B$ and $R$ the disturbing function. +" We can express this Hamiltonian in a form adequate for perturbation theory: F=Fo+&Fj. where Fo = + ny F,= UEcos., and &=Ging/ag is a small parameter that serves as a guide of the relative magnitudes between the perturbation term Fy and the unperturbed integrable Hamiltonian Fo."," We can express this Hamiltonian in a form adequate for perturbation theory: $F = F_0 + \varepsilon F_1$, where F_0 = + n_B F_1 = +, and $\varepsilon = {\cal G} m_B/a_B$ is a small parameter that serves as a guide of the relative magnitudes between the perturbation term $F_1$ and the unperturbed integrable Hamiltonian $F_0$." + For the disturbing function. we adopt a Legendre expansion. truncated to fourth order in the ratio ¢/ag: 1n other words. we approximate the perturbation by F< (e eps). where P;(cosó) is the Legendre polynomial of degree i.," For the disturbing function, we adopt a Legendre expansion, truncated to fourth order in the ratio $a/a_B$ ; in other words, we approximate the perturbation by F_1 = ( )^i ( )^i ( P_i ), where $P_i(\cos{\phi})$ is the Legendre polynomial of degree $i$." +" Switching from a power series in cosó to a harmonic decomposition in @ and transforming them to orbital elements. we can obtain a truncated expansion of the disturbing function leading to ΕΞ Diggeéencos(kM where M and Mj are the mean longitudes of both bodies. and D;j,, may be obtained in terms of the Hansen coefficients (see Beaugé and Michtehenko 2003)."," Switching from a power series in $\cos{\phi}$ to a harmonic decomposition in $\phi$ and transforming them to orbital elements, we can obtain a truncated expansion of the disturbing function leading to F_1 = e^i e_B^j where $M$ and $M_B$ are the mean longitudes of both bodies, and $D_{i,j,k,l}$ may be obtained in terms of the Hansen coefficients (see Beaugé and Michtchenko 2003)." + Having an explicit expression for Fy i mean variables. we may now apply Horr's method.," Having an explicit expression for $F_1$ in mean variables, we may now apply Hori's method." +" The idea is to search for a Lie-type canonical transformation B=6B, &Bs... toa new set of variables (L.A.(G{ήννιcr) such that the transformed Hamiltonian F is independent of Ul and ορ."," The idea is to search for a Lie-type canonical transformation $B = \varepsilon B_1 + \varepsilon^2 B_2 + \ldots$ to a new set of variables $(L^*,\Lambda^*,(G-L)^*,\lambda^*,\lambda_B^*,\varpi^*)$ such that the transformed Hamiltonian $F^*$ is independent of $\lambda^*$ and $\lambda_B^*$." + Up to second order in the small parameter. the new Hamiltonian function may be written às Cete JH where Aw”=wo—cy.," Up to second order in the small parameter, the new Hamiltonian function may be written as ^*) = F_0^* + F_1^* + ^2 F_2^* where $\Delta \varpi^* = \varpi^* - \varpi_B$." +" The different orders in expression (13)) are given by E0 = Γρ. A? Fi Ga», Fy = GU. + Ε.Β), where {} is the Poisson bracket. (1, denotes the averaging with respect to both mean longitudes (keeping all other variables fixed). and B, ts the first-order generating function of Horr's method."," The different orders in expression \ref{eq13}) ) are given by F_0^* = F_0 ^*) F_1^* = F_1 F_2^* = (F_1 + F_1^*), B_1 where $\{ \}$ is the Poisson bracket, $\langle \rangle_{\lambda,\lambda_B}$ denotes the averaging with respect to both mean longitudes (keeping all other variables fixed), and $B_1$ is the first-order generating function of Hori's method." + In terms of the adopted expansion for the disturbing function (12)). it is given by ⋅ where the function must be evaluated in the new variables.," In terms of the adopted expansion for the disturbing function \ref{eq12}) ), it is given by B_1 = ^i ^j, where the function must be evaluated in the new variables." + The construction of the new secular Hamiltonian F'((G—Ly.Aw’:L.A‘) is cumbersome. although fairly straightforward when using an algebraic manipulator.," The construction of the new secular Hamiltonian $F^*((G-L)^*,\Delta \varpi^*;L^*,\Lambda^*)$ is cumbersome, although fairly straightforward when using an algebraic manipulator." + Fortunately. it will hot be necessary to write al explicit expression here.," Fortunately, it will not be necessary to write an explicit expression here." +" Let it suffice to say that F constitutes a second-order model of the secular system and a single degree of freedom system in variables ((G—Ly.Aw"")."," Let it suffice to say that $F^*$ constitutes a second-order model of the secular system and a single degree of freedom system in variables $((G-L)^*,\Delta \varpi^*)$." + Employing the inverse transformation from Delaunay variables to orbital elements. we can also obtain an expression for F(e.Acid) in terms of the mean eccentricity e? and the proper semimajor axis c.," Employing the inverse transformation from Delaunay variables to orbital elements, we can also obtain an expression for $F^*(e^*,\Delta \varpi^*;a^*)$ in terms of the mean eccentricity $e^*$ and the proper semimajor axis $a^*$." + Since the latter orbital element is constant. 1t appears in the Hamiltonian as an external parameter.," Since the latter orbital element is constant, it appears in the Hamiltonian as an external parameter." + Finally. after solving the secular system and obtaining both e and Ac as functions of time. we may invoke the inverse Hori transformation to obtain the short-period variations of the original osculating variables.," Finally, after solving the secular system and obtaining both $e^*$ and $\Delta \varpi^*$ as functions of time, we may invoke the inverse Hori transformation to obtain the short-period variations of the original osculating variables." + For the eccentricity. this yields ena yu Because δι explicitly depends on the mean longitudes. the second term models the short-period variations 1n. the eccentricity. while the first term (e () gives the main secular contributions.," For the eccentricity, this yields e^2(t) ^2(t) + Because $B_1$ explicitly depends on the mean longitudes, the second term models the short-period variations in the eccentricity, while the first term ${e^*}^2(t)$ ) gives the main secular contributions." + Since the eccentricity is a positively defined function. the magnitude of the second term also specifies the minimum mean eccentricity ¢* of the secular system for any given proper semimajor axis «.," Since the eccentricity is a positively defined function, the magnitude of the second term also specifies the minimum mean eccentricity $e^*$ of the secular system for any given proper semimajor axis $a^*$ ." + At the same time. it also gives the averaged semi-amplitude of the short-period variations Ae in the same orbital element.," At the same time, it also gives the averaged semi-amplitude of the short-period variations $ \Delta e$ in the same orbital element." + Figure 2. shows an application of our second-order model to the same generic binary system as was discussed in Figure |..., Figure \ref{fig2} shows an application of our second-order model to the same generic binary system as was discussed in Figure \ref{fig1}. . +continua from the 35 decay of orthopositronimm and the broad lines froma a reactions.,continuum from the $\gamma$ decay of orthopositronium and the broad lines from $\alpha-\alpha$ reactions. + Orthopositroniu will ouly survive collisional disruption before decay at low deusities: thus. a 511 keV line with little σοιτα directly below it can be taken as a sien of annihilation at moderately high density but not exeat depth.," Orthopositronium will only survive collisional disruption before decay at low densities; thus, a 511 keV line with little continuum directly below it can be taken as a sign of annihilation at moderately high density but not great depth." + Shareetal.(2001) found that if the 511 keV line was produced under 57 & 2. the Compton continua would be simular to what is seen below the line byAILESSI trom the N17 flare of 2003 October 28.," \citet{share04} found that if the 511 keV line was produced under 5–7 g $^-2$, the Compton continuum would be similar to what is seen below the line by from the X17 flare of 2003 October 28." + Our simulations show that a significant fraction of positrons anuihilate at just this depth if they originate from pious., Our simulations show that a significant fraction of positrons annihilate at just this depth if they originate from pions. + Positrous from | decay of spallation products will probably have a shallower distribution since they can be created by more nuucerous. lower-energv protons of tous of MeV that do not penetrate to these depths.," Positrons from $\beta +$ decay of spallation products will probably have a shallower distribution since they can be created by more numerous, lower-energy protons of tens of MeV that do not penetrate to these depths." + This flare. the second largest iu the “Walloween storms” of 20023. occurred near disk center at a heliocentric angle of arecos(O0.587)..," This flare, the second largest in the “Halloween storms” of 2003, occurred near disk center at a heliocentric angle of $\arccos(0.87)$." +REESST inissed the rapid rise phase auc peak of the flare because it was crossing the South Atlautic Anomaly and ouly provides data after 11:06 UT., missed the rapid rise phase and peak of the flare because it was crossing the South Atlantic Anomaly and only provides data after 11:06 UT. + The data extend from 3 keV to 17 MeV. with cucrey resolution of —110 keV across this range.," The data extend from 3 keV to 17 MeV, with energy resolution of $\sim$ 1–10 keV across this range." + The high-cuerey spectrum of the flare is shown in Figure 9.. using data from he rear seginenuts oftheRIEESSI ecrimanium detectors (Sunithetal.2002).," The high-energy spectrum of the flare is shown in Figure \ref{fig:spec}, using data from the rear segments of the germanium detectors \citep{smith02}." +. The 511 keV line and the 2.2 MeV line from jeutron capture ou ambicut protous are most clearly visible., The 511 keV line and the 2.2 MeV line from neutron capture on ambient protons are most clearly visible. + Since this spectrum is uncorrected for iustruuent respouse. uauv of the counts are shifted to lower cuereics by Compton scattering in the instrument.," Since this spectrum is uncorrected for instrument response, many of the counts are shifted to lower energies by Compton scattering in the instrument." + A spectral accumulation aken 15 orbits (about one day) carlicr has been subtracted as backeround. since the geographical position and radiation history of the spacecraft was simular at that time.," A spectral accumulation taken 15 orbits (about one day) earlier has been subtracted as background, since the geographical position and radiation history of the spacecraft was similar at that time." + Iu Table 3.. we list the ratio between 511 keV line flux aud the continua around 200 keV and δ15 MeV for comparison ο our simulations: the results are shown eraphically in Figure 10..," In Table \ref{tab:ob}, we list the ratio between 511 keV line flux and the continua around 200 keV and 8–15 MeV for comparison to our simulations; the results are shown graphically in Figure \ref{fig:ratio}." + We find that if all or most of the 511 keV line Hux resulted from pion iuteractious. there would have been more 815 MeV σοι observed. regardless of the aneular distribution of the injected protons (Table 2)).," We find that if all or most of the 511 keV line flux resulted from pion interactions, there would have been more 8–15 MeV continuum observed, regardless of the angular distribution of the injected protons (Table \ref{tab:p}) )." + Most of the positrous are therefore from other sources. either >| decays (not simulated here) or bremsstrahlung eias from lieh-cucrey flare clectrous (Table 11).," Most of the positrons are therefore from other sources, either $\beta+$ decays (not simulated here) or bremsstrahlung gammas from high-energy flare electrons (Table \ref{tab:e}) )." + If all or most of the 511 keV line flux came from accelerated. clectrous. the 815 MeV. coutinnun would also be overproduced for an isotropic distribution.," If all or most of the 511 keV line flux came from accelerated electrons, the 8–15 MeV continuum would also be overproduced for an isotropic distribution." + Either a domination of the positron source by >| decay or by mostly dowmward electrous is allowed., Either a domination of the positron source by $\beta+$ decay or by mostly downward electrons is allowed. + Iu the comparison above. we did not consider the effect of 35 anmililation ou the 511 keV line.," In the comparison above, we did not consider the effect of $\gamma$ annihilation on the 511 keV line." + Most of the annihilation in our model occurs below the plotospliere. where the deusity is high enough that orthopositroniua will be destroved by collisions before decay. thus we believe that this is à eood approximation.," Most of the annihilation in our model occurs below the photosphere, where the density is high enough that orthopositronium will be destroyed by collisions before decay, thus we believe that this is a good approximation." + IHToxcever. if there were any 25 annililation. it would male the 511 keV line to 815 MeV ratios even siualler. thus strengthening the conclusion that pion decay does not dominate positron production in this fare.," However, if there were any $\gamma$ annihilation, it would make the 511 keV line to 8–15 MeV ratios even smaller, thus strengthening the conclusion that pion decay does not dominate positron production in this flare." + We lave used the GEANT1 package to simulate the spectra produced by the interactions of high-encrey flare particles in the Sun. cmphasizing clectrou breimisstraliluue aud piou production by protons.," We have used the GEANT4 package to simulate the spectra produced by the interactions of high-energy flare particles in the Sun, emphasizing electron bremsstrahlung and pion production by protons." +2].,. + Lor cosmic rav. ionisation In regionso where thermal ionisation is the dominant source. the laver can be approximated with Now we can fit the whole active laver surface density analvticallv.," For cosmic ray ionisation In regions where thermal ionisation is the dominant source, the layer can be approximated with Now we can fit the whole active layer surface density analytically." + In Fig., In Fig. + G6 we show the analytic approximation to the surface density in the active laver is a good fit for high critical magnetic Revnolds number. Learcrit100.," \ref{analytic} we show the analytic approximation to the surface density in the active layer is a good fit for high critical magnetic Reynolds number, $Re_{\rm M,crit} \gtrsim 100$." + Note that even though we have only shown one temperature and surface density clistribution in this work. these fits are valid for any cistribution.," Note that even though we have only shown one temperature and surface density distribution in this work, these fits are valid for any distribution." + The accretion rate through the laver can be approximated. by in regions where cosmic ray ionisation is the dominant source., The accretion rate through the layer can be approximated by in regions where cosmic ray ionisation is the dominant source. + The minimum accretion rate through the disc occurs where cosmic rav ionisation takes over from thermal ionisation., The minimum accretion rate through the disc occurs where cosmic ray ionisation takes over from thermal ionisation. + By finding where the surface densities in equations (27)) ancl (28)) are. equal. we find this occurs ab a temperature of Z7zclo?Ix.," By finding where the surface densities in equations \ref{fit}) ) and \ref{fit2}) ) are equal, we find this occurs at a temperature of $T\approx 10^3\,\rm K$." + The radius corresponding to this temperature has the smallest. aceretion. rate. (see lig. 5))., The radius corresponding to this temperature has the smallest accretion rate (see Fig. \ref{mdot}) ). + As explained in Section 3 the accretion on to the central object will be limited. by this minimum over a viscous timescale at that radius.," As explained in Section \ref{ar}, the accretion on to the central object will be limited by this minimum over a viscous timescale at that radius." + If the viscosity à parameter is smaller than the value we have taken in this work. of 0.1. then both the active laver surface clensity ancl accretion rate would be smaller than predicted here (see equations 27. ancl 28)).," If the viscosity $\alpha$ parameter is smaller than the value we have taken in this work, of 0.1, then both the active layer surface density and accretion rate would be smaller than predicted here (see equations \ref{fit} and \ref{fit2}) )." + The disc would. become even more unstable to the gravo-magneto instability., The disc would become even more unstable to the gravo-magneto instability. + Lhe results shown here represent an upper limit to the surface density in the active laver., The results shown here represent an upper limit to the surface density in the active layer. + There are three non-iceal MILD. effects in the generalised Ohnm's law. Ohmic resistivity. Hall. effect ancl ambipolar ilFusion. that dominate for dillerent regimes.," There are three non-ideal MHD effects in the generalised Ohm's law, Ohmic resistivity, Hall effect and ambipolar diffusion, that dominate for different regimes." + The Obmic term. that we have used. here. dominates at. high. density and very low ionisation.," The Ohmic term, that we have used here, dominates at high density and very low ionisation." + However. the ambipolar cilfusion ominates for low density ancl high ionisation and the Llall οσοι dominates in a region between these two extremes Wardle1997).," However, the ambipolar diffusion dominates for low density and high ionisation and the Hall effect dominates in a region between these two extremes \citep{wardle97}." +. Recent work suggests that the MIU in the surface lavers of dises may. be dictated by ambipolar cillusion (Perez-Decker&Chiang2011a.b:DaiStonePOLL) or the Hall effect. (Wardle&Salmeron2011). rather than Ohmic resistivity as we have assumed here.," Recent work suggests that the MRI in the surface layers of discs may be dictated by ambipolar diffusion \citep{perezbecker11a,perezbecker11b,bai11} or the Hall effect \citep{wardle11} rather than Ohmic resistivity as we have assumed here." + Wardle&Salmeron(2011). applied. a model with all three elfects to 1e minimum mass solar nebula and found that at a radius X LAU there is around an order of magnitude increase or ecrease in the active [aver surface density. depending on whether the field is parallel or antiparallel to the rotation axis. respectively. compared. with a disc with only Ohmic resistivity.," \cite{wardle11} applied a model with all three effects to the minimum mass solar nebula and found that at a radius of $1\,\rm AU$ there is around an order of magnitude increase or decrease in the active layer surface density, depending on whether the field is parallel or antiparallel to the rotation axis, respectively, compared with a disc with only Ohmic resistivity." + These extra elfects. could. change the surface density in the active [aver and the acerction rate through the dise predicted. here by around. an order of magnitude., These extra effects could change the surface density in the active layer and the accretion rate through the disc predicted here by around an order of magnitude. + However. Olmic resistivity. has the advantage of being independent of the magnetic field (Fleming2000) and the values it procluces for the surface density of the active laver represent an average for the values obtained over a range of vertical magnetic fields (e.g.Warelle&Salmeron2011).," However, Ohmic resistivity has the advantage of being independent of the magnetic field \citep{fleming00} and the values it produces for the surface density of the active layer represent an average for the values obtained over a range of vertical magnetic fields \citep[e.g.][]{wardle11}." +. Fromang.Terquem.&Balbus(2002) use à similar approach to the work presented here but find that the active [aver in the disc decreases with radius such that the dead: zone surface density is approximately constant., \cite{fromang02} use a similar approach to the work presented here but find that the active layer in the disc decreases with radius such that the dead zone surface density is approximately constant. + The emperature distribution they use. shown in their Figure 1. jt a very steep radial dependence in the region where he dead: zone forms.," The temperature distribution they use, shown in their Figure 1, has a very steep radial dependence in the region where the dead zone forms." + With the analytical fits given here. it is clear that the constant active [aver surface density can »* recovered. if the temperature of the disc has à radius dependence TxRot.," With the analytical fits given here, it is clear that the constant active layer surface density can be recovered if the temperature of the disc has a radius dependence $T\propto R^{-9/4}$." + Lf the power is even smaller. 9/1. then the active [aver will decrease with radius as found w Fromang.Terquem&Balbus(2002).," If the power is even smaller, $<-9/4$ , then the active layer will decrease with radius as found by \cite{fromang02}." +. Phe analytical fits »esented here in Section 4 would provide an approximation o the disc in this case too because they can describe any surface density and temperature distribution., The analytical fits presented here in Section \ref{an} would provide an approximation to the disc in this case too because they can describe any surface density and temperature distribution. + If cosmic rays are present. the depth of the active laver is insensitive to the presence of X-rays because they do not," If cosmic rays are present, the depth of the active layer is insensitive to the presence of X-rays because they do not" + 107? 241O* ~3 50 cooling imflow., $10^{59}$ $2\times 10^8$ $\sim3$ $50$ cooling inflow. + Iu general. however. ceutral black holes are unable to provide the optiual or umn feedback cnerey that must be deposited at every radius in the cluster eas just sufficient to shu down black hole accretion of locally coolingo eas.," In general, however, central black holes are unable to provide the optimal or minimum feedback energy that must be deposited at every radius in the cluster gas just sufficient to shut down black hole accretion of locally cooling gas." +Oo Iusteac. black holes typically over-veact im aochuusy fashion. depositing πιο] nore energev than the nmüunmuiun required. much of it in distant regious of the cluster where the radiative cocling time exceeds the age of the cuxter.," Instead, black holes typically over-react in a clumsy fashion, depositing much more energy than the minimum required, much of it in distant regions of the cluster where the radiative cooling time exceeds the age of the cluster." + After a few 105 vrs following a feedback event most of the feedback cucrey couverts to poteutial energy. as the eutire gaseous cTuster atmosphere adiabatically expands outward (Matrews Briehenuti 2008).," After a few $10^8$ yrs following a feedback event most of the feedback energy converts to potential energy, as the entire gaseous cluster atmosphere adiabatically expands outward (Mathews Brighenti 2008)." + Consequently. the increased ¢uster gas entropv Is necessarily related to a reduction of the cluster gas density relative to the local dark mater.," Consequently, the increased cluster gas entropy is necessarily related to a reduction of the cluster gas density relative to the local dark matter." +" We discuss here au approximate estination of the toal feedback energv received by cluster Ooeas duringC» the cluser lifeiue bv comparingOo, gas potential enerev profiles iu observed clusters with that of idealized eas deusitv disrbutious resulting from ""adiabatic"" eyavitatioial colapse into the cluster halo in the absence of radiative COCying aud associated feedback.", We discuss here an approximate estimation of the total feedback energy received by cluster gas during the cluster lifetime by comparing gas potential energy profiles in observed clusters with that of idealized gas density distributions resulting from “adiabatic” gravitational collapse into the cluster halo in the absence of radiative cooling and associated feedback. + We show that fus encvevs ~1005 coves. far exceeds the euergv lost by raclation during the cluster lifetime and cousequenlv the mmm euergv required merely to stop the cooline infow.," We show that this energy, $\sim10^{63}$ ergs, far exceeds the energy lost by radiation during the cluster lifetime and consequently the minimum energy required merely to stop the cooling inflow." + The collective cucrey from all superuovae aSO provides a negligible fraction of the total feedback cucrey., The collective energy from all supernovae also provides a negligible fraction of the total feedback energy. + Since only LO percent of the hot barvoulc ooOas du nniassive clusters cools to form stars. star formation cau also be ignored in our estinate of the elobalenergetiesof the," Since only 10 percent of the hot baryonic gas in massive clusters cools to form stars, star formation can also be ignored in our estimate of the globalenergeticsof the" +For this SED type the colour correction at the 247m band is small (<3 per cent) and we choose not to apply it.,For this SED type the colour correction at the $\rm \mu m$ band is small $<$ 3 per cent) and we choose not to apply it. + In the 70 and θά data processing. the first step was © fit ramps to the reads to derive slopes. during which readout jumps and cosmic ray hits were also removed and an electronic nonlinearity correction was applied.," In the 70 and $\rm 160 \mu m$ data processing, the first step was to fit ramps to the reads to derive slopes, during which readout jumps and cosmic ray hits were also removed and an electronic nonlinearity correction was applied." +i] Next. the stim flash frames aken by the instrument were used as responsivity corrections.," Next, the stim flash frames taken by the instrument were used as responsivity corrections." + The dark current was subtracted from the data. an illumination correction was applied. and short term variations in the the signal (often referred to as drift) were removed.," The dark current was subtracted from the data, an illumination correction was applied, and short term variations in the the signal (often referred to as drift) were removed." + Next. a robust statistical analysis was applied to cospatial pixels from different frames in which statistical outliers (e.g. pixels affected by cosmic rays) were masked out.," Next, a robust statistical analysis was applied to cospatial pixels from different frames in which statistical outliers (e.g. pixels affected by cosmic rays) were masked out." + Once this was done. final mosaics were made using square pixels of aaresee for the ται data and aaresec for the πι data.," Once this was done, final mosaics were made using square pixels of arcsec for the $\rm 70 \mu m$ data and arcsec for the $\mu$ m data." + The residual backgrounds were measured and subtracted from the images., The residual backgrounds were measured and subtracted from the images. + Finally. flux calibration factors were applied to the data.," Finally, flux calibration factors were applied to the data." + Theται calibration factors given by ? are 702+35 MIy sr! [MIPS instrumental 1. and the 1605 calibration factor is given by 2 as 41.7£5 MIv + [MIPS instrumental .," The$\rm 70 \mu m$ calibration factors given by \citet{Gordon2007} are $702 \pm 35$ MJy $^{-1}$ [MIPS instrumental $^{-1}$ , and the $\rm 160 \mu m$ calibration factor is given by \citet{Stansberry2007} as $41.7\pm5$ MJy $^{-1}$ [MIPS instrumental $^{-1}$ ." + For the photometry we use apertures with radii 4.5 and aaresec at 70 and 160;rm respectively., For the photometry we use apertures with radii 4.5 and arcsec at 70 and $\rm 160 \mu m$ respectively. + In this case. the correction factors that account for PSF losses are 1.30 and 1.857 respectively.," In this case, the correction factors that account for PSF losses are 1.30 and 1.87 respectively." + Colour corrections for the MIPS 70 and 1607/3 bands are typically smaller than the calibration uncertainties and are therefore not applied to the data., Colour corrections for the MIPS 70 and $\rm 160 \mu m$ bands are typically smaller than the calibration uncertainties and are therefore not applied to the data. + In the case of non-detection we assign an upper limit to the flux density which corresponds to 5 times the standard deviation of the background., In the case of non-detection we assign an upper limit to the flux density which corresponds to 5 times the standard deviation of the background. + Optical spectroscopy for the target sources was carried out at the Kitt Peak National Observatory (KPNO) 4-m telescope and the 4.2m William Herschel Telescope (WHT)., Optical spectroscopy for the target sources was carried out at the Kitt Peak National Observatory (KPNO) 4-m telescope and the 4.2m William Herschel Telescope (WHT). + The KPNO observations used the Ritchey-Chretien spectrograph in single-slit mode with the 1181 grism blazed at 7500., The KPNO observations used the Ritchey-Chretien spectrograph in single-slit mode with the 181 grism blazed at $\rm \AA$. + This setup provides a resolution of about in the wavelength range 5500)O500A., This setup provides a resolution of about in the wavelength range $\rm 5500-9500\AA$. + An exposure time of 20min was adopted., An exposure time of 20min was adopted. + These observations were carried out in March 10 2006., These observations were carried out in March 10 2006. + The WHT spectroscopy used the ISIS (Intermediate dispersion Spectrograph and Imaging System) double armed spectrograph during service time in June 17 and July 8 2007., The WHT spectroscopy used the ISIS (Intermediate dispersion Spectrograph and Imaging System) double armed spectrograph during service time in June 17 and July 8 2007. + The observations were made using the dichroic and the R300B and RISSR gratings in the blue and red arms of the spectrograph respectively., The observations were made using the dichroic and the R300B and R158R gratings in the blue and red arms of the spectrograph respectively. + The spectral resolution was about for the red arm and for the blue arm spectrum., The spectral resolution was about for the red arm and for the blue arm spectrum. + The total on-source integration time was mmin split into two mmin exposures., The total on-source integration time was min split into two min exposures. + The data were reduced following standard methods as implemented in the package ofIRAP., The data were reduced following standard methods as implemented in the package of. + After subtraction of the bias. the data were flat-tielded using observations of interna calibration lamps.," After subtraction of the bias, the data were flat-fielded using observations of internal calibration lamps." + Cosmic ray events were removed using the Laplacian Cosmic Ray Identification package (LACOSMIC::2)., Cosmic ray events were removed using the Laplacian Cosmic Ray Identification package \citep[{\sc lacosmic};. + The one dimensional spectra were extracted and wavelength calibrated using observations of CuNe and CuAr are lamps., The one dimensional spectra were extracted and wavelength calibrated using observations of CuNe and CuAr arc lamps. + For the flux calibration observations of the spectrophotometric standard stars BD 282411 and BD 332642 were used., For the flux calibration observations of the spectrophotometric standard stars BD 282411 and BD 332642 were used. + Because of the apparen faintness of our targets at wavelengths shorter than the WHT/ISIS blue arm spectra did not show any signal and are therefore not presented in this paper., Because of the apparent faintness of our targets at wavelengths shorter than the WHT/ISIS blue arm spectra did not show any signal and are therefore not presented in this paper. + Near-infrared spectroscopy of. SDSS/2MASS EROs was obtained in queue mode on the UK Infrared Telescope (UKIRT)., Near-infrared spectroscopy of SDSS/2MASS EROs was obtained in queue mode on the UK Infrared Telescope (UKIRT). + The observations used the UKIRT Imaging SpecTrometer (UIST) in long slit mode with a mixture of the IJ and HK grisms. the exact selection depending on the expected redshift of the object based on photometric redshift estimation.," The observations used the UKIRT Imaging SpecTrometer (UIST) in long slit mode with a mixture of the IJ and HK grisms, the exact selection depending on the expected redshift of the object based on photometric redshift estimation." + The observations were carried out in clear conditions on [8. 22. 23 June. 2007.," The observations were carried out in clear conditions on 18, 22, 23 June, 2007." + Integration times were ~ {νο hours for the HK grism and ~ 45 minutes for the IJ grism., Integration times were $\sim$ 1.5 hours for the HK grism and $\sim$ 45 minutes for the IJ grism. + The data were reduced using the automated ORACDR system which performed flat fielding. wavelength calibration based on are spectra. subtracted the chopped images and coadded separate sub-exposures.," The data were reduced using the automated ORACDR system which performed flat fielding, wavelength calibration based on arc spectra, subtracted the chopped images and coadded separate sub-exposures." + Flux calibration was carried out using the BS5019 and BSS spectrophotometrie standards., Flux calibration was carried out using the BS5019 and BS8 spectrophotometric standards. + No correction for slit losses were applied so the flux calibration is correct in a relative sense., No correction for slit losses were applied so the flux calibration is correct in a relative sense. + The spectra were then analyzed using a combination of IRAF and IDL routines to determine redshifts and to extract relevant emission line parameters., The spectra were then analyzed using a combination of IRAF and IDL routines to determine redshifts and to extract relevant emission line parameters. + Spectroscopic redshifts are available for 8/10 2MASS sources. 7 from our own observations and | from the literature.," Spectroscopic redshifts are available for 8/10 2MASS sources, 7 from our own observations and 1 from the literature." + The lack of spectroscopic redshift determinations for ? sources in the sample is because of low S/N optical spectra., The lack of spectroscopic redshift determinations for 2 sources in the sample is because of low S/N optical spectra. + The optical and near-IR spectra of the sources with successful redshift determinations are shown in Figure 2.., The optical and near-IR spectra of the sources with successful redshift determinations are shown in Figure \ref{fig_spec}. + The redshifts are presented in Table 2. and estimates of the FWHM (Full Width Half Maximum) of emission lines are discussed in the Appendix and are listedin Table 3 , The redshifts are presented in Table \ref{tab_obs2} and estimates of the FWHM (Full Width Half Maximum) of emission lines are discussed in the Appendix and are listedin Table \ref{tab_restframe} . +The edobserved optical to mid-IR Spectral Energy Distribution (SED) of the sample sources are modeled following the methods fully described in ??..," The observed optical to mid-IR Spectral Energy Distribution (SED) of the sample sources are modeled following the methods fully described in \cite{rowan2005,rowan2008}. ." + In brief the (-bandto 4.5sanaphotometric data are fit using a library of 8 templates described by ?.. 6," In brief the $U$ -bandto $\rm 4.5\,\mu +m$photometric data are fit using a library of 8 templates described by \cite{Babbedge2004}, , 6" +undergoing contact have been included for the reasons given in this subsection and also because their exclusion would lead to the production of a too small number of Algol type binaries.,undergoing contact have been included for the reasons given in this subsection and also because their exclusion would lead to the production of a too small number of Algol type binaries. + The accuracy of the semi-detached scenario is restricted by the value of the radiative efficiency of accretion A which defines the quantity {ΚΚ exerting the radiation pressure of a hot spot., The accuracy of the semi-detached scenario is restricted by the value of the radiative efficiency of accretion $\tilde{K}$ which defines the quantity $L_{acc}$$\times$$\tilde{K}$ exerting the radiation pressure of a hot spot. +" Lj, is. that part of roLil. = GxMoxMRUU—, that is available after reduction due to the fact that matter impinging on the gainer starts at the first Lagrangian point and not at infinity.", $L_{acc}$ is that part of $L_{acc}^{\infty}$ = $\times \frac {M_{g}\times M_{d}^{RLOF}}{R_{g}}$ that is available after reduction due to the fact that matter impinging on the gainer starts at the first Lagrangian point and not at infinity. + This accretion luminosity is weakened by the fact that only a fraction can be converted into radiation and strengthened because the energy of the Impacting material is concentrated in a hot spot which ts significantly smaller than the entire gainer's surface., This accretion luminosity is weakened by the fact that only a fraction can be converted into radiation and strengthened because the energy of the impacting material is concentrated in a hot spot which is significantly smaller than the entire gainer's surface. + Van Rensbergen et al. (2008)), Van Rensbergen et al. \cite{Walter2}) ) + defined a quantity A which enables the calculation of the contribution of the hot spot to the total luminosity of the gainer., defined a quantity $K$ which enables the calculation of the contribution of the hot spot to the total luminosity of the gainer. + It is easier to visualize the action of the hot spot using K=t as given by relation (1)): Unfortunately. there are only 11. reliable hot spot temperatures available in the literature.," It is easier to visualize the action of the hot spot using $\tilde{K}$ $\frac{1}{K}$ as given by relation \ref{Ktilde}) ): Unfortunately, there are only 11 reliable hot spot temperatures available in the literature." + Eight systems (VW Cep. CN And. KZ Pav. V361 Lyr. RT Scl. U Cep. U Sge. and SV Cen) are direct impact systems. whereas three of them (SW Cyg. V356 Ser andP Lyr) have a transient accretion disk.," Eight systems (VW Cep, CN And, KZ Pav, V361 Lyr, RT Scl, U Cep, U Sge, and SV Cen) are direct impact systems, whereas three of them (SW Cyg, V356 Sgr and $\beta$ Lyr) have a transient accretion disk." +" In the case of the formation of a hot spot on the edge of an accretion disk we have to replace in equation (1)): Ry by Ru and Terre by Tj,4:4."," In the case of the formation of a hot spot on the edge of an accretion disk we have to replace in equation \ref{Ktilde}) ): $R_{g}$ by $R_{disk}$ and $T_{eff,g}$ by $T_{edge,disk}$." +" Our liberal evolutionary calculations have thus been gauged with small number statistics. producing an empirical relation for the radiative efficiency of accretion & concentrated in a hot spot. increasing with the total mass of the system as: Radiative efficiency. 7. 1s usually defined through the lumimosity Loy, which is added to a system as a consequence of the transfer of matter at a rate M: A numerical value can hence be calculated from relation (2)) for the radiative efficiency of mass accretion by a Main Sequence gainer: The factor D is the geometric factor taking into account that matter does not fall onto the gainer from infinity but from the first Lagarangian point."," Our liberal evolutionary calculations have thus been gauged with small number statistics, producing an empirical relation for the radiative efficiency of accretion $\tilde{K}$ concentrated in a hot spot, increasing with the total mass of the system as: Radiative efficiency, $\eta$, is usually defined through the luminosity $L_{add}$ which is added to a system as a consequence of the transfer of matter at a rate $\dot{M}$: A numerical value can hence be calculated from relation \ref{Ktildenumber}) ) for the radiative efficiency of mass accretion by a Main Sequence gainer: The factor $D$ is the geometric factor taking into account that matter does not fall onto the gainer from infinity but from the first Lagarangian point." + This factor is zero for a contact system and goes to unity as LZ; goes to infinity., This factor is zero for a contact system and goes to unity as $L_{1}$ goes to infinity. + The factor S is the fractional surface area of the hot spot., The factor $S$ is the fractional surface area of the hot spot. + Consequently we can compare the values of 77 calculated with relation (4)) with values that are well known from fundamental physics: y = 0.007 for complete nuclear fusion of hydrogen. 77) grows smoothly from 0.057 for a mass gaining non-rotating black hole to 0.32 for a black hole rotating at maximum plausible spin (Thorne 1974)).," Consequently we can compare the values of $\eta$ calculated with relation \ref{etanumber}) ) with values that are well known from fundamental physics: $\eta$ = 0.007 for complete nuclear fusion of hydrogen, $\eta$ grows smoothly from 0.057 for a mass gaining non-rotating black hole to 0.32 for a black hole rotating at maximum plausible spin (Thorne \cite{Thorne}) )." + All the systems in the grid have been calculated both with strong and weak tidal interaction., All the systems in the grid have been calculated both with strong and weak tidal interaction. + The formalism for the tidal interaction was taken from Zahn (1977)). who gives a suitable approximation for the synchronisation time-scale: This expression uses the semi major axis a of the binary and a mass-ratio q. in which the star that has to be synchronized is in the denominator.," The formalism for the tidal interaction was taken from Zahn \cite{Zahn}) ), who gives a suitable approximation for the synchronisation time-scale: This expression uses the semi major axis $a$ of the binary and a mass-ratio $q$ , in which the star that has to be synchronized is in the denominator." + This is the gainer in our case. so that 4—-WoMg," This is the $gainer$ in our case, so that ${q}={M_{d}\over M_{g}}$." +" Tidal interactions modulate the angular velocity of the gainer wy with the angular velocity «,,, of the system.", Tidal interactions modulate the angular velocity of the gainer $\omega_{g}$ with the angular velocity $\omega_{orb}$ of the system. + According to Tassoul (2000)) one can write: ..Tidal interactions spin the gainer down when wy>Warp., According to Tassoul \cite{Tassoul}) ) one can write: Tidal interactions spin the gainer down when $\omega_{g} > \omega_{orb}$. + Tides spin the gainer up when ων5 MJup:," That process can easily reproduce the apsidal motion, but pumping the mutual inclination up to the observed values is difficult and probably requires the removal of a planet with mass $> 5$ $_\textrm{Jup}$." + Removing (wo planets does not increase (his probability significantly., Removing two planets does not increase this probability significantly. +" The other important constraint on the scattering hypothesis is (he svstenrs close proximity to the stability boundary. 3dof//:,.;;."," The other important constraint on the scattering hypothesis is the system's close proximity to the stability boundary, $\beta/\beta_{crit}$." + Collisions may leave asvstem near that boundary. whereas ejections tend to spread out the planets.," Collisions may leave a system near that boundary, whereas ejections tend to spread out the planets." +" Furthermore. we find (hat collisions tend to produce svslenms with low ο/η and low WV. while ejections produce a broad range of V. but large values of 32/5,4;."," Furthermore, we find that collisions tend to produce systems with low $\beta/\beta_{crit}$ and low $\Psi$, while ejections produce a broad range of $\Psi$, but large values of $\beta/\beta_{crit}$." + Nonetheless. Fig.," Nonetheless, Fig." + 3. demonstrates (hat scattering can produce svstenis similar to c And., \ref{fig:example} demonstrates that scattering can produce systems similar to $\upsilon$ And. + Although scattering is à reasonable process to produce the observed. architecture. we cannot determine the triggering mechanism.," Although scattering is a reasonable process to produce the observed architecture, we cannot determine the triggering mechanism." + Did scattering occur because D destabilized (he planetary system?, Did scattering occur because B destabilized the planetary system? + Or did the planet lormation process itsell. independent of D. ultimately lead to instabilities?," Or did the planet formation process itself, independent of B, ultimately lead to instabilities?" + The presence of D makes distinguishing these possibilities very difficult., The presence of B makes distinguishing these possibilities very difficult. + A larger census of mutual inclinations and stellar companions can resolve this open Issue., A larger census of mutual inclinations and stellar companions can resolve this open issue. + Alternatively. our decisions about the svstem at the onset of scattering could be mistaken.," Alternatively, our decisions about the system at the onset of scattering could be mistaken." + We assumed (he planets formed inside (he original protoplanetary disk wilh inclinations <1°., We assumed the planets formed inside the original protoplanetary disk with inclinations $<1^\circ$. + ]t may be that larger initial inclinations are possible prior to scattering. in which case the planets could be pumped to larger mutual inclinations (Chatterjee 2008).," It may be that larger initial inclinations are possible prior to scattering, in which case the planets could be pumped to larger mutual inclinations (Chatterjee 2008)." + Llowever. il remains to be seen if such configurations are possible prior (ο scattering.," However, it remains to be seen if such configurations are possible prior to scattering." + Future studies should explore the inclinations of giant planets during formation., Future studies should explore the inclinations of giant planets during formation. + We have also ignored the effects of planet b. stellar companion D. and a possible fourth," We have also ignored the effects of planet b, stellar companion B, and a possible fourth" +All of our simulations start with uniform gas density (pj) and gas pressure (7).,All of our simulations start with uniform gas density $\rho_0$ ) and gas pressure $P_0$ ). + The elobal gas pressure gradient is set to be ;=—0.04., The global gas pressure gradient is set to be $\beta=-0.04$. +" The initial eas angular velocity prolile is given bx unperturbed Ixeplerian flow (—(2/2)4) and a small reduction due to global gas pressure gradient. (360,/2). à,=ολα)450,/2."," The initial gas angular velocity profile is given by unperturbed Keplerian flow $-(3/2)x\Omega$ ) and a small reduction due to global gas pressure gradient $\beta c_{s}/2$ ), $u_{\rm y}=-(3/2)x\Omega+\beta c_{s}/2$." +" Initial disturbances are given {ο the gas radial velocity with the amplitude ο,=0.001c..", Initial disturbances are given to the gas radial velocity with the amplitude $\left|\delta u_{x}\right|=0.001c_{s}$. + Test particles are initially orbiting at the Kepler angular velocity., Test particles are initially orbiting at the Kepler angular velocity. + The particles move inwarel in (he initial stage because thev lose (heir angular momentum by the heacwind that thev feel due to the global pressure eraclient., The particles move inward in the initial stage because they lose their angular momentum by the headwind that they feel due to the global pressure gradient. + This is the dust infall problem described in Introduction., This is the dust infall problem described in Introduction. + Initially 3 particles per gird are distributed., Initially 8 particles per gird are distributed. + Since typical grid we use is (250—950)x10050 (Table 3)). totally ~O(10*) particles are distributed.," Since typical grid we use is $(250-950) \times 100 \times 50$ (Table \ref{tab:1}) ), totally $\sim O(10^7)$ particles are distributed." +" The non-uniformity in the MBI growth is set either bv non-uniform resistivity (CASEL) or non-uniform vertical (2) component of the magnetic field (CASE2),", The non-uniformity in the MRI growth is set either by non-uniform resistivity (CASE1) or non-uniform vertical $z$ ) component of the magnetic field (CASE2). + We describe these cases in details in the following., We describe these cases in details in the following. + In CASEL. gas ionization degree is set to be racially inhomogeneous under the uniform magnetic field.," In CASE1, gas ionization degree is set to be radially inhomogeneous under the uniform magnetic field." + The linear analvsis for MIRI causecl by vertical magnetic field shows that the larger resistivity makes unstable wavelength longer (Jin1996:Sano&Alivama.1999).," The linear analysis for MRI caused by vertical magnetic field shows that the larger resistivity makes unstable wavelength longer \citep{jin96, sam99}." +. The upper limit to (he wavelength. À.44. is scale height for actual disks while in our simulation. it is the size of the simulation box in the z direction (L.).," The upper limit to the wavelength, $\lambda_{z, {\rm crit}}$, is scale height for actual disks while in our simulation, it is the size of the simulation box in the $z$ direction $L_{z}$ )." + The critical value of resistivity with whieh the modes with wavelength shorter Chan À.44; cannot grow is where Ayei Is− (he wave number corresponding− A- eri.," The critical value of resistivity with which the modes with wavelength shorter than $\lambda_{z, {\rm crit}}$ cannot grow is where $k_{z, {\rm crit}}$ is the wave number corresponding $\lambda_{z, {\rm crit}}$ ." + Here Sposa=⋅⋅↽≻2301/03.> is: the plasma beta., Here $\beta_{plasma} ={2c^2_{s}}/v^2_{{\rm A}z}$ is the plasma beta. + la our case (here is no growing mocle if the resistivity makes A.μι larger (han L..," In our case there is no growing mode if the resistivity makes $\lambda_{z,{\rm crit}}$ larger than $L_{z}$." + In CASEL. we sel ρω=4000 and By=(0.0.D.).," In CASE1, we set $\beta_{plasma}=4000$ and $\mathbf{B}_0=(0, 0, B_{z})$." + Resistivity varies in the radial direction such that MRI grows only in a limitedzone in the center of the simulation box., Resistivity varies in the radial direction such that MRI grows only in a limitedzone in the center of the simulation box. + The resistivity distribution is not changed throughout runs., The resistivity distribution is not changed throughout runs. + The radial distribution is shown in Figure 2aa. In this paper. the zone at the center where resistivity is initially sub-critical is relerred to as the “unstable” region.," The radial distribution is shown in Figure \ref{fig:ini}a a. In this paper, the zone at the center where resistivity is initially sub-critical is referred to as the ""unstable"" region." +" The radial width of the stable and unstable regionsare denoted by £L, and L£,. respectively."," The radial width of the stable and unstable regionsare denoted by $L_{\rm s}$ and $L_{\rm u}$ , respectively." +We thank the staff at LUCCA observatory for time allocation and assistance during the observations.,We thank the staff at IUCCA observatory for time allocation and assistance during the observations. + This work made use of the SIMDAD astronomical database. operated at CDS. Strasbourg. France. and the NASA ADS. USA.," This work made use of the SIMBAD astronomical database, operated at CDS, Strasbourg, France, and the NASA ADS, USA." + We thank Prof. A. V. Raveendran for useful discussions., We thank Prof. A. V. Raveendran for useful discussions. + Sreeja S. Ixartha is a JRF in the DST project 5R/52/1IEP-09/2007: [funding from this project is greatfully acknowledged., Sreeja S. Kartha is a JRF in the DST project SR/S2/HEP-09/2007; funding from this project is greatfully acknowledged. +Tt can be seen that both methods correctly indicate the area of couverecuce. but ATR inereases for all particles in the convergence region.,"It can be seen that both methods correctly indicate the area of convergence, but $\cal{NK}$ increases for all particles in the convergence region." + D is raised for most particles in the couvergeuce zone. but is also incorrectly raised for aligninents of particles which are not iu the convergence gone.," $B$ is raised for most particles in the convergence zone, but is also incorrectly raised for alignments of particles which are not in the convergence zone." + The mean value of AK within the convergence zoue is 0.78. and .06 outside wlile mean B is ouly 0.116 inside the zone aud 0.052 outside.," The mean value of $\cal{NK}$ within the convergence zone is 0.78, and .06 outside while mean $B$ is only 0.116 inside the zone and 0.052 outside." + The ring spreading test was repeated usine the AX factor. aud the results are presented in Table 2.," The ring spreading test was repeated using the $\cal{NK}$ factor, and the results are presented in Table \ref{efold}." + VK kept AV switched off and the ring did uot spread at all., $\cal{NK}$ kept AV switched off and the ring did not spread at all. + There was also only a very simall increase in the erowth of prograde lear aliguments (frou 18 to 19% ) when the NK factor was used., There was also only a very small increase in the growth of prograde linear alignments (from $18$ to $19\%$ ) when the $\cal{NK}$ factor was used. + When pressure forces were added to the simmlation. the AK factor did not completely suppress the formation of aliguimmenuts. but performed iuch better than B aud ΤΟΝ.," When pressure forces were added to the simulation, the $\cal{NK}$ factor did not completely suppress the formation of alignments, but performed much better than $B$ and TDV." + Finally. to test the A method with a more realistic siuulation. an isothermal disk was evolved containing a Jupiteranass object.," Finally, to test the $\cal{NK}$ method with a more realistic simulation, an isothermal disk was evolved containing a Jupiter-mass object." +" Tuitial couditious were isothermal. T=10K. surface density “=σαRiau)oe. Moise= OOLAL... Mu,=LAL..."," Initial conditions were isothermal, T=10K, surface density $\Sigma=\Sigma(1 AU) (R/au)^{-7/4}$, $M_{disk}=0.01 M_{\odot}$ . $M_{star}=1M_{\odot}$." + The disk exteuded from 5 to 15 au aud planet mass was 1 AL; a radius 10 au., The disk extended from 5 to 15 au and planet mass was 1 $M_{J}$ at radius 10 au. +" un10,000 SPIT particles were used aud the simulation ran for LfOvrs. about 15 orbital periods of the planet."," 500,000 SPH particles were used and the simulation ran for 470yrs, about 15 orbital periods of the planet." + The results are shown in Fie. 5.., The results are shown in Fig. \ref{planet}. + It can be secu that ACA was effective at capturing the shocks. aud the predicted spiral wave was observed.," It can be seen that $\cal{NK}$ was effective at capturing the shocks, and the predicted spiral wave was observed." + For comparison. the same simulation was performed using P. aud the results are similar. but the PAorals aud shocks are slightly. better defined when using +10 AK inethod.," For comparison, the same simulation was performed using $B$, and the results are similar, but the spirals and shocks are slightly better defined when using the $\cal{NK}$ method." + The SPI estimate of the divergence of viscosity ιν (Eqn. 1))," The SPH estimate of the divergence of viscosity ${\mid\nabla \cdot \bf v\mid}$, (Eqn. \ref{divv}) )" + when used in a EKepleriau Disk. is dominated by the Poisson noise arising frou the impertectly spaced SPI particles (Cartwright et al 2009).," when used in a Keplerian Disk, is dominated by the Poisson noise arising from the imperfectly spaced SPH particles (Cartwright et al 2009)." + As the estimate of |Vev is the key factor in calculating both B aud ΤΩΝ. both of these methods erroucouslv register the apparent convergence of overtaking neiglibours as a signal that AV should be applied.," As the estimate of ${\mid\nabla \cdot \bf v\mid}$ is the key factor in calculating both $B$ and TDV, both of these methods erroneously register the apparent convergence of overtaking neighbours as a signal that AV should be applied." + D ds prone to au aligument artifact. varviug periodically with a frequency ~ 23 times the orbital frequency. which is the overtaking frequency for neighbours.," $B$ is prone to an alignment artifact, varying periodically with a frequency $\sim $ 3 times the orbital frequency, which is the overtaking frequency for neighbours." + This is independent of h aud therefore independent of the umber of SPIT particles used., This is independent of $h$ and therefore independent of the number of SPH particles used. + ΤΙΝ is also not ideal for use in IKepleriau disks if used with Vev|gprr as a source term.," TDV is also not ideal for use in Keplerian disks if used with $\nabla \cdot \bf v\mid_{SPH}$, as a source term." + Vev|gprr is the source of the low frequency aliguiment artifact which compromises D. aud applving a low pass filter to it does not remove the effect.," $\nabla \cdot \bf v\mid_{SPH}$ is the source of the low frequency alignment artifact which compromises $B$, and applying a low pass filter to it does not remove the effect." + AX jf applied. even at quite a low level iu a Iseplerian Disk. results iu the formation of aligumoenuts of particles iu the prograde direction.," AV if applied, even at quite a low level, in a Keplerian Disk, results in the formation of alignments of particles in the prograde direction." + This can be quantified bv calculating the correlation cocficieut cce of close ucighbours of particles. positive values ee20.5 indicating prograde alieunmienuts. ce0.5 indicating retrograde alieuments.," This can be quantified by calculating the correlation coefficient $cc$ of close neighbours of particles, positive values $cc>0,5$ indicating prograde alignments, $cc<-0.5$ indicating retrograde alignments." + A randomly populated disk of particles has no excess of either. having about I8 of cach.," A randomly populated disk of particles has no excess of either, having about $18\%$ of each." + The balance is unaffected if the disk is evolved with only pressure forces aud no AV., The balance is unaffected if the disk is evolved with only pressure forces and no AV. + However. as soon as AV is used. even at low evels using D. the particles start to form an excess of 12.16% prograde aliguments.," However, as soon as AV is used, even at low levels using $B$, the particles start to form an excess of $12-16\%$ prograde alignments." + Using pressure forces in addition to AV causes an even larger surplus of alieuimients to appear.up to 21% beime measured when μια AV was implemented.," Using pressure forces in addition to AV causes an even larger surplus of alignments to appear,up to $24\%$ being measured when maximum AV was implemented." + This should be of exeat concern for the disk-imocdelling community., This should be of great concern for the disk-modelling community. + Normally. disk," Normally, disk" +eap between moderately. metal-poor thin disk stars and the thick disk is much smaller. and. the present uncertainties in the age determinations allow for the possibility that the thin disk formed üunmecdiately after (IL Cyr) alter the thick disk aud halo.,"gap between moderately metal-poor thin disk stars and the thick disk is much smaller, and the present uncertainties in the age determinations allow for the possibility that the thin disk formed immediately after $< 1$ Gyr) after the thick disk and halo." + We are extremely gratefull to Dana Dinescu for providing us with the routines to calculate space velocities o the field stars. for calculating the orbits of the stars and for ceross-referenciug her membership list for NGC 188 with the photometry from Sarajediui et al.," We are extremely gratefull to Dana Dinescu for providing us with the routines to calculate space velocities of the field stars, for calculating the orbits of the stars and for cross-referencing her membership list for NGC 188 with the photometry from Sarajedini et al." + We would like to think the anonymous referee aud the editor Jim Liebert whose numerous suggestious led to a considerable improvement in this paper., We would like to think the anonymous referee and the editor Jim Liebert whose numerous suggestions led to a considerable improvement in this paper. + This research was supported by NASA through the NASA/New Hampshire Space Graut. an LTSA award NACG5-9225 (BC). by a Burke Research Crant from Dartirouth College (BC) and. used the SIMBAD database. operated by operated at CDS. Strasbourg. France.," This research was supported by NASA through the NASA/New Hampshire Space Grant, an LTSA award NAG5-9225 (BC), by a Burke Research Grant from Dartmouth College (BC) and used the SIMBAD database, operated by operated at CDS, Strasbourg, France." + BC acknowledges the hospitality of the Aspen Center of Physics. where he revised the paper.," BC acknowledges the hospitality of the Aspen Center of Physics, where he revised the paper." +Interestingly. 2 report a ~55% pulsed fraction at 100 keV as observed by GDBM —230/— 10 minutes before the BAT trigger.,"Interestingly, \citet{kgk+10} report a $\sim$ pulsed fraction at $\sim$ 100 keV as observed by GBM $\sim$ 30–40 minutes before the BAT trigger." + They report that this is the first time that pulsatious unrelated to a eiut flare have becu observed at 7100 keV for anL., They report that this is the first time that pulsations unrelated to a giant flare have been observed at $\sim$ 100 keV for an. + However. ANPs lave previously been shown to exhibit pulsations at 100 keV with pulsed fractions ax ligh as (e.c.7).," However, AXPs have previously been shown to exhibit pulsations at $\sim$ 100 keV with pulsed fractions as high as \citep[e.g.][]{khhc06}." + Thus it is possible that the measure actually decreased from à higher pulsed fraction leading up to the outburst event. ie. the ~100 keV pulsed fraction iav have behaved sinularly to that iu the 1l10 keV band.," Thus it is possible that the measured actually decreased from a higher pulsed fraction leading up to the outburst event, i.e. the $\sim$ 100 keV pulsed fraction may have behaved similarly to that in the 1–10 keV band." +" Future lard A-rayv telescopes with focusing optics. such asTAR, will allow wich easier measurements of the pulsed fraction of maguetars at high N-ray energies."," Future hard X-ray telescopes with focusing optics, such as, will allow much easier measurements of the pulsed fraction of magnetars at high X-ray energies." +" Previous studies of SGR bursts have shown that their energies. aud thus fluences. follow a power-law distribution ανοxE."" witha equal to ~5/3 (27?).."," Previous studies of SGR bursts have shown that their energies, and thus fluences, follow a power-law distribution $dN/dE \propto E^{-\alpha}$ with $\alpha$ equal to $\sim$ 5/3 \citep{cegy96,gwk+99,gwk+00}." + It has been noted that this is simular to the Ciuteubere- law for earthquakes aud to energy distributions of solar flares (??)..," It has been noted that this is similar to the Gutenberg-Richter law for earthquakes and to energy distributions of solar flares \citep{cad93,lhmb93}." + Both LE 1517. 5108 and LE 2259|586 also follow this distribution., Both 1E $-$ 5408 and 1E 2259+586 also follow this distribution. + In this work. the fluence distribution of LE 5108 is found to have a law iudex of 0.640.1 which corresponds to dN/dE E," In this work, the fluence distribution of 1E $-$ 5408 is found to have a power-law index of $-0.6\pm 0.1$ which corresponds to $dN/dE \propto E^{-1.6}$ ." +t)? find ane of L.F40-1 for 1E 2259|586. similar to the values found for SCRs. further reiufordus the similarity in this particular behavior among ANPs aud SCR.," \citet{gkw04} find an $\alpha$ of $1.7\pm0.1$ for 1E 2259+586, similar to the values found for SGRs, further reinforcing the similarity in this particular behavior among AXPs and SGRs." + For the 2009 outburst. observations which cover an enerev range of >SO keV. show differeut burst properties from those determined using the NRT observations.," For the 2009 outburst, observations which cover an energy range of $>80$ keV, show different burst properties from those determined using the XRT observations." + 7. report a 68-1üu8 mean duration derived οι a log-normal distributiou with a scatter of 30 - 155 aus., \citet{snb+10} report a 68-ms mean duration derived from a log-normal distribution with a scatter of 30 - 155 ms. + This is much shorter than the 305-115 duration determined in this work (see Table tj)., This is much shorter than the 305-ms duration determined in this work (see Table \ref{ta:mags}) ). + This discrepency may be due to the difference in energy coverage: perhaps bursts have different iiorphologies at different cucreics., This discrepency may be due to the difference in energy coverage; perhaps bursts have different morphologies at different energies. + ILlowever. the definition of duration used by ?7/— differs from the τω definition used here.," However, the definition of duration used by \citet{snb+10} differs from the $T_{90}$ definition used here." + 7?/— define the burst duration as the time between the moment when the count rate rises above 5o to when the count rate drops below 3c., \citet{snb+10} define the burst duration as the time between the moment when the count rate rises above $\sigma$ to when the count rate drops below $\sigma$. + When applvius their definition of duration to the bursts identified in our study. we fiud. for a lognormal distribution. a niean duration of LOL 1s and a range for oue standard deviation of 59 - 173 mis. closer to but still somewhat longer than their measurement. suggesting a possible euergv dependeuce of burst duration.," When applying their definition of duration to the bursts identified in our study, we find, for a log-normal distribution, a mean duration of 101 ms and a range for one standard deviation of 59 - 173 ms, closer to but still somewhat longer than their measurement, suggesting a possible energy dependence of burst duration." + We do not. however. detect ay sigeuificaut difference iu the duratious meastred using 0.510 keV counts with those measured using 210 keV counts.," We do not, however, detect any significant difference in the durations measured using 0.5–10 keV counts with those measured using 2–10 keV counts." + The properties of bursts from the 2009 outburst even of LE 5108 are reminiscent of those from the outburst of LE 2259|586 (7).., The properties of bursts from the 2009 outburst event of 1E $-$ 5408 are reminiscent of those from the outburst of 1E 2259+586 \citep{gkw04}. + Both have a siguificanr ΠΠΟΙ of short spikes like those fouud iu SCRs. aud a set of bursts with long pulsating tails like those fond in burst studies of other ANPs.," Both have a significant number of short spikes like those found in SGRs, and a set of bursts with long pulsating tails like those found in burst studies of other AXPs." + Although we do uo find any bursts with lone pulsating tails in the NRT observations. ? and ? πια two such bursts.," Although we do not find any bursts with long pulsating tails in the XRT observations, \citet{snb+10} and \citet{mgw+09} find two such bursts." + These were nof found in our analysis becauseSusff was no observing IE 5108 when they occured., These were not found in our analysis because was not observing 1E $-$ 5408 when they occured. + Table 1 conrpares the properties of bursts from LE 5108 o those frou outbursts from other maguetars., Table \ref{ta:mags} compares the properties of bursts from 1E $-$ 5408 to those from outbursts from other magnetars. + We note hat the average durations of bursts from LE 5Los appear to be longer than for those iu other sources., We note that the average durations of bursts from 1E $-$ 5408 appear to be longer than for those in other sources. + However. this could be an artifact as the burst properties or the other tabulated sources were determined withRNTE.," However, this could be an artifact as the burst properties for the other tabulated sources were determined with." +" The huwger collecting area ofRANTLE allows it o detect bursts that are fainter than thoseSuvft can detect,", The larger collecting area of allows it to detect bursts that are fainter than those can detect. +" Tf faint. short bursts are missed by the NRT. he mean burst duration (as well as £, aud f5) may overestimated."," If faint, short bursts are missed by the XRT, the mean burst duration (as well as $t_r$ and $t_f$ ) may be overestimated." + Also. the cucrev range of RNTE (26 τον). probes higher cuereics aud so differences may be due to the energy depeudauce of burst properties.," Also, the energy range of RXTE (2–60 keV) probes higher energies and so differences may be due to the energy dependance of burst properties." + A detailed statistical study. of LE 5108 bursts withRNTE is needed to clarity this point., A detailed statistical study of 1E $-$ 5408 bursts with is needed to clarify this point. + AlthoughSwift NRT is not ideal for probiug the spectra of magnetar bursts. which have siguificaut fiux above 10 keV. we were still able to draw the following conclusions from our analysis.," Although XRT is not ideal for probing the spectra of magnetar bursts, which have significant flux above 10 keV, we were still able to draw the following conclusions from our analysis." + While we do not observe a hardness-Huence correlation for 1E 5108. this could be due to our limited energy rauge.," While we do not observe a hardness-fluence correlation for 1E $-$ 5408, this could be due to our limited energy range." + Iudecd. there is à hint of a correlation between P aud fiueuce. however is is not statistically significaut.," Indeed, there is a hint of a correlation between $\Gamma$ and fluence, however is is not statistically significant." + Note however that we do observe a significant [-fux correlation (Fig. 17)). 7..," Note however that we do observe a significant $\Gamma$ -flux correlation (Fig. \ref{fig:fluxgamma}) ). \citet{snb+10}," +" using data of the 2009 οπανί, fiud a correlation between burst harducss aud count rate."," using data of the 2009 outburst, find a correlation between burst hardness and count rate." + Their harduecss ratio is defined as the ratio between the Auti-Coincidence Shield. (ACS) fux. which is seusitive to photous above NO keV. aud a 20-60 keV fux from the ISCRI iustruueut.," Their hardness ratio is defined as the ratio between the Anti-Coincidence Shield (ACS) flux, which is sensitive to photons above 80 keV, and a 20-60 keV flux from the ISGRI instrument." + This is also cousistent with a correlation between harducss aud burst magnitude for 1E 5108., This is also consistent with a correlation between hardness and burst magnitude for 1E $-$ 5408. + 7. also fiud a correlation between hardiucss and fiueuce for IE 2259|586., \citet{gkw04} also find a correlation between hardness and fluence for 1E 2259+586. + For the SCRs. ou the other laud. an auti-correlation between larducss aud fluence has been observed (??7).. Table lL also shows that the IE ΙΟΣ bursts from0Η are much harder than those from LE 2259|586.," For the SGRs, on the other hand, an anti-correlation between hardness and fluence has been observed \citep{gwk+99,gwk+00}.. Table \ref{ta:mags} also shows that the 1E $-$ 5408 bursts from are much harder than those from 1E 2259+586." + Du light of the observed harducss-flnence correlation in ANP bursts. this Is not a suprising result.," In light of the observed hardness-fluence correlation in AXP bursts, this is not a suprising result." + The 28 most fluent bursts from LE 2259|586 for which spectral indices were measured. ive flucuces of ~1007)10 Scere ? (2).," The 28 most fluent bursts from 1E 2259+586 for which spectral indices were measured, have fluences of $\sim10^{-9} - 10^{-8}$ erg $^{-2}$ \citep{gkw04}." + This is to ve compared with the 16 most fuent bursts for which Dowas neasured here for TE 5108. that span a HBuence range of ~10ο* ere 7.," This is to be compared with the 46 most fluent bursts for which $\Gamma$ was measured here for 1E $-$ 5408, that span a fluence range of $\sim10^{-8} - 10^{-7}$ erg $^{-2}$." + This may account for the harder average spectral iudex for bursts rom LE 5105., This may account for the harder average spectral index for bursts from 1E $-$ 5408. + Tn the magnetar model. two imechanisnis have been sugeested for producing magnetar bursts.," In the magnetar model, two mechanisms have been suggested for producing magnetar bursts." + 2 sugeest hat stresses due to the stroug maguctic fields prescut inside magnetars are able to crack the crust of the jieutron star., \citet{td95} suggest that stresses due to the strong magnetic fields present inside magnetars are able to crack the crust of the neutron star. + This cracking releases a plasma fireball into the magnetosphere., This cracking releases a plasma fireball into the magnetosphere. + The strong maeuetic fields can hold the fireball above the fracture site., The strong magnetic fields can hold the fireball above the fracture site. + The suspended fireball can heat the surface thus causing an extended cooling tail., The suspended fireball can heat the surface thus causing an extended cooling tail. + Since the strouecst surface ficlds are located near the polar caps. these fracture events would occur prefercutially near the poles which would result in an observed phase dependence of the musts.," Since the strongest surface fields are located near the polar caps, these fracture events would occur preferentially near the poles which would result in an observed phase dependence of the bursts." + Another mechnanisni proposed by ?..suggests hat bursts are caused by reconnection events initiated w the development of a tearing node instability. in he maenetically dominated relativistic plasima in the nagnctosplere.," Another mechanism, proposed by \citet{lyu03}, ,suggests that bursts are caused by reconnection events initiated by the development of a tearing mode instability in the magnetically dominated relativistic plasma in the magnetosphere." + Tn this case. bursts occur randomly iu," In this case, bursts occur randomly in" +"within the experimental errors affecting the measurements of ευ (ορ!το): its & peak is found at ~ 1.3 aud ~ Ll eV by Taft aud Philipp (1965) aud Tosatti and Bassai (1970).. respectively,","within the experimental errors affecting the measurements of $\epsilon_{2}$ (graphite): its $\pi$ peak is found at $\sim$ 4.3 and $\sim$ 4 eV by Taft and Philipp \cite{tp} and Tosatti and Bassani \cite{tb}, respectively." + Had we adopted the intermediate value L1. in Sec.," Had we adopted the intermediate value 4.1, in Sec." + 2. the peaks in Fig.," 2, the peaks in Fig." + 2 would have been shifted to the IS position., 2 would have been shifted to the IS position. + Thus. our model is able to satisfv the simultancous constraints of variable feature width and ucarly constant peak position.," Thus, our model is able to satisfy the simultaneous constraints of variable feature width and nearly constant peak position." + This is effected by chaugiug ouly the muuber of eraphene lavers per stack. which is positively correlated with the degree of eraphitization of the stacks in the erai. and hence to the amount of processing of the dust by UV heating.," This is effected by changing only the number of graphene layers per stack, which is positively correlated with the degree of graphitization of the stacks in the grain, and hence to the amount of processing of the dust by UV heating." + Figure 1 illustrates the chanee of properties cucompassed by this mocel. between its extremes: eraphene and eraphite.," Figure 1 illustrates the change of properties encompassed by this model, between its extremes: graphene and graphite." + Note that the model does uot specify the nuuber of stacks per grain., Note that the model does not specify the number of stacks per grain. + A grain could well consist of oulv one stack (brick)., A grain could well consist of only one stack (brick). + While this model exhibits a far UV rise in extinction. it should be stressed that possible contiuuun contributions to extinction by other carriers are outside the scope of this work.," While this model exhibits a far UV rise in extinction, it should be stressed that possible continuum contributions to extinction by other carriers are outside the scope of this work." + The arguineut developed above hinges upou the grapliene properties., The argument developed above hinges upon the graphene properties. + However. erapliene theory assuies au infinite plane.," However, graphene theory assumes an infinite plane." + Can this be applied to our model eraplitic bricks?, Can this be applied to our model graphitic bricks? + The latter mist be imch sinaller than the average erain size. which is itself lamited to ~300 by the Ravleigh condition for 2175.," The latter must be much smaller than the average grain size, which is itself limited to $\sim300$ by the Rayleigh condition for 2175." +. We have to cuquire if the properties of eraplene still apply at simaller sizes., We have to enquire if the properties of graphene still apply at smaller sizes. + These properties are determined by the interactions between an atom and its neighbours., These properties are determined by the interactions between an atom and its neighbours. + Obviously. these interactions fade away as the distance to the central atom increases.," Obviously, these interactions fade away as the distance to the central atom increases." + Iu order to find the “cut-off distance. we therefore considered successively compact clusters of carbon rugs of mereastug size.," In order to find the “cut-off"" distance, we therefore considered successively compact clusters of carbon rings of increasing size." + With the help ofa conunercial quautuim cheuistry package (EHypereube. Προολο T) their structure was optimized by secking the niuiainua total binding euergx. using the semi-cmpirical ΔΑΤΠΕ method.," With the help of a commercial quantum chemistry package (Hypercube, Hyperchem 7), their structure was optimized by seeking the minimum total binding energy, using the semi-empirical AM1/UHF method." + Figure 3 shows the variation of the binding euergy per atom. ορ. as a function of the nuniber of rings. Ny.," Figure 3 shows the variation of the binding energy per atom, $e_{b}$, as a function of the number of rings, $_{\rm{r}}$." + Bevoud about 10 rings. or SL atoms. the binding cuerey reaches. for all practical purposes. an asviuptotie value of 182 kcal/mol or 8 eV per atom. which is indeed about the eraphite sublimation eucrev.," Beyond about 40 rings, or 84 atoms, the binding energy reaches, for all practical purposes, an asymptotic value of 182 kcal/mol or 8 eV per atom, which is indeed about the graphite sublimation energy." + The correspouding diameter of the structure is about 1.5 nui, The corresponding diameter of the structure is about 1.5 nm. + A similar couclusion was reached by Robertson (1986). on the basis of a simpler Wiieckel caleulation., A similar conclusion was reached by Robertson \cite{rob} on the basis of a simpler Hücckel calculation. + Thus. the," Thus, the" +"all cases but the 2.5Me, Z=0.004 model, where [Ge/Fe] = 0.77.","all cases but the $\Msun$ , $Z=0.004$ model, where [Ge/Fe] = 0.77." +" Models with no '?CC pocket little Ge and Ga, except in the case of the 6.5Mo producedsolar verymetallicity models."," Models with no C pocket produced very little Ge and Ga, except in the case of the $\Msun$ solar metallicity models." +" For these massive AGB models, neutrons are released by efficient activation of the ?NNe neutron source during TPs and the increase of Ge at the tip of the TP-AGB is factor of ~ 1.5 above solar."," For these massive AGB models, neutrons are released by efficient activation of the Ne neutron source during TPs and the increase of Ge at the tip of the TP-AGB is a factor of $\sim\,$ 1.5 above solar." +" In comparison the 5Mo, Z=0.02a model produced little Ge with ([Ge/Fe] = 0.112) or without (0.04) a PMZ."," In comparison the $\Msun$, $Z=0.02$ model produced little Ge with ([Ge/Fe] = 0.112) or without (0.04) a PMZ." +" The 2.5Μ9, Z20.004 model produced the most Ge, partly because efficient TDU results in a large amount of matter dredged from the core into the envelope (see Table 1))."," The $\Msun$, $Z=0.004$ model produced the most Ge, partly because efficient TDU results in a large amount of matter dredged from the core into the envelope (see Table \ref{models}) )." +" Another reason is that the efficiency of the PCC(a,n)600 neutron source does not depend on the initial Z, and that means more neutrons per Fe-seed nuclei are produced at lower metallicity."," Another reason is that the efficiency of the $\alpha,n$ O neutron source does not depend on the initial $Z$, and that means more neutrons per Fe-seed nuclei are produced at lower metallicity." + Table 1 from Goriely&Mowlavi(2000) also shows more Ge in the dredged-up matter with decreasing Z., Table 1 from \citet{goriely00} also shows more Ge in the dredged-up matter with decreasing $Z$. +" Gallinoetal.(1998) Figures 18 and 20 show the s-process enhancement factors in the intershell material cumulatively dredged into the envelope in 2M; models with Z=0.01 and Z=0.0005, respectively."," \citet{gallino98} Figures 18 and 20 show the $s$ -process enhancement factors in the intershell material cumulatively dredged into the envelope in $\Msun$ models with $Z=0.01$ and $Z=0.0005$, respectively." +" The lower Z model clearly shows an increase in the production of the Ge isotopes, with atomic mass &70."," The lower $Z$ model clearly shows an increase in the production of the Ge isotopes, with atomic mass $\approx 70$." +" Our results compare favorably with the 3 Mo Z=0.02 model computed with the FRANEC evolutionary code (Stranieroetal.1997) by Gallinoetal.(1998) with their standard PCC pocket (hereafter: theTorino models), who finds the final [Ge/Fe], [Ga/Fe], [Zr/Fe] and [Ba/Fe] equal to 0.46, 0.43, 1.03 and 0.93, respectively."," Our results compare favorably with the 3 $\Msun$ $Z=0.02$ model computed with the FRANEC evolutionary code \citep{straniero97} by \citet{gallino98} with their standard C pocket (hereafter: the models), who finds the final [Ge/Fe], [Ga/Fe], [Zr/Fe] and [Ba/Fe] equal to 0.46, 0.43, 1.03 and 0.93, respectively." +" The 1.5Mo, Z=0.02 produced values equal to 0.28, 0.29, 0.75 and 0.65, respectively."," The $\Msun$, $Z=0.02$ produced values equal to 0.28, 0.29, 0.75 and 0.65, respectively." +" The 5M; Z=0.02 model produced a final [Ge/Fe]=0.57, higher than our equivalent model, owing to the choice of the Reimers(1975) mass loss (with η= 10) which results in more TPs (48) compared to our computation (24)."," The $\Msun$ $Z=0.02$ model produced a final [Ge/Fe]=0.57, higher than our equivalent model, owing to the choice of the \citet{reimers75} mass loss (with $\eta = 10$ ) which results in more TPs (48) compared to our computation (24)." +" Massive AGB stars have been suggested as the progenitors of Type I bipolar PNe owing to their high He and N/O abundances (Stanghellinietal.2006),, as well as kinematics (Corradi&Schwarz1995)."," Massive AGB stars have been suggested as the progenitors of Type I bipolar PNe owing to their high He and N/O abundances \citep{stanghellini06}, as well as kinematics \citep{corradi95}." +". Sterling&Dinerstein(2005) and Sterling(2006) find a correlation between PNe morphology and s-process overabundances, where elliptical PNe are more enriched than bipolar PNe, which show little or no enhancement."," \citet{sterling05c} and \citet{sterlingThesis} find a correlation between PNe morphology and s-process overabundances, where elliptical PNe are more enriched than bipolar PNe, which show little or no enhancement." +" These observations suggest that Reimers type mass loss is inadequate for modeling massive AGB stars, and formulae with a superwind (such1993) are favored."," These observations suggest that Reimers type mass loss is inadequate for modeling massive AGB stars, and formulae with a superwind \citep[such as][]{vw93} are favored." + None of the AGB models lost all of their envelopes before the computation finished., None of the AGB models lost all of their envelopes before the computation finished. +" That is, all of the models were near the tip of the AGB but had not proceeded to the post-AGB phase."," That is, all of the models were near the tip of the AGB but had not proceeded to the post-AGB phase." +" Some of these models could in principle experience further TPs and TDUs, and we refer to these asTPs."," Some of these models could in principle experience further TPs and TDUs, and we refer to these as." +" The amount of Ge expected after the i'"" TP can be estimated according to X!=(MLIX!4+AMge)/Mi,,, where AMge=AAMiutershe is the mass of Ge dredged into the envelope, A is the TDU efficiency and AMintershen is the mass of Ge in the intershell."," The amount of Ge expected after the $i^{\rm th}$ TP can be estimated according to $X^{i} = (M_{\rm env}^{i-1}X^{i-1} + \Delta M_{\rm Ge})/ M_{\rm env}^{i}$, where $\Delta M_{\rm Ge} = \lambda \Delta M_{\rm intershell}$ is the mass of Ge dredged into the envelope, $\lambda$ is the TDU efficiency and $\Delta M_{\rm intershell}$ is the mass of Ge in the intershell." + In Figure |we show the intershell abundances for selected Ge isotopes for two models., In Figure \ref{intershell} we show the intershell abundances for selected Ge isotopes for two models. +" A Ge pocket can be seen in both cases, and although this will be diluted by one order of magnitude by intershell convection, the post-pulse abundances are still enhanced compared to solar."," A Ge pocket can be seen in both cases, and although this will be diluted by one order of magnitude by intershell convection, the post-pulse abundances are still enhanced compared to solar." +"Although our arguments are analytical. we [find it useful to illustrate our points with numerical simulations that were recently. presented by Cha&Navakshin(2010).. who simulated fragmentation and. evolution of a massive. Al,=OAAL.. eas disc around a parent star of mass Al,=0.6M..","Although our arguments are analytical, we find it useful to illustrate our points with numerical simulations that were recently presented by \cite{ChaNayakshin10}, who simulated fragmentation and evolution of a massive, $M_d = 0.4 \msun$, gas disc around a parent star of mass $M_* = 0.6 +\msun$." + The eas component was modelled with a 3D SPILL code utilising an analytical approximation to the radiative cooling. whereas the dust. was treated as a second Iluid under the inlluence of gravity and the drag force from the eas.," The gas component was modelled with a 3D SPH code utilising an analytical approximation to the radiative cooling, whereas the dust was treated as a second fluid under the influence of gravity and the drag force from the gas." + Phe grains were allowed to grow via a stick-and-hit mechanism saturated at a maximum impact velocity of 3 m i, The grains were allowed to grow via a stick-and-hit mechanism saturated at a maximum impact velocity of $3$ m $^{-1}$. + As expected. the dise fragmented. on a dozen or so gascous clumps with masses between 5 and 20 Al; at a distance of 70 to 150 AU.," As expected, the disc fragmented on a dozen or so gaseous clumps with masses between 5 and 20 $M_J$ at a distance of $\sim 70$ to $\sim$ 150 AU." + Some of the clumps merge with one another. others interact strongly gravitationally.," Some of the clumps merge with one another, others interact strongly gravitationally." + Several clumps make it into the inner few tens of AU., Several clumps make it into the inner few tens of AU. + The less dense ones are destroved.by tidal shear releasing their dust content at 15 AU., The less dense ones are destroyedby tidal shear releasing their dust content at $\sim 15$ AU. + One particular embryo was dense enough to spiral in closer before being completely destroved., One particular embryo was dense enough to spiral in closer before being completely destroyed. + ὃν virtue of its higher density the embryo also contained larger dust grains and a gravitationallv collapsed dust core of mass 7.5Mq.," By virtue of its higher density the embryo also contained larger dust grains and a gravitationally collapsed dust core of mass $\sim 7.5 +\mearth$." + The vsuper-Earth” core was deposited in a low cecentricity orbit with the semi-major axis of zzS AU., The “super-Earth” core was deposited in a low eccentricity orbit with the semi-major axis of $\approx 8$ AU. + Figure 1. shows the face-on eas column density map centred on a typical uncisturbed embryo at a large distance from the star at time /=4880 vears2010)., Figure \ref{fig:embryo_disc} shows the face-on gas column density map centred on a typical undisturbed embryo at a large distance from the star at time $t=4880$ years. +. The collection of evan dots in the centre of the figure is the dust. grain particles with size greater than LO cm., The collection of cyan dots in the centre of the figure is the dust grain particles with size greater than 10 cm. + The grain concentration is not vet high enough to vield a collapsed solid core at the time of the snapshot., The grain concentration is not yet high enough to yield a collapsed solid core at the time of the snapshot. + Black arrows show the velocity field of the gas with respect to the velocity of the densest part of the embryo., Black arrows show the velocity field of the gas with respect to the velocity of the densest part of the embryo. + The spin direction is the same as that of the parent disc around the star. save for offset by about 5°.," The spin direction is the same as that of the parent disc around the star, save for offset by about $5^\circ$." + The origin of prograde rotation of the embryo may be in the shape of streamlines on the “horse-shoe orbits” of gas near massive planets (seeLubowetal.1999)., The origin of prograde rotation of the embryo may be in the shape of streamlines on the “horse-shoe orbits” of gas near massive planets \citep[see][]{LubowEtal99}. +. Phe magnitude of velocity vectors in the figure first increase with distance from the centre (to the distance of a few AW). and then stay roughly constant or perhaps decrease slightly further out.," The magnitude of velocity vectors in the figure first increase with distance from the centre (to the distance of a few AU), and then stay roughly constant or perhaps decrease slightly further out." + A sulliciently viscous gaseous body may be expected to rotate at a constant angular frecuencey. c.g.. as à solid body.," A sufficiently viscous gaseous body may be expected to rotate at a constant angular frequency, e.g., as a solid body." + Lor a constant density embryo model (Navakshin2010c).. the maximum break-up angular frequency. of rotation is where po is the density of the embryo.," For a constant density embryo model \citep{Nayakshin10a}, the maximum break-up angular frequency of rotation is where $\rho_0$ is the density of the embryo." + We define the rotational break-up velocity of the embryo as where r=Lag ds the projected. distance to the embryos centre., We define the rotational break-up velocity of the embryo as where $r = \sqrt{x^2 + y^2}$ is the projected distance to the embryo's centre. + To analyse the rotation pattern of embryo from figure 1. further. we normalise the velocity field on Copes taking po to be the mean eas density in the embryo.," To analyse the rotation pattern of embryo from figure \ref{fig:embryo_disc} further, we normalise the velocity field on $v_{\rm + break}$, taking $\rho_0$ to be the mean gas density in the embryo." + The left panel of Figure 2. shows the embryo in the same face-on projection as in figure 1.. whereas the right. panel of the figure shows the projection of the embryo along the gy-direction (e.g.. in the plane of the disc).," The left panel of Figure \ref{fig:rotating_embryo} shows the embryo in the same face-on projection as in figure \ref{fig:embryo_disc}, whereas the right panel of the figure shows the projection of the embryo along the $y$ -direction (e.g., in the plane of the disc)." + Velocity vectors normalised on Phreak ave also plotxd., Velocity vectors normalised on $v_{\rm break}$ are also plotted. + ]t is clear from Fig., It is clear from Fig. + 2 that the embryo spins nearly as a solid body in the central few AU. e.g. with a constant angular frequenev.," 2 that the embryo spins nearly as a solid body in the central few AU, e.g., with a constant angular frequency." + Furthermore. the right panel shows that the rotation is significant enough to deform the embryo's shape from a spherical shape to that of an oblate spheroid Iattened. along the spin vector.," Furthermore, the right panel shows that the rotation is significant enough to deform the embryo's shape from a spherical shape to that of an oblate spheroid flattened along the spin vector." + The amplitude of rotation Q is close to 0.1., The amplitude of rotation $\Omega$ is close to $0.1\Omega_{\rm break}$. + Our final example of rotating embryos found in simulations is shown in Figure 3. which shows the facc-on projection of an embryo closest to the star in the left panel of ligure 4 o£ Cha&Navakshin(2010)., Our final example of rotating embryos found in simulations is shown in Figure \ref{fig:disturbed_embryo} which shows the face-on projection of an embryo closest to the star in the left panel of figure 4 of \cite{ChaNayakshin10}. +. Phe embryo is within slightly less than 40 AU from the parent star (located south-west in the figure) ancl has just. interacted with another embryo outside of the figure ancl located north-west., The embryo is within slightly less than 40 AU from the parent star (located south-west in the figure) and has just interacted with another embryo outside of the figure and located north-west. + This is an example of an embryo significantly. perturbed by the tidal field of the star and other interactions in the disc., This is an example of an embryo significantly perturbed by the tidal field of the star and other interactions in the disc. + The central dot in the left panel of the figure is the super-Larth solid. core (we do not show grains smaller than 100 cm in this figure)., The central dot in the left panel of the figure is the super-Earth solid core (we do not show grains smaller than 100 cm in this figure). + Phe right panel of figure 3. shows the central part of this embryo. centred on the solid core.," The right panel of figure \ref{fig:disturbed_embryo} shows the central part of this embryo, centred on the solid core." + Note that the rotation pattern of the gas component is ollset by about 0.15 AU from the solid core in this case., Note that the rotation pattern of the gas component is offset by about $0.15$ AU from the solid core in this case. + The spin axis of this embryo is more strongly inclined away [rom the disc axis of svmmetry: the inclination angle for the embryo is slightly larger than 307., The spin axis of this embryo is more strongly inclined away from the disc axis of symmetry; the inclination angle for the embryo is slightly larger than $30^\circ$ . + This is very likely to be the result of at least two interactions that the embryo have had earlier., This is very likely to be the result of at least two interactions that the embryo have had earlier. + In particular. the embryo had merged with," In particular, the embryo had merged with" +irradiation models.,irradiation models. + The current parameters of the system (2). are based on the SuperWASP discovery photometry and a partial transit ight curve taken with RISE., The current parameters of the system \citep{Bouchy2010} are based on the SuperWASP discovery photometry and a partial transit light curve taken with RISE. + However. the lack of a high precision complete transit light curve required the assumption of the main sequence mass-radius relation which tends to bias the estimate of he inclination.," However, the lack of a high precision complete transit light curve required the assumption of the main sequence mass-radius relation which tends to bias the estimate of the inclination." + Furthermore. the age derived for WASP-21 is longer han the main-sequence life time of a 1.01M... star.," Furthermore, the age derived for WASP-21 is longer than the main-sequence life time of a $1.01 \Msun$ star." + This suggests hat WASP-21 could be evolved which would invalidate the main-sequence assumption and bias the parameters of the system., This suggests that WASP-21 could be evolved which would invalidate the main-sequence assumption and bias the parameters of the system. + To test he main-sequence assumption we obtained further observations of WASP-2l., To test the main-sequence assumption we obtained further observations of WASP-21. + In this paper. we present transit observations of WASP-21b with RISE including a full transit light curve.," In this paper, we present transit observations of WASP-21b with RISE including a full transit light curve." + Our high precision light curves allow us derive the planetary and stellar radii without assuming the main-sequence mass-radius relation for the host star., Our high precision light curves allow us derive the planetary and stellar radii without assuming the main-sequence mass-radius relation for the host star. + We describe our observations in Section 2., We describe our observations in Section 2. + In Section 3. we discuss our transit model and present the updated parameters of the system in Section +.," In Section 3, we discuss our transit model and present the updated parameters of the system in Section 4." + Finally. we discuss and summarise our results in Section 5.," Finally, we discuss and summarise our results in Section 5." + WASP-21b was observed with RISE (?). mounted at the auxiliary Cassegrain focus of the robotic 2.0m Liverpool Telescope on La Palma. Canary Islands.," WASP-21b was observed with RISE \citep{rise2008} mounted at the auxiliary Cassegrain focus of the robotic 2.0m Liverpool Telescope on La Palma, Canary Islands." + This is a focal reducer system utilizing a frame transfer e2v CCD sensor., This is a focal reducer system utilizing a frame transfer e2v CCD sensor. + The detector has a pixel scale of 0.54 aresec/pixel that results in a 94 = 9.4 aremin field of view., The detector has a pixel scale of 0.54 arcsec/pixel that results in a 9.4 $\times$ 9.4 arcmin field of view. +" RISE has a wideband filter covering ~ 500—700 nm which corresponds approximately to VR. The instrument has no moving parts,"," RISE has a wideband filter covering $\sim 500$ $700\,$ nm which corresponds approximately to V+R. The instrument has no moving parts." + The Liverpool Telescope has a library of flat tields which are taken manually every couple of months., The Liverpool Telescope has a library of flat fields which are taken manually every couple of months. + RISE flats are taken during twilight at different rotator angles so that there is a uniform illumination of the CCD., RISE flats are taken during twilight at different rotator angles so that there is a uniform illumination of the CCD. + The exposure times of the images are automatically adjusted so that the peak counts in the individual flats are below the non-linearity limit of the CCD at 45000 counts., The exposure times of the images are automatically adjusted so that the peak counts in the individual flats are below the non-linearity limit of the CCD at 45000 counts. + Typically. the individual flats have between 20000 and 40000 counts.," Typically, the individual flats have between 20000 and 40000 counts." + Due to the fast readout. we can obtain approximately 200 flat frames in a run. these are combined to create a master flat.," Due to the fast readout, we can obtain approximately 200 flat frames in a run, these are combined to create a master flat." + For each observation run we use the master flat that is closest in time. although we note that these are very stable.," For each observation run we use the master flat that is closest in time, although we note that these are very stable." + On 2009-09-09 we obtained a full transit of WASP-2, On 2009-09-09 we obtained a full transit of WASP-21b. + A total of 6581 exposures in the 2 binning mode with an exposure1b. time of 2.7 seconds were taken., A total of 6581 exposures in the $2 \times 2$ binning mode with an exposure time of 2.7 seconds were taken. +" The telescope was defocussed by -1.2mm which resulted in à FWHM of ~11"".", The telescope was defocussed by -1.2mm which resulted in a FWHM of $\sim 11$. +. For defocussed photometry. the star profiles are not Gaussian.," For defocussed photometry, the star profiles are not Gaussian." + However. we found that. in our case. a Gaussian provided a good fit to the wings of the star profile. and could be use as a rough estimate of the profile width.," However, we found that, in our case, a Gaussian provided a good fit to the wings of the star profile, and could be use as a rough estimate of the profile width." + Therefore. we estimated the FHWM in the usual way by cross-correlating a Gaussian profile with that of the star.," Therefore, we estimated the FHWM in the usual way by cross-correlating a Gaussian profile with that of the star." + A second full transit observation of WASP-21b was attempted on 2010-11-24., A second full transit observation of WASP-21b was attempted on 2010-11-24. + In this case. deteriorating weather terminated the observations shortly after the mid-transit. by which time. 4008 integrations had been obtained.," In this case, deteriorating weather terminated the observations shortly after the mid-transit, by which time, 4008 integrations had been obtained." +" During these observations. the FWHM was 12.5""."," During these observations, the FWHM was $\sim 12.5$." +. Both data-sets were reduced using the ULTRACAM pipeline (?) which is optimized for time-series photometry., Both data-sets were reduced using the ULTRACAM pipeline \citep{Ultracam} which is optimized for time-series photometry. + Initially. we bias subtracted the data while we investigated systematic effects that were introduced by the flat fielding process.," Initially, we bias subtracted the data while we investigated systematic effects that were introduced by the flat fielding process." + We performed differential photometry relative to five comparison stars in the field. confirmed to be non variable. and we sampled different aperture radii and ehose the aperture radius that minimised the noise.," We performed differential photometry relative to five comparison stars in the field, confirmed to be non variable, and we sampled different aperture radii and chose the aperture radius that minimised the noise." +" For the first night. we used a 22 pixel aperture radius (~12"")). and for the second transit. a 32 pixel aperture radius (~17""))."," For the first night, we used a 22 pixel aperture radius $\sim +12$ ), and for the second transit, a 32 pixel aperture radius $\sim 17$ )." + The photometric errors include the shot noise. readout and background noises.," The photometric errors include the shot noise, readout and background noises." + We also included in our analysis. the previously published egress of WASP-21 taken with RISE (?)..," We also included in our analysis, the previously published egress of WASP-21 taken with RISE \citep{Bouchy2010}." + For consistency. we reduced the original data using the same method as for the other two observations.," For consistency, we re-reduced the original data using the same method as for the other two observations." + On 2008-10-07. 2220 exposures of sec duration were taken.," On 2008-10-07, 2220 exposures of 5 sec duration were taken." +" We estimated a FWHM of ~2.7"".. 5therefore. the levelof defocussing was lower than in our observations."," We estimated a FWHM of $\sim 2.7$, therefore, the levelof defocussing was lower than in our observations." +" The best aperture radius was found to be 15 pixel (~ 8"")).", The best aperture radius was found to be 15 pixel $\sim 8$ ). + Our results agree well with the previous published light curve., Our results agree well with the previous published light curve. + The final high precision photometrie light curves are shown in Figure | along with the best-tit model described in Section 3.3.., The final high precision photometric light curves are shown in Figure \ref{photolc} along with the best-fit model described in Section \ref{model}. + We overplot the model residuals and the estimated uncertainties which are discussed in Section 3.2.., We overplot the model residuals and the estimated uncertainties which are discussed in Section \ref{errors}. + As mentioned above. defocusing is commonly used in exoplanet transit observations.," As mentioned above, defocusing is commonly used in exoplanet transit observations." + ?. caleulated the optimum exposure time for the DFOSC imager mounted on the [.54m Danish Telescope., \citet{Southworth2009} calculated the optimum exposure time for the DFOSC imager mounted on the 1.54m Danish Telescope. + We follow the same procedure and apply it to RISE mounted on the Liverpool Telescope and hence. we account for readout noise. photon. background and scintillation noise.," We follow the same procedure and apply it to RISE mounted on the Liverpool Telescope and hence, we account for readout noise, photon, background and scintillation noise." + Similar to ?.. we do not include flat-fielding noise. assuming that the profile position is stable.," Similar to \citet{Southworth2009}, , we do not include flat-fielding noise, assuming that the profile position is stable." +SED modeling is difficult.,SED modeling is difficult. + Here. AKARI’s mid-IR bands are advantageous in directly observing redshifted restframe 8/:m flux in one of the AKARFSs filters. leading to more reliable measurement of 8j/m LFs without uncertainty from the SED modeling.," Here, AKARI's mid-IR bands are advantageous in directly observing redshifted restframe $\mu$ m flux in one of the AKARI's filters, leading to more reliable measurement of $\mu$ m LFs without uncertainty from the SED modeling." + Pérez-Gonzálezetal.(2005) investigated the evolution of restframe 12j/m LFs using the Spitzer CDF-S and HDF-N data., \citet{2005ApJ...630...82P} investigated the evolution of restframe $\mu$ m LFs using the Spitzer CDF-S and HDF-N data. + We overplot their results in similar redshift ranges as the cyan dot-dashed lines in Fig.8.., We overplot their results in similar redshift ranges as the cyan dot-dashed lines in \ref{fig:12umlf}. + Considering both LFs have significant error bars. these LFs are in good agreement with our ΕΕ». and show significant evolution in the 12;j/m LFs compared with the :zO {μην LF by Rush.Malkan.&Spinoglio(1993).," Considering both LFs have significant error bars, these LFs are in good agreement with our LFs, and show significant evolution in the $\mu$ m LFs compared with the $z$ =0 $\mu$ m LF by \citet{1993ApJS...89....1R}." +. The agreement 15 in a stark contrast to the comparison in 8j/im LFs in 52?.. where we suffered from differnces of a factor of several.," The agreement is in a stark contrast to the comparison in $\mu$ m LFs in $\S$ \ref{sec:8umLF_comp}, where we suffered from differnces of a factor of several." +" A possible reason for this 1s that {μην is sufficiently redder than 8j/m. that it is easier to be extrapolated from 55, in case of the Spitzer work."," A possible reason for this is that $\mu$ m is sufficiently redder than $\mu$ m, that it is easier to be extrapolated from $S_{24\mu m}$ in case of the Spitzer work." + In fact. at «Ξ1. both the Spitzer 247m band and AKARI L21 observe the restframe 12/:m directly.," In fact, at $z$ =1, both the Spitzer $\mu$ m band and AKARI $L24$ observe the restframe $\mu$ m directly." + In additon. mid-IR SEDs around 12;:m are flatter than at 847m. where PAH emissions are prominent.," In additon, mid-IR SEDs around $\mu$ m are flatter than at $\mu$ m, where PAH emissions are prominent." + Therefore. SED models can predict the flux more accurately.," Therefore, SED models can predict the flux more accurately." + In fact. this is part of the reason why Pérez-Gonzálezetal.(2005) chose to investigate 12j/m LFs.," In fact, this is part of the reason why \citet{2005ApJ...630...82P} chose to investigate $\mu$ m LFs." +" Pérez-Gonzalezetal.(2005) used Chary&Elbaz (2001)""7s SED to extrapolate μμ and yet. they agree well with AKARI results. which are derived from filters that cover the restframe 12;m. However. in other words. the discrepancy in 8j/m LFs highlights the fact that the SED models are perhaps still imperfect in the 8y/m. wavelength range. and thus. MIR-spectroscopic data that covers wider luminosity and redshift ranges will be necessary to refine SED models in the mid-IR."," \citet{2005ApJ...630...82P} used \citet{2001ApJ...556..562C}' 's SED to extrapolate $S_{24\mu m}$ , and yet, they agree well with AKARI results, which are derived from filters that cover the restframe $\mu$ m. However, in other words, the discrepancy in $\mu$ m LFs highlights the fact that the SED models are perhaps still imperfect in the $\mu$ m wavelength range, and thus, MIR-spectroscopic data that covers wider luminosity and redshift ranges will be necessary to refine SED models in the mid-IR." + AKARI’s mid-IR slitless spectroscopy survey (Wada.2008) may help in this regard., AKARI's mid-IR slitless spectroscopy survey \citep{2008cosp...37.3370W} may help in this regard. + Lastly. we compare our TIR. LPs (Fig.14)) with those in the literature.," Lastly, we compare our TIR LFs \ref{fig:TIR_LF}) ) with those in the literature." + Although the TIR. LFs can also be obtained by converting 8j/m LFs or 12j/m LFs. we already compared our results in these wavelengths in the last subsections.," Although the TIR LFs can also be obtained by converting $\mu$ m LFs or $\mu$ m LFs, we already compared our results in these wavelengths in the last subsections." + Here. wecompare our TIR LFs to LeFlochetal.(2005) and Magnellietal. (2009).. LeF," Here, wecompare our TIR LFs to \citet{2005ApJ...632..169L} and \citet{2009A&A...496...57M}." +loc'hetal.(2005) obtained TIR LFs using the Spitzer CDF-S data., \citet{2005ApJ...632..169L} obtained TIR LFs using the Spitzer CDF-S data. + They have used the best-fit SED among various templates to estimate τιν., They have used the best-fit SED among various templates to estimate $L_{TIR}$. + We overplot their total LFs in Fig.14 with the cyan dash-dotted lines., We overplot their total LFs in \ref{fig:TIR_LF} with the cyan dash-dotted lines. + Only LFs that overlap with our redshit ranges are shown., Only LFs that overlap with our redshit ranges are shown. + The agreement at 0.3.