ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Iu Fig., In Fig.3 1 we report the PDS aud MECS spectra obtained by sumauing tle spectra of the two observations., 1 we report the PDS and MECS spectra obtained by summing the spectra of the two observations.4 The PDS background subtracted combiued count rate is .1514-0.011 counts st in the 15-10() keV energy rauge at the confidence level of L1o.," The PDS background subtracted combined count rate is $\pm$ 0.011 counts $^{-1}$ in the 15-100 keV energy range at the confidence level of $\sim514\sigma$."6 The PDS data of the first observation has been reanalyzed using tle same procedure utilized for the secoud longer observation., The PDS data of the first observation has been reanalyzed using the same procedure utilized for the second longer observation.7 The MECS spectrum is iu he range ~2-10 keV obtained from a circular region of 8’ corresponding to about 0.5 Mpc cente'ed ou the primary emission peak., The MECS spectrum is in the range $\sim$ 2-10 keV obtained from a circular region of $'$ corresponding to about 0.5 Mpc centered on the primary emission peak.8 The PSPC radial profile indicates that ~TO% of the otal cluster eiission falls within this radius (see Fusco-Femiano 2000 for details τόσαΟΙ1& MECS datareductiou. the cross-correlation between MECS aud PDS and results for ouly OBS1).," The PSPC radial profile indicates that $\sim 70\%$ of the total cluster emission falls within this radius (see Fusco-Femiano 2000 for details regarding MECS data reduction, the cross-correlation between MECS and PDS and results for only OBS1)."9 The total exdose time 380.1 ks., The total exposure time is 386.4 ks.10 The spectral analysis of the NECS data alone gives a teumperature of kT = 0.1011! iskeV using the MEKAL code on the XSPEC package. while the sinilaneous fit to tre MECSS and PDS data gives κ...1T keV (the MECS aud PDS normalizatious are treated as ree paraiueters).," The spectral analysis of the MECS data alone gives a temperature of kT = $^{+0.19}_{-0.14}$ keV using the MEKAL code on the XSPEC package, while the simultaneous fit to the MECS and PDS data gives $\pm$ 0.17 keV (the MECS and PDS normalizations are treated as free parameters)."11 This value of the temperature is consistent. with the meastwements of (ni(232-3:T.TO keV: Hatsukade LO89) with a fied of view comparable to that of the PDS. MPC (6.7-8.1 keV: David 1993). CIS (6.78-7.14 keV: Heuriksen 1999) aud with he more recent joint analysis of aud (PCA HENTE) data (7.664 0.12 keV: Rephaeli Gruber 20()3).," This value of the temperature is consistent with the measurements of (7.32-7.70 keV; Hatsukade 1989) with a field of view comparable to that of the PDS, MPC (6.7-8.1 keV; David 1993), GIS (6.78-7.44 keV; Henriksen 1999) and with the more recent joint analysis of and (PCA HEXTE) data $\pm$ 0.12 keV; Rephaeli Gruber 2003)."12 las reportec several emission regions giving evidence for the oesenuce of a mereer event (Sun 20un., has reported several emission regions giving evidence for the presence of a merger event (Sun 2002).13" ΤΙese detections slow temperature variaious with a nean value of 6.70.2 keV in the central S. ""mquare.", These detections show temperature variations with a mean value of $\pm$ 0.2 keV in the central $8'.3$ square.14 Also the flux of ~5.1x1011erecmn?s1 in the 2-1Q keV energy range measured by is cousisteut with previous observations., Also the flux of $\sim 5.4\times 10^{-11}\erg$ in the 2-10 keV energy range measured by is consistent with previous observations.15 The iron abundauce is 0.010.037 in agreement with he results (Markeviteh Vikhlinin 1997).," The iron abundance is $^{+0.01}_{-0.03}$, in agreement with the results (Markevitch Vikhlinin 1997)."16 The presence of au excess with respect to the thermal emission in the spectrum of A2256 is evidenced a) by the fit to the PDS data aloie in the 15-80 keV energy rauge with a thermal component that determines a temperalure of i5 keV well above the average gas temperature eiven by in the interval7.2-7.7() keV (David 1993): b) by the fit to the PDS data alone with a bremsstrahluug component at the fixed temperature of 7.6 keV. derived by the NECS," The presence of an excess with respect to the thermal emission in the spectrum of A2256 is evidenced a) by the fit to the PDS data alone in the 15–80 keV energy range with a thermal component that determines a temperature of $^{+4.3}_{-3.2}$ keV well above the average gas temperature given by in the interval 7.32-7.70 keV (David 1993); b) by the fit to the PDS data alone with a bremsstrahlung component at the fixed temperature of 7.6 keV, derived by the MECS"17principal effect of increasing N is to reduce the amplitude of initial density fluctuations.,principal effect of increasing $N$ is to reduce the amplitude of initial density fluctuations.18" The swing-amplifier quickly polarizes the disc, creating trailing spiral responses having an amplitude proportional to the input noise signal T"," The swing-amplifier quickly polarizes the disc, creating trailing spiral responses having an amplitude proportional to the input noise signal \citep{TK91}."19"he larger the particle number the smaller the initial ∙∙amplitude, and it is clear from Fig."," The larger the particle number the smaller the initial amplitude, and it is clear from Fig."20 that the swing-amplified noise has too small an amplitude to cause heating at first when N= 20M. We do not expect global instabilities in a smooth disc for m>2 because small-amplitude disturbances at most reasonable pattern speeds will be damped at an citepMark74.., \ref{Qtplot} that the swing-amplified noise has too small an amplitude to cause heating at first when $N=20$ M. We do not expect global instabilities in a smooth disc for $m>2$ because small-amplitude disturbances at most reasonable pattern speeds will be damped at an \\citep{Mark74}.21" Thus the later increase in the spiral amplitude must be a non-linear effect, perhaps related to the recurrent instability cycle reported by ∙∙"," Thus the later increase in the spiral amplitude must be a non-linear effect, perhaps related to the recurrent instability cycle reported by \cite{SL89}."22" Whatever the cause, the similar heating rate and final Q value is consistent with spiral amplitudes that are independent of N at later times."," Whatever the cause, the similar heating rate and final $Q$ value is consistent with spiral amplitudes that are independent of $N$ at later times."23 The origin of multi-arm spiral waves will be followed up in future work., The origin of multi-arm spiral waves will be followed up in future work.24 Fig., Fig.25" shows that even with N= 20M, heating begins after just [5]15 disc rotations."," \ref{Qtplot} shows that even with $N=20$ M, heating begins after just 15 disc rotations."26 This should be contrasted with the case where forces were restricted to m=2 where no visible bi-symmetric features appeared in 40 rotations even with the ten times larger seed amplitude implied by 100 times fewer particles., This should be contrasted with the case where forces were restricted to $m=2$ where no visible bi-symmetric features appeared in 40 rotations even with the ten times larger seed amplitude implied by 100 times fewer particles.27" It should be further noted that real spiral galaxy discs have large star clusters and giant molecular clouds that imply much larger seed density fluctuations than arise from N= 20M randomly-placed, equal-mass particles."," It should be further noted that real spiral galaxy discs have large star clusters and giant molecular clouds that imply much larger seed density fluctuations than arise from $N=20$ M randomly-placed, equal-mass particles."28" While these simulations explicitly test just one of the many models presented in BLLT, all the cases that they regard of most interest have strongly sub-maximal discs in order that swing amplification is ineffective for m=2; this aspect is essential so that the model possess only slowly-growing, tightly-wrapped, bi-symmetric spiral modes."," While these simulations explicitly test just one of the many models presented in BLLT, all the cases that they regard of most interest have strongly sub-maximal discs in order that swing amplification is ineffective for $m=2$; this aspect is essential so that the model possess only slowly-growing, tightly-wrapped, bi-symmetric spiral modes."29" However, the vigour of the swing-amplifier for m>2 makes it inevitable that every one of their galaxy models with a low-mass disk will be subject to stronger activity due to disturbance forces with m>2, which will quickly heat the outer disc and destroy the conditions they require, as just demonstrated."," However, the vigour of the swing-amplifier for $m>2$ makes it inevitable that every one of their galaxy models with a low-mass disk will be subject to stronger activity due to disturbance forces with $m>2$, which will quickly heat the outer disc and destroy the conditions they require, as just demonstrated."30 Thus the “basic state” invoked by BLLT for the modes they favour to account for bi-symmetric spiral patterns could not survive in real discs that permit disturbances of all sectoral harmonics., Thus the “basic state” invoked by BLLT for the modes they favour to account for bi-symmetric spiral patterns could not survive in real discs that permit disturbances of all sectoral harmonics.31" As this conclusion depends largely on the results from simulations, one must worry whether they can be trusted."," As this conclusion depends largely on the results from simulations, one must worry whether they can be trusted."32 The principal source of concern is that the origin of the multi-arm patterns that heat the disc remains obscure., The principal source of concern is that the origin of the multi-arm patterns that heat the disc remains obscure.33" Simulations of this kind over many years (e.g. have manifested recurrent multi-arm spiral patterns, and the behaviour has not changed as numerical quality has risen and the codes have passed many tests."," Simulations of this kind over many years \citep[\eg][]{SC84,Fuji10} have manifested recurrent multi-arm spiral patterns, and the behaviour has not changed as numerical quality has risen and the codes have passed many tests."34" However, the possibility that the behaviour could result from some artefact in the simulations cannot be excluded altogether until a satisfactory explanation is provided."," However, the possibility that the behaviour could result from some artefact in the simulations cannot be excluded altogether until a satisfactory explanation is provided."35" Note that to doubt the result on these grounds calls into question all simulations of isolated discs over the past 40 years, as well as those that model the formation of disc galaxies."," Note that to doubt the result on these grounds calls into question all simulations of isolated discs over the past 40 years, as well as those that model the formation of disc galaxies."36" Other possible criticisms, such as the simulations could be unreliable because of gravity softening, particle noise, or the restriction to 2D, are more readily rebutted."," Other possible criticisms, such as the simulations could be unreliable because of gravity softening, particle noise, or the restriction to 2D, are more readily rebutted."37" First, the very same code has been shown to reproduce modes predicted from linear stability analyses of other models, as cited above."," First, the very same code has been shown to reproduce modes predicted from linear stability analyses of other models, as cited above."38" Also, Plummer softening in simulations with particles confined to aplane provides a reasonable allowance for finite disc thickness and anyway the same behaviour persists in simulations of discs with finite thickness si"," Also, Plummer softening in simulations with particles confined to aplane provides a reasonable allowance for finite disc thickness and anyway the same behaviour persists in simulations of discs with finite thickness \citep{Rosk08,Fuji10}."39"nce the only variation in the behaviourFurther, as N is increased 100-fold is an increasing delay due to a decreasing seed amplitude, with no other qualitative differences, an argument that simulations cannot be trusted because N is too small is somewhat threadbare."," Further, since the only variation in the behaviour as $N$ is increased 100-fold is an increasing delay due to a decreasing seed amplitude, with no other qualitative differences, an argument that simulations cannot be trusted because $N$ is too small is somewhat threadbare."40 One might also worry that the stellar dynamical realization I have created differs from the model that BLLT analyzed in the hydrodynamic approximation — essentially I have replaced pressure in their hydrodynamic calculations with velocity spreads; a more direct test would require a prediction of a slowly-growing spiral in a stellar-dynamical model., One might also worry that the stellar dynamical realization I have created differs from the model that BLLT analyzed in the hydrodynamic approximation – essentially I have replaced pressure in their hydrodynamic calculations with velocity spreads; a more direct test would require a prediction of a slowly-growing spiral in a stellar-dynamical model.41" However, it is hard to see why this minor difference should matter, especially in this case where the dispersion is a small fraction of the orbit speed almost everywhere; the exception is at the centre where Q is so large that the disc is (by design) dynamically inert."," However, it is hard to see why this minor difference should matter, especially in this case where the dispersion is a small fraction of the orbit speed almost everywhere; the exception is at the centre where $Q$ is so large that the disc is (by design) dynamically inert."42" The simulations here have not, of course, made any allowance for the influence of the gas component, whichcan offset the heating effects from transient spiral patterns to some extent."," The simulations here have not, of course, made any allowance for the influence of the gas component, whichcan offset the heating effects from transient spiral patterns to some extent."43" However, found that simulations that included a very crude form of cooling still settled to 1.5SQ<2."," However, \cite{SC84}44 found that simulations that included a very crude form of cooling still settled to $1.5 \la Q \la 2$."45" Short-lived recurrent spiral patterns have developed spontaneously in simulations of isolated galaxies, from the first studies by modern simulations that include more [Agertz,sophisticatedTeyssier &physicalMoore processes (e.g.[RosarefaL00S) 2010).."," Short-lived recurrent spiral patterns have developed spontaneously in simulations of isolated galaxies, from the first studies by \cite{MPQ70} and \cite{HB74}, , right through to modern simulations that include more sophisticated physical processes \citep[\eg][]{Rosk08,ATM10}. ."46 Claims of long-lived spiral waves, Claims of long-lived spiral waves47»hotometric bin. lo test the accuracy in this determination of Ας) we have selected: all those galaxies in our sample that are also included in the 2SLAQ. spectroscopic (~6000 objects) and computed their distribution of true redshifts as well as N(z) according to Ίσα. (43).,"photometric bin, To test the accuracy in this determination of $N(z)$ we have selected all those galaxies in our sample that are also included in the 2SLAQ spectroscopic $\sim 6000$ objects) and computed their distribution of true redshifts as well as N(z) according to Eq. \ref{eq:Nzestimator}) )."48 These two distributions are remarkably. similar as shown in Fig. 6..., These two distributions are remarkably similar as shown in Fig. \ref{fig:dndzPDFvs2SLAQ}.49 A Gaussian fit to each of them shows that their peak dillers by less than X and their width by less than 0%2°., A Gaussian fit to each of them shows that their peak differs by less than $1\%$ and their width by less than $9\%$.50") ""phis dillerence is in perfect agreement with the intrinsic scatter in true redshift distributions obtained from dillerent. photo-z codes (e.g. see Table AT in 2))).", This difference is in perfect agreement with the intrinsic scatter in true redshift distributions obtained from different photo-z codes (e.g. see Table A1 in \cite{2011MNRAS.412.1669T}) ).51 Notice that we can not use 25LAQ to estimate Ας) for our complete catalog since our LAG selection is dillerent from that in 25LAQ (in particular the magnitude cuts)., Notice that we can not use 2SLAQ to estimate $N(z)$ for our complete catalog since our LRG selection is different from that in 2SLAQ (in particular the magnitude cuts).52 Nonetheless the previous study shows the degree of unknown in the red shift distribution., Nonetheless the previous study shows the degree of unknown in the red shift distribution.53 Hence we will use Eq. (4)), Hence we will use Eq. \ref{eq:Nzestimator}) )54 to estimate IN(2) for our red shift bins and will cliscuss in Sec., to estimate $N(z)$ for our red shift bins and will discuss in Sec.55 4.3. how our results vary when the width and/or peak change by 9% and 1% respectively., \ref{sec:systematics} how our results vary when the width and/or peak change by $9\%$ and $1\%$ respectively.56 In this wav. our selected. sample of LRGs have a distribution in true red shifts that peaks at z0.5 and extends roughly from 0.4 to ~0.65.," In this way, our selected sample of LRGs have a distribution in true red shifts that peaks at $z \sim 0.5$ and extends roughly from $\sim 0.4$ to $\sim570.65$."58 For our analysis we will mostly refer to a single top-hat photometric redshifts bin inthe range 0.5—0.6]., For our analysis we will mostly refer to a single top-hat photometric redshifts bin in the range $\left[0.5-0.6\right]$.59 Figure 7 shows the true distribution of galaxies in this bin., Figure \ref{fig:dndz0506} shows the true distribution of galaxies in this bin.60 The number of objects in this bin. after the photo-z quality cut. is 664870.," The number of objects in this bin, after the photo-z quality cut, is $664870$."61 Notice that the bin width is slightly. larger than our typical photometric error at this redshift (0.~ 0.05) hence choosing à narrower bin would vield almost the same distribution of galaxies but ab the expense of increasing the noise in the measurement, Notice that the bin width is slightly larger than our typical photometric error at this redshift $\sigma_z \sim 0.05$ ) hence choosing a narrower bin would yield almost the same distribution of galaxies but at the expense of increasing the noise in the measurement62 healingfromactivegalaclienucleiandradialivecooling.,from active galactic nuclei and radiative cooling.63Dolhsimulatedetustersevhibilhisbehaviaurwaithiparadiusojf Name Data i200DA EFETT Pike LOOkpe. and their. gas properties. diverge. considerably. in. this region.," Both simulated clusters exhibit this behaviour within a radius of $\la64100\,\rmn{kpc}$ , and their gas properties diverge considerably in this region."65 We therefore choose to ignore the central cluster core in fitting to the data since the high eas density. and hence X-ray. surface. brightness.. will. stronely bias. the results.," We therefore choose to ignore the central cluster core in fitting to the data since the high gas density, and hence X-ray surface brightness, will strongly bias the results."66 Mock SZ data and X-ray. surface. brightnesse cata are constructed. from. the simulated. cluster maps using the method described in sections 2? and ??.., Mock SZ data and X-ray surface brightness data are constructed from the simulated cluster maps using the method described in sections \ref{section:mock_sz_data} and \ref{section:mock_xray_data}. .67 We fit the entropy- model to both highR and low signal-to-noiseR simulatedR data in. order to investigate. possible. svstematies. introduced thetl lerivedderived. clusterclus properties., We fit the entropy-based model to both high and low signal-to-noise simulated data in order to investigate possible systematics introduced into the derived cluster properties.68ü .ForVor the hiehhigh sisignal-to-oc uIthedatacase. we fit toicleali idealised dataprol with very? low experimental within no calibration errors. and no intrinsic CALB signal mass the SZ data.," For the high signal-to-noise case we fit to idealised data with very low experimental error, no calibration errors, and no intrinsic CMB signal in the SZ data."69 Conversely lor low signal-to-noise data we cent larger experimental error. and introduce calibration error and an intrinsic CMD component in the SZ data.," Conversely for low signal-to-noise data we simulate larger experimental error, and introduce calibration error and an intrinsic CMB component in the SZ data."70 The calibration errors are introduced as nuisance parameters to be marginalisedover and are distributed bv a Gaussian prior with gag given by the (quoted. error value., The calibration errors are introduced as nuisance parameters to be marginalised over and are distributed by a Gaussian prior with $\sigma_\rmn{cal}$ given by the quoted error value.71 X. calibration error of pper cent is used for the SZ data. typical of the calibration of 1192 visibility data. and the N-ray. surface brightness data typically contain a calibration error. of pper cent (?)..," A calibration error of per cent is used for the SZ data, typical of the calibration of CBI2 visibility data, and the X-ray surface brightness data typically contain a calibration error of per cent \citep{Andersson:2004}. ."72" refeure:kav,mutations...rays noiseSZandX raydala", \\ref{figure:kay_simulations_sz_xrays_only} shows the constraints introduced from separately fitting to high signal-to-noise SZ and X-ray data.73 ThesZdataconstrainthe integrated sighlpressurcandthereforegeneraleanantiThe/model. corrclationbebweenthecentraleleetrondensibtyandbempoeraturepare, The SZ data constrain the integrated line-of-sight pressure and therefore generate an anti-correlation between the central electron density and temperature parameters.74omdbdinosk medelit ibuthe sla! eot icDlrePEÉBet floe glargecenti , In addition the SZ data reduce the likelihood of having large central electron density and temperature values since these would generate large SZ signals that are inconsistent with the data.75raysur facebrighinessdalaareproportionallotheinlegratedsquarcefülpadison with sightelectrondensityandthere forestrongiyconstrainthecen| mattiide provides:Ευ Ραbke, The X-ray surface brightness data are proportional to the integrated square of the line-of-sight electron density and therefore strongly constrain the central electron density parameter.76 Πο raydalaisofrelativelyhigherresolitionthanthesZdataandisthe élldsy) vago atdyptdfsi leprocidings and a., The X-ray data is of relatively higher resolution than the SZ data and is therefore much more dependent upon the shape of the entropy profile providing strong constraints on $r_\rmn{core}$ and $\alpha$.77 The high signal-to-noise surface. brightness data do not provide a strong constraint on the temperature and mass of the cluster., The high signal-to-noise surface brightness data do not provide a strong constraint on the temperature and mass of the cluster.78 In the case of EDI the X-ray surface brightness data appear to generate a series of high likelihood peaks within parameter space., In the case of FB1 the X-ray surface brightness data appear to generate a series of high likelihood peaks within parameter space.79 However the data are unable to distinguish between these in the absence of an additional constraint [rom the SZ data., However the data are unable to distinguish between these in the absence of an additional constraint from the SZ data.80" Results from fitting simultancously to both data sets. for both the high and low signal-to-noise cases. are shown nlyshoustheconstramisintrodimediatelanseparatelyfiltinglohighsignaladtable:simulation, roperiicsandbiquresGand?..whercestimateso"," Results from fitting simultaneously to both data sets, for both the high and low signal-to-noise cases, are shown in \\ref{table:simulation_properties} and Figures \ref{figure:kay_simulations_entropy_params} and \ref{figure:kay_simulations_entropy_results}, where estimates of the posterior distribution for the model parameters, profiles of the cluster properties and selected enclosed quantities are plotted."81 fihep parameters are. constrained by the , The model parameters are constrained by the combination of both data sets.82pam the known simulated cluster properties the κιλα trueroo value. and rafbetohakdvat caleykou dapawtid radius.," For the purposes of comparison with the known simulated cluster properties the radial profiles are scaled by the known true$r_{200}$ value, and allglobal quantities are calculated by integrating within this radius."83 In the high edopewasignal-to-noise regime the radial profiles, In the high signal-to-noise regime the radial profiles84Brown dwarfs may be thought of as failed stars.,Brown dwarfs may be thought of as failed stars.85" These low mass (<70 Maij, Burrowsetal. 20013). cool objects are the lowest mass objects that the star formation process ean produce."," These low mass $\leq$ 70 $_{\rm Jup}$ \citealt{burrows01}) ), cool objects are the lowest mass objects that the star formation process can produce."86 The majority of the brown dwarfs that have been discovered to date are field objects found using surveys such as the Two Micron All Sky Survey (2MASS: Skrutskieetal.2006.. see Leggettetal.2002. for examples). the DEep Near-Infrared Sky survey (DENIS: DENISConsortium 2005.. see Delfosseetal..1999. for examples). the Sloan Digital Sky Survey (SDSS:Yorketal.2000. see Hawleyet for examples) and the UKIRT Deep Infrared Sky Survey (UKIDSS: Lawrenceetal.2007.. see Kendalletal.2007:Lodieual.2007a for examples).," The majority of the brown dwarfs that have been discovered to date are field objects found using surveys such as the Two Micron All Sky Survey (2MASS; \citealt{skrutskie06}, see \citealt{leggett02} for examples), the DEep Near-Infrared Sky survey (DENIS; \citealt{denis05}, see \citealt{delfosse99} for examples), the Sloan Digital Sky Survey \citealt{york00} see \citealt{hawley02} for examples) and the UKIRT Deep Infrared Sky Survey (UKIDSS; \citealt{lawrence06}, see \citealt{kendall07, lodieu07b} for examples)."87 However. to study brown dwarfs in depth. a knowledge of their age is essential. which means we must study brown dwarfs in open star clusters or moving groups.," However, to study brown dwarfs in depth, a knowledge of their age is essential, which means we must study brown dwarfs in open star clusters or moving groups."88 Once a brown dwarf has been proved to belong to an open star cluster. or a moving group. then its age is known. allowing meaningful comparisons to evolutionary models to be made.," Once a brown dwarf has been proved to belong to an open star cluster, or a moving group, then its age is known, allowing meaningful comparisons to evolutionary models to be made."89 The most recent example of this is the study done by Bannister&Jameson(2007). who used existing proper motions and parallax measurements to show that a selection of field dwarfs in fact belong to the Ursa Major and Hyades moving groups., The most recent example of this is the study done by \citet{bannister07} who used existing proper motions and parallax measurements to show that a selection of field dwarfs in fact belong to the Ursa Major and Hyades moving groups.90 The importance of this study. is that these are the first brown dwarfs to be associated with an older cluster or group (age 7200 Myr).," The importance of this study, is that these are the first brown dwarfs to be associated with an older cluster or group (age $>$ 200 Myr)."91 Older clusters such as the Hyades are expected to contain very few or no brown dwarfs or low mass members. due to the dynamical evolution of the cluster over time CAdamsetal.2002).," Older clusters such as the Hyades are expected to contain very few or no brown dwarfs or low mass members, due to the dynamical evolution of the cluster over time \citep{adams02}."92. However. these escaped low mass objects may remain members of the much larger moving group that surrounds the cluster.," However, these escaped low mass objects may remain members of the much larger moving group that surrounds the cluster."93 Jamesonetal.(2008a) followed this work by using the wide field camera (WFCAM. Casalietal. 2007)) on the United Kingdom Infrared Telescope (UKIRT) to image 143 known field L dwarfs.," \citet{jameson08} followed this work by using the wide field camera (WFCAM, \citealt{casali07}) ) on the United Kingdom Infrared Telescope (UKIRT) to image 143 known field L dwarfs."94 These images provided a second epoch for proper motion measurements. when combined with existing 2MASS images. typically taken 7 years previously.," These images provided a second epoch for proper motion measurements, when combined with existing 2MASS images, typically taken 7 years previously."95 Using the proper motions and a distance calculated using the spectral type of the L dwarf given by Cruzetal.(2003).. the moving group method was applied. and all 143 objects were scrutinised to check if their direction and magnitude of motion made them candidates of the many moving groups known.," Using the proper motions and a distance calculated using the spectral type of the L dwarf given by \citet{cruz03}, the moving group method was applied, and all 143 objects were scrutinised to check if their direction and magnitude of motion made them candidates of the many moving groups known."96 Members of the Hyades. Ursa Major and Pleiades moving groups were found.," Members of the Hyades, Ursa Major and Pleiades moving groups were found."97" Radial velocity measurements such as those of ZapateroOsorioetal.(2007). are required however. before it can be determined if these moving group members are cluster members that have ""escaped"" as the cluster has dynamically evolved (Adamsetal.2002)."," Radial velocity measurements such as those of \citet{zapatero07} are required however, before it can be determined if these moving group members are cluster members that have “escaped” as the cluster has dynamically evolved \citep{adams02}."98. Is should also be noted that galactic resonances ean produce effects similar to moving groups. and so all members may not be coeval (Dehnen1998).," Is should also be noted that galactic resonances can produce effects similar to moving groups, and so all members may not be coeval \citep{dehnen98}."99. To continue the study started. by Bannister&Jame-(2007) and Jamesonetal.(2008)... we have measured proper motions for the majority of the remaining known feld L dwarfs listed in the online Lo and. T dwarf archive (http://spider.ipac.caltech.edu/staft/davy/ARCHIVE/).," To continue the study started by \citet{bannister07} and \citet{jameson08}, we have measured proper motions for the majority of the remaining known field L dwarfs listed in the online L and T dwarf archive (http://spider.ipac.caltech.edu/staff/davy/ARCHIVE/)."100 This has again been accomplished using the WFCAM on UKIRT and for the more southern objects. Son of ISAAC (Soff) on the 3.58m ESO New Technology Telescope (NTT).," This has again been accomplished using the WFCAM on UKIRT and for the more southern objects, Son of ISAAC (SofI) on the 3.58m ESO New Technology Telescope (NTT)."101 Using these wide field images and existing catalogue data. we have measured proper motions for an additional 126 L and T dwarfs listed in the dwarf archive.," Using these wide field images and existing catalogue data, we have measured proper motions for an additional 126 L and T dwarfs listed in the dwarf archive."102 These proper motion data may be put to a number of uses., These proper motion data may be put to a number of uses.103 Using reduced proper motion diagrams they ean be used as an approximate measure of distance., Using reduced proper motion diagrams they can be used as an approximate measure of distance.104 The proper motion measurements can also be used to help identify objects as members of a star cluster or members of a moving group via the moving cluster method., The proper motion measurements can also be used to help identify objects as members of a star cluster or members of a moving group via the moving cluster method.105 Taken with measured radial velocities and, Taken with measured radial velocities and106We have analyzed all the currently available high energy data keV)) of aand continued the long term variability study of the source in the soft X-ray range (<10 keV). confirming the flux-hardness correlation proposed by ?. and ?..,"We have analyzed all the currently available high energy data ) of and continued the long term variability study of the source in the soft X-ray range $\la$ 10 keV), confirming the flux-hardness correlation proposed by \cite{roz05} and \cite{campana07}."107 Moreover. we report for the first time the discovery of hard X-ray long term flux changes. and show that there is a possible correlation. with the flux variations detected at lower energies.," Moreover, we report for the first time the discovery of hard X-ray long term flux changes, and show that there is a possible correlation with the flux variations detected at lower energies."108 Thanks to the dense monitoring of the last years. we are able to correlate these variations with the presence of the two new glitches (discussedin ?)..," Thanks to the dense monitoring of the last years, we are able to correlate these variations with the presence of the two new glitches \citep[discussed in][]{israel07}."109 The only other magnetar for which long term variability in this band has been reported is SGR 1806-20. for which the spectral hardening appears to be correlated with a burst rate increase (?)..," The only other magnetar for which long term variability in this band has been reported is SGR 1806–20, for which the spectral hardening appears to be correlated with a burst rate increase \citep{gotz07}."110 As proposed in 9?.. ?.. and ??.. an increase in the source activity (bursts. glitches) and a simultaneous spectral hardening may be caused by à growing twist in the magnetosphere: this may be also responsible for the transient appearance of a cyclotron line during the “high” emission state (??)..," As proposed in \cite{tlk02}, \cite{roz05}, and \cite{campana07}, an increase in the source activity (bursts, glitches) and a simultaneous spectral hardening may be caused by a growing twist in the magnetosphere; this may be also responsible for the transient appearance of a cyclotron line during the “high” emission state \citep{rea03,roz05}."111 If this is the case. data presented here support models in which also the hard X-ray tails are produced by mechanisms whose strength increases with the twist.," If this is the case, data presented here support models in which also the hard X-ray tails are produced by mechanisms whose strength increases with the twist."112 Indeed. 1t may also be that the flux variations m the hard X-rays dominate and drive those detected at lower energies. if the hard X-ray component does not sharply cut off below ~10 keV (as it may be the case for a synchrotron component).," Indeed, it may also be that the flux variations in the hard X-rays dominate and drive those detected at lower energies, if the hard X-ray component does not sharply cut off below $\sim$ 10 keV (as it may be the case for a synchrotron component)."113 Quite recently. ? discussed how soft gamma-rays may be produced in a twisted magnetosphere. proposing two different scenarios: either thermal bremsstrahlung emission from the surface region heated by returning currents. or synchrotron emission from pairs created higher up (~ 100 km) in the magnetosphere.," Quite recently, \cite{thompson05} discussed how soft gamma-rays may be produced in a twisted magnetosphere, proposing two different scenarios: either thermal bremsstrahlung emission from the surface region heated by returning currents, or synchrotron emission from pairs created higher up $\sim$ 100 km) in the magnetosphere."114 While both scenarios predict a power-law-like spectral distribution for the 20-100 keV photons. the cut-offs of the high energy emission are markedly different in the two cases. vs. | MeV. A third sceario involving resonant magnetic Compton up-scattering of soft X-ray photons by a non-thermal population of highly relativistic electrons has been proposed by ?..," While both scenarios predict a power-law-like spectral distribution for the 20-100 keV photons, the cut-offs of the high energy emission are markedly different in the two cases, vs. 1 MeV. A third scenario involving resonant magnetic Compton up-scattering of soft X-ray photons by a non-thermal population of highly relativistic electrons has been proposed by \cite{baring07}."115 In this contest we notice that. as for 4U 01424614 (?).. another member of the AXP class. multi-band spectral observations seems to disfavor the thermal bremsstrahlung model.," In this contest we notice that, as for 4U 0142+614 \citep{rea07}, another member of the AXP class, multi-band spectral observations seems to disfavor the thermal bremsstrahlung model."116 In fact. for any choice of temperature. a model which fits well the data below -150kkeV. will over-predict by more than a factor of 5 the COMPTEL upper limits derived in the MeV band (?).," In fact, for any choice of temperature, a model which fits well the data below $\sim$ keV, will over-predict by more than a factor of 5 the COMPTEL upper limits derived in the MeV band \citep{kuiper06}."117 However. these observations are not simultaneous and due to the variability of the source. no firm conclusion can be IBIS data confirm the large pulsed fraction25%—60%.. growing with energy. which has been reported earlier at high energies for other AXPs (and for uusing a different data set) by ?..," However, these observations are not simultaneous and due to the variability of the source, no firm conclusion can be IBIS data confirm the large pulsed fraction, growing with energy, which has been reported earlier at high energies for other AXPs (and for using a different data set) by \citet{kuiper06}. ."118 There is a clear indication for a phase difference of Δό~0.3—0.4 between the maxima of the soft («8 keV) and hard (28 keV) X-rays light curves measured in the 2004 with ISGRI/PCA data (see reffig:corr))., There is a clear indication for a phase difference of $\Delta\phi \sim 0.3-0.4$ between the maxima of the soft $<$$8$ keV) and hard $>$$8$ keV) X-rays light curves measured in the 2004 with ISGRI/PCA data (see \\ref{fig:corr}) ).119 The same phase shift was already present in the 2001 MECS/PDS data: within the errors. we find no evidence for any significant evolution in. Aó or pulsed flux. despite the three glitches that occurred between the observations.," The same phase shift was already present in the 2001 MECS/PDS data: within the errors, we find no evidence for any significant evolution in $\Delta\phi$ or pulsed flux, despite the three glitches that occurred between the observations."120 The phase shift. similar to the one detected at lower energies (?).. still lacks a clear interpretation 1n the magnetar framework.and it may indicate that the location of production of the two (soft/hard) component is different. but stable with time.," The phase shift, similar to the one detected at lower energies \citep{rea03}, still lacks a clear interpretation in the magnetar framework,and it may indicate that the location of production of the two (soft/hard) component is different, but stable with time."121 The top panel of Figure 9. shows the cilferential and cumulative distributions of τομ for penetrating encounters (b<L1: solid lines) and for encounters with b&1 (dotted lines).,= = t. The top panel of Figure \ref{fig:coll3} shows the differential and cumulative distributions of $\tau_{coll}$ for penetrating encounters $b<1$: solid lines) and for encounters with $b\ge 1$ (dotted lines).122 For this distribution we used all the data of Figure S.. excluding those contributing to the Ieftmost solid. svmbol.," For this distribution we used all the data of Figure \ref{fig:coll2}, excluding those contributing to the leftmost solid symbol."123 The median disruption time for b«1 is toycLl Cr. corresponding to a median mass loss of (Amin)~0.15.," The median disruption time for $b<1$ is $\tau_{coll} \simeq 11$ Gyr, corresponding to a median mass loss of $(\Delta m/m)^\prime \simeq 0.15$."124 The percentage of satellites dissolved by collisions over a Llubble time is 52 per cent., The percentage of satellites dissolved by collisions over a Hubble time is 52 per cent.125 On the other hand. encounters with 6>l1 have negligible mass loss. and. median ToryFgabbr. a result consistent with the data shown in the top iuiel of Figure 8..," On the other hand, encounters with $b\ge 1$ have negligible mass loss, and median $\tau_{coll} \gg t_{Hubble}$ , a result consistent with the data shown in the top panel of Figure \ref{fig:coll2}."126 The bottom panel of Figure 9. shows the same statistic or satellites with mm.fA.«0.01. which correspond. to ealaxy-size haloes falling onto a cluster.," The bottom panel of Figure \ref{fig:coll3} shows the same statistic for satellites with $m_v/M_v <0.01$, which correspond to galaxy-size haloes falling onto a cluster."127 In this case mass osses due to penetrating encounters are smaller. with median value Amn=0.05. corresponding to a median disruption time /230 Cir. with 42 per cent. of satellites xng dissolved over a Hubble time.," In this case mass losses due to penetrating encounters are smaller, with median value $\Delta m/m = 0.05$, corresponding to a median disruption time $t\simeq 30$ Gyr, with 42 per cent of satellites being dissolved over a Hubble time."128 We can usethe data in the first panel of Figure 7.. on the requency of penetrating encounters in satellites. to quantify he statistical significance of encounters.," We can use the data in the first panel of Figure \ref{fig:coll1}, on the frequency of penetrating encounters in satellites, to quantify the statistical significance of encounters."129 Since 60 per cent of all satellites have one or more penetrating encounters. rom the top panel of Figure 9 we can sav that at. least 30 per cent ofad satellites are dissolved in LL Gar or less yw penetrating encounters alone. and a comparable fraction is dissolved. over a Hubble time.," Since 60 per cent of all satellites have one or more penetrating encounters, from the top panel of Figure \ref{fig:coll3} we can say that at least 30 per cent of satellites are dissolved in 11 Gyr or less by penetrating encounters alone, and a comparable fraction is dissolved over a Hubble time."130" Similarly. 23. per cent. of satellites with miM,«0.01 are dissolved by penetrating encounters in less than a Llubble time."," Similarly, 23 per cent of satellites with $m_v/M_v <0.01$ are dissolved by penetrating encounters in less than a Hubble time."131 These numbers are an estimate of mass loss ancl disruption time due only. to penetrating encounters., These numbers are an estimate of mass loss and disruption time due only to penetrating encounters.132 Total mass losses and total survival times are those presented in Section ??.., Total mass losses and total survival times are those presented in Section \ref{sec:surv}.133" Finally, we found that these distributions are fairly robust to variations of parameters."," Finally, we found that these distributions are fairly robust to variations of parameters."134 We obtain essentially the same results if we change the requirements on the fraction of initial satellite mass which must be sell-bound at the time of the encounter. or if we only consider encounters at larger distances A(7)/HR. from the center of the main halo.," We obtain essentially the same results if we change the requirements on the fraction of initial satellite mass which must be self-bound at the time of the encounter, or if we only consider encounters at larger distances $R(\tau)/R_v$ from the center of the main halo."135 llere. we investigate the evolution of the internal structure of satellites.," Here, we investigate the evolution of the internal structure of satellites."136 ALL the particles composing the satellite just before the merging time define the density ancl the velocity. profile at cach time., All the particles composing the satellite just before the merging time define the density and the velocity profile at each time.137 We can thus investigate how the internal structure of a satellite changes after the merging time. and how its mass is redistributed within the main halo.," We can thus investigate how the internal structure of a satellite changes after the merging time, and how its mass is redistributed within the main halo."138 Vhe internal structure evolution of satellites is different for sma and large mass satellites., The internal structure evolution of satellites is different for small and large mass satellites.139 The density of the environment surrounding a satellite suffers an abrupt change when the satellite enters the main halo., The density of the environment surrounding a satellite suffers an abrupt change when the satellite enters the main halo.140 The tidal radius drastically decreases (Figure 5)) and. particles with enough kinetic energy. escape the satellite., The tidal radius drastically decreases (Figure \ref{fig:tidal}) ) and particles with enough kinetic energy escape the satellite.141 This process leaves low mass satellites with particles having a smaller velocity (Figure 11)). producing an overall effect. of cooling and a slight mass concentration. (Figure. 10)).," This process leaves low mass satellites with particles having a smaller velocity (Figure \ref{fig:vprof}) ), producing an overall effect of cooling and a slight mass concentration (Figure \ref{fig:mprof}) )."142 Escaped particles quickly thermalize to the main halo velocity. clispersion., Escaped particles quickly thermalize to the main halo velocity dispersion.143action of a large ununber of iudepenudoeut processes.,action of a large number of independent processes.144 These actors need not be physical processes. as assu in nodes of the origin of the stellar IME.," These factors need not be physical processes, as assumed in models of the origin of the stellar IMF."145 The iudepoeueut Xocesses nieht eqially well include those discussed iu refsec:define.. niaev thines like the addition of raioni zunonuuts of nolse to each chup. random errors iu he assiguiuent of chunp boundaries by chuup-fiuclue algoritlaus. and t1 perturbations fo cach chunip's Lass caused by convolution with other clumps and superposition along the line of sieht.," The independent processes might equally well include those discussed in \\ref{sec:define}, namely things like the addition of random amounts of noise to each clump, random errors in the assignment of clump boundaries by clump-finding algorithms, and the perturbations to each clump's mass caused by convolution with other clumps and superposition along the line of sight."146 Indeed. as the pots in Fieure ll show. he combined effects of large inouts of noise and very coarse angular resolution do not ruin he lognormal shape of the mass uction.," Indeed, as the plots in Figure \ref{fig:logncmfs} show, the combined effects of large amounts of noise and very coarse angular resolution do not ruin the lognormal shape of the mass function."147 Qur reference mass function already has a lognormal orm., 	Our reference mass function already has a lognormal form.148 The ouly post-processing recmired to coustruct that uass function was the use of a chuup-fiuidiug aleorithin: (XCOSSIVE Oise ald Coarse anguar resolution are nof ‘actors., The only post-processing required to construct that mass function was the use of a clump-finding algorithm; excessive noise and coarse angular resolution are not factors.149 Adding noise aud coatsene the resolution 6ft the simulation appears to cmange the width and iorinalizatiou of the lognormal chump mass function. mt not to make it anv less k»s]ornmal," Adding noise and coarsening the resolution of the simulation appears to change the width and normalization of the lognormal clump mass function, but not to make it any less lognormal."150 This is the ychavior oue expects if the Cemval Limit Theorem is, This is the behavior one expects if the Central Limit Theorem is151problem can be found in Benedetto (1992).,problem can be found in Benedetto (1992).152 llowever. the Frame Theory solution for inregular sampling often leads to functional inversions (hat are numerically diffieult and which. when the data are not well-oversampled. can be ill-conditioned. even in the absence of noise.," However, the Frame Theory solution for irregular sampling often leads to functional inversions that are numerically difficult and which, when the data are not well-oversampled, can be ill-conditioned, even in the absence of noise."153" This produces very laree computational costs (Werther 1999, Aldroubi aud Groechenig 2001)."," This produces very large computational costs (Werther 1999, Aldroubi and Gröcchenig 2001)."154 Thus the Frame Theory approach is rarely used in practice., Thus the Frame Theory approach is rarely used in practice.155 Instead. iterative reconstruction techniques have been developed to solve for a band-limited function in the case of irregularly. sampled data (c.f," Instead, iterative reconstruction techniques have been developed to solve for a band-limited function in the case of irregularly sampled data (c.f."156 Feichtinger and Grocchenie 1994. Werther 1999. Grócchenig and Strolmer 2001 }.," Feichtinger and Gröcchenig 1994, Werther 1999, Gröcchenig and Strohmer 2001 )."157 Here I present a new iterative reconstruction method., Here I present a new iterative reconstruction method.158 In essence itis an improvement upon a simple but powerful iterative technique. the Voronoi or nearest neiglibor approximation (c.f.," In essence it is an improvement upon a simple but powerful iterative technique, the Voronoi or nearest neighbor approximation (c.f."159 Werther 2004)., Werther 2004).160 In the nethod introduced here. (he astronomical imagine algorithm. Drizzle. replaces the nearest jeiehbor approximation.," In the method introduced here, the astronomical imaging algorithm, Drizzle, replaces the nearest neighbor approximation."161 Drizzle allows (his method to handle {ο geometric distortion. and combines (he data using the full statistical power of the individual images.," Drizzle allows this method to handle to geometric distortion, and combines the data using the full statistical power of the individual images."162 In the absence of 10lse (his method converges directly to the band-Iimited image., In the absence of noise this method converges directly to the band-limited image.163 In (he presence of noise. the nuethod introduces a small increase in statistical noise. but the svstematic high-frequency 1oise introduced by Drizzle (see Figure 6)) is removed.," In the presence of noise, the method introduces a small increase in statistical noise, but the systematic high-frequency noise introduced by Drizzle (see Figure \ref{fig-ACS-driz}) ) is removed."164 One might imagine (hat one could take (he total set of irregularly sampled. data which evervwhere meets the Nyquist criterion. perform a direct Fourier transform. remove any frequencies above the cutoll frequency. ancl the use the inverse Fourier transform (o arrive al the Que band-limited image.," One might imagine that one could take the total set of irregularly sampled data which everywhere meets the Nyquist criterion, perform a direct Fourier transform, remove any frequencies above the cutoff frequency, and the use the inverse Fourier transform to arrive at the true band-limited image."165 Unfortunately. a direct Fourier transform of irreeularly-samplecl data throws a great. deal of power out of the original passbancl.," Unfortunately, a direct Fourier transform of irregularly-sampled data throws a great deal of power out of the original passband."166 This simple method. (hus fails terribly., This simple method thus fails terribly.167 It is in fact. more effective to first put the data onto a regular Nyquist. erid bv simply taking the value of the nearest neiehbor before doing the Fourier trausform., It is in fact more effective to first put the data onto a regular Nyquist grid by simply taking the value of the nearest neighbor before doing the Fourier transform.168 The inverted. band-imited function tuis out to be a much (truer approximation (han the direct transform case.," The inverted, band-limited function turns out to be a much truer approximation than the direct transform case."169 This approximation is know as (he Voronoi approximatioΕν, This approximation is know as the Voronoi approximation.170 The Voronoi approximation is band-limited funcetion and thus can be sinc interpolated to the irregular gril of the data., The Voronoi approximation is band-limited function and thus can be sinc interpolated to the irregular grid of the data.171 One can therefore subtract the Voronoi approximation from the original function at all of the data points., One can therefore subtract the Voronoi approximation from the original function at all of the data points.172 Furthermore. this smaller difference funelion is itself a band-mited function. so one can repeat (he process and get a further refined approximation to the underlying band-limited funcüon.," Furthermore, this smaller difference function is itself a band-limited function, so one can repeat the process and get a further refined approximation to the underlying band-limited function."173 This procedure is known to converge geometrically (see Theorem 8.13 in Feichtinger and Grócchenig 1994)., This procedure is known to converge geometrically (see Theorem 8.13 in Feichtinger and Gröcchenig 1994).174 The nearest neighbor approximation is. however. lar from ideal for astronomical imaging.," The nearest neighbor approximation is, however, far from ideal for astronomical imaging."175llirose.IXxrolik.&Stone(2005). started with an initial condition corresponding {ο an annulus at 300 CU/c? around a black hole of mass Af=6.62 M...,\citet{hir05} started with an initial condition corresponding to an annulus at 300 $GM/c^2$ around a black hole of mass $M=6.62$ $_\odot$.176 The surface density of the annulus matched (hat of a Shakura-Sunyaev disk with a=0.02 and a luminosity equal to 0.066 times the Eddington rate. assuming 10 percent radiative efficiency.," The surface density of the annulus matched that of a Shakura-Sunyaev disk with $\alpha=0.02$ and a luminosity equal to 0.066 times the Eddington rate, assuming 10 percent radiative efficiency."177 After including a weak magnetic field with no net poloidal flux. (he MRI erows aud produces turbulence which saturates by about (en orbits. and a rough balance between heating and radiative cooling is thereafter established until à numerical problem at the boundaries interferes αἱ about. 60 orbits.," After including a weak magnetic field with no net poloidal flux, the MRI grows and produces turbulence which saturates by about ten orbits, and a rough balance between heating and radiative cooling is thereafter established until a numerical problem at the boundaries interferes at about 60 orbits."178 At anv specifie time. thermal balance is not exact. as there are significant [Inctuations in both heating and radiative cooling.," At any specific time, thermal balance is not exact, as there are significant fluctuations in both heating and radiative cooling."179 In addition. significant asvimmetries above and below (he midplane exist. and the flux emergine Irom one side can exceed (hat from the other bv factors of 2-3 over Gime scales as long as 5-10- orbits.," In addition, significant asymmetries above and below the midplane exist, and the flux emerging from one side can exceed that from the other by factors of 2-3 over time scales as long as 5-10 orbits."180 Spatial variations in the horizontal direction come and go as well., Spatial variations in the horizontal direction come and go as well.181 It would be interesting in future to compute the instantaneous emergent spectrum [from ihe annulus using three dimensional. (ime ancl frequency-dependent radiative transfer. but our scope here is much less ambitious.," It would be interesting in future to compute the instantaneous emergent spectrum from the annulus using three dimensional, time and frequency-dependent radiative transfer, but our scope here is much less ambitious."182 We simply wish (to examine the overall effects. of (he dissipation and magnetic pressure profiles on the (ime-averaged spectrum., We simply wish to examine the overall effects of the dissipation and magnetic pressure profiles on the time-averaged spectrum.183 We therefore horizontally averaged all [bud quantities in the simulation at every lime step. and then computed a time average from 10 to 60 orbits of these variables at every height. [," We therefore horizontally averaged all fluid quantities in the simulation at every time step, and then computed a time average from 10 to 60 orbits of these variables at every height. ["184We (δα (wo (vpes of averages of euantities related to energv and. pressure (e.g flux. pressure eradients. dissipation rate): a straight lime average and a lime average weighted bv the total instantaneous magnetic plus thermal energy in the annulus.,"We tried two types of averages of quantities related to energy and pressure (e.g flux, pressure gradients, dissipation rate): a straight time average and a time average weighted by the total instantaneous magnetic plus thermal energy in the annulus."185 Both approaches gave very nearly identical results.|, Both approaches gave very nearly identical results.]186 The time-averaged profiles still had small asvmmetries about the midplane (as much as 20 percent in (he case of the magnetic pressure eradients). so as a final step. we averaged all the vertical profiles above and below the disk midplane.," The time-averaged profiles still had small asymmetries about the midplane (as much as 20 percent in the case of the magnetic pressure gradients), so as a final step, we averaged all the vertical profiles above and below the disk midplane."187 The surface densitv and emergent flux [rom the resulting averaged structure still matches that of a Shakura-Sunvaev. annulis at a radius of 3006ο around a6.62 M. black hole. now accreting al L.1xLOM ος (corresponding to a luminosity of 0.095 in units of Eddington for 10 percent radiative efficiency) aud with a=0.016.," The surface density and emergent flux from the resulting averaged structure still matches that of a Shakura-Sunyaev annulus at a radius of $300 GM/c^2$ around a6.62 $_\odot$ black hole, now accreting at $1.1\times10^{18}$ g/s (corresponding to a luminosity of 0.095 in units of Eddington for 10 percent radiative efficiency) and with $\alpha=0.016$."188 Figure 9 depicts the average energy dissipation per unit mass e. together with the average verlical radiative flux gradient divided by density: pIdF/dz=—dF/dim. as a function of column mass densitv 2 measured [rom the surface inward.," Figure \ref{figdfdm} depicts the average energy dissipation per unit mass $\epsilon$, together with the average vertical radiative flux gradient divided by density: $\rho^{-1}dF/dz=-dF/dm$, as a function of column mass density $m$ measured from the surface inward."189 In a stationary. siructure. radiative equilibrium would require these (wo proliles to be identical. but the average profiles from the simulation are not quite in such agreement.," In a stationary, one-dimensional structure, radiative equilibrium would require these two profiles to be identical, but the average profiles from the simulation are not quite in such agreement."190 Following IIubeny& (1998).. we fit the profile of dF/din with a broken power," Following \citet{hub98}, , we fit the profile of $dF/dm$ with a broken power"191supermassive black hole and its surrounding matter.,supermassive black hole and its surrounding matter.192 To do this we compare both physical and phenomenological models of Sgr A* to the mm-VLBI visibilities., To do this we compare both physical and phenomenological models of Sgr A* to the mm-VLBI visibilities.193 This requires the computation of model visibilities., This requires the computation of model visibilities.194" Given a trial image intensity distribution, /(a,8), where a and ( are angular coordinates, we may compute the visibilities in the standard fashion: Here we describe three classes of model images: those associated with radiatively inefficient accretion flows (RIAFs) of the form discussed in ?,, symmetric and asymmetric "," Given a trial image intensity distribution, $I(\alpha,\beta)$, where $\alpha$ and $\beta$ are angular coordinates, we may compute the visibilities in the standard fashion: Here we describe three classes of model images: those associated with radiatively inefficient accretion flows (RIAFs) of the form discussed in \citet{Brod-Loeb:06a}, symmetric and asymmetric gaussians."195We also summarize the effects of interstellar electron gaussians.scattering., We also summarize the effects of interstellar electron scattering.196" We employ a suite of radiatively inefficient accretion flow (RIAF) models, first described in ?,, and based upon those of ?.."," We employ a suite of radiatively inefficient accretion flow (RIAF) models, first described in \citet{Brod-Loeb:06a}, and based upon those of \citet{Yuan-Quat-Nara:03}."197" Here these models, which henceforth we refer to as BLO06, are summarized."," Here these models, which henceforth we refer to as BL06, are summarized."198" Sgr A* transitions from an inverted, presumably optically thick to an optically thin spectrum near millimeter wavelengths."," Sgr A* transitions from an inverted, presumably optically thick spectrum to an optically thin spectrum near millimeter wavelengths."199" spectrumThis implies that near 1.3mm Sgr A* is only becoming optically thin, and thus in the surrounding medium is likely to be important."," This implies that near 1.3mm Sgr A* is only becoming optically thin, and thus absorption in the surrounding medium is likely to be important."200" This absorptiontransition does not occur isotropically, at longer wavelengths for that is receding and at shorter happeningwavelengths for gas that is approaching."," This transition does not occur isotropically, happening at longer wavelengths for gas that is receding and at shorter wavelengths for gas that is approaching."201"gas Therefore, the structure and relativistic radiative transfer is properlycrucial to modelingproducing high fidelity images."," Therefore, properly modeling the structure and relativistic radiative transfer is crucial to producing high fidelity images."202" Although Sgr A* is vastly sub-Eddington, its bolometric luminosity, roughly 10?9ergs""!, is still large in absolute terms, Like AGN, in the radio Sgr A* exhibits the nearly-flat, power-lawmany spectrum associated with non-thermal sources, with the emitted (vL,) peaking at synchrotronmillimeter wavelengths."," Although Sgr A* is vastly sub-Eddington, its bolometric luminosity, roughly $10^{36}\,\erg\s^{-1}$, is still large in absolute terms, Like many AGN, in the radio Sgr A* exhibits the nearly-flat, power-law spectrum associated with non-thermal synchrotron sources, with the power emitted $\nu L_\nu$ ) peaking at millimeter wavelengths."203" As a powerconsequence, it has been widely accepted that Sgr A* is accretion powered, implying a minimum accretion rate of 107"," As a consequence, it has been widely accepted that Sgr A* is accretion powered, implying a minimum accretion rate of $10^{-10}\Ms\yr^{-1}$."204" It is presently unclear how this emission is produced, M;syr""!.evidenced by the"," It is presently unclear how this emission is produced, evidenced by the variety of models that have been proposed \citep[e.g.,][]{Nara_etal:98,Blan-Bege:99,Falc-Mark:00,Yuan-Mark-Falc:02,Yuan-Quat-Nara:03,Loeb-Waxm:07}."205" Models in which the emission arises directly from the accreting gas have been subsumed into the general class of RIAFs, defined by the generally weak coupling between the electrons, which radiate rapidly, and the ions, which efficiently convert gravitational potential energy into heat (?).."," Models in which the emission arises directly from the accreting gas have been subsumed into the general class of RIAFs, defined by the generally weak coupling between the electrons, which radiate rapidly, and the ions, which efficiently convert gravitational potential energy into heat \citep{Nara_etal:98}."206 This coupling may be sufficiently weak to allow accretion rates in excess of that required to explain the observed substantiallyluminosity with a canonical AGN radiative efficiency of 10%., This coupling may be sufficiently weak to allow accretion rates substantially in excess of that required to explain the observed luminosity with a canonical AGN radiative efficiency of $10\%$.207" However, the detection of linear polarization in Sgr A* above 100GHz (????) and measurements of the Faraday rotation measure (??),, have subsequentimplied that the accretion rate near the black hole is much less than the Bondi rate, requiring the existence of large-scale outflows (??).."," However, the detection of linear polarization in Sgr A* above $100\GHz$ \citep{Aitk_etal:00,Bowe_etal:01,Bowe_etal:03,Marr_etal:06}208 and subsequent measurements of the Faraday rotation measure \citep{Macq_etal:06,Marr_etal:07}, have implied that the accretion rate near the black hole is much less than the Bondi rate, requiring the existence of large-scale outflows \citep{Agol:00,Quat-Gruz:00}."209 the outflow to the properties of the accretion flow Relatingrequires an ab initio calculation that is presently not possible., Relating the outflow to the properties of the accretion flow requires an ab initio calculation that is presently not possible.210" Nevertheless, a number of authors have studied this relationship in the context of a variety of with general-relativistic simplifyingmagnetohydrodynamicassumptions, and radiative-hydrodynamiclarge-scal"," Nevertheless, a number of authors have studied this relationship in the context of a variety of simplifying assumptions, with large-scale general-relativistic magnetohydrodynamic and radiative-hydrodynamic simulations playing a central role \citep{DeVi-Hawl-Krol-Hiro:05,McKi:06,Hawl-Krol:06,Beck-Hawl-Krol:08,McKi-Blan:09,Tche-Nara-McKi:10,Dext-Agol-Frag-McKi:10,Penn_etal:10,Kuro-Prog:09}."211e has been found that the structure and dynamics of the outflow critically depends upon the initial conditions., In these it has been found that the structure and dynamics of the outflow critically depends upon the initial conditions.212" The applicability of the MHD prescription to Sgr A* is still unclear, where the accretion rate is sufficiently low that non-MHD effects become important (??).."," The applicability of the MHD prescription to Sgr A* is still unclear, where the accretion rate is sufficiently low that non-MHD effects may become important \citep{Shar-Hamm-Quat-Ston:06,Shar-Quat-Hamm-Ston:07}."213" More most of these mayapproaches do not model the electronimportantly, heating (beyond ad hoc prescriptions) and none model the production of nonthermal electrons (see,e.g.???).."," More importantly, most of these approaches do not model the electron heating (beyond ad hoc prescriptions) and none model the production of nonthermal electrons \citep[see, e.g.,][]{Mosc_etal:09,Dext-Agol-Frag-McKi:10,Shch-Penn-McKi:10}."214" Furthermore, simulations are computationally expensive to produce."," Furthermore, simulations are computationally expensive to produce."215" For these reasons we adopt a simple, self-similar model for the accretion flow which includes substantial mass loss."," For these reasons we adopt a simple, self-similar model for the accretion flow which includes substantial mass loss."216" For concreteness, as in ?,, we follow ? and employ a model in which the accretion flow has a Keplerian velocity distribution, a population of thermal electrons with density and temperature and and a toroidal magnetic field in approximate (6= 10) respectively,equipartition with the ions (which are responsible for the majority of the pressure), i.e., In all of these, rs=2GM/c? is the Schwarzschild radius, pis the cylindrical radius and z is the vertical coordinate."," For concreteness, as in \citet{Brod-Loeb:06a}, we follow \citet{Yuan-Quat-Nara:03} and employ a model in which the accretion flow has a Keplerian velocity distribution, a population of thermal electrons with density and temperature and respectively, and a toroidal magnetic field in approximate $\beta=10$ ) equipartition with the ions (which are responsible for the majority of the pressure), i.e., In all of these, $\Rs=2GM/c^2$ is the Schwarzschild radius, $\rho$ is the cylindrical radius and $z$ is the vertical coordinate."217 Inside of the innermost-stable circular orbit ISCO) we assume the gas is plunging upon ballistic trajectories., Inside of the innermost-stable circular orbit (ISCO) we assume the gas is plunging upon ballistic trajectories.218 In principle the plunging, In principle the plunging219depends on mass.,depends on mass.220 For massive haloes. the central galaxies inside these haloes are a bit more massive than the galaxies within the same mass of haloes at 2=0.," For massive haloes, the central galaxies inside these haloes are a bit more massive than the galaxies within the same mass of haloes at $z=0$."221 For less massive haloes. the mass of central galaxies is smaller at higher redshift.," For less massive haloes, the mass of central galaxies is smaller at higher redshift."222 For satellite galaxies. however. the mass of galaxies is much smaller toward higher redshift at all mass scales.," For satellite galaxies, however, the mass of galaxies is much smaller toward higher redshift at all mass scales."223 In à recent paper. ? claim that stellar mass function alone is enough to constrain the relation between galaxy stellar mass and its hosting halo mass. since the [it to correlation functions has a much wider range at its \ minimum than the fit to stellar mass functions.," In a recent paper, \citet{moster2009} claim that stellar mass function alone is enough to constrain the relation between galaxy stellar mass and its hosting halo mass, since the fit to correlation functions has a much wider range at its $\chi^2$ minimum than the fit to stellar mass functions."224 However. this may not be true for higher redshift case.," However, this may not be true for higher redshift case."225 In. Fig. 5..," In Fig. \ref{fig:bestSMFfit},"226 we show the derived. stellar mass function and. correlation functions for the best-fit model when fitting only the stellar mass function of VVDS observation., we show the derived stellar mass function and correlation functions for the best-fit model when fitting only the stellar mass function of VVDS observation.227 The results show that the clustering of galaxies is generally over-precictecl in this ease., The results show that the clustering of galaxies is generally over-predicted in this case.228 Pherclore. we believe that fitting both stellar mass function and the correlation functions simultaneously is required to get reasonable fit. at least for the current observational data we can get.," Therefore, we believe that fitting both stellar mass function and the correlation functions simultaneously is required to get reasonable fit, at least for the current observational data we can get."229 From high redshift to the present day. dark matter haloes ect larger through mergers. and galaxics inside then also become bigger in size.," From high redshift to the present day, dark matter haloes get larger through mergers, and galaxies inside them also become bigger in size."230 The ealaxies gain their masses through either mergers with other galaxies. or by forming new stars.," The galaxies gain their masses through either mergers with other galaxies, or by forming new stars."231 Using the model we build in Sec., Using the model we build in Sec.232 2. we already know the galaxy masses at redshift of 0.83., \ref{sec:model} we already know the galaxy masses at redshift of $0.83$.233 We also have ealaxy stellar masses of today according to the model built al 2=0 from ?.., We also have galaxy stellar masses of today according to the model built at $z=0$ from \citet{wang2006}.234 The galaxy mass of today is a total amount of stellar component of galaxy. stellar mass that already exists at recshift of 0.83. the mass increase resulting from mergers with other galaxies. and in addition the newly formed stars during the time interval.," The galaxy mass of today is a total amount of stellar component of galaxy stellar mass that already exists at redshift of $0.83$, the mass increase resulting from mergers with other galaxies, and in addition the newly formed stars during the time interval."235 By tracing the merger histories of haloes/subhaloes and hence the galaxies that reside in these haloes/subhaloes. the amount of stellar mass that was added through mergers can be calculated.," By tracing the merger histories of haloes/subhaloes and hence the galaxies that reside in these haloes/subhaloes, the amount of stellar mass that was added through mergers can be calculated."236 Combined with the stellar mass of galaxies at both 2=0.83 and z=0. the stars that were newly formed during the time interval between these two redshift epochs can be predicted.," Combined with the stellar mass of galaxies at both $z=0.83$ and $z=0$, the stars that were newly formed during the time interval between these two redshift epochs can be predicted."237 lor à galaxy that resides in a halo of given mass at =0.we trace back through merger trees to its most massive progenitor at z=0.88.," For a galaxy that resides in a halo of given mass at $z=0$,we trace back through merger trees to its most massive progenitor at $z=0.83$."238 We plot in Fig., We plot in Fig.239 6 the meclian relation between the stellar mass of the most massive progenitor at z=0.83 of a galaxy ancl the mass of its host halo at present dav in black solid. line., \ref{fig:massincrease} the median relation between the stellar mass of the most massive progenitor at $z=0.83$ of a galaxy and the mass of its host halo at present day in black solid line.240 Among the galaxies that merge into this most massive progenitor. some of them are galaxies that alreacky exist. at 2=0.83. including both central and satellite galaxies at that time.," Among the galaxies that merge into this most massive progenitor, some of them are galaxies that already exist at $z=0.83$, including both central and satellite galaxies at that time."241 Phe other galaxies are newly formed galaxies after Ξ0.83. and merge into the main group before the present day.," The other galaxies are newly formed galaxies after $z=0.83$, and merge into the main group before the present day."242 From our fitted: mocel results we know that the M.-M;s relation evolves with time., From our fitted model results we know that the $M_{stars}$ $M_{infall}$ relation evolves with time.243 Fherefore. at the time of each parmerger. the mass of the merged. galaxy should. not be the same as its mass at the time of redshift 0.83.," Therefore, at the time of each merger, the mass of the merged galaxy should not be the same as its mass at the time of redshift $0.83$."244 We ect the galaxy mass at the time of each merger by interpolating ανω λενpar relation between 2=0.83 and z=0. assuming that the moclel parameters evolve linearly. with recshilt.," We get the galaxy mass at the time of each merger by interpolating $M_{stars}$ $M_{infall}$ relation between $z=0.83$ and $z=0$, assuming that the model parameters evolve linearly with redshift."245 In Fig. 6.," In Fig. \ref{fig:massincrease},"246 the dotted. black line is the sum of the stellar masses at 2=0.83 of the most massive progenitor and of its satellites merged. in., the dotted black line is the sum of the stellar masses at $z=0.83$ of the most massive progenitor and of its satellites merged in.247 Vhe Rec solid line is the result when the merged mass from central galaxies is added. including both the stellar mass existing at z=0.83 and those newly formed. since then.," The Red solid line is the result when the merged mass from central galaxies is added, including both the stellar mass existing at $z=0.83$ and those newly formed since then."248 The contribution from the merged central galaxies is much smaller compared with the mass [from merged satellite galaxies., The contribution from the merged central galaxies is much smaller compared with the mass from merged satellite galaxies.249 Blue lines are the mass of galaxies of present day. according to our model fit result for SDSS observation(?).," Blue lines are the mass of galaxies of present day, according to our model fit result for SDSS \citep{wang2006}."250. In the bottom panel of Fig. 6..," In the bottom panel of Fig. \ref{fig:massincrease},"251 the corresponding mass ratio of cach component to the galaxy of the present day is shown., the corresponding mass ratio of each component to the galaxy of the present day is shown.252 From Fig., From Fig.253 6 we can tell that for galaxies that reside in haloes of mass less than 10775.AL... the mergers since 2=0.83 contributes to the stellar mass growth by a very small fraction. which can even be ignored.," \ref{fig:massincrease} we can tell that for galaxies that reside in haloes of mass less than $10^{12}h^{-1}M_{\odot}$, the mergers since $z=0.83$ contributes to the stellar mass growth by a very small fraction, which can even be ignored."254 Compared. with the galaxy mass at present day. their most massive progenitors contribute from about 20 percent to around 60 percent of the present day mass. while the rest of the mass of z=0 galaxies should come from star formation of the central galaxy itself.," Compared with the galaxy mass at present day, their most massive progenitors contribute from about 20 percent to around 60 percent of the present day mass, while the rest of the mass of $z=0$ galaxies should come from star formation of the central galaxy itself."255 However. for high mass galaxies whose hosting halo masses are more than 10775.ΑΗ. the story is totally dilferent.," However, for high mass galaxies whose hosting halo masses are more than $10^{12.5}h^{-1}M_{\odot}$, the story is totally different."256 The mass of the most massive progenitor galaxy at z=0.83 is comparable to its present day mass., The mass of the most massive progenitor galaxy at $z=0.83$ is comparable to its present day mass.257 When taking into account the stellar component of other merged galaxies. the total mass is significantly larger than the galaxy mass of the present day.," When taking into account the stellar component of other merged galaxies, the total mass is significantly larger than the galaxy mass of the present day."258 This paradoxical result is the consequence of hierarchical merging in the current cosmological moclel., This paradoxical result is the consequence of hierarchical merging in the current cosmological model.259 Lere we have adopted the merger trees constructed by ?. for ealaxies by taking into account the dynamical time scales., Here we have adopted the merger trees constructed by \citet{lucia2006} for galaxies by taking into account the dynamical time scales.260 We found that the merged fraction of stellar mass does not change when the merger time scale of 2. is adopted., We found that the merged fraction of stellar mass does not change when the merger time scale of \citet{jiang2008} is adopted.261 There are several possibilities to reconcile the observations at. low and high redshifts in the hierarchical model., There are several possibilities to reconcile the observations at low and high redshifts in the hierarchical model.262 One is that satellite galaxies are tically clisrupted in a significant amount of stellar mass before merged into the central galaxies (27?)..," One is that satellite galaxies are tidally disrupted in a significant amount of stellar mass before merged into the central galaxies \citep{yang2009,wetzel2009}."263 llowever. as we see in 4. the significant tidal cüsruption is not stronely required by current observational data. because the unified model (details in 4) in which we assume no tidal disruption. matches the observational data equally well.," However, as we see in 4, the significant tidal disruption is not strongly required by current observational data, because the unified model (details in 4) in which we assume no tidal disruption matches the observational data equally well."264 Another possibility is that central galaxy mass observationally determined. may diller from the galaxy mass defined. in simulation. due to the limit size of the observed. central region of a galaxy.," Another possibility is that central galaxy mass observationally determined may differ from the galaxy mass defined in simulation, due to the limit size of the observed central region of a galaxy."265 Josides. when counting for the merged mass in simulation. all stellar masses of the merged. galaxies is added. while observationallv. the more extended stellar halo around the central galaxy may not be fully counted in.," Besides, when counting for the merged mass in simulation, all stellar masses of the merged galaxies is added, while observationally, the more extended stellar halo around the central galaxy may not be fully counted in."266 Pherefore observationally determined galaxy mass can be smaller than he simulated total mass., Therefore observationally determined galaxy mass can be smaller than the simulated total mass.267" With the model advocated. here. we expect to study. and: discriminate these possibilities when the model parameters can be determined better with ""ture high redshift samples of galaxies."," With the model advocated here, we expect to study and discriminate these possibilities when the model parameters can be determined better with future high redshift samples of galaxies."268 Future observations of intra-cluster (group) stars can also help testing these xossible mechanisms., Future observations of intra-cluster (group) stars can also help testing these possible mechanisms.269 In any case. qualitatively we should be able to conclude hat for low mass galaxies. they gain quite a fraction of their esent day mass through star formation [from z=0.83 to odav. while for high mass galaxies. most of their. present clay mass already exist at redshift of 0.83. and star formation is not active for these galaxies.," In any case, qualitatively we should be able to conclude that for low mass galaxies, they gain quite a fraction of their present day mass through star formation from $z=0.83$ to today, while for high mass galaxies, most of their present day mass already exist at redshift of $0.83$ and star formation is not active for these galaxies."270 This is consistent with the result o£ ? where they constrain the star formation histories of galaxies by fitting the spectral distribution properties of, This is consistent with the result of \citet{wang2007} where they constrain the star formation histories of galaxies by fitting the spectral distribution properties of271The τμ dependence on Ry is such that τρ does not depend on Ry.,The $z_0$ dependence on $R_0$ is such that $z_0/R_0$ does not depend on $R_0$.272 As a consequence the parameter A (defined in $5) does not depend on Ry., As a consequence the parameter $\Lambda$ (defined in 5) does not depend on $R_0$.273 Concerning the Y parameter. à change of 10 percent produces a negligible change of ~1 percent on zy.," Concerning the $V_0$ parameter, a change of 10 percent produces a negligible change of $\sim1$ percent on $z_0$."274" The vertical ο, and radial 75, kinematic scale lengths have been supposed equal because the data do not allow us to determine separately the two scale lengths.", The vertical $R_{\sigma_w}$ and radial $R_{\sigma_r}$ kinematic scale lengths have been supposed equal because the data do not allow us to determine separately the two scale lengths.275 They have certainly the same (large) order of magnitude. (, They have certainly the same (large) order of magnitude. (276"The kinematic radial scale length A, is about 9 kpe for giants. Neese Yoss. 1988.. Lewis et Freeman 1989.. a value large compared to the Pille:ensity scale length.","The kinematic radial scale length $R_{\sigma_r}$ is about 9 kpc for giants, Neese Yoss, \cite{ny88}, Lewis et Freeman \cite{lf89}, a value large compared to the density scale length."277 For younger populations the kinematic cale length should be even larger)., For younger populations the kinematic scale length should be even larger).278 Now considering the distribution function. (Eq., Now considering the distribution function (Eq.279" 1). a ""Secrease of 2, (at constant 2) has the effect of increasing the vertical dispersion for velocities smaller than Vi and ""Secreasing for velocities larger than Vy (Figs. 7--8))."," 1), a decrease of $R_{\sigma_w}$ (at constant $R_{\sigma}$ ) has the effect of increasing the vertical dispersion for velocities smaller than $V_0$ and decreasing for velocities larger than $V_0$ (Figs. \ref{fig7}- \ref{fig8}) )."280" The apparent change on the tsocontours would mimic a change of the ;,, parameter.", The apparent change on the isocontours would mimic a change of the $z_o$ parameter.281" We notice it also changes the velocity ""Sistribution f(eg.ος=0) and then the two effects (changes on A5, and τν ) could be distinguished."," We notice it also changes the velocity distribution $f(v_{\theta}, v_z=0)$ and then the two effects (changes on $R_{\sigma_w}$ and $z_o$ ) could be distinguished."282" Finally. modifying ndependently both 7; and £75, in the range 6-15 Κρο, gives a range of values for fitted :, from 3.8 to 6 kpe that is nearly about the range of the errors given by the maximum likelihood."," Finally, modifying independently both $R_{\sigma}$ and $R_{\sigma_w}$ in the range 6-15 kpc, gives a range of values for fitted $z_o$ from 3.8 to 6 kpc that is nearly about the range of the errors given by the maximum likelihood."283 In building the 3D kinematic model. we defined the parameter τω that is a measure of the radial bending of the potential.," In building the 3D kinematic model, we defined the parameter $z_o$ that is a measure of the radial bending of the potential."284" It is also tightly related to ὁ the vertical tilt of the velocity ellipsoidgiven by Hori Liu (1963)) shown that in à Stücckel potential the tilt 6 depends only on the positions: The change of the alt close to the galactic plane (where >= 0.6=O and first order vertical derivatives of o,.,. and 7...are null) is and for a Stücckel potential (at ;= 0) A general and approximate expression valid at 2=0 (exact in the case of Stiicckel potentials) is given by Amendt Cuddeford (1991)) (see also Cuddeford Amendt. 199].. 1992)) where A(} depends on potential derivatives: They show that A(r) may be strongly linked to the mass gradient in the galactic plane."," It is also tightly related to $\delta$ the vertical tilt of the velocity ellipsoidgiven by Hori Liu \cite{hl63}) ) shown that in a Stäcckel potential the tilt $\delta$ depends only on the positions: The change of the tilt close to the galactic plane (where $z=0$, $\delta=0$ and first order vertical derivatives of $\sigma_{r,r}$ and $\sigma_{z,z}$are null) is and for a Stäcckel potential (at $z=0$ ) A general and approximate expression valid at $z=0$ (exact in the case of Stäcckel potentials) is given by Amendt Cuddeford \cite{ac91}) ) (see also Cuddeford Amendt, \cite{ca91}, \cite{ca92}) ) where $\Lambda(r)$ depends on potential derivatives: They show that $\Lambda(r)$ may be strongly linked to the mass gradient in the galactic plane."285" For the simplest cases we have that: D) for a spherical potential. τν=0. A=1 and the velocity ellipsoid points towards the galactic center. 2) while for a cylindrical potential. ;,,=x. A=0 and the ellipsoid stays everywhere parallel to the galactic plane."," For the simplest cases we have that: 1) for a spherical potential, $z_o=0$, $ \Lambda= 1 $ and the velocity ellipsoid points towards the galactic center, 2) while for a cylindrical potential, $z_o=\infty$, $ \Lambda= 0 $ and the ellipsoid stays everywhere parallel to the galactic plane."286" We measure ($44.1) +, directly from Hipparcos data using the distribution function Eq.", We measure 4.1) $z_o$ directly from Hipparcos data using the distribution function Eq.287 1., 1.288" Better constraints are obtained using a sample with 3D velocities since ο, Is strongly tied to the coupling between vy and e; components ($44.2).", Better constraints are obtained using a sample with 3D velocities since $z_o$ is strongly tied to the coupling between $v_\theta$ and $v_z$ components 4.2).289 Figure 7 shows the f(c.«) marginal velocity distribution for the 3D velocity sample and Fig.," Figure \ref{fig7} shows the $f(v,w)$ marginal velocity distribution for the 3D velocity sample and Fig."290" 8. the isocontours for three models: the first model is the best fit model ο,=5.7 kpc) and two similar models just changing τν to 0 and x.", \ref{fig8} the isocontours for three models: the first model is the best fit model $z_o=5.7\kpc$ ) and two similar models just changing $z_o$ to 0 and $\infty$ .291 We remark that these three models are strictly identical on the two axis ον—0) and f(e=c4.w) (see Appendix). and that the differences are important for large velocities both in ο and uw.," We remark that these three models are strictly identical on the two axis $f(v,w=0)$ and $f(v=v_{circ},w)$ (see Appendix), and that the differences are important for large velocities both in $v$ and $w$ ."292"delayed by roughly 0.3 Myr compared to star formation in the latter, and that the mean mass of the stars that form is noticeably larger.","delayed by roughly 0.3 Myr compared to star formation in the latter, and that the mean mass of the stars that form is noticeably larger."293" However, this has a simple explanation."," However, this has a simple explanation."294" At a given density and temperature, the Jeans mass scales with the mean molecular weight pas M;οςw~°/?."," At a given density and temperature, the Jeans mass scales with the mean molecular weight $\mu$ as $M_{J} \propto \mu^{-3/2}$."295" In run B, the gas is fully atomic at all densities, and so µ—1.27amu (where we have assumed a helium fraction of 0.1 by number, relative to hydrogen)."," In run B, the gas is fully atomic at all densities, and so $\mu = 1.27 \: {\rm amu}$ (where we have assumed a helium fraction of 0.1 by number, relative to hydrogen)."296" On the other hand, in runs C, D1 and D2, the hydrogen in the densest gas is almost fully molecular, as illustrated in Figure 4,, and so 4=2.33amu."," On the other hand, in runs C, D1 and D2, the hydrogen in the densest gas is almost fully molecular, as illustrated in Figure \ref{rhoh2}, and so $\mu = 2.33 \: {\rm amu}$."297" Therefore, for any given choice of density and temperature within the dense gas, the Jeans mass is roughly a factor of 2.5 times larger in run B than in runs C, D1 or D2."," Therefore, for any given choice of density and temperature within the dense gas, the Jeans mass is roughly a factor of 2.5 times larger in run B than in runs C, D1 or D2."298" If we assume that gas is assembled into dense filaments and cores at roughly the same rate in all of these runs, which seems likely given the similar temperature-density relationship, then this implies that in run B it will take longer for these structures to grow to the point at which they become gravitationally unstable, and hence that the onset of star formation will be delayed."," If we assume that gas is assembled into dense filaments and cores at roughly the same rate in all of these runs, which seems likely given the similar temperature-density relationship, then this implies that in run B it will take longer for these structures to grow to the point at which they become gravitationally unstable, and hence that the onset of star formation will be delayed."299" It also suggests that the stars that do form will have systematically larger masses, in agreement with what we find in our simulations."," It also suggests that the stars that do form will have systematically larger masses, in agreement with what we find in our simulations."300 We can gain additional insight into the physical processes determining the star formation rate in our model clouds by examining the probability density function (PDF) of gas density generated in the different runs., We can gain additional insight into the physical processes determining the star formation rate in our model clouds by examining the probability density function (PDF) of gas density generated in the different runs.301" In Figure 3,, we show the mass-weighted density PDF of the gas in runs B, C, D1 and D2 immediately prior to the onset of star formation in these four runs."," In Figure \ref{rhopdf}, we show the mass-weighted density PDF of the gas in runs B, C, D1 and D2 immediately prior to the onset of star formation in these four runs."302" For comparison, we also show the density PDF in run A at a similar physical time, t=2.3Myr."," For comparison, we also show the density PDF in run A at a similar physical time, $t = 2.3 \: {\rm Myr}$."303" In the four star-forming runs, the density PDF is broad, and shows evidence for a power-law tail at high densities, n>107cm?."," In the four star-forming runs, the density PDF is broad, and shows evidence for a power-law tail at high densities, $n > 10^{4} \: {\rm cm^{-3}}$."304" Similar features have been found in previous simulations of selfgravitating supersonic turbulence (e.g.Wagner 2011),, in which run-away gravitational collapse has occurred."," Similar features have been found in previous simulations of self-gravitating supersonic turbulence \citep[e.g.][]{klessen00,fed08,knw11}, in which run-away gravitational collapse has occurred."305 There is also now observational evidence for the presence of power-law tails in the density PDFs of active star-forming regions in real molecular clouds (Kainulainenetal. 2011)..," There is also now observational evidence for the presence of power-law tails in the density PDFs of active star-forming regions in real molecular clouds \citep{kain09,lom10,kain11}."306" In contrast, the density PDF in run A is much narrower, and appears to have a log-normal form, as would be expected in a cloud in which gravitational collapse has not yet occurred."," In contrast, the density PDF in run A is much narrower, and appears to have a log-normal form, as would be expected in a cloud in which gravitational collapse has not yet occurred."307" The higher gas temperatures in run A compared to the other runs mean that the turbulence has a much smaller root-mean-squared Mach number, and hence produces weaker compressions, leading to a significantly narrower PDF (Padoan,Nordlund&Jones1997;Federrath,Klessen,&Schmidt2008;PadoanNordlund 2011)."," The higher gas temperatures in run A compared to the other runs mean that the turbulence has a much smaller root-mean-squared Mach number, and hence produces weaker compressions, leading to a significantly narrower PDF \citep{pnj97,fks08,pn11}."308". As a result, none of the gas in run A has yet reached a high enough density to become locally self-gravitating and to decouple from the larger-scale flow, while in the other four runs, a significant fraction of the gas mass is found in collapsing, self-gravitating structures."," As a result, none of the gas in run A has yet reached a high enough density to become locally self-gravitating and to decouple from the larger-scale flow, while in the other four runs, a significant fraction of the gas mass is found in collapsing, self-gravitating structures."309 The fact that the four star-forming runs have very similar density PDFs is a consequence of the fact that they have very similar temperature distributions., The fact that the four star-forming runs have very similar density PDFs is a consequence of the fact that they have very similar temperature distributions.310" It is therefore easy to understand why they form stars at very similar rates: in all four cases, the amount of dense gas available for star formation is very similar, and the rate at which this dense gas is converted into stars is limited primarily by the local free-fall time, which does not depend upon the nature of the gas coolants."," It is therefore easy to understand why they form stars at very similar rates: in all four cases, the amount of dense gas available for star formation is very similar, and the rate at which this dense gas is converted into stars is limited primarily by the local free-fall time, which does not depend upon the nature of the gas coolants."311" In Figure 4,, we plot the fractional abundance of Ho, ΦΗ., as a function of the hydrogen nuclei number density n in runs C, D1 and D2 at a time shortly before the onset of star formation in these simulations."," In Figure \ref{rhoh2}, we plot the fractional abundance of $_{2}$, $x_{\rm H_{2}}$, as a function of the hydrogen nuclei number density $n$ in runs C, D1 and D2 at a time shortly before the onset of star formation in these simulations."312" For comparison, we also plot vg, versus n at a similar output time in run A. We show no results from run B because zu,=0 by design in this run."," For comparison, we also plot $x_{\rm H_{2}}$ versus $n$ at a similar output time in run A. We show no results from run B because $x_{\rm H_{2}} = 0$ by design in this run."313" We define xy, as the ratio of the H2 number density ng, and the hydrogen nuclei number density n, which means that in fully molecular gas, ry,=0.5n/n0.5."," We define $x_{\rm H_{2}}$ as the ratio of the $_{2}$ number density $n_{\rm H_{2}}$ and the hydrogen nuclei number density $n$, which means that in fully molecular gas, $x_{\rm H_{2}} = 0.5 n / n= 0.5$."314" If we compare the results from runs C, D1 and D2, we see that in each case, the cloud is predominantly molecular at the point at which it forms stars."," If we compare the results from runs C, D1 and D2, we see that in each case, the cloud is predominantly molecular at the point at which it forms stars."315" The mean H» fractional abundance falls significantly below 0.5 only for densities n«100cm?, corresponding to warm, unshielded gas at the boundaries of the clouds."," The mean $_{2}$ fractional abundance falls significantly below 0.5 only for densities $n < 100 \: {\rm cm^{-3}}$, corresponding to warm, unshielded gas at the boundaries of the clouds."316" The rapidity with which He forms within the clouds is a consequence of the many transient density enhancements produced by the supersonic turbulence, which boost the overall H2 formation rate in the cloud by a factor of a few (formoredetails,seee.g.Glover&MacLow2007;Milosavljevicetal. 2011)."," The rapidity with which $_{2}$ forms within the clouds is a consequence of the many transient density enhancements produced by the supersonic turbulence, which boost the overall $_{2}$ formation rate in the cloud by a factor of a few \citep[for more details, see e.g.][]{gm07,mili11}."317". The main difference of note between runs C, D1 and D2 is the larger scatter in xy, at high densities in runs C and D1 than in run D2."," The main difference of note between runs C, D1 and D2 is the larger scatter in $x_{\rm H_{2}}$ at high densities in runs C and D1 than in run D2."318" This reflects the difference in initial conditions between these runs: runs C and D1 start with all of their hydrogen in atomic form, and although most of it has become molecular by t~2.5Myr there are still a few regions that retain a high atomic fraction."," This reflects the difference in initial conditions between these runs: runs C and D1 start with all of their hydrogen in atomic form, and although most of it has become molecular by $t \sim 2.5 \: {\rm Myr}$ there are still a few regions that retain a high atomic fraction."319" In run D2, on the other hand, the hydrogen is initially in fully molecular form, and atomic hydrogen is"," In run D2, on the other hand, the hydrogen is initially in fully molecular form, and atomic hydrogen is"320span several local scale heights in both height and width see Reynolds&Miller 2009)).,span several local scale heights in both height and width see \citealt{2009ApJ...692..869R}) ).321" The average ratio of gas-to-magnetic(e.g., pressure is initialized to 6e1000.", The average ratio of gas-to-magnetic pressure is initialized to $\beta\approx1000$.322 The following analysis treats the disk only after it has relaxed away from its initial conditions., The following analysis treats the disk only after it has relaxed away from its initial conditions.323" Specifically, we allow the disk to evolve for 150 ISCO orbits (»9200 GM/c?) and define t—0 to correspond to the end of this initialization period."," Specifically, we allow the disk to evolve for $150$ ISCO orbits $>9200$ $^3$ ) and define $t=0$ to correspond to the end of this initialization period."324" The simulation is then followed post-initialization for more than 1500 ISCO orbits, from t=0 to tz9.8x10* GM/c?."," The simulation is then followed post-initialization for more than 1500 ISCO orbits, from $t=0$ to $t\approx9.8\times 10^4$ $^3$."325" During and after the initialization, the disk naturally evolves to a turbulent state as a result of the MRI."," During and after the initialization, the disk naturally evolves to a turbulent state as a result of the MRI."326" Deferring a detailed discussion of the full disk evolution to a future work, we focus here on an interesting set of coherent behaviors that emerge from this turbulence."," Deferring a detailed discussion of the full disk evolution to a future work, we focus here on an interesting set of coherent behaviors that emerge from this turbulence."327 Figure 1 shows the azimuthal field strength (also azimuthally as a function of both time and elevation from the averaged)midplane for three distinctradii., Figure 1 shows the azimuthal field strength (also azimuthally averaged) as a function of both time and elevation from the midplane for three distinctradii.328" At all radii, the disk midplane is located at 0=7/2, while A=0.05 corresponds to one scaleheight for fixed h/r."," At all radii, the disk midplane is located at $\theta=\pi/2$, while $\Delta \theta =0.05$ corresponds to one scaleheight for fixed $h/r$."329 Each panel of the figure shows that the azimuthal field at a given location reverses sign multiple times., Each panel of the figure shows that the azimuthal field at a given location reverses sign multiple times.330" This variation can be seen for several scale heights above and below the disk midplane, forming a “butterfly” pattern analogous to that which has been observed in shearing box simulations of accretion disks."," This variation can be seen for several scale heights above and below the disk midplane, forming a “butterfly” pattern analogous to that which has been observed in shearing box simulations of accretion disks."331" The period of field reversal is generally longer for larger distances from the central object, although there are also some common features seen at all radii."," The period of field reversal is generally longer for larger distances from the central object, although there are also some common features seen at all radii."332" While it is difficult to tell from these diagrams whether the variability is truly periodic, it appears that the reversals in field orientation take place on timescales on the order of tens of local orbital periods."," While it is difficult to tell from these diagrams whether the variability is truly periodic, it appears that the reversals in field orientation take place on timescales on the order of tens of local orbital periods."333" Near the maxima of the field cycles, the azimuthal field strength can be twice as strong as the RMS value of the azimuthal field measured over the simulation duration in the same region."," Near the maxima of the field cycles, the azimuthal field strength can be twice as strong as the RMS value of the azimuthal field measured over the simulation duration in the same region."334" 'To explore this variability in more detail, we show in Figure 2 the power spectral density (PSD), defined as P(v)=n|f(v)?, where η is a normalization constant and f(v) is the Fourier transform of a time series f(t)."," To explore this variability in more detail, we show in Figure 2 the power spectral density (PSD), defined as $P(\nu)=\eta|\bar{f}(\nu)|^2$, where $\eta$ is a normalization constant and $\bar{f}(\nu)$ is the Fourier transform of a time series $f(t)$."335" In each panel, the azimuthal magnetic field has been azimuthally averaged and summed over a radial range comparable to the local scale height before the PSD is computed for a location two scale heights above the disk midplane."," In each panel, the azimuthal magnetic field has been azimuthally averaged and summed over a radial range comparable to the local scale height before the PSD is computed for a location two scale heights above the disk midplane."336" In this case, the time series is taken to be the duration of the simulation after initialization."," In this case, the time series is taken to be the duration of the simulation after initialization."337" All three panels show strong power enhancements at frequencies roughly comparable to ten to twenty local orbital periods 0.05—0.1Vorb, where Vorb is the local orbital frequency)."," All three panels show strong power enhancements at frequencies roughly comparable to ten to twenty local orbital periods $0.05-0.1~\nu_{\rm orb}$, where $\nu_{\rm orb}$ is the local orbital frequency)."338"(4.e., It is interesting to note that all radii also show multiple peaks, suggesting that the phenomenon is not always simply related to the local orbital period."," It is interesting to note that all radii also show multiple peaks, suggesting that the phenomenon is not always simply related to the local orbital period."339" In fact, there is some overlap between adjacent radii, as seen in the shared frequency of the strongest peaks for both R=15rg and R=20rg."," In fact, there is some overlap between adjacent radii, as seen in the shared frequency of the strongest peaks for both $R=15~{\rm r}_g$ and $R=20~{\rm r}_g$."340" As a coarse estimate of the significance of these peaks, we can compare their strengths to the mean power as estimated from nearby frequencies."," As a coarse estimate of the significance of these peaks, we can compare their strengths to the mean power as estimated from nearby frequencies."341" For a PSD of a single time series, the mean is comparable to the standard deviation of the power distribution Pressetal. 1992)), implying that the ratio of peak-to-mean(e.g., power can be used to estimate peak significance."," For a PSD of a single time series, the mean is comparable to the standard deviation of the power distribution \citealt{1992nrca.book.....P}) ), implying that the ratio of peak-to-mean power can be used to estimate peak significance."342" In the case of R=15rg, for example, the two highest peaks are approximately 15-20 times the mean power as extrapolated from nearby frequency ranges."," In the case of $R=15~{\rm r}_g$, for example, the two highest peaks are approximately 15-20 times the mean power as extrapolated from nearby frequency ranges."343" The case of R=20 is even more convincing as the primary peak is approximatelyr, 90 times stronger than the mean while the secondary peak is roughly 40 times above the mean.", The case of $R=20~{\rm r}_g$ is even more convincing as the primary peak is approximately 90 times stronger than the mean while the secondary peak is roughly 40 times above the mean.344" Even if our approximations somehow underestimate the mean power by factors of a few, each radius features multiple peaks that stand significantly above the noise."," Even if our approximations somehow underestimate the mean power by factors of a few, each radius features multiple peaks that stand significantly above the noise."345" 'To further evaluate the significance of these features, we also construct the average power spectral density (PSD), defined as P(v)—(1/N)S5Ps(v) over a set of N independent time series "," To further evaluate the significance of these features, we also construct the average power spectral density $\overline{\rm PSD}$ ), defined as $\displaystyle \overline{P}(\nu) = (1/N)\sum\limits_{i=1}^N P_i(\nu)$ over a set of $N$ independent time series $f_i(t)$ ."346This approach has the advantage of reducing the standardf;(¢). deviation of the PSD features at the expense of the available frequency, This approach has the advantage of reducing the standard deviation of the PSD features at the expense of the available frequency347Because SDSS surveys primarily low-redshitt ealaxies. the best sampled clusters are both uearby and massive.,"Because SDSS surveys primarily low-redshift galaxies, the best sampled clusters are both nearby and massive."348 We therefore search N-rav cluster catalogs derived frou the ROSAT Al-Sly Survey for clusters in DRL., We therefore search X-ray cluster catalogs derived from the ROSAT All-Sky Survey for clusters in DR4.349 RASS is a shallow survev but it is suffiicicutly deep to inchide uearby. massive clusters.," RASS \citep{rass} is a shallow survey but it is sufficiently deep to include nearby, massive clusters."350 RASS covers virtually the eutire sky and is thus the most complete N-ray cluster survey for nearby clusters., RASS covers virtually the entire sky and is thus the most complete X-ray cluster survey for nearby clusters.351 RASS was conducted with the PSPC (Position Sensitive Proportional Counter) iustiunent., RASS was conducted with the PSPC (Position Sensitive Proportional Counter) instrument.352 Published cluster catalogs derived from the RASS inchide the X-ray Brightest Abell Cluster Survey (NBACS). the Bright Cluster Survey (BCS). the NOrtheru ROSAT AlL-Sky eulaxy cluster survey (NORAS). and the ROSAT-ESO flux limited ταν galaxy cluster survey (REFLEN).," Published cluster catalogs derived from the RASS include the X-ray Brightest Abell Cluster Survey (XBACS), the Bright Cluster Survey (BCS), the NOrthern ROSAT All-Sky galaxy cluster survey (NORAS), and the ROSAT-ESO flux limited X-ray galaxy cluster survey (REFLEX)."353" NBACS is ""au essentially complete. all-sky. Noay flus-limited sample of 212 Abell clusters” from RASS L(?).. the first processing of the RASS."," XBACS is “an essentially complete, all-sky, X-ray flux-limited sample of 242 Abell clusters” from RASS I \citep{xbacs}, the first processing of the RASS."354 BCS is the Brielt Cluster Survey (7). and eBCS is an extension of this survey to a smaller limiting flux (?).., BCS is the Bright Cluster Survey \citep{bcs} and eBCS is an extension of this survey to a smaller limiting flux \citep{2000MNRAS.318..333E}.355 NBAC'Ss and BCS/eBCS were coustructed first by searching for N-rav sources around known optical clusters from the Abell aud Zwicky catalogs: they then use a Vorouoi Tesselation aud Percolation (VIP) algorithin to identify extended N-rav sources (frou a aster catalog of N-rav point sources) not associated with optical clusters., XBACs and BCS/eBCS were constructed first by searching for X-ray sources around known optical clusters from the Abell and Zwicky catalogs; they then use a Voronoi Tesselation and Percolation (VTP) algorithm to identify extended X-ray sources (from a master catalog of X-ray point sources) not associated with optical clusters.356 PSPC count rates are converted to total fluxes (in the 0.1-2.1 keV energy baud) using Wine models to account for missing flix at large radi and corrected for Calactic absorption aud Jy corrected using either temperatures from ? or a correction frou the LyT relation from an iterative process., PSPC count rates are converted to total fluxes (in the 0.1-2.4 keV energy band) using King models to account for missing flux at large radii and corrected for Galactic absorption and $K$ corrected using either temperatures from \citet{david93} or a correction from the $L_X-T$ relation from an iterative process.357" BCS/eBCS covers the northern lemisphere at high Galactic latitudes (ó =O"" and [5] >20°).", BCS/eBCS covers the northern hemisphere at high Galactic latitudes $\delta \geq$ $^\circ$ and $|b|>$ $^\circ$ ).358 The flux Inuits of BCS and eBCS are LE aud 2.8410. erestem P respectively., The flux limits of BCS and eBCS are 4.4 and $\times 10^{-12}$ erg $^{-1}$ $^{-2}$ respectively.359 2 estimate the completeness to these limits is approximately audSOC. where the missing clusters are extended sources not iucluded in the master catalog of X-ray point sources.," \citet{bcs} estimate the completeness to these limits is approximately and, where the missing clusters are extended sources not included in the master catalog of X-ray point sources."360 NORAS (7) also covers the northern hemisphere at high Galactic latitudes (8 207 and |b] 7207)., NORAS \citep{2000ApJS..129..435B} also covers the northern hemisphere at high Galactic latitudes $\delta \geq$ $^\circ$ and $|b|>$ $^\circ$ ).361 The initial source catalog consists of exteuded objects detected in RASS I with their properties determined from RASS II (thesecondprocessingofRASS.7) data.," The initial source catalog consists of extended objects detected in RASS I with their properties determined from RASS II \citep[the second processing of RASS, ][]{rass} data."362 The fluxes are coluputed using a method called growth curve analysis and are corrected for missing flux by fitting the euissiou profile to a .J model (2?) and extrapolating to 12 core radi., The fluxes are computed using a method called growth curve analysis and are corrected for missing flux by fitting the emission profile to a $\beta$ model \citep{cff} and extrapolating to 12 core radii.363 The NORAS fluxes agree well with BCS/cBCS fluxes for clusters in common., The NORAS fluxes agree well with BCS/eBCS fluxes for clusters in common.364 Both surveys are expected to be incomplete., Both surveys are expected to be incomplete.365 Comparing NORAS and REFLEN. ? estimate that the completeness of NORAS is aboutἄ," Comparing NORAS and REFLEX, \citet{noras} estimate that the completeness of NORAS is about."366ν In a subset of NORAS (an area of sky between ascensious 9 and LL! aud declinations 6>0). the uleteness Increases to with the addition of several itional clusters found in a thorough search of Abell ster positions aud extended sources in the RASS II catalog ?..," In a subset of NORAS (an area of sky between right ascensions $^h$ and $^h$ and declinations $\delta$$>$ 0), the completeness increases to with the addition of several additional clusters found in a thorough search of Abell cluster positions and extended sources in the RASS II catalog \citet{noras}."367 We include these clusters iu our sample., We include these clusters in our sample.368 REFLEN (?7?) is analogous to NORAS but. for the southern hemisphere.," REFLEX \citep{2001A&A...369..826B,2004A&A...425..367B} is analogous to NORAS but for the southern hemisphere."369 Both NORAS aud REFLEX extend to sinaller N-vav fluxes than NBACS., Both NORAS and REFLEX extend to smaller X-ray fluxes than XBACS.370 The catalog construction is cdittercut for cach survey: NBAC's aud BCS/eBCS initially search for exteuded N-rav sources around known optical clusters: DCS/eDCS iucludes additional N-rav selected clusters selected from a aster catalog of point sources., The catalog construction is different for each survey: XBACs and BCS/eBCS initially search for extended X-ray sources around known optical clusters; BCS/eBCS includes additional X-ray selected clusters selected from a master catalog of point sources.371 NORAS is selected from extended. N-rav sources with no explicit optical selection., NORAS is selected from extended X-ray sources with no explicit optical selection.372 Finally. REFLEX matches ταν flux overdensities with ealaxv overdeusities aud is therefore selected joiuthy in X-ray aud optical waveleusths.," Finally, REFLEX matches X-ray flux overdensities with galaxy overdensities and is therefore selected jointly in X-ray and optical wavelengths."373 The REFLEX &uxes are calculated iu the same manucr as NORAS., The REFLEX fluxes are calculated in the same manner as NORAS.374 When multiple N-rav fluxes are available for a cluster. we use the most recently published value.," When multiple X-ray fluxes are available for a cluster, we use the most recently published value."375 The order of preferences is therefore: REFLEX. NORÀS. BCS/cBCS. NBACs.," The order of preferences is therefore: REFLEX, NORAS, BCS/eBCS, XBACs."376 We define à flux-limited aud redshift-liamited sample of clusters with the criteria fy23<10tere stom 2 (01-2.] keV) aud z<0.10.," We define a flux-limited and redshift-limited sample of clusters with the criteria $f_X\geq 3\times37710^{-12}$ erg $^{-1}$ $^{-2}$ (0.1-2.4 keV) and $z\leq$ 0.10."378 Note that variations in the method of determining flux in different catalogs av affect the precise fux luit., Note that variations in the method of determining flux in different catalogs may affect the precise flux limit.379 The oulv cluster with an NBACS flux is AlT5O0b. the southern component of A1T50.," The only cluster with an XBACs flux is A1750b, the southern component of A1750."380 We follow ? and treat AT750 as a single source rather than two separate sources as in NBACSs., We follow \citet{2004A&A...425..367B} and treat A1750 as a single source rather than two separate sources as in XBACs.381 Similarly. he ealaxy NGC5813 is bound to the NCC5&l6 eroup (?)..," Similarly, the galaxy NGC5813 is bound to the NGC5846 group \citep{mahdavi05}."382 Because the dvuamucs of NCC5S13 are dominated w the NCCS5&L6 system. we eliniuate αςΟδ]. from the salple.," Because the dynamics of NGC5813 are dominated by the NGC5846 system, we eliminate NGC5813 from the sample."383 We inspect the redshift data around cach cluster o coufiri the cluster redshift aud find that A2061 has an incorrect redshift (aud N-ray Iuninosityv) listed in NORAS., We inspect the redshift data around each cluster to confirm the cluster redshift and find that A2064 has an incorrect redshift (and X-ray luminosity) listed in NORAS.384 The correct redshift is 0.0738 instead of 0.1076., The correct redshift is 0.0738 instead of 0.1076.385 We correct he X-rav huniuositv accordingly., We correct the X-ray luminosity accordingly.386 The redshift of A2119 is listed as :20.1068 in NORAS and 2-=0.0675 in eDC'S., The redshift of A2149 is listed as $z$ =0.1068 in NORAS and $z$ =0.0675 in eBCS.387 Because the N-rav peak of the RASS image lies ucar au apparent BCG at the latter redshift (see 81)). we adopt the eDCS value aud adjust the N-vav Iuninosity accordingly.," Because the X-ray peak of the RASS image lies near an apparent BCG at the latter redshift (see $\S$ \ref{individual}) ), we adopt the eBCS value and adjust the X-ray luminosity accordingly."388 Our final flux and redshift hiuited sample contains clusters within the SDSS DRI spectroscopic footprint., Our final flux and redshift limited sample contains clusters within the SDSS DR4 spectroscopic footprint.389 We will refer to this sample as the CIRS (Cluster Infall Reeious in SDSS) clusters hereafter., We will refer to this sample as the CIRS (Cluster Infall Regions in SDSS) clusters hereafter.390 The completeness of the CIRS salple is limited by the completeness of the uuderlviug cluster catalogs., The completeness of the CIRS sample is limited by the completeness of the underlying cluster catalogs.391 Ilowewer. bv combining clusters from the various catalogs we should be more complete than any individual catalog.," However, by combining clusters from the various catalogs we should be more complete than any individual catalog."392 For our purposes. this modest potential incompleteness is not important.," For our purposes, this modest potential incompleteness is not important."393 The clusters are an unbiased sample: the sclection of the CIRS sample is based purely on X-ray flux aud the footprint of the SDSS DR1 spectroscopic survey., The clusters are an unbiased sample: the selection of the CIRS sample is based purely on X-ray flux and the footprint of the SDSS DR4 spectroscopic survey.394 We first test for the ubiquitv of caustic or iufall patterus around N-ray clusters., We first test for the ubiquity of caustic or infall patterns around X-ray clusters.395 Analogous to CAIRNS. we plotted racius-redshitt diagrams for all clusters in the X-ray cluster catalogs covered by DRtl with : «0.20.," Analogous to CAIRNS, we plotted radius-redshift diagrams for all clusters in the X-ray cluster catalogs covered by DR4 with $z<$ 0.20."396 Clusters with 2 200 have few spectroscopically confirmed members in DRL (see 52.1))., Clusters with $z>$ 0.10 have few spectroscopically confirmed members in DR4 (see $\S$ \ref{sdssdesc}) ).397 The caustic patter is a superposition of the “finger-ofGod” clongation in redshift space of the virialized galaxies in the cluster ceuter aud the flattening due to infall at large radi., The caustic pattern is a superposition of the “finger-of-God” elongation in redshift space of the virialized galaxies in the cluster center and the flattening due to infall at large radii.398 The resulting iufall pattern is a characteristic trumpet shape in plase space (27.D99).., The resulting infall pattern is a characteristic trumpet shape in phase space \citep[][D99]{kais87}.399 Substructure in the iufall region sincars out the sharp cnhauccments iu phase space predicted by simple spherical infall so the infall pattern should be apparent as a deuse euvelope of galaxies iu phase space with well-defined edges (D99).," Substructure in the infall region smears out the sharp enhancements in phase space predicted by simple spherical infall, so the infall pattern should be apparent as a dense envelope of galaxies in phase space with well-defined edges (D99)."400 The detailed appearance of the redshift-radius diagrams depends on the line-of- of the observer. so the contrast between the dense iufall cuvelope aud. foreground. and background: ealaxics is subject to projection effects (D99).," The detailed appearance of the redshift-radius diagrams depends on the line-of-sight of the observer, so the contrast between the dense infall envelope and foreground and background galaxies is subject to projection effects (D99)."401 We assign a, We assign a402magnetic field configurations. which can be understood from Fig. 1:,"magnetic field configurations, which can be understood from Fig. \ref{fig:slices}:"403 the extent of the magnetized region above B~[πα is indeed not fundamentally modified by the chosen distribution and the photon flux is hardly more sensitive to the overall intensity of the field (in. particular. we tested that a value of By=10 nG does not affect the results of more than a factor 2. for all magnetic configurations).," the extent of the magnetized region above $B\sim 1~$ nG is indeed not fundamentally modified by the chosen distribution and the photon flux is hardly more sensitive to the overall intensity of the field (in particular, we tested that a value of $B_0=10$ nG does not affect the results of more than a factor 2, for all magnetic configurations)."404" All in all. for a quite reasonable normalization of the magnetic field. meaning an average By~0.1— IOnG at density contrast unity. and for various scalings of the nagnetic field with density profile. the variations in flux remain smaller than an order of magnitude in the range E,~10—1000 GeV. Figure 2. also illustrates that the energy at which the signal peaks depends only weakly on the normalization of the magnetic field Bo. anc this remains true up to a few nano-"," All in all, for a quite reasonable normalization of the magnetic field, meaning an average $B_0\sim0.1-10\,$ nG at density contrast unity, and for various scalings of the magnetic field with density profile, the variations in flux remain smaller than an order of magnitude in the range $E_\gamma \sim 10-1000\,$ GeV. Figure \ref{fig:angles_fil} also illustrates that the energy at which the signal peaks depends only weakly on the normalization of the magnetic field $B_0$, and this remains true up to a few nano-Gauss."405 This can be understood qualitatively. assuming for simplicity the field to be homogeneous over the area of interest. with strength Bo.," This can be understood qualitatively, assuming for simplicity the field to be homogeneous over the area of interest, with strength $B_0$."406" For Bo=] nG. the electron cross-over energy E, beyond which electrons radiate in synchrotron reads E,=10! eV (see the discussion in Sec. 2)."," For $B_0=1\,$ nG, the electron cross-over energy $E_\times$ beyond which electrons radiate in synchrotron reads $E_\times\simeq 10^{18}\,$ eV (see the discussion in Sec. \ref{section:B}) )."407" However. the energy spectrum F.dN,/dE, of secondary electrons deposited in the source vicinity peaks at ~10'? eV. as a result of the competition between the opposite scalings with energy of the abundance of parent protons and of the parent proton energy loss rate."," However, the energy spectrum $E_e {\rm408 d}N_e/{\rm d}E_e$ of secondary electrons deposited in the source vicinity peaks at $\sim10^{19}\,$ eV, as a result of the competition between the opposite scalings with energy of the abundance of parent protons and of the parent proton energy loss rate."409" Therefore. the synchrotron signal is expected to peak at E,~10GeV. see Eq."," Therefore, the synchrotron signal is expected to peak at $E_\gamma \sim 10\,{\rm410 GeV}$, see Eq."411" 2 with Bo= 1nG and E,=10!"" eV. Now. for Bo=0.1 πα. the cross-over energy Ey=~4x10! eV so that one should use E,=4xI0 eV in Eq."," \ref{eq:Esyn} with $B_0=1\,$ nG and $E_e=10^{19}\,$ eV. Now, for $B_0=0.1\,$ nG, the cross-over energy $E_\times \simeq 4\times 10^{19}\,$ eV so that one should use $E_e=4\times 10^{19}\,$ eV in Eq."412" 2. with By= nG. giving E,~10 GeV again: the larger typical electron energy (among those radiating in synchrotron) compensates for the smaller value of Bo."," \ref{eq:Esyn} with $B_0=0.1\,$ nG, giving $E_\gamma \sim 10\,$ GeV again: the larger typical electron energy (among those radiating in synchrotron) compensates for the smaller value of $B_0$."413 As Bo is increased significantly above | nG. the peak location of the gamma-ray signal will increase in proportion. as most of the secondary electron flux can be radiated in synchrotron.," As $B_0$ is increased significantly above $1\,$ nG, the peak location of the gamma-ray signal will increase in proportion, as most of the secondary electron flux can be radiated in synchrotron."414" Note that the flux should be cut off above E,~10 TeV due to the opacity of the Universe to photons above this energy.", Note that the flux should be cut off above $E_{\gamma}\sim 10$ TeV due to the opacity of the Universe to photons above this energy.415 This effect is hot represented in these plots for simplicity. as its precise spectral shape depends on the distance d to the source (while the sub-TeV gamma ray flux seales in proportion to Lafd).," This effect is not represented in these plots for simplicity, as its precise spectral shape depends on the distance $d$ to the source (while the sub-TeV gamma ray flux scales in proportion to $L_{\rm416 cr}/d^2$ )."417" At lower energy (E,<| GeV). the flux intensity can vary by more than two orders of magnitude depending on the chosen magnetic configuration."," At lower energy $E_{\gamma}\lesssim 1$ GeV), the flux intensity can vary by more than two orders of magnitude depending on the chosen magnetic configuration."418 In the low energy range. magnetic confinement indeed starts to play an important role.," In the low energy range, magnetic confinement indeed starts to play an important role."419 Furthermore. the inverse Compton energy loss length shortens drastically at these energies so that only strong magnetic fields can help avoiding the formation of an electromagnetic cascade and lead instead to synchrotron emission in the filament.," Furthermore, the inverse Compton energy loss length shortens drastically at these energies so that only strong magnetic fields can help avoiding the formation of an electromagnetic cascade and lead instead to synchrotron emission in the filament."420 In this section. we discuss the effect of the injected chemical composition and of the spectral index at the source.," In this section, we discuss the effect of the injected chemical composition and of the spectral index at the source."421 As discussed above. there are conflicting claims as to the measured chemical compositiot at ultrahigh energies: in particular. the HiRes experiment reports a light composition (?) while the Pierre Auger Observatory measurements point toward a composition that becomes increasingly heavier at energies above the ankle (?)..," As discussed above, there are conflicting claims as to the measured chemical composition at ultrahigh energies; in particular, the HiRes experiment reports a light composition \citep{Hires10} while the Pierre Auger Observatory measurements point toward a composition that becomes increasingly heavier at energies above the ankle \citep{Auger10}."422 Theory ts here of little help. as the source of ultrahigh energy cosmic rays is unknown: protons are usually considered as prime candidates because of their large cosmic abundance. but at the same time one may argue that a large atomic number facilitates acceleration to high energy.," Theory is here of little help, as the source of ultrahigh energy cosmic rays is unknown; protons are usually considered as prime candidates because of their large cosmic abundance, but at the same time one may argue that a large atomic number facilitates acceleration to high energy."423 In this framework. ? have proposed a test of the chemical composition of ultra-high energy cosmic rays on the sky. using the anisotropy patterns measured at various energies. instead of relying on measurements of the depth of maximum shower development.," In this framework, \cite{LW09} have proposed a test of the chemical composition of ultra-high energy cosmic rays on the sky, using the anisotropy patterns measured at various energies, instead of relying on measurements of the depth of maximum shower development."424 It is shown i particular that. at equal magnetic rigidities E/Z. one should observe a comparable or stronger anisotropy signal from the proton component than from the heavy nuclei component emitted by the source. even if the source injects protons and heavy nuclei in equal numbers at a given energy.," It is shown in particular that, at equal magnetic rigidities $E/Z$, one should observe a comparable or stronger anisotropy signal from the proton component than from the heavy nuclei component emitted by the source, even if the source injects protons and heavy nuclei in equal numbers at a given energy."425 When compared to the ο]., When compared to the c.l.426 anisotropy signal reported by the Pierre Auger Observatory at energies above 5.7x10 ev (22).. one concludes that: if the composition ts heavy at these energies. and if the source injects protons in at least equal number (at a given energy) as heavy nuclei. then one should observe a comparable or stronger anisotropy pattern above 5.7x10'?/ZeV. Future data will hopefully cast light on this issue. but in the meantime it Is necessary to consider a large set of possible chemical compositions.," anisotropy signal reported by the Pierre Auger Observatory at energies above $5.7\times10^{19}\,$ eV \citep{Auger1,Auger2}, one concludes that: if the composition is heavy at these energies, and if the source injects protons in at least equal number (at a given energy) as heavy nuclei, then one should observe a comparable or stronger anisotropy pattern above $5.7\times10^{19}/Z\,$ eV. Future data will hopefully cast light on this issue, but in the meantime it is necessary to consider a large set of possible chemical compositions."427 We thus consider the following injection spectra:, We thus consider the following injection spectra:428sensitive to the eutropy floor level of any aud all scaling relations that we have explored.,sensitive to the entropy floor level of any and all scaling relations that we have explored.429 If we exclude A1835 aud RXJ1317.5-1115 frou the fit. the cutropy floor is essentially unchanged (Wy=305!M keV cm?) but the fit is inproved (4Z=22.37/181.21).," If we exclude A1835 and RXJ1347.5-1145 from the fit, the entropy floor is essentially unchanged $K_0 = 305^{+80}_{-65}$ keV $^2$ ) but the fit is improved $\chi^2_{\nu} =43022.37/18 = 1.24$ )."431 Iu addition. we verify that splitting the sample by cooling flow status does not signuificautly modify the best-fit value 0.1iu of Avy.," In addition, we verify that splitting the sample by cooling flow status does not significantly modify the best-fit value 0.1in of $K_0$."432 As mentioned above. there appears to be a slight difference in the normalizations of the yyPy relatious for low aud high redshift clusters.," As mentioned above, there appears to be a slight difference in the normalizations of the $y_0-T_X$ relations for low and high redshift clusters."433 Is this difference siguificant?, Is this difference significant?434 If we restrict the fit to low redshift ἐν< 0.3) clusters only. we find a best-fit value of Ay=370!UM keV em? (AZ=9.69/12— (.81).," If we restrict the fit to low redshift $z < 0.3$ ) clusters only, we find a best-fit value of $K_0 = 435370^{+130}_{-95}$ keV $^2$ $\chi^2_{\nu} = 9.69/12 = 0.81$ )."436 This is cousisteut with thebest-fit for the whole sample., This is consistent with thebest-fit for the whole sample.437" Fitting ouly high redshift (5> 0.3) clusters we find a best-fit value of Ay=220!a"" keV cnm? (AZ=7961/5 1.53)."," Fitting only high redshift $z > 0.3$ ) clusters we find a best-fit value of $K_0 = 220^{+100}_{-70}$ keV $^2$ $\chi^2_{\nu} = 7.64/5 = 4381.53$ )."439 Therefore. there is oulv à marginal statistical difference between the best-fit values of Ay frou the low and high redshift clusters.," Therefore, there is only a marginal statistical difference between the best-fit values of $K_0$ from the low and high redshift clusters."440" A very similar result is deduced from an examination of the S,4,.7f£,Ty relation (which is nof as sensitive as the yo£x relation to the eutropv floor: MBIIDO3). where the low redshift clusters are best fit by eutropy floormodels with Ay~300 keV cu? while the high redshift clusters are best fit ly eutropy floor models with Wy~200 keV au?."," A very similar result is deduced from an examination of the $S_{\nu,arc}/f_{\nu}-T_X$ relation (which is not as sensitive as the $y_0 - T_X$ relation to the entropy floor; MBHB03), where the low redshift clusters are best fit by entropy floormodels with $K_0 \sim 300$ keV $^2$ while the high redshift clusters are best fit by entropy floor models with $K_0 \sim 200$ keV $^2$."441 The theoretical yyLx relations have the iuterestiug properties that they do not evolve strongly with redshift and. more iportautly. are virtually insensitive to the presence of an cutropy floor.," The theoretical $y_0-L_X$ relations have the interesting properties that they do not evolve strongly with redshift and, more importantly, are virtually insensitive to the presence of an entropy floor."442 The reason why this happens to be the case is not because the individual quantities. yy and Ly. aro unaffected by an eutropy fior (on the contrary. they are ereatly modified). but because they are both affected iu a very simular manner.," The reason why this happens to be the case is not because the individual quantities, $y_0$ and $L_X$, are unaffected by an entropy floor (on the contrary, they are greatly modified), but because they are both affected in a very similar manner."443 Therefore. this correlation is less than ideal when it comes to probing the nom-eravitational cutropy of galaxy clusters.," Therefore, this correlation is less than ideal when it comes to probing the non-gravitational entropy of galaxy clusters."444 However. the relation is still of exeat interest because it provides a valuable consistency check of the other scaling relations studied here.," However, the relation is still of great interest because it provides a valuable consistency check of the other scaling relations studied here."445 Figure 6 is a plot of the observed goLy rolatiou., Figure 6 is a plot of the observed $y_0-L_X$ relation.446 This ∩∙∐∐ ↕↴∖↴↴∖↴∏↻↸∖↥⋅↕∐∏⋯↴∖↴↸∖≼↧∪∐↑∐↸∖↻↥⋅↸∖≼∐↸⊳↑↸∖≼↧−∙∶∩∙⊇⇈↕∏↸⊳↨↘↽ ∐∐↸∖↴∖↴⋟⋜⋯≼↧∶∶∩∙⋅↱⊐⋖↑↕∐∐∐∐↸∖↴∖↴⋟↥⋅↸∖↕⋜↧↑↕∪∐↴∖↴↕≯∪↥⋅↑↕∐∖↴∖↴↸∖∐∟ simular model (dotted) aud the Ay = 100 (short-dashed). 300 (loug-dashed). 500. (dot-dashed). and 700 keV cui? (solid) eutropy floor models.," This 0.1in is superimposed on the predicted $z = 0.2$ (thick lines) and $z = 0.5$ (thin lines) relations for the self-similar model (dotted) and the $K_0$ = 100 (short-dashed), 300 (long-dashed), 500 (dot-dashed), and 700 keV $^2$ (solid) entropy floor models."447 Since the theoretical jjLx relations do not evolve strouely with redshift (compare the hin aud thick lines). a qualitative “by eve” comparison is »ossible.," Since the theoretical $y_0-L_X$ relations do not evolve strongly with redshift (compare the thin and thick lines), a qualitative “by eye” comparison is possible."448 A clear correlation between a clusters central Compton xuaneter audits bolometric X-ray luinosity is apparent in Figure 6., A clear correlation between a cluster's central Compton parameter and its bolometric X-ray luminosity is apparent in Figure 6.449 The relation is quite tight and follows he predicted treuds., The relation is quite tight and follows the predicted trends.450 Even the two massive cooling flow clusters AlsS35 and RNJI317.5-1115 secur to follow the xedieted trends., Even the two massive cooling flow clusters A1835 and RXJ1347.5-1145 seem to follow the predicted trends.451 Thus. the observed yyLx relation eives us confidence that our general understanding of ICM ds basically correct.," Thus, the observed $y_0-L_X$ relation gives us confidence that our general understanding of ICM is basically correct."452 That being said. the quality of the ft is uot ereat im a statistical sense (42-67.36/16= L211).," That being said, the quality of the fit is not great in a statistical sense $\chi^2_{\nu} = 67.36/16 = 4.21$ )."453 The high value of A uudoubtedlv arises from the randoni scatter present in the observed relation., The high value of $\chi^2_{\nu}$ undoubtedly arises from the random scatter present in the observed relation.454 The preseuce of this scatter may be inconsistent with theoretical predictions., The presence of this scatter may be inconsistent with theoretical predictions.455 We note. however. that observational systematic macertaities for yy and Ly are ou the order of cach (Reese et al.," We note, however, that observational systematic uncertainties for $y_0$ and $L_X$ are on the order of each (Reese et al."456 2002)., 2002).457 Ta addition. Abushotzkv Scharf (1997) have found that estimates of the N-rav huuinosities of clusters can vary from stucly to study bv up to20%.. most likely attributable to different measurement techniques.," In addition, Mushotzky Scharf (1997) have found that estimates of the X-ray luminosities of clusters can vary from study to study by up to, most likely attributable to different measurement techniques."458 Couscrvatively estimating the tof?wucertainty ou Ly to be 20%.. we find a significantly improved fit of \2=19.76/16 L2L ," Conservatively estimating the uncertainty on $L_X$ to be , we find a significantly improved fit of $\chi^2_{\nu} = 19.76/16 = 1.24$ ."459As expected. the eutropv floor level is not coustrained by the cata.," As expected, the entropy floor level is not constrained by the data."460 While the y).£x relation is insensitive to the cutropy, While the $y_0-L_X$ relation is insensitive to the entropy461While there ids a strong evidence for the existence of non-barvonie dark matter. little is known about its origius.,"While there is a strong evidence for the existence of non-baryonic dark matter, little is known about its origins."462 In ΤΕ popular scenario. dark matter particles aud antiparticles start iu thermal equilibrium with radiation.," In the currently popular scenario, dark matter particles and antiparticles start in thermal equilibrium with radiation."463" When temperature drops below the particle mass. mx. their comoving deusitv beeins an exponential fall uutil the annihilation time-scale. f,,,=GixGann) t becomes lavecr than the ase of the Universe."," When temperature drops below the particle mass, $m_X$, their comoving density begins an exponential fall until the annihilation time-scale, $t_{ann}=(n_X\left<\sigma_{ann}v\right>)^{-1}$ , becomes larger than the age of the Universe."464 Frou this point the comoving density of dark matter particles is assuuced frozen., From this point the comoving density of dark matter particles is assumed frozen.465" For the relic abundance of dark matter particles to be consistent with the present value of Qay, their aunibhilation rate at the time of freeze-out must equal (I&olb Turner 1989) Uuiless dark iatter is of non-thermal origin (Chnuug. Iolb Riotto 1995]. lower values of (Cann€; Would overclose the uuiverse aud therefore can be excluded."," For the relic abundance of dark matter particles to be consistent with the present value of $\Omega_{\rm dm}$ their annihilation rate at the time of freeze-out must equal (Kolb Turner 1989) Unless dark matter is of non-thermal origin (Chung, Kolb Riotto 1998), lower values of $\left<\sigma_{ann}v\right>$ would overclose the universe and therefore can be excluded."466 If dark matter particles interact through any known force. during the decoupling epoch. when Toong. their annihilation cross-section cau uot ↸∖⊼∩∖↸∖≺⇂⊔⋯⋯⋞⊰∩⊺−∿∩∣⊔⇀−∖⊳∙↕↴↴∖↴↕∐∶↴∙⊾↑∐↕↴∖↴↕⋜↧↸⊳↑∙:»Doge ⋅⋟," If dark matter particles interact through any known force, during the decoupling epoch, when $T\sim m_X$, their annihilation cross-section can not exceed $\sigma_{ann} \lsim \alpha/T^2\sim467\alpha/m_{X}^{2} $."468 ≼∶↥⋅↕↸∖↴∖↴↑∙∖↽↕↘⊽⋜⋯∐∪↕∐↘↽∪↖↖↽↴∖↨↘↽↕⋖↕∩∩↭∪↴⋝↑⋜↧↕↕∐∖≼⊔⋟↥⋅∪⋯∐⊔ an upper lait ou the mass of dark matter particles However. in this paper we point out that dark iatter candidates with higher mass and ower απμπαπο cross-section are uot necessarily inconsistent with the present value of O44.," Using this fact, Griest Kamionkowski (1990) obtained from \ref{ann}) ) an upper limit on the mass of dark matter particles However, in this paper we point out that dark matter candidates with higher mass and lower annihilation cross-section are not necessarily inconsistent with the present value of $\Omega_{\rm dm}$."469 Uulike he standard inodel which assunes the dark uatter coinoviug deusitv freezes out soon affer he temperature of the Universe drops below imxy. we show that it is possible for it to drop again ater. after dark matter particles form virialized ialos.," Unlike the standard model, which assumes the dark matter comoving density freezes out soon after the temperature of the Universe drops below $m_X$, we show that it is possible for it to drop again later, after dark matter particles form virialized halos."470" Unlike the standard model. where the matter becomes dominant only around 2~101, ina Universe with low σι) and lieh my the initial transition to matter domination happens much earlier."," Unlike the standard model, where the matter becomes dominant only around $z\sim 10^4$, in a Universe with low $\left<\sigma_{ann}v\right>$ and high $m_X$ the initial transition to matter domination happens much earlier."471 Consequceutly the erowth of density perturbations aud the formation of the first, Consequently the growth of density perturbations and the formation of the first472rangethe authors consider this redshift determination only ‘tentative’.,range–the authors consider this redshift determination only `tentative'.473 Lt is true however that other identifications that would put the redshift in agreement. with the photometric measurement A1900 or ÀAAI548.1551) are also problematic because of the absence of other important lines in the observed range.," It is true however that other identifications that would put the redshift in agreement with the photometric measurement $\lambda1909$ or $\lambda\lambda$ 1548,1551) are also problematic because of the absence of other important lines in the observed range."474 We have checked: our photometry and do not see any particular problem with the object.it is isolated. and it does not look likely that light from nearby objects could. either fool our photometry or produce spurious emission lines.," We have checked our photometry and do not see any particular problem with the object–it is isolated, and it does not look likely that light from nearby objects could either fool our photometry or produce spurious emission lines."475 It is not clear what is causing the divergence., It is not clear what is causing the divergence.476 In order to check that the confidence intervals we are calculating are consistent. we perform the following test: for each object. we observe whether the spectroscopic (real?) redshift is consistent with our value to within a le. 27. 30 or none of them.," In order to check that the confidence intervals we are calculating are consistent, we perform the following test: for each object, we observe whether the spectroscopic (`real') redshift is consistent with our value to within a $1\sigma$, $2\sigma$, $3\sigma$ or none of them."477 Given the uncertainty about 11419 discussed in the previous paragraph. we do not include it in this calculation.," Given the uncertainty about 1419 discussed in the previous paragraph, we do not include it in this calculation."478 Phe results are listed in Table 2. together with a comparison with the expectations for a pure normal distribution.," The results are listed in Table 2, together with a comparison with the expectations for a pure normal distribution."479 Lt must be noticed that the object which is further than 3m is actually only marginally so: the spectroscopic redshift is τομ= 0.483. with the three sigma interval around sn=0.230 being 0.0000.473].," It must be noticed that the object which is further than $3\sigma$ is actually only marginally so: the spectroscopic redshift is $z_{\rm sp}=0.483$ , with the three sigma interval around $z_{\rm ph}=0.230$ being [0.000–0.473]."480 In any case. the presence of a»3a deviation in a sample of 151 members is. as indicated in the table. not particularly remarkable.," In any case, the presence of a $>3\sigma$ deviation in a sample of 151 members is, as indicated in the table, not particularly remarkable."481 The results in Table 2 are indicative of the accuracy of our error estimates., The results in Table 2 are indicative of the accuracy of our error estimates.482 We think that this proves that the method. here described is a consistent and efficient. way to estimate the errors associated to the photometric redshift measurements. and that this method should be used in order to obtain error estimates of any quantity which is measured based on catalogues of photometric redshilts.," We think that this proves that the method here described is a consistent and efficient way to estimate the errors associated to the photometric redshift measurements, and that this method should be used in order to obtain error estimates of any quantity which is measured based on catalogues of photometric redshifts."483 We have presented a complete analysis of the sources of error present in the photometric redshift determination technique., We have presented a complete analysis of the sources of error present in the photometric redshift determination technique.484 After showing in a previous paper (11901) that photometric redshilts are at least as reliable as traditional spectroscopic redshifts when it comes to the measurement of faint galaxies. we show in this paper that the photometric redshifts have an additional advantage: the error in the measurement can be completely characterised by means of a redshift probability 'unction.," After showing in a previous paper (FS01) that photometric redshifts are at least as reliable as traditional spectroscopic redshifts when it comes to the measurement of faint galaxies, we show in this paper that the photometric redshifts have an additional advantage: the error in the measurement can be completely characterised by means of a redshift probability function."485 We have described how this probability. function. can x» obtained for each individual object. making use of he redshift’ likelihood function. (whieh accounts. for the ohotometric uncertainties) anc of the error. component hat is added as a svstematic ellect by our technique.," We have described how this probability function can be obtained for each individual object, making use of the redshift likelihood function (which accounts for the photometric uncertainties) and of the error component that is added as a systematic effect by our technique."486 We jwe mocdelled this component as a gaussian with variable variance. σι=δα|z). and measured the parameter Nom0.065 from a large sample of reliable recshilts.," We have modelled this component as a gaussian with variable variance, $\sigma_z=\Sigma (1+z)$, and measured the parameter $\Sigma=0.065$ from a large sample of reliable redshifts."487 By convolving both error components we obtain a Cor cach object. that casily allows for the determination of confidence intervals associated to the value of the photometric recshilt.," By convolving both error components we obtain a for each object, that easily allows for the determination of confidence intervals associated to the value of the photometric redshift."488 We have checked that the confidence limits thus calculated. are consistent. and suggest that any quantity (ο be measured. from. photometric redshift catalogues in. the future should. make use of similar techniques. in order to account for the errors inherent to the process of redshift determination.," We have checked that the confidence limits thus calculated are consistent, and suggest that any quantity to be measured from photometric redshift catalogues in the future should make use of similar techniques, in order to account for the errors inherent to the process of redshift determination."489 We would like to thank our referee. Mark Lacy. for his insightful comments that have improved the clarity of the paper.," We would like to thank our referee, Mark Lacy, for his insightful comments that have improved the clarity of the paper."490 ABS gratefully. acknowledges thesupport. of the European Commission through a Alarie CurieFellowship., AFS gratefully acknowledges thesupport of the European Commission through a Marie CurieFellowship.491fall in the 15” radius GRB extraction region.,fall in the $''$ radius GRB extraction region.492 Thus we finally obtain an estimate of 50319 jet afterglow counts in the 0.210 keV energy baud (3341 3 in the PN camera alouc)., Thus we finally obtain an estimate of $\pm$ 19 net afterglow counts in the 0.2–10 keV energy band $\pm$ 13 in the PN camera alone).493 An alternative approach cousists in directly 1ieasuriug the backeround and ACN contamination based on au appropriate extraction region close to the afterglow position. ax was done in Ticneoetal.(2003).," An alternative approach consists in directly measuring the background and AGN contamination based on an appropriate extraction region close to the afterglow position, as was done in \cite{tiengo}."494".. Tn this wav we obtain 51419 net afterelow counts in tc 15"" CRD extraction region (sec Fie.", In this way we obtain $\pm$ 19 net afterglow counts in the $''$ GRB extraction region (see Fig.495 1)., 1).496 As a further test we developed a maxima likelihood analysis program aud used it to model tie region of 1 0.210. keV PN image containing aud ιο AGN., As a further test we developed a maximum likelihood analysis program and used it to model the region of the 0.2–10 keV PN image containing and the AGN.497 We used the appropriate PSF and let the TOS1ος and intensities of the two sources. as wel as 16 background level. as free paraineters.," We used the appropriate PSF and let the positions and intensities of the two sources, as well as the background level, as free parameters."498" This vielded an sootensity normalization for the afterglow correspoudine to 31 PN couuts within a radius of 15"",", This yielded an intensity normalization for the afterglow corresponding to 34 PN counts within a radius of $''$.499 The source positions. 16 background level and the AGN intensity derived in his wav were also consistent with the values fouud with the ucthods described above.," The source positions, the background level and the AGN intensity derived in this way were also consistent with the values found with the methods described above."500 Iu conclusion. since all methods eave consistent restIts. in the following we adopt the count estimate obtained with he first method. which corresponds to a 2.70 detection.," In conclusion, since all methods gave consistent results, in the following we adopt the count estimate obtained with the first method, which corresponds to a $\sigma$ detection."501 Since the small statistics docs not permit to carry out a detailed spectral analysis. a spectral model must be ASSTLLLULCE to convert count rates to plivsical flux units.," Since the small statistics does not permit to carry out a detailed spectral analysis, a spectral model must be assumed to convert count rates to physical flux units."502 The spectra measured in the previous X.rav observations were well fitted by a power law., The spectra measured in the previous X–ray observations were well fitted by a power law.503 Iu the first observation. the photon iudex could be tightly coustrained at T=2.17!M., In the first observation the photon index could be tightly constrained at $\Gamma$ $_{-0.03}^{+0.04}$.504 The followiug observations. performed by.. eave a strone upper limit on the jieutral bydrogcen column density. which cannot differ substantially from the Galactic value of Nyp=2 <1yeu 7.," The following observations, performed by, gave a strong upper limit on the neutral hydrogen column density, which cannot differ substantially from the Galactic value of $_{\rm H}$ $\times10^{20}$ $^{-2}$ ."505 We have then verified that a1 absorbed power law with [T=2.17 aud Aqὃς10°? ? gives au acceptable fit to all the Nrav spectra of the afterglow micasured up to now., We have then verified that an absorbed power law with $\Gamma$ =2.17 and $N_{\rm H}=2\times10^{20}$ $^{-2}$ gives an acceptable fit to all the X–ray spectra of the afterglow measured up to now.506 We thus asstme such a Spectitlu. which vields an observed flux (ne. uot corrected for the absorption) of (6.22.3) «10i6 cre »s liu. the 2 keV range.," We thus assume such a spectrum, which yields an observed flux (i.e. not corrected for the absorption) of $\pm$ $\times10^{-16}$ erg $^{-2}$ $^{-1}$ in the 0.5--2 keV range."507 To derive the long teria fux history of the afterglow in a consistent wav. we have re-analyzed the two observations of May. 2003 usine the procedures described above.," To derive the long term flux history of the afterglow in a consistent way, we have re-analyzed the two observations of May 2003 using the procedures described above."508 In particular. we reprocessed the PN data with the new cleaning algorithim aud verified that the different wavs of estimating the AGN contamination eave consistent results.," In particular, we reprocessed the PN data with the new cleaning algorithm and verified that the different ways of estimating the AGN contamination gave consistent results."509 As for the December observation. we finally adopt the values based ou the first method: 501-425 and 1002425 uet afterglow counts for the first aud second observation. respectively.," As for the December observation, we finally adopt the values based on the first method: $\pm$ 25 and $\pm$ 25 net afterglow counts for the first and second observation, respectively."510 The light curve from the three observations is well fit by a power law decay with iudex 6=1. 1540.2 (Fie., The light curve from the three observations is well fit by a power law decay with index $\delta$ $\pm$ 0.2 (Fig.511 2)., 2).512 For a power law spectu with P=2.17 aud Ay=)10?P D7. the above couut rates correspond to 0.52 seV observed fluxes of (1307) «10.19 and (7945) «10.19 ere cin? +t. respectively.," For a power law spectrum with $\Gamma$ =2.17 and $N_{\rm H}=2\times10^{20}$ $^{-2}$, the above count rates correspond to 0.5–2 keV observed fluxes of $\pm$ $\times10^{-16}$ and $\pm$ $\times10^{-16}$ erg $^{-2}$ $^{-1}$, respectively."513"""n7.. These flix estimates. do not change significantly if the spectral parameters are allowed ο vary within their confidence intervals (Ticugo ct al.", These flux estimates do not change significantly if the spectral parameters are allowed to vary within their confidence intervals (Tiengo et al.514 2003)., 2003).515 To draw a complete Xrav light curve containing both he aud data. an extrapolation of the Nrav spectrum is unavoidable.," To draw a complete X–ray light curve containing both the and data, an extrapolation of the X–ray spectrum is unavoidable."516 In fact. most of he counts detected by EPIC have energies below 2 keV. while the PCA instrument of the satellite is not sensitive to such low energv photons.," In fact, most of the counts detected by EPIC have energies below 2 keV, while the PCA instrument of the satellite is not sensitive to such low energy photons."517 We herefore extracted the 0.52 keV fluxes of the observations from the best fit absorbed power aw model to cach PCA spectrum. obtaining the values reported in Table 1.," We therefore extracted the 0.5–2 keV fluxes of the observations from the best fit absorbed power law model to each PCA spectrum, obtaining the values reported in Table 1."518 The correspoucding errors take mto account the uncertainties on the spectral shape., The corresponding errors take into account the uncertainties on the spectral shape.519 The resulting lieht curve is shown in Figure 3., The resulting light curve is shown in Figure 3.520 Fitting it with a single power law vields a time decay with à-1. 7840.02 aud reduced. 47D of tas2.6., Fitting it with a single power law yields a time decay with $\delta$ $\pm$ 0.02 and reduced $\chi^2$ of 2.6.521- As shown above. a siuele power luv decav gives a mnareinally acceptable 61.)," As shown above, a single power law decay gives a marginally acceptable c.l.)"522 description of the Nrav afterelow from 5 hours to almost nine months from the burst., description of the X–ray afterglow from 5 hours to almost nine months from the burst.523 The data presented in Tiengoetal.(2003) Were consistent with a break in the XN.ray light curve at t0.[5 davs., The data presented in \cite{tiengo} were consistent with a break in the X–ray light curve at $\sim$ 0.45 days.524 Similarly to the optical data available at that time. 1e decay slope changed from ~0.9 to —1.9.," Similarly to the optical data available at that time, the decay slope changed from $\sim$ 0.9 to $\sim$ 1.9."525 Notethat in Tiengoetal.(2003) we used fluxes inthe 2.10 keV energy ας. Which was optimal to represent the observed fux iu ιο PCA range. but implied a substautial extrapolation," Notethat in \cite{tiengo} we used fluxes in the 2–10 keV energy band, which was optimal to represent the observed flux in the PCA range, but implied a substantial extrapolation"526 The bulge of a galaxv. though consisting of mainlv old stars. is a mecca of activities.," The bulge of a galaxy, though consisting of mainly old stars, is a mecca of high-energy activities."527 Low-mass X-ray binaries (LAINBs). in the huninositv range of," Low-mass X-ray binaries (LMXBs), in the luminosity range of"528"simulations presented here, this curvature is small and probably does not influence the results significantly.","simulations presented here, this curvature is small and probably does not influence the results significantly."529" The parameter has technical significance, however, because it also controls the opening of the lateral boundaries."," The parameter has technical significance, however, because it also controls the opening of the lateral boundaries."530" The remaining two numbers are chosen to be fy:=8mpo/B?, which controls the strength of the magnetic field, and the Mach number M,:=vob/6.0. Which determines the speed of rotation."," The remaining two numbers are chosen to be $\betab \coloneqq 8\pi p_0 / B_\bnd^2$, which controls the strength of the magnetic field, and the Mach number $\Mb \coloneqq \vphimax /531\cso$, which determines the speed of rotation."532" Note that in the emerging field model (E), B is a measure of the field strength but not a local plasma-beta value, since the pressure entering its definition is not measured at the same location as the field strength."," Note that in the emerging field model (E), $\betab$ is a measure of the field strength but not a local plasma-beta value, since the pressure entering its definition is not measured at the same location as the field strength."533" For the sake of clarity, we usually omit the units in the presentation of the results."," For the sake of clarity, we usually omit the units in the presentation of the results."534 The concerned quantity is then measured in terms of the associated normalization unitlisted in Table 1.., The concerned quantity is then measured in terms of the associated normalization unitlisted in Table \ref{tab:units}.535 As explained in Sect., As explained in Sect.536" 2 above, the calculations were done with different models for the rotating magnetic field configuration."," \ref{sec:models} above, the calculations were done with different models for the rotating magnetic field configuration."537" It turns out that some of these cases produce long-lived jets, others only transient flows or flows that dissipate in the atmosphere close to the source."," It turns out that some of these cases produce long-lived jets, others only transient flows or flows that dissipate in the atmosphere close to the source."538" The results presented in the following subsection were obtained with setup D (Sect. 3.1.1)),"," The results presented in the following subsection were obtained with setup D (Sect. \ref{sec:setupD}) ),"539 those in the subsequent subsections were obtained with setup E (Sect. 3.1.2))., those in the subsequent subsections were obtained with setup E (Sect. \ref{sec:setupE}) ).540 Simulation setup D with the field geometry in Fig., Simulation setup D with the field geometry in Fig.541" laa was found to produce extended, collimated outflows."," \ref{fig:emergecases}a a was found to produce extended, collimated outflows."542" However, the magnetic field at the base of the jet decays in this case (hence the “D”) and is not replenished, for which reason these jets are not permanent."," However, the magnetic field at the base of the jet decays in this case (hence the “D”) and is not replenished, for which reason these jets are not permanent."543 The forced rotation at the lower boundary stretches the magnetic field lines in azimuthal (y) direction around the axis of rotation (y)., The forced rotation at the lower boundary stretches the magnetic field lines in azimuthal $\varphi$ ) direction around the axis of rotation $y$ ).544 The gas is accelerated upwards and the magnetic field assumes a tangled helical structure., The gas is accelerated upwards and the magnetic field assumes a tangled helical structure.545 A good momentary acceleration was obtained with the parameters (f 18).," A good momentary acceleration was obtained with the parameters $(\betab=1/4,\Mb=18)$ ."546 The magnetic field in this case is depicted in Fig. 4.., The magnetic field in this case is depicted in Fig. \ref{fig:flinesD}.547 The jet diameter is resolved with about 35 grid cells in this simulation., The jet diameter is resolved with about 35 grid cells in this simulation.548" The jet attains a height of about 30 times its initial diameter, the factor of expansion being about 7."," The jet attains a height of about 30 times its initial diameter, the factor of expansion being about 7."549 It reaches velocities that are close to Mp and about a factor of 10 above the escape speed., It reaches velocities that are close to $\Mb$ and about a factor of $10$ above the escape speed.550" The field lines are closing with the lower boundary: inside the jet. the radial magnetic field has the same polarity as on the disk, whereas the net radial magnetic flux fB,dA, integrated over the r—const surface, is virtually zero at all times and all radii."," The field lines are closing with the lower boundary: inside the jet, the radial magnetic field has the same polarity as on the disk, whereas the net radial magnetic flux $\int B_r \, \de A$, integrated over the $r=\const$ surface, is virtually zero at all times and all radii."551" The “absolute flux” f|B,|dA decreases linearly with time near the lower boundary.", The “absolute flux” $\int \abs{B_r} \de A$ decreases linearly with time near the lower boundary.552" Increased temperatures near the outside of the rotating surface indicate that a substantial amount of magnetic field is being dissipated there, see Fig. 5.."," Increased temperatures near the outside of the rotating surface indicate that a substantial amount of magnetic field is being dissipated there, see Fig. \ref{fig:lic}."553" Due to the rotation, the magnetic field assumes a vortex-like structure, at the border of which magnetic field lines of opposite polarities become entangled."," Due to the rotation, the magnetic field assumes a vortex-like structure, at the border of which magnetic field lines of opposite polarities become entangled."554 This leads to a continuous decay of the magnetic field., This leads to a continuous decay of the magnetic field.555" Such a decay of the magnetic field, through wrapping up of field lines followed by cancellation through diffusion, is called “convective expulsion” in overturning flows (e.g.??).."," Such a decay of the magnetic field, through wrapping up of field lines followed by cancellation through diffusion, is called “convective expulsion” in overturning flows \citep[e.g.][]{1956Zeldovich,1963Parker}."556 The magnetic field in the physical source of a successful jet evidently must be of a different nature., The magnetic field in the physical source of a successful jet evidently must be of a different nature.557 This calls for a modification of the boundary conditions at the base of our simulations., This calls for a modification of the boundary conditions at the base of our simulations.558 Such cases are discussed in the following sections., Such cases are discussed in the following sections.559" Simulation setup E, in which the magnetic field loops above the rotating surface are continuously replenished, produced long-lasting jets that propagate considerable distances."," Simulation setup E, in which the magnetic field loops above the rotating surface are continuously replenished, produced long-lasting jets that propagate considerable distances."560" Before presenting big simulations with long jets in the next two sections, we discuss the influence of the parameters (B5,Mp) on the results by comparing a series of smaller, computationally cheaper simulations in which these parameters are varied."," Before presenting big simulations with long jets in the next two sections, we discuss the influence of the parameters $(\betab,\Mb)$ on the results by comparing a series of smaller, computationally cheaper simulations in which these parameters are varied."561" Although the proximity of the upper boundary possibly influences the results (see discussion of instabilities below), the small simulations give clear indications about which parameters yield efficient jets."," Although the proximity of the upper boundary possibly influences the results (see discussion of instabilities below), the small simulations give clear indications about which parameters yield efficient jets."562" The simulations cover the relatively short distance of 20 length units (40 disk radii), with 10«r30 and 6,9=7/2x 1/9, the resolution being 256x9696."," The simulations cover the relatively short distance of $20$ length units $40$ disk radii), with $10<r<30$ and $\theta,\phi=\pi/2\pm\pi/9$ , the resolution being $256\times96\times96$."563 The atmospheric density differs by a factor 27 between the lower and upper boundaries., The atmospheric density differs by a factor $27$ between the lower and upper boundaries.564 The simulations were pursued until f~ 100., The simulations were pursued until $t\approx100$ .565" In the cases where a jet was successfully launched, this suffices"," In the cases where a jet was successfully launched, this suffices"566random variables. one can derive analyical expressions for the distributions of total intensity. polarization. and fractional polarization. as well as distributions for the orientation angles of the polarization vector.,"random variables, one can derive analytical expressions for the distributions of total intensity, polarization, and fractional polarization, as well as distributions for the orientation angles of the polarization vector."567 The main result [rom the model for the purposes of this paper is the derivation of the conditional density of the polarization vectors orientation angles., The main result from the model for the purposes of this paper is the derivation of the conditional density of the polarization vector's orientation angles.568 The conditional density is (he joint probability density of (he vectors colatitude. 9. and longitude. © at a fixed value of polarization amplitude. +.," The conditional density is the joint probability density of the vector's colatitude, $\theta$, and longitude, $\phi$, at a fixed value of polarization amplitude, $r_o$."569 It captures the functional form of the more general joint density in a simple analviical expression., It captures the functional form of the more general joint density in a simple analytical expression.570 H is known as (he Bineham-Aarcia (Dingham Marclia 1978). or von Mises-Fisher. distribution.," It is known as the Bingham-Mardia (Bingham Mardia 1978), or von Mises-Fisher, distribution."571 The conditional clensity is parameterized by (he constants & and 5 ancl is normalized by the constant ic., The conditional density is parameterized by the constants $\kappa$ and $\gamma$ and is normalized by the constant $w$.572 The constant & can be regarded as a signal-to-nolse ratio in polarization., The constant $\kappa$ can be regarded as a signal-to-noise ratio in polarization.573 The constant 5 satisfies the relation |5|€1., The constant $\gamma$ satisfies the relation $|\gamma|\le 1$.574 By construction. the distribution is symmetric in longitude. which is uniformly. distributed over 27.," By construction, the distribution is symmetric in longitude, which is uniformly distributed over $2\pi$."575 The vectors longitude and colatitude are statistically independent of one another., The vector's longitude and colatitude are statistically independent of one another.576 The plus signs in the argument of the exponential in Equation 1l occur when the polarization fluctuations are predominantly parallel to the mode diagonal., The plus signs in the argument of the exponential in Equation \ref{eqn:BM} occur when the polarization fluctuations are predominantly parallel to the mode diagonal.577 They are caused by the randomly varving intensities of the OPMs., They are caused by the randomly varying intensities of the OPMs.578 In this case. the functional form of the colatitude conditional clensity is generally. bimodal.," In this case, the functional form of the colatitude conditional density is generally bimodal."579 The polarization pattern formed by a projection of the conditional densitv generally consists of a set of concentric circular contours in each hemisphere of the projection., The polarization pattern formed by a projection of the conditional density generally consists of a set of concentric circular contours in each hemisphere of the projection.580 The circular shape of the pattern arises [rom the svmnietrvy in longitude., The circular shape of the pattern arises from the symmetry in longitude.581 The minus signs in the argument of the exponentail in Equation 1. occur when the polarization [Iuctuations are predominantly perpendicular to the mode diagonal., The minus signs in the argument of the exponentail in Equation \ref{eqn:BM} occur when the polarization fluctuations are predominantly perpendicular to the mode diagonal.582 The origin ol these perpendieular fluctuations is not known. but is discussed in the following section.," The origin of these perpendicular fluctuations is not known, but is discussed in the following section."583 In this case. the conditional densitv is always unimodal because it is normal in cos8.," In this case, the conditional density is always unimodal because it is normal in $\cos\theta$."584 The polarization pattern lormed by (he projection of this conditional densitv is generally a complete annulus in only one of the two projection hemispheres (Mcelxinnon 2009)., The polarization pattern formed by the projection of this conditional density is generally a complete annulus in only one of the two projection hemispheres (McKinnon 2009).585 The general applicability of Equation 1. can be illustrated. with a few special cases., The general applicability of Equation \ref{eqn:BM} can be illustrated with a few special cases.586 When &=0. the polarization fluctuations are dominated by instrumental noise. and the conditional density becomes isotropic. as one would expect for pure noise.," When $\kappa=0$, the polarization fluctuations are dominated by instrumental noise, and the conditional density becomes isotropic, as one would expect for pure noise."587 When &lI. the fluctuations are very small in comparison to the polarized signal. and the conditional density becomes a Fisher distribution (Fisher et al.," When $\kappa\gg 1$, the fluctuations are very small in comparison to the polarized signal, and the conditional density becomes a Fisher distribution (Fisher et al."588 1987)., 1987).589 When +=0 and the fluctuations, When $\gamma=0$ and the fluctuations590An even tighter constraint on the dark matter interaction can be obtained [rom bulge svstems if compression of the dark halo is allowed for.,	An even tighter constraint on the dark matter interaction can be obtained from bulge systems if compression of the dark halo is allowed for.591 In Appendix D we show that condensation of barvons results in a steeper inner density profile with a’=f(a.£). where a and o! are the inner clark matter profile exponents before and after compression respectively. and € is (he exponent of (he inner profile of the total mass density (barvous plus dark matter) aller compression.," In Appendix B we show that condensation of baryons results in a steeper inner density profile with $\alpha^{\prime}=f(\alpha,\xi)$, where $\alpha$ and $\alpha^{\prime}$ are the inner dark matter profile exponents before and after compression respectively, and $\xi$ is the exponent of the inner profile of the total mass density (baryons plus dark matter) after compression."592 Specifically. we show that. in the collisionless (À/r2»1) and highly collisional (A/r< 1) limits. the final dark matter cusp slope is For a final Hat rotation curve. typical of normal bulge dominated galaxies. £=2. giving (he simple result The most likely CDM. value of a=1.3. gives à!=1.74.," Specifically, we show that, in the collisionless $\lambda/r \gg 1$ ) and highly collisional $\lambda/r \ll 1$ ) limits, the final dark matter cusp slope is For a final flat rotation curve, typical of normal bulge dominated galaxies, $\xi=2$, giving the simple result The most likely CDM value of $\alpha=1.3$, gives $\alpha^{\prime}=1.74$."593 The tightest constraint is obtained by comparing to the bulge svstem that lies on the observed Mg—υ relation. since roughly speaking the Mp;—¢ scaling for SIDM black holes is as steep as or shallower than that observed.," The tightest constraint is obtained by comparing to the bulge system that lies on the observed $M_{BH}-v$ relation, since roughly speaking the $M_{BH}-v$ scaling for SIDM black holes is as steep as or shallower than that observed."594 To this end. we compare to the black hole at the galactic Mp23.0x10AL. (Genzel et al.," To this end, we compare to the black hole at the galactic $M_{BH}\approx 3.0\times 10^6 \ M_{\odot}$ (Genzel et al."595 2000). which is the smallest reliable mass estimate that lies on the observed. Mg;—e (Ferrarese Merritt2000: Gebhardt et al.," 2000), which is the smallest reliable mass estimate that lies on the observed $M_{BH}-v$ (Ferrarese Merritt2000; Gebhardt et al."596 2000: Merritt Ferrarese 2001)., 2000; Merritt Ferrarese 2001).597 Using this value in eqn. (5.1)).," Using this value in eqn. \ref{sig33}) ),"598" with à and p; determinedfrom the scaling relations for Mj,=3.0x107AL. gives. σαLelog"," with $r_s$ and $\rho_s$ determinedfrom the scaling relations for $M_{halo} = 3.0 \times 10^{12} \ M_{\odot}$ gives, _1"599day.,day.600 Including the time required to apply the nonlinear filter. which for the laptop used takes ~4s per light curve per filter duration. this would increase to ~3d (using three dilferent filter durations).," Including the time required to apply the nonlinear filter, which for the laptop used takes $\sim 4\,$ s per light curve per filter duration, this would increase to $\sim 3\,$ d (using three different filter durations)."601 This is achieved at no cost in elliciency: in white noise only. the algorithm is capable of detecting transits down to approximately the same S/N limit as that quoted by ?. for their BLS method. which has been the most successful method to date in terms ofpractical results. being used by the OGLE team to discover most of their cancidate ransits. sce (??)..," This is achieved at no cost in efficiency: in white noise only, the algorithm is capable of detecting transits down to approximately the same $S/N$ limit as that quoted by \citet{kzm02} for their BLS method, which has been the most successful method to date in terms of practical results, being used by the OGLE team to discover most of their candidate transits, see \citep{uzs+02,ups+03}."602 This approach is preclicatech on the assumption of »eriodic transits hidden in random noise. usually assumed to ος superposed on a flat continuum with regular continuous sampling.," This approach is predicated on the assumption of periodic transits hidden in random noise, usually assumed to be superposed on a flat continuum with regular continuous sampling."603 In the real world. stellar (micro) variability is expected to be the dominant. signal component.," In the real world, stellar (micro) variability is expected to be the dominant signal component."604 We have hen shown how to generalise the transit finding method to he more realistic scenario where complex stellar variability. irregular sampling and long gaps in the data. are all present.," We have then shown how to generalise the transit finding method to the more realistic scenario where complex stellar variability, irregular sampling and long gaps in the data, are all present."605 The two filtering methods developed to deal with this case share some advantages both can be applied to data with gaps but they also have different properties., The two filtering methods developed to deal with this case share some advantages – both can be applied to data with gaps – but they also have different properties.606 The least-squaresi fittinge method. is capable of making. use of the time information in cata with irregular sampling., The least-squares fitting method is capable of making use of the time information in data with irregular sampling.607ὃν lt also allows a theoretically optimal filter tthe Wiener or matched filter) to be combined with a pre-whitening filter. although from the point of view of detection. the matched filler is the main active component of any maximum likelihood-basecl detection. algorithm.," It also allows a theoretically optimal filter the Wiener or matched filter) to be combined with a pre-whitening filter, although from the point of view of detection, the matched filter is the main active component of any maximum likelihood-based detection algorithm."608 As à by. product. of the filtering. the stellar signal can also be reconstructed.," As a by product of the filtering, the stellar signal can also be reconstructed."609 llowever. this is computationally intensive. particularly if one wishes to [it higher frequencies.," However, this is computationally intensive, particularly if one wishes to fit higher frequencies."610 Lts performance also depends quite critically on concordance between the cluration of the reference transit and that of any true transit., Its performance also depends quite critically on concordance between the duration of the reference transit and that of any true transit.611 On the other hand. iterative non-linear filtering is simple to implement ancl fast. but ignores any local time information (except for the long gaps which are detected automatically).," On the other hand, iterative non-linear filtering is simple to implement and fast, but ignores any local time information (except for the long gaps which are detected automatically)."612 This means that its performance is likely to degrade if the sampling is seriously irregular., This means that its performance is likely to degrade if the sampling is seriously irregular.613 However. it is he most efficient method in cases such as those investigated iere.," However, it is the most efficient method in cases such as those investigated here."614 By removing any signal on timescales longer than wo-three times the estimated transit duration. it is likely o be less alfected. by the value chosen for that duration.," By removing any signal on timescales longer than two-three times the estimated transit duration, it is likely to be less affected by the value chosen for that duration."615 Although more work is needed to establish quantitatively he relative merits of the two approaches. it seems. more ellicient. given the results so far. to use the iterative non-inear filtering method prior to a general transit search.," Although more work is needed to establish quantitatively the relative merits of the two approaches, it seems more efficient, given the results so far, to use the iterative non-linear filtering method prior to a general transit search."616 The cast-squares fitting method could be emploved in the more cdillicult vvery irregular sampling) or borderline (as in Sect. 4.2.2)), The least-squares fitting method could be employed in the more difficult very irregular sampling) or borderline (as in Sect. \ref{sec:borderline}) )617 cases. where the additional information used about the transit shape may Lead to better performance.," cases, where the additional information used about the transit shape may lead to better performance."618 Whatever the method used. there is a fundamental limit o what can be achieved.," Whatever the method used, there is a fundamental limit to what can be achieved."619 Stellar variability can only be iltered out if an orthogonal decomposition of the transit and stellar signal is possible. if the two signatures in the requency domain do not overlap by too much.," Stellar variability can only be filtered out if an orthogonal decomposition of the transit and stellar signal is possible, if the two signatures in the frequency domain do not overlap by too much."620 Therefore. very rapidly rotating stars where the rotation perioc is close to the transit curation. or stars showing much more power than the Sun on timescales of minutes to hours thigher meso- or super-granulation) will be problematic argets.," Therefore, very rapidly rotating stars where the rotation period is close to the transit duration, or stars showing much more power than the Sun on timescales of minutes to hours higher meso- or super-granulation) will be problematic targets."621 Even in the hypothetical situation where all stellar noise is removed. the remaining white noise will also place a imit on the performance of the transit detection algorithm. and hence on the apparent magnitude of star around which transits of a certain depth can be found.," Even in the hypothetical situation where all stellar noise is removed, the remaining white noise will also place a limit on the performance of the transit detection algorithm, and hence on the apparent magnitude of star around which transits of a certain depth can be found."622 In white Gaussian noise. any transit vielding a signal-to-noise ratio above a fixed threshold. (estimated to be zz6 in Sect. 4.2.1))," In white Gaussian noise, any transit yielding a signal-to-noise ratio above a fixed threshold (estimated to be $\approx 6$ in Sect. \ref{sec:photonly}) )"623 should be detectable., should be detectable.624 Considering photon noise alone. for a given stellar racius. orbital period and transit duration. the smallest. detectable planet radius. would therefore scale as D orexp(m/10) where D and m are the star's apparent brightness and magnitude respectively.," Considering photon noise alone, for a given stellar radius, orbital period and transit duration, the smallest detectable planet radius would therefore scale as $B^{-1/4}$ or $\exp(m/10)$ where $B$ and $m$ are the star's apparent brightness and magnitude respectively."625 The natural progression of this work will be further quantification of the performances attained. and the identification of the best method to use for a given situation sstar-planet combination. instrument characteristics and/or sampling).," The natural progression of this work will be further quantification of the performances attained, and the identification of the best method to use for a given situation star-planet combination, instrument characteristics and/or sampling)."626 As in the present paper. this can be done hrough Monte Carlo simulations. and more realistic noise xoliles can be included in the light curves instrumental noise).," As in the present paper, this can be done through Monte Carlo simulations, and more realistic noise profiles can be included in the light curves instrumental noise)."627 Extensive simulations can be performed for a given arget field. by coupling the stellar variability. model to a galactic population model and any available extinction information on the field., Extensive simulations can be performed for a given target field by coupling the stellar variability model to a galactic population model and any available extinction information on the field.628 However. it will only be meaningful ο carry out such simulations when the design. target Liclels and observing strategies of the missions in question are inalised and when more information about stellar. micro-variability is available.," However, it will only be meaningful to carry out such simulations when the design, target fields and observing strategies of the missions in question are finalised and when more information about stellar micro-variability is available."629 Our main conclusion if that even with realistic contamination fron stellar. variability. irregular. sampling. anc gaps in the data record. it ds still. possible to detect. transiting planets with an efficiency. close to. the idealised theoretical bound.," Our main conclusion if that even with realistic contamination from stellar variability, irregular sampling, and gaps in the data record, it is still possible to detect transiting planets with an efficiency close to the idealised theoretical bound."630 In particular. space missions are tantalisingly close to being capable of detecting carth-like planets around C ancl Ix. cwarfs.," In particular, space missions are tantalisingly close to being capable of detecting earth-like planets around G and K dwarfs."631 AA. acknowledges support. from ΑΟ studentship number PDPAX/5/5/2003/03183 and from the Isaac Newton ‘Trust., A. acknowledges support from PPARC studentship number PPA/S/S/2003/03183 and from the Isaac Newton Trust.632 We are grateful to EbFavata and Gilmore [or their careful. reading of the manuscript and. helpful comments., We are grateful to Favata and Gilmore for their careful reading of the manuscript and helpful comments.633 In this appendix we brielly outline the method. used to simulate the light curves shown in Figs., In this appendix we briefly outline the method used to simulate the light curves shown in Figs.634 5. δι. TUS, \ref{fig:lc} \ref{fig:lc_g}. \citet{dee99}'635 IDL based Universal Transit Modeller (OPAL was used to simulate noise-free light. curves., 's IDL based Universal Transit Modeller (UTM) was used to simulate noise-free light curves.636 UTM includes a linear limb-darkening law. and Dimb-darkening cocllicients [rom 2 were used.," UTM includes a linear limb-darkening law, and limb-darkening coefficients from \citet{ham93} were used."637 For à given star-planet. configuration. the other input parameters were the ratio of planetary to stellar radius. the planets orbital period. and. distance. and the sampling time and duration.," For a given star-planet configuration, the other input parameters were the ratio of planetary to stellar radius, the planet's orbital period and distance, and the sampling time and duration."638 For the latter. values of 10 min and 3 vr respectively were used. as appropriate for. in planet-linding mode (2)..," For the latter, values of 10 min and 3 yr respectively were used, as appropriate for in planet-finding mode \citep{fav03}."639 Phe output is in units of relative lux. normalised to an out-of-transit. value of 1.0.," The output is in units of relative flux, normalised to an out-of-transit value of 1.0."640 These units are used throughout., These units are used throughout.641 Note that no rellect light from the planet is included. and that all orbits are assumeded," Note that no reflected light from the planet is included, and that all orbits are assumed"642preferred. although better geometrical constraints are needed for most sources to establish them as aligned rotators.,"preferred, although better geometrical constraints are needed for most sources to establish them as aligned rotators."643 Other plausible peculiarities for PSR J065914 exist: for example it has the lowest light cylinder field Όσες. of any LAT radio pulsar., Other plausible peculiarities for PSR J0659+1414 exist; for example it has the lowest light cylinder field $B_{LC}$ of any LAT radio pulsar.644 Table | lists Bye: for our candidates.,	 Table 1 lists $B_{LC}$ for our candidates.645 No strong trend is evident. and certainly the few kG fields of PSRs JO358+45413. J053842817 and J17404-1000 are quite typical of those of detected LAT pulsars.," No strong trend is evident, and certainly the few kG fields of PSRs J0358+5413, J0538+2817 and J1740+1000 are quite typical of those of detected LAT pulsars."646 For these objects. at least. orientation seems more promising.," For these objects, at least, orientation seems more promising."647 Since several of our sub-luminous candidates have limits on luminosity approaching the 70659-1414. level. it will be important to see If increased LAT exposure or pulsed searches can detect evidence of similar low level ~-ray emission.," 	Since several of our sub-luminous candidates have limits on luminosity approaching the J0659+1414 level, it will be important to see if increased LAT exposure or pulsed searches can detect evidence of similar low level $\gamma$ -ray emission."648" Any such pulse detections for these sources must then represent an atypical ""sub-Iuminous"" mechanism.", Any such pulse detections for these sources must then represent an atypical `sub-luminous' mechanism.649 The phasing of such pulses can be used to cement the geometrical location and their spectrum and dependence on spin properties should help lock down the emission physics., The phasing of such pulses can be used to cement the geometrical location and their spectrum and dependence on spin properties should help lock down the emission physics.650 The prospect of using the LAT to probe a second domain of pulsar particle acceleration. i addition to the established high luminosity outer magnetosphere emittors. is very exciting. (Manchesteretal.2005)..," The prospect of using the LAT to probe a second domain of pulsar particle acceleration, in addition to the established high luminosity outer magnetosphere emittors, is very exciting. \citep{met05}."651values of the viewing angle vary from ~07 to 11 (Lopez.2002).,"values of the viewing angle vary from $\sim$$\degr$ to $\degr$ \citep{lopez1995,roddier1995,menshchikov2002}."652. These viewing angles would. correspond to inclination angles between ~ 90° to 79., These viewing angles would correspond to inclination angles between $\sim$ $\degr$ to $\degr$.653 Dujarrabalctal.(2005) fined that an intermediate value of 5° fits their data yest. which would correspond to an inclination angle of 85.," \citet{bujarrabal2005} find that an intermediate value of $\degr$ fits their data best, which would correspond to an inclination angle of $\degr$."654 At the centre of the cavity in the cireumbinary cise are the components of the binary system: the photonietric wimary (a mass-losine post-AGB star). ancl the secondary (à main sequence star with an accretion disc and hieh-velocity jet).," At the centre of the cavity in the circumbinary disc are the components of the binary system: the photometric primary (a mass-losing post-AGB star), and the secondary (a main sequence star with an accretion disc and high-velocity jet)."655 For simplicity we shall refer to the photometric παν as the primary star throughout this paper., For simplicity we shall refer to the photometric primary as the primary star throughout this paper.656 The wimarv star has an effective temperature of 7.700 Ix. an estimated mass of0.8 M. a luminosity of about 6.000 . (Menshehikovetal.2002)... and a racdius of 0.21 AU (Witt 2009).," The primary star has an effective temperature of 7,700 K, an estimated mass of0.8 $_{\odot}$, a luminosity of about 6,000 $_{\odot}$ \citep{menshchikov2002}, and a radius of 0.21 AU \citep{witt2009}."657. The secondary has a mass of roughly 0.9 M. and is believed to be a main sequence star (Wittet.al. 2009)., The secondary has a mass of roughly 0.9 $_{\odot}$ and is believed to be a main sequence star \citep{witt2009}.658. In the work of Wittetal.(2009). the dependence of the Ho line on orbital phase was investigated. revealing a high velocity jet (tna.~560 kms 1) originating [rom an accretion disc around the secondary.," In the work of \citet{witt2009} the dependence of the $\alpha$ line on orbital phase was investigated, revealing a high velocity jet $v_{max} \sim~560$ km $^{-1}$ ) originating from an accretion disc around the secondary."659 The accretion disc around the secondary is powered by mass transfer from the primary star via Itoche-Iobe overflow at periastron (Wittet 2009)., The accretion disc around the secondary is powered by mass transfer from the primary star via Roche-lobe overflow at periastron \citep{witt2009}.660. The ionizingphotons from the hot inner regions of the accretion cise provide the necessary energy to excite the Extended. Red Emission (IRIS)., The ionizingphotons from the hot inner regions of the accretion disc provide the necessary energy to excite the Extended Red Emission (ERE).661 The ERIE requires ultraviolet photons with energies I5 > 0.5 eV. (Wittetal. 2006)., The ERE requires far-ultraviolet photons with energies E $>$ 10.5 eV \citep{witt2006}.662. The accretion disc also provides the energy source to maintain the region inside the cavity of the optically-thick circumbinary disc that was suggested by Jura.Turner.&Balm (1997)., The accretion disc also provides the energy source to maintain the region inside the cavity of the optically-thick circumbinary disc that was suggested by \citet{jura1997}.663 The near cdge-on optically-thick cireumbinary disc preventsa direct line-of-sight) view of the binary., The near edge-on optically-thick circumbinary disc preventsa direct line-of-sight view of the binary.664 Light originating inside the cavity can only be observed via scattering olf material located above and below the clisc., Light originating inside the cavity can only be observed via scattering off material located above and below the disc.665 This obseurecl view of the binary. illustrated in. Fig. L..," This obscured view of the binary, illustrated in Fig. \ref{fig1},"666 will be referred. to as the indirect line-of-sight) απ is responsible for the dillieult interpretation of the spectra., will be referred to as the indirect line-of-sight and is responsible for the difficult interpretation of the spectra.667 The indirect. line-of-sight to the central object was. first stucied by Waelkensetal.(1996)... who determined. the elective inclination angle to be 35.," The indirect line-of-sight to the central object was first studied by \citet{waelkens1996}, who determined the effective inclination angle to be $\degr$."668 Theeffective inclination angle is the angle at which light from the central binary is scattered into our line-ol-sieht bv the material near the top and bottom of the disc., Theeffective inclination angle is the angle at which light from the central binary is scattered into our line-of-sight by the material near the top and bottom of the disc.669 This viewing geometry has been confirmed by high-resolution optical (Osterbart.Langer.&Weigelt.1907:Cohenctal.2004). and. infrared. imaging CPathilletal.2002).," This viewing geometry has been confirmed by high-resolution optical \citep{osterbart1997, cohen2004} and infrared imaging \citep{tuthill2002}."670. For light from the central source (which can only been seen via scattering). we adopt the effective inclination angle of 35° in our calculations.," For light from the central source (which can only been seen via scattering), we adopt the effective inclination angle of $\degr$ in our calculations."671 The outer regions of the nebula are. however. seen directlv.," The outer regions of the nebula are, however, seen directly."672 To properly study emission processes that originate in the outer nebula one must use the inclination angle of the nebula (857) rather than the effective inclination angle (35)., To properly study emission processes that originate in the outer nebula one must use the inclination angle of the nebula $\degr$ ) rather than the effective inclination angle $\degr$ ).673 Since LID 44179 can only be studied via scattered light. it is important to discuss the known uncertainties.," Since HD 44179 can only be studied via scattered light, it is important to discuss the known uncertainties."674 The ellective angle at which we are viewing the stars is likely the mean scattering angle., The effective angle at which we are viewing the stars is likely the mean scattering angle.675 Phe variation of the scattering angle over the duration of the orbit. which best fits the 0.14 mag variation in the light curve. is 1.67 (Waclkensetal.1996).," The variation of the scattering angle over the duration of the orbit, which best fits the 0.14 mag variation in the light curve, is $\degr$ \citep{waelkens1996}."676. The average value for the scattering angle corresponds to the effective inclination angle of 35., The average value for the scattering angle corresponds to the effective inclination angle of $\degr$.677 In addition. the tilt of the svstem implies that the scattering angle for light from the north and the south of the nebula is. slightly cilferent (of order 5°).," In addition, the tilt of the system implies that the scattering angle for light from the north and the south of the nebula is slightly different (of order $\degr$ )."678 Therefore. the effective inclination angle is just that. an elfective value that we use in order to make progress in understanding this complex. svstem.," Therefore, the effective inclination angle is just that, an effective value that we use in order to make progress in understanding this complex system."679 The variation in the value for the ellective inclination angle will cause uncertainties in: the orbital elements. the derived velocities. and the mass of the secondary.," The variation in the value for the effective inclination angle will cause uncertainties in; the orbital elements, the derived velocities, and the mass of the secondary."680 The properties of the stars also depend. upon the estimation of the laminosity (Menshehikoyetal.2002)., The properties of the stars also depend upon the estimation of the luminosity \citep{menshchikov2002}.681. Phe luminosity depends on the uncertain distance to the star. assumptions about the geometry of the circumbinarv-disc. and the evolutionary state of the svstem.," The luminosity depends on the uncertain distance to the star, assumptions about the geometry of the circumbinary-disc, and the evolutionary state of the system."682 Since this a close binary. it is likely that there has been some interaction in the past resulting in a complex evolutionary history.," Since this a close binary, it is likely that there has been some interaction in the past resulting in a complex evolutionary history."683 Pherefore. it is likely that the evolutionary track of the stars. eliller from that of single stars. as in Vassiliadis&Wood(1994) ancl Bloecker(1995).," Therefore, it is likely that the evolutionary track of the stars differ from that of single stars, as in \citet{Vassiliadis1994} and \citet{bloecker1995}."684.. As a result. the quoted values that we have used for the mass ancl luminosity of the primary remain uncertain.," As a result, the quoted values that we have used for the mass and luminosity of the primary remain uncertain."685 At present. these uncertainties can not be aclelressecl with current observational data.," At present, these uncertainties can not be addressed with current observational data."686 Studying the nebular outflow: and. its mechanisms is important for understanding how stellar material is returned o the interstellar medium., Studying the nebular outflow and its mechanisms is important for understanding how stellar material is returned to the interstellar medium.687 The detectable emission of the La recombination line in our spectra is limited to the inner xuts of the nebula., The detectable emission of the $\alpha$ recombination line in our spectra is limited to the inner parts of the nebula.688 Phe Ho emission is not observed in the j-conical lobes far away [rom the central source., The $\alpha$ emission is not observed in the bi-conical lobes far away from the central source.689 Studying he D-lines. easily excited. resonance lines.allows us o probe the mass-loss to much greater distances from the central source.," Studying the D-lines, easily excited resonance lines,allows us to probe the mass-loss to much greater distances from the central source."690 The D-lines also allow us to directly study the mass-loss rom the primary star., The D-lines also allow us to directly study the mass-loss from the primary star.691 The details of the observations. and the radial velocity (RV) measurements are given in 2..," The details of the observations, and the radial velocity (RV) measurements are given in \ref{sec-observation}."692 The determination of he orbital parameters is discussed in 3.., The determination of the orbital parameters is discussed in \ref{sec-orbital}.693 In 4. we discuss he abundance and the model atmosphere. used. to determine the photospherie line profiles., In \ref{sec-abundance} we discuss the abundance and the model atmosphere used to determine the photospheric line profiles.694 The behaviour of he photospheric lines and the processing of light in the RR is discussed in 5.., The behaviour of the photospheric lines and the processing of light in the RR is discussed in \ref{sec-lineshape}.695 Phe origins ancl measurements of the components of the D-line profile are discussed in 6.., The origins and measurements of the components of the D-line profile are discussed in \ref{sec-naprofiles}.696 In 7. the origin of the single and double peaks are discussed., In \ref{sec-singlevsdouble} the origin of the single and double peaks are discussed.697 The conclusions are presented in δ.., The conclusions are presented in \ref{sec-conclusions}.698 In the present paper we examine 33 high-resolution écchelle μαvectra Of LED 44179., In the present paper we examine 33 high-resolution écchelle spectra of HD 44179.699 The data set includes the 17 spectra used in the work of Wittetal.(2009)., The data set includes the 17 spectra used in the work of \citet{witt2009}.700.. The observation ates are detailed in Table 1.., The observation dates are detailed in Table \ref{table1}. .701 Phe orbital coverage of the observations is illustrated in Fig. 2.., The orbital coverage of the observations is illustrated in Fig. \ref{fig2}. .702 Vhe details of Fig., The details of Fig.703 will be discussed in 3.., \ref{fig2} will be discussed in \ref{sec-orbital}. .704 Phe spectra were obtained. with 16 ARCES cechelle spectrograph (Wangetal.2003). on 1e 3.5-m telescope at the Apache Point Observatory., The spectra were obtained with the ARCES écchelle spectrograph \citep{wang2003} on the 3.5-m telescope at the Apache Point Observatory.705 The μα»ectral range of the spectrograph is 3.700 to 10.000 ata resolving power of /?= 38.000.," The spectral range of the spectrograph is 3,700 to 10,000 at a resolving power of $R = 38,000$ ."706 Phe velocity resolution, The velocity resolution707ln future work each of these problems must be addressed.,In future work each of these problems must be addressed.708 The gradual convergence of the svstem towards lower and lower dilfusivities is “merely” a computational challenge. which can in principle be solved.," The gradual convergence of the system towards lower and lower diffusivities is “merely” a computational challenge, which can in principle be solved."709 There is hope that for low enough cdilfusivities the system reaches an asvmptotie state which is more-or-less independent. of the Ekman parameters., There is hope that for low enough diffusivities the system reaches an asymptotic state which is more-or-less independent of the Ekman parameters.710 Asvmptotic analyses. following the steps of IxIecorin ct al. (," Asymptotic analyses, following the steps of Kleeorin et al. ("7111998) for instance. may provide a wav of by-passing boundary. lavers in the flow by providing Jumpconditions across the lavers.,"1998) for instance, may provide a way of by-passing boundary layers in the flow by providing jump-conditions across the layers."712 This would greatly help reducing some of the numerical dilficulties., This would greatly help reducing some of the numerical difficulties.713 Llowever. looking a ) importance of geometric or nonlinear ellects in he svstem. it is unlikely that an asvmptotic analysis could provide a full solution of the problem.," However, looking at the importance of geometric or nonlinear effects in the system, it is unlikely that an asymptotic analysis could provide a full solution of the problem."714 The problem ol 10 representation of the cdvnamical interaction of he tachocline and the convection zone through adequate »oundary conditions is a strong theoretical challenge. which will be looked. into in the future.," The problem of the representation of the dynamical interaction of the tachocline and the convection zone through adequate boundary conditions is a strong theoretical challenge, which will be looked into in the future."715 The most obvious route is through the inclusion of the convection zone in the computational domain. and the ad-hoc prescription of lievnolds stresses which would [ead to the observed rotation profile.," The most obvious route is through the inclusion of the convection zone in the computational domain, and the ad-hoc prescription of Reynolds stresses which would lead to the observed rotation profile."716 But comparing the relative importance of all the points mentionned in this section. it is clear that the next step towards improving the model is through the inclusion of the elfects of compressibility. energy. transport and stratification on the dvnamies of the svstem. which will allow a correct quantitative representation of the baroclinic driving of the meridional motions as well as the effects. of the strong stratification in the radiative zone.," But comparing the relative importance of all the points mentionned in this section, it is clear that the next step towards improving the model is through the inclusion of the effects of compressibility, energy transport and stratification on the dynamics of the system, which will allow a correct quantitative representation of the baroclinic driving of the meridional motions as well as the effects of the strong stratification in the radiative zone."717 This is work which will be presented in a subsequent. paper., This is work which will be presented in a subsequent paper.718 This paper presents a numerical analysis of the nonlinear interaction between a primordial field anc large-scale {uid Hlows in the solar radiative zone when a [atitudinal shear is imposed from the convection zone through a combination of magnetic and. viscous stresses., This paper presents a numerical analysis of the nonlinear interaction between a primordial field and large-scale fluid flows in the solar radiative zone when a latitudinal shear is imposed from the convection zone through a combination of magnetic and viscous stresses.719 Within the scope of some simplifving assumptions (axisvmetry. steady-state. incompressibilitv). Che presence of a large-scale. field. in the radiative zone was shown to lead to three dynamical regimes. which depend: essentially on the strength of the underlving field.," Within the scope of some simplifying assumptions (axisymetry, steady-state, incompressibility), the presence of a large-scale field in the radiative zone was shown to lead to three dynamical regimes, which depend essentially on the strength of the underlying field."720 When the Elsasser number is low. the llow is dominated by the Proucdman constraint. which enforces a rotation profile roughly constant on cvlindrical surfaces throughout most of the radiative zone.," When the Elsasser number is low, the flow is dominated by the Proudman constraint, which enforces a rotation profile roughly constant on cylindrical surfaces throughout most of the radiative zone."721 When the Elsasser number is high. the magnetic field »opagates the shear to a large part of the interior according o the Ferraro isorotation law. and only within the outermost closed field line does one observe uniform. rotation.," When the Elsasser number is high, the magnetic field propagates the shear to a large part of the interior according to the Ferraro isorotation law, and only within the outermost closed field line does one observe uniform rotation."722 When he Elsasser number is of order of unitv. the magnetic iclcl is weak enough to be advected by meridional motions driven by Ekman-eHEartmann pumping on the boundary.," When the Elsasser number is of order of unity, the magnetic field is weak enough to be advected by meridional motions driven by Ekman-Hartmann pumping on the boundary."723 This advection process stretches the field. along the boundary hereby reducing the magnetic stresses connecting the convection zone and the radiative zone) ancl pushes the »»boidal field deeper into the interior., This advection process stretches the field along the boundary (thereby reducing the magnetic stresses connecting the convection zone and the radiative zone) and pushes the poloidal field deeper into the interior.724 As a result. the shear is confined to some shallow [aver below the convection zone. which can be likened to the tachocline.," As a result, the shear is confined to some shallow layer below the convection zone, which can be likened to the tachocline."725 Conversely. 10 meridional circulation is kept from burrowing into the mπιολανο zone by the accumulation of magnetic Dux below 10 tachocline.," Conversely, the meridional circulation is kept from burrowing into the radiative zone by the accumulation of magnetic flux below the tachocline."726 The structure of the solution in the intermecdiate-feld case is in qualitative agreement with the angular-velocity observations. as well as the precictions of the Gough Alelntvre (1998) model," The structure of the solution in the intermediate-field case is in qualitative agreement with the angular-velocity observations, as well as the predictions of the Gough McIntyre (1998) model."727 The simulations also show the presence of cllicicnt mixing in the tachocline which would influence the abundances of chemical elements in. that region: this can also be detected observationallv (elliott Cough. 1999. Brun. Turck-Chiezze Zahn. 1999).," The simulations also show the presence of efficient mixing in the tachocline which would influence the abundances of chemical elements in that region; this can also be detected observationally (Elliott Gough, 1999, Brun, Turck-Chièzze Zahn, 1999)."728 As expected. the quantitative agreement between the model and the observations is poor: this is due on the one hand to the large dilfusivities used in the simulations. and on the other hand to some oversimplification of the dvnamics involved. (through the boundary conditions chosen. anc also the assumption of incompressibilitv. which drive a meridional [Dow quantitatively cillerent from what one coulc expect in the tacheoline).," As expected, the quantitative agreement between the model and the observations is poor; this is due on the one hand to the large diffusivities used in the simulations, and on the other hand to some oversimplification of the dynamics involved (through the boundary conditions chosen, and also the assumption of incompressibility, which drive a meridional flow quantitatively different from what one could expect in the tachcoline)."729 Both of these problems wil »* addressed. in future work: in particular. the effects. of compressibility will be studied in a following paper.," Both of these problems will be addressed in future work; in particular, the effects of compressibility will be studied in a following paper."730 1n conclusion. although the dynamical behaviour of he sun is likely to be far more complex than that of he simulations presented in this paper. it is clear tha hese simulations can >grasp. and explain. some of thefundamental aspects of the dvnamies of the observed solar cillerential rotation.," In conclusion, although the dynamical behaviour of the sun is likely to be far more complex than that of the simulations presented in this paper, it is clear that these simulations can grasp, and explain, some of the aspects of the dynamics of the observed solar differential rotation."731" Moreover. they [av a strong basis for ""ture improvements of the models along the lines described above."," Moreover, they lay a strong basis for future improvements of the models along the lines described above."732 his work was funded by New Hall. PPARC and the Isaac Newton Studentship at various stages of its completion.," This work was funded by New Hall, PPARC and the Isaac Newton Studentship at various stages of its completion."733 None of this work would have been possible without the constant encouragements and tremendous. insight of Professor D. O. Gough., None of this work would have been possible without the constant encouragements and tremendous insight of Professor D. O. Gough.734 | thank Professors M. 1t. DE. Proctor.," I thank Professors M. R. E. Proctor,"735 s7!). but mostly sample populations of objects at z~2.,"$^{-1}$ ), but mostly sample populations of objects at $z\sim 2$."736 The measured space density of CT AGN at these high redshifts is in general as large as expected from XRB synthesis models or possibly even larger (see eg. ?))., The measured space density of CT AGN at these high redshifts is in general as large as expected from XRB synthesis models or possibly even larger (see eg. ).737 Another way to select obscured QSOs is through their high-ionization narrow optical emission lines. which are thought to be produced on physical scales (from ~0.1 toa few kpe) mostly free from nuclear obscuration.," Another way to select obscured QSOs is through their high-ionization narrow optical emission lines, which are thought to be produced on physical scales (from $\sim0.1$ to a few kpc) mostly free from nuclear obscuration."738 Recently. the [O |264 line has been used to select obscured AGN among galaxies observed with Spirzer/IRS.," Recently, the [O $\mu m$ line has been used to select obscured AGN among galaxies observed with /IRS."739 However. since this line quickly moves out of the observable IR bands as redshift increases. this selectiol mostly concerns the nearby Universe(??).," However, since this line quickly moves out of the observable IR bands as redshift increases, this selection mostly concerns the nearby Universe."740. The most commonly used marker of obscured nuclear activity therefore remains the [O IIL]|5007 emission line. which is strong. falls in the optical domain. and allows object selection up to z~0.8.," The most commonly used marker of obscured nuclear activity therefore remains the [O III]5007 emission line, which is strong, falls in the optical domain, and allows object selection up to $z\sim 0.8$."741 The 2-10 keV to [O III|5007 flux ratio (X/OIID has been often used as a diagnostic for heavy obscuration in sources with poor X-ray photon statistics(222). being low X/OIII ratios (€3. see e.g. Fig.," The 2-10 keV to [O III]5007 flux ratio (X/OIII) has been often used as a diagnostic for heavy obscuration in sources with poor X-ray photon statistics, being low X/OIII ratios $\lesssim 3$, see e.g. Fig."742 + of ?)) highly suggestive of heavy nuclear absorption., 4 of ) highly suggestive of heavy nuclear absorption.743 Based on the [ο III|5007 emission line. and identified in the Sloan Digital Sky Survey (SDSS) a population of obscured QSOs at a median redshift of z~0.3. at least as abundant as that of type-1 QSOs at the same redshifts(?).," Based on the [O III]5007 emission line, and identified in the Sloan Digital Sky Survey (SDSS) a population of obscured QSOs at a median redshift of $z\sim0.3$, at least as abundant as that of type-1 QSOs at the same redshifts."744. These results have been extended to lower luminosities by ?.. who measured the luminosity function of [O III]-selected type-2 AGN in the zCOSMOS spectroscopic survey(?).. finding that the fraction of obscured AG is decreasing with luminosity. in agreement with what is observed in X-ray surveys.," These results have been extended to lower luminosities by , who measured the luminosity function of [O III]-selected type-2 AGN in the zCOSMOS spectroscopic survey, finding that the fraction of obscured AGN is decreasing with luminosity, in agreement with what is observed in X-ray surveys."745 X-ray observations of small samples drawn from the catalog. suggest that about half of luminous type-2 QSOs (οσο>9.3 Li) could be CT for X-ray observations of lower luminosity SDSS type-2AGN).," X-ray observations of small samples drawn from the catalog, suggest that about half of luminous type-2 QSOs $L_{O III}>9.3\;L_{\odot}$ ) could be CT for X-ray observations of lower luminosity SDSS type-2."746 Since [O III] selection is likely missing objects in which also the Narrow Line Region (NLR) is extincted (ike e.g. in the prototype CT AGN NGC 4945 and NGC 6240). the estimated type-2 QSO abundances should be considered as lower limitsVIO).," Since [O III] selection is likely missing objects in which also the Narrow Line Region (NLR) is extincted (like e.g. in the prototype CT AGN NGC 4945 and NGC 6240), the estimated type-2 QSO abundances should be considered as lower limits."747 In this work we explore the possibility of using the high-ionization [Ne V]3426 emission line. rather than. the [ο II1]|5007 line. às a tracer of obscured nuclear activity.," In this work we explore the possibility of using the high-ionization [Ne V]3426 emission line, rather than the [O III]5007 line, as a tracer of obscured nuclear activity."748 Despite being on average a factor of ~9 weaker than [ο I11|5007 and suffering stronger dust extinction. the [Ne V]3426 line is commonly observed in nearby Seyfert galaxies and. given that high energy photons (20.1 keV) are required to further ionize NelV. it is considered an unambiguous sign of nuclear activity2).," Despite being on average a factor of $\sim 9$ weaker than [O III]5007 and suffering stronger dust extinction, the [Ne V]3426 line is commonly observed in nearby Seyfert galaxies and, given that high energy photons $\gtrsim 0.1$ keV) are required to further ionize NeIV, it is considered an unambiguous sign of nuclear activity."749. In addition. the [Ne V|3426 emission line is observable up to z~1.5 before being redshifted out of the optical bands. whereas the [O 111]5007 line is observable only up to z~0.7—0.8.," In addition, the [Ne V]3426 emission line is observable up to $z\sim 1.5$ before being redshifted out of the optical bands, whereas the [O III]5007 line is observable only up to $z\sim7500.7-0.8$."751 Indeed. only 13 out of 887 [O III]-selected QSOs in the sample lie at z2»0.7. with only3 at z>0.8. [," Indeed, only 13 out of 887 [O III]-selected QSOs in the sample lie at $z>0.7$, with only3 at $z>0.8$. ["752Ne V]-selection may then be used to reveal nuclear activity in obscured sources at z~1. 1.9. at the epoch where most of the XRB light is thought to be produced.,"Ne V]-selection may then be used to reveal nuclear activity in obscured sources at $z\sim 1$, i.e. at the epoch where most of the XRB light is thought to be produced."753 The structure of the paper is the following: in Section 2 we present and discuss the sample of nearby Seyfert galaxies used to calibrate the relation between [Ne V] and X-ray emission (the details of the sample are given in the Appendix)., The structure of the paper is the following: in Section 2 we present and discuss the sample of nearby Seyfert galaxies used to calibrate the relation between [Ne V] and X-ray emission (the details of the sample are given in the Appendix).754 In Section 3 we present the X/NeV diagnostic diagram and apply it to obscured and unobscured QSO population drawn from the SDSS., In Section 3 we present the X/NeV diagnostic diagram and apply it to obscured and unobscured QSO population drawn from the SDSS.755 In Section 4 we present oobservations of a sample of 9 [Ne V]-selected obscured QSOs at z~| in the SDSS and use the X/NeV diagnostic to estimate the fraction of CT objects among them., In Section 4 we present observations of a sample of 9 [Ne V]-selected obscured QSOs at $z\sim 1$ in the SDSS and use the X/NeV diagnostic to estimate the fraction of CT objects among them.756 In Section 5 we discuss efficiency and biases of [Ne V] selection together with its application to sky areas with deep optical spectroscopy and X-ray coverage., In Section 5 we discuss efficiency and biases of [Ne V] selection together with its application to sky areas with deep optical spectroscopy and X-ray coverage.757 In the same Section. the evidence of enhanced star formation in obscured QSOs at z=0.4-1.5 is also highlighted.," In the same Section, the evidence of enhanced star formation in obscured QSOs at z=0.4-1.5 is also highlighted."758 The conclusions are drawn in Section 6., The conclusions are drawn in Section 6.759 We searched in the literature for nearby (z«0.1) AGN for which both [Ne V] and X-ray data are available., We searched in the literature for nearby $z<0.1$ ) AGN for which both [Ne V] and X-ray data are available.760 A total sample of 74 objects were found with measured [Ne V] flux. 2-10 keV flux and X-ray column density Λη.," A total sample of 74 objects were found with measured [Ne V] flux, 2-10 keV flux and X-ray column density $N_H$."761 The most difficult nformation to obtain was that on [Ne V] flux. since optical spectra are often limited at wavelengths >3700A.," The most difficult information to obtain was that on [Ne V] flux, since optical spectra are often limited at wavelengths $>3700\AA$."762 On the contrary. the Nj; and the 2-10 keV flux values for bright earby objects are more easily obtained either from published papers or from archival X-ray data.," On the contrary, the $N_H$ and the 2-10 keV flux values for bright nearby objects are more easily obtained either from published papers or from archival X-ray data."763" The main catalogs of optical/near-UV Seyfert spectra providing the [Ne V] fluxes used in this work are those published by ?..2..?., 2.2 as well as the compilation by?."," The main catalogs of optical/near-UV Seyfert spectra providing the [Ne V] fluxes used in this work are those published by , as well as the compilation by."764. A public catalog of HST/STIS spectra of nearby AGN has been released by?., A public catalog of HST/STIS spectra of nearby AGN has been released by.765". We note that the HST/STIS spectra have been extracted 1n apertures of 0.2""x0.2"", thus sampling physical scales of a few tens of parsees at the typical source redshift."," We note that the HST/STIS spectra have been extracted in apertures of $0.2''\times0.2''$, thus sampling physical scales of a few tens of parsecs at the typical source redshift."766 This physical scale is often too small to fully encompass the NLR. which indeed may extend up to a few kpe.," This physical scale is often too small to fully encompass the NLR, which indeed may extend up to a few kpc."767 We verified that the [O III] and [Ne V] fluxes as measured on the spectra are often significantly lower (an order of magnitude or more) than those measured on larger apertures. especially in those objects in which an extended NLR has been revealed(?).," We verified that the [O III] and [Ne V] fluxes as measured on the spectra are often significantly lower (an order of magnitude or more) than those measured on larger apertures, especially in those objects in which an extended NLR has been revealed."768. Therefore. we avoided using measurements obtained with HST/STIS and considered only those taken with larger apertures.," Therefore, we avoided using measurements obtained with HST/STIS and considered only those taken with larger apertures."769" All the [Ne V] fluxes used in this work come from apertures >L5"".", All the [Ne V] fluxes used in this work come from apertures $\gtrsim1.5''$.770 Whenever more than one measurement is available for the [Ne VJ flux. we preferred the one obtained with the largest aperture.," Whenever more than one measurement is available for the [Ne V] flux, we preferred the one obtained with the largest aperture."771 For 6 objects we measured the [Ne V] line flux directly on the calibrated spectrum drawn from the catalog of 99 UV-optical spectra of nearby galaxies released by Storchi-Bergmann etal., For 6 objects we measured the [Ne V] line flux directly on the calibrated spectrum drawn from the catalog of 99 UV-optical spectra of nearby galaxies released by Storchi-Bergmann et.772 Since our main aim is to calibrate a diagnostic which can be applied to distant objects. we did not attempt to correct the [Ne V] fluxes for the reddening which may be intrinsic to the NLR.," Since our main aim is to calibrate a diagnostic which can be applied to distant objects, we did not attempt to correct the [Ne V] fluxes for the reddening which may be intrinsic to the NLR."773 Indeed. while for local objects the extinction to the NLR can be easily measured through e.g. the ratio between the narrow components of Ha and Hp. in distant AGN either He or both Ho and Hp are not observable and measuringthe," Indeed, while for local objects the extinction to the NLR can be easily measured through e.g. the ratio between the narrow components of $H\alpha$ and $H\beta$ , in distant AGN either $H\alpha$ or both $H\alpha$ and $H\beta$ are not observable and measuringthe"774When the review on phenomena in clusters of galaxies by Rephaeli. Nevalainen. Ohashi Bykov 2008 (astro-ph05010052: hereafter. RNOBOS) appeared on (he WEB we sent our conunents to Prof YRephaeli.,"When the review on phenomena in clusters of galaxies by Rephaeli, Nevalainen, Ohashi Bykov 2008 (astro-ph/08010982; hereafter, RNOB08) appeared on the WEB we sent our comments to Prof. Y.Rephaeli."775" But the answer of the Editor. Dr J.IxXaastra. of the book: ""Clusters of galaxies: bevond the thermal view’. was that he has checked with Springer. but unfortunately (heir process is already (oo Lar to make any changes to (he paper."," But the answer of the Editor, Dr J.Kaastra, of the book: ""Clusters of galaxies: beyond the thermal view"", was that he has checked with Springer, but unfortunately their process is already too far to make any changes to the paper."776 For this reason we have decided to put on the WEB these comments., For this reason we have decided to put on the WEB these comments.777" The comments regard: the boring controversial between the analysis of the data of the Coma cluster with the software package NAS by Fusco-Femiano 2004 (hereafter. FFO4) and the Rossetti Molendi analysis with a different software SANDAS (hereafter. RAIO4): the a hard excess in A?199, A?163 and the Bullet cluster."," The comments regard: the boring controversial between the analysis of the data of the Coma cluster with the software package XAS by Fusco-Femiano 2004 (hereafter, FF04) and the Rossetti Molendi analysis with a different software SAXDAS (hereafter, RM04); the a hard excess in A2199, A2163 and the Bullet cluster."778" In 2007 Fusco-Femiano. Landi Orlandini (hereafter. FF07) have the PDS data using the same software of ΗΛΙΟ showing that it is possible to obtain (he same results of FFO4 explaining of course (he reasons of (he cliscrepancy between FFO4 and ΗΛΙΟ,"," In 2007 Fusco-Femiano, Landi Orlandini (hereafter, FF07) have re-analyzed the PDS data using the same software of RM04 showing that it is possible to obtain the same results of FF04 explaining of course the reasons of the discrepancy between FF04 and RM04."779 RossetG Molencli replied to our paper (FEQ7) with an electronic preprint only (RALOT) ancl we were obliged to a new reply (FFOTR)., Rossetti Molendi replied to our paper (FF07) with an electronic preprint only (RM07) and we were obliged to a new reply (FF07R).780 Unfortunately. the authors of the review have not read with the due attention the papers FF04. FFOT and FFOTR (the last is not reported in (he review) and (his is a serious mistake," Unfortunately, the authors of the review have not read with the due attention the papers FF04, FF07 and FF07R (the last is not reported in the review) and this is a serious mistake"781presenting differcut resistance to the propagation of the jets. and thus producing differcut size arms.,"presenting different resistance to the propagation of the jets, and thus producing different size arms."782 Although these hree effects could act iu a combines Inauner. we can try to constrain the possible reasons of asvuuuetry in our sguuple.," Although these three effects could act in a combined manner, we can try to constrain the possible reasons of asymmetry in our sample."783 First we note that the wealth of observatious of the tuner jets in radio galaxies am quasars do not show evidence for intrinsic differences in the properties of jets aud couuter-jets., First we note that the wealth of observations of the inner jets in radio galaxies and quasars do not show evidence for intrinsic differences in the properties of jets and counter-jets.784 The observe differeuces are readily explained through the effects of relativistic aberration in sviunietric. auti-parallel jets (0.8. Ciovannid et al. 2X1:," The observed differences are readily explained through the effects of relativistic aberration in symmetric, anti-parallel jets (e.g. Giovannini et al. \cite{giov01};"785 Laine Bridle 2002))., Laing Bridle \cite{laing1}) ).786 In the following. we thus c'onceutrate in distinguishing between the external imiediuni or source orientation as the main reason of asvnuuetrv.," In the following, we thus concentrate in distinguishing between the external medium or source orientation as the main reason of asymmetry."787 We have considered ac Padeonmilv oricuted sanup (PUO)xsii10 P standing for probability) of iutriusicallv sviunietric radio galaxies with a Gaussian advance velociv distributio1 of tje jet head., We have considered a randomly oriented sample $P(\theta)\propto\sin\theta$; $P$ standing for probability) of intrinsically symmetric radio galaxies with a Gaussian advance velocity distribution of the jet head.788 Uider these assuimiptious. we are aldle to obtain reasonable approxinations the shape of the observed aruiccheth ratio distribution solely on the basis of orientation effects for both. FR I and FR II radio sources. usiie different jet velociv distributiois for cach type of radio galaxw (see Fig. 3)).," Under these assumptions, we are able to obtain reasonable approximations to the shape of the observed arm-length ratio distribution solely on the basis of orientation effects for both, FR I and FR II radio sources, using different jet velocity distributions for each type of radio galaxy (see Fig. \ref{arm}) )."789 But what is relevant here. our model requires too high (and thus unrealistic) jet-head αναwe velocities for FR Is and FR UIs.," But what is relevant here, our model requires too high (and thus unrealistic) jet-head advance velocities for FR Is and FR IIs."790 For example. a veocitv distribution larrowly centered. around 0.25€ is required to expla- he axi-leusth ratio distribution of FR II radio galaxies. while most models aud. observational «ata sugecstOO much ower expausion velocities (0.5. Lougair Riley 1979: Alexander Leahy 1987: Scheuer 1995)).," For example, a velocity distribution narrowly centered around 0.25c is required to explain the arm-length ratio distribution of FR II radio galaxies, while most models and observational data suggest much lower expansion velocities (e.g. Longair Riley \cite{longair}; Alexander Leahy \cite{alexander}; Scheuer \cite{scheuer2}) )."791 Moreover. even with unacceptable jetlead velocities. the model still oediets more sVvuuduetric sources than observed which wieght reflect the influence of the external medium not accounted for.," Moreover, even with unacceptable jet–head velocities, the model still predicts more symmetric sources than observed which might reflect the influence of the external medium not accounted for."792 As a second argument. we fid an strikiuslv large ractiou ( THM) of FR II radio galaxies with a stronger lobe ou the shorter arm of the radio structure.," As a second argument, we find an strikingly large fraction $\sim 75$ ) of FR II radio galaxies with a stronger lobe on the shorter arm of the radio structure."793 A similar behavior is also found by Machalski et al. (2001)), A similar behavior is also found by Machalski et al. \cite{machalski}) )794 im a sample of GRGs., in a sample of GRGs.795 To compute this percentage we have excluded. quasi-svuuuetric sources (with 0.9<r&€ 1) to avoid confusion.," To compute this percentage we have excluded quasi-symmetric sources (with $0.9\le796r \le 1$ ) to avoid confusion."797 We uote that in an orieutation based asviunietzy. if is expectec that the shorter iur corresponds to the receding jet aud i the ο froun the lobes is at least moderately beamed (e.g. Ceoreanopoulos Ἱνασαπας 2003)). it is expected that the receding lobe preseuts weaker cmission than the approaching one.," We note that in an orientation based asymmetry, it is expected that the shorter arm corresponds to the receding jet and if the emission from the lobes is at least moderately beamed (e.g. Georganopoulos Kazanas \cite{georga}) ), it is expected that the receding lobe presents weaker emission than the approaching one."798 Therefore we sugecst that orientation cannot be the aiu reason of asviuuetry., Therefore we suggest that orientation cannot be the main reason of asymmetry.799 The asvuunetry could be explained if the external medium were uot isotropic., The asymmetry could be explained if the external medium were not isotropic.800" Iu hat Case the shorter lobe would be the one fiudiug strouger resistance to its expansion iu the external ποπα, which shows up as a lieher surface brightness"," In that case the shorter lobe would be the one finding stronger resistance to its expansion in the external medium, which shows up as a higher surface brightness."801 Supporting this idea. the sources for which we have polarization nieasuremienuts present also a tendency of stronger polarized ciission in the shorter and stronser lobe. consistent with a conipression of the maeguetic field against the exterial medium. but this fact needs to be confirmed throieh more detailed observations.," Supporting this idea, the sources for which we have polarization measurements present also a tendency of stronger polarized emission in the shorter and stronger lobe, consistent with a compression of the magnetic field against the external medium, but this fact needs to be confirmed through more detailed observations."802 Moreover. the anisotropics iu the external medi most plausibly explain the existence of several sources with pairs of jets showing markedly differeit properties or with a hybrid FR ΤΠ morpholoey.," Moreover, the anisotropies in the external medium most plausibly explain the existence of several sources with pairs of jets showing markedly different properties or with a hybrid FR I/II morphology."803 The most dramatic case is (see Paper D. with p—0.00.," The most dramatic case is (see Paper I), with $r=0.09$."804 Iu conclusion. with the necessary caution required due to the uncertainties in the aruileugth ratio determinations iu FR IL. we obtain from the orientation based asviaunuetrv luoel and from the fact that many sources show the stronger lobe on the shorter arm. that the external mediuἩ nust be the donünaut effect du nost of the asviuuetrie sources of our sample.," In conclusion, with the necessary caution required due to the uncertainties in the arm-length ratio determinations in FR Is, we obtain from the orientation based asymmetry model and from the fact that many sources show the stronger lobe on the shorter arm, that the external medium must be the dominant effect in most of the asymmetric sources of our sample."805 However. we cannot exclude that orieutation effects Ιστ plav their role to explain certain degree of asviunetry in FR Is aud," However, we cannot exclude that orientation effects might play their role to explain certain degree of asymmetry in FR Is and"806consistelt with those of Cowley et al. (,consistent with those of Cowley et al. (8071988) and MeClintock Remilard (1990).,1988) and McClintock Remillard (1990).808 Curiously. à much larger variation is found i the systemic velocity y. as has also been noted by Torres et al. (," Curiously, a much larger variation is found in the systemic velocity $\gamma$, as has also been noted by Torres et al. ("8092002).,2002).810 We obtain a y intermediate to the values reported earlier., We obtain a $\gamma$ intermediate to the values reported earlier.811 We do not have an explanation for this discrepancy. which in principle could be due to the use of an erroneous heliocentric radial velocity for the template stars.," We do not have an explanation for this discrepancy, which in principle could be due to the use of an erroneous heliocentric radial velocity for the template stars."812 Our value for P has a correspondingly large uncertainty as a result of our relatively short observing baseline with respect to. e.g. Torres et al. (," Our value for $P$ has a correspondingly large uncertainty as a result of our relatively short observing baseline with respect to, e.g. Torres et al. ("8132002).,2002).814 The radial velocity curve. after folding with our best ephemeris. is shown in Fig. [..," The radial velocity curve, after folding with our best ephemeris, is shown in Fig. \ref{curve}."815 It is highly sinusoidal 1.1) despite the point at phase 0.75., It is highly sinusoidal ${\chi^2}_{\nu}=1.1$ ) despite the point at phase 0.75.816 This point is not due to instrumental problems (such as telescope flexure) and we also note that a similar effect is seen in the radial velocity curve of Cen X-4 measured by Torres et al. (, This point is not due to instrumental problems (such as telescope flexure) and we also note that a similar effect is seen in the radial velocity curve of Cen X-4 measured by Torres et al. (8172002): however there is no clear explanation for such behaviour.,2002); however there is no clear explanation for such behaviour.818 We have produced an average spectrum of Cen X-4 in the rest frame of the companion star after Doppler shifting every individual spectrum using our orbital solution and the orbital period of Torres et al. (, We have produced an average spectrum of Cen X-4 in the rest frame of the companion star after Doppler shifting every individual spectrum using our orbital solution and the orbital period of Torres et al. (8192002).,2002).820 The spectrum shows prominent He. Hel 45876. 26678 emission as well as absorption features typical of late type stars (e.g. TIO 26161. Fell 26361 and Fell 26494. Fig. 2)).," The spectrum shows prominent ${\alpha}$, HeI $\lambda$ 5876, $\lambda$ 6678 emission as well as absorption features typical of late type stars (e.g. TiO $\lambda$ 6161, FeII $\lambda$ 6361 and FeII $\lambda$ 6494, Fig. \ref{tot_spectrum}) )."821 A spectral classification can be derived by taking different templates degraded appropriately with a Gaussian bandpass to match the broadening of our NTT observations., A spectral classification can be derived by taking different templates degraded appropriately with a Gaussian bandpass to match the broadening of our NTT observations.822 These templates were then multiplied by a factor οςf<l. representing the fractional contribution of light from the secondary star and subtracted from the target average (after masking interstellar. night-sky and emission lines. and rebinning to a uniform velocity scale).," These templates were then multiplied by a factor $0823\leq f \leq 1$, representing the fractional contribution of light from the secondary star and subtracted from the target average (after masking interstellar, night-sky and emission lines and rebinning to a uniform velocity scale)."824 The best fit is obtained for templates K3 V-K5 V and f=0.59—0.62. although a K7 III also provides an acceptable fit (see Table 3)).," The best fit is obtained for templates K3 V–K5 V and $f=0.59-0.62$, although a K7 III also provides an acceptable fit (see Table \ref{template}) )."825 More importantly. in. the Doppler-corrected. average. Li I 16708 absorption becomes prominent.," More importantly, in the Doppler-corrected average, Li I $\lambda$ 6708 absorption becomes prominent."826 The detection of a strong Li 46708 absorption feature in such a late-type companion would normally be unexpected since the star's initial Li I content should be rapidly depleted by à contamination of convective mixing and mass transfer to the compact object., The detection of a strong Li $\lambda$ 6708 absorption feature in such a late-type companion would normally be unexpected since the star's initial Li I content should be rapidly depleted by a contamination of convective mixing and mass transfer to the compact object.827 Such unusual abundances of Li I have already been found by other authors (e.g. Martin et al., Such unusual abundances of Li I have already been found by other authors (e.g. Martin et al.828 1994. Torres et al.," 1994, Torres et al."829 2002)., 2002).830 This significant and anomalous abundance of Li Lin Cen X-4 (and other transients) finds various explanations in the literature. such as synthesis in a supernova explosion of the compact primary’s progenitor. or c-r reactions during the repeated strong outbursts that characterize transient X-ray binaries (Martin et al.," This significant and anomalous abundance of Li I in Cen X-4 (and other transients) finds various explanations in the literature, such as synthesis in a supernova explosion of the compact primary's progenitor, or $\alpha$ $\alpha$ reactions during the repeated strong outbursts that characterize transient X-ray binaries (Martin et al."831 1994). a relatively recent formation of the system (Gonzalez Hernandez et al.," 1994), a relatively recent formation of the system (Gonzalez Hernandez et al."832 2005). or an effect related to the tidally-locked rotation of the two stars. which leads to a slower lithium destruction rate (Maccarone et al.," 2005), or an effect related to the tidally-locked rotation of the two stars, which leads to a slower lithium destruction rate (Maccarone et al."833 2005)., 2005).834 An alternative approach to the spectral classification consists of comparing the ratio of the equivalent width of the absorption lines in Cen X-4 with different templates., An alternative approach to the spectral classification consists of comparing the ratio of the equivalent width of the absorption lines in Cen X-4 with different templates.835 We consider the ratios 6361(Felb/t6l61 ιο) and A6494(FelD/Z16161. (TIO). which also classify the secondary of Cen X-4 as a KS V-K7 V star (see Table 4)).," We consider the ratios $\lambda$ $\lambda$ 6161 (TiO) and $\lambda$ $\lambda$ 6161 (TiO), which also classify the secondary of Cen X-4 as a K5 V–K7 V star (see Table \ref{ratio}) )."836 We therefore conclude that the most likely spectral type for Cen X-4 is a K3-7 V star., We therefore conclude that the most likely spectral type for Cen X-4 is a K3–7 V star.837where the funetion A(x.fx’.) involves a sum over all paths P connecting the initial and final states with fo/: where D is an appropriate measure on the set of classical space-time trajectories.,"where the function $K({\bf x}, t; {\bf x'}, t')$ involves a sum over all paths $\Gamma$ connecting the initial and final states with $t>t'$: where ${\cal D}$ is an appropriate measure on the set of classical space-time trajectories."838 For a particle moving in a potential V(x./)=mó(x.l) the action 9 for a given path E is given by Note the presence of the Gaussian field in equation (21) and hence in the exponential of the integrand on the right-1andeaside of equation (20)).," For a particle moving in a potential $V({\bf x}, t)=m\phi({\bf x}, t)$ the action $S$ for a given path $\Gamma$ is given by Note the presence of the Gaussian field in equation (21) and hence in the exponential of the integrand on the right-hand-side of equation \ref{eq:Green}) )."839 To get an approximate solution o this svstem we can follow the same reasoning as Zeldovich et al. (, To get an approximate solution to this system we can follow the same reasoning as Zeldovich et al. (8401985. LOST) and Jones (1999). ignoring time-varving erms. using the Ciaussian properties anc counting the dominant contributions to the path integral to deduce that he integral produces a solution of lognormal form.,"1985, 1987) and Jones (1999), ignoring time-varying terms, using the Gaussian properties and counting the dominant contributions to the path integral to deduce that the integral produces a solution of lognormal form."841 This vat of the argument is identical to that advanced by Jones. except that the solution is for c rather than νο and since p is Jur then one directly obtains a lognormal distribution for he desired ensity p(x.().," This part of the argument is identical to that advanced by Jones, except that the solution is for $\psi$ rather than $\varphi$ and since $\rho$ is $|\psi^2|$ then one directly obtains a lognormal distribution for the desired density $\rho({\bf x}, t)$."842 It should be stressed that. although the present approach clearly provides a more elegant formulation of the problem. the deduction. of lognormality remains approximate: the lognormal is not the exact solution to the system to either Jones! equation (15) or the present equation (16).," It should be stressed that, although the present approach clearly provides a more elegant formulation of the problem, the deduction of lognormality remains approximate; the lognormal is not the exact solution to the system to either Jones' equation (15) or the present equation (16)."843 Low accurately this approximate form applies is open to doubt. and will have to be checked bv full numerical solutions., How accurately this approximate form applies is open to doubt and will have to be checked by full numerical solutions.844 Interestingly. however. d0 is known to apply quite accurately in (quantum systems such as clisorderecl mesoscopic electron. configurations (Janssen 1998).," Interestingly, however, it is known to apply quite accurately in quantum systems such as disordered mesoscopic electron configurations (Janssen 1998)."845 As mentioned above. the Schrodinger approach vields a wavefunction c which is directly. related to the particle ensitv p via p=fel.," As mentioned above, the Schrodinger approach yields a wavefunction $\psi$ which is directly related to the particle density $\rho$ via $\rho=|\psi|^2$."846 Such quantum systems also display lognormal scaling for properties such as the conductance. which depends on felt.," Such quantum systems also display lognormal scaling for properties such as the conductance, which depends on $|\psi|^4$ ."847" Lt is a property of the lognormal istribution that if a random variable .X is lognormal. then so is .X""."," It is a property of the lognormal distribution that if a random variable $X$ is lognormal, then so is $X^n$."848 In such svstems the role of the gravitational potential © is plaveck by a potential that. describes. the isorder ofa solid. perhaps caused by the presence of defects.," In such systems the role of the gravitational potential $\phi$ is played by a potential that describes the disorder of a solid, perhaps caused by the presence of defects."849 Such systems display.foeafisalion at low temperature which is similar in some wavs to the original idea of Ancerson location (Anderson 1958)., Such systems display at low temperature which is similar in some ways to the original idea of Anderson location (Anderson 1958).850 The formation of strongly non-linear structures by gravity is thus directly analogous to the e&eneration of localised wavefunctions in condensed matter πμο..., The formation of strongly non-linear structures by gravity is thus directly analogous to the generation of localised wavefunctions in condensed matter systems.851 Finally. ancl perhaps most. promisinglv for future work. the equation (16)) ollers a relatively straightforward: way of modelling the behaviour of collisional material.," Finally, and perhaps most promisingly for future work, the equation \ref{eq:schrod}) ) offers a relatively straightforward way of modelling the behaviour of collisional material."852 The addition to the potential of a term of the form a[o|72 Gvith o an appropriately-chosen constant). converts the original equation (16)) into a nonlinear Sehroclelinger equation: (Sulem Sulem 1999).," The addition to the potential of a term of the form $\alpha |\psi|^2$ (with $\alpha$ an appropriately-chosen constant), converts the original equation \ref{eq:schrod}) ) into a nonlinear Schröddinger equation: (Sulem Sulem 1999)."853 Phis equation is now equivalent to those that. describe the flow of a barotropic Luicl: see Spiegel (1980)., This equation is now equivalent to those that describe the flow of a barotropic fluid; see Spiegel (1980).854 This svstem can therefore be usec to model pressure effects. which are otherwise only handled ellectively using numerical methocs such as. smoothed-particle hydrodynamical approximations (e.g. Monaghan 1992).," This system can therefore be used to model pressure effects, which are otherwise only handled effectively using numerical methods such as smoothed-particle hydrodynamical approximations (e.g. Monaghan 1992)."855 In the context of quantum systems. the nonlinear term ds used. to describe the formation of Bose-Einstcin condensates (e.g. Choi Niu 1999 and reference therein)," In the context of quantum systems, the nonlinear term is used to describe the formation of Bose-Einstein condensates (e.g. Choi Niu 1999 and reference therein)."856 In this short. paper 1 have sketched out. an. approach to the study evolving cosmological density lluctuations that relics on a transformation of the Vlasov-DPoisson. svsteni into a Sehrodcinger-Poisson system., In this short paper I have sketched out an approach to the study evolving cosmological density fluctuations that relies on a transformation of the Vlasov-Poisson system into a Schröddinger-Poisson system.857 The. transformation is not a new idea. but despite the ellorts of Widrow Ixaiser (1993) it does not seem to be well known in the astronomical community.," The transformation is not a new idea, but despite the efforts of Widrow Kaiser (1993) it does not seem to be well known in the astronomical community."858 The immediate: advantage of this new formalism is that it vields a rather more convincing approach to understanding the origin of spatial intermitteney ancl approximate lognormalitv in the galaxy distribution than that ollered by Jones (1999)., The immediate advantage of this new formalism is that it yields a rather more convincing approach to understanding the origin of spatial intermittency and approximate lognormality in the galaxy distribution than that offered by Jones (1999).859 It also makes a connection in the underlving physies with other systems that clisplay similar phenomena., It also makes a connection in the underlying physics with other systems that display similar phenomena.860 On the other hand. one must be aware of the approximations also inherent in the present approach.," On the other hand, one must be aware of the approximations also inherent in the present approach."861 The Schréddinger equation is not exact. and its usefulness. as an approximate tool is restricted by a number of conditions outlined by Widrow Kaiser (1993): see also Spiegel (1980).," The Schröddinger equation is not exact, and its usefulness as an approximate tool is restricted by a number of conditions outlined by Widrow Kaiser (1993); see also Spiegel (1980)."862 Furthermore. the lognormal solution of the svstem is a further approximation and may not be valid. especially in the stronglv-Huctuating limit.," Furthermore, the lognormal solution of the system is a further approximation and may not be valid especially in the strongly-fluctuating limit."863 Although it neatly. bypasses some of the problems inherent in the Jones (1999) mocel. the nonlinear wave equation is by no means easy to solve in eeneral situations.," Although it neatly bypasses some of the problems inherent in the Jones (1999) model, the nonlinear wave equation is by no means easy to solve in general situations."864 Numerical methods will still have to be emploved to understanding other aspects of the evolution of cosmic structure within this framework as indeed they are in other branches of physics., Numerical methods will still have to be employed to understanding other aspects of the evolution of cosmic structure within this framework as indeed they are in other branches of physics.865 One particular issue worth exploring using this approach is to understand the limits of the approach in strongly non-linear situations., One particular issue worth exploring using this approach is to understand the limits of the approach in strongly non-linear situations.866 As it stanels. the justification for the lognormal approximation arises from the weakly non-linear behaviour of collisionless matter moving in an almost constant potential field.," As it stands, the justification for the lognormal approximation arises from the weakly non-linear behaviour of collisionless matter moving in an almost constant potential field."867" ""Taking into account the expansion of the Universe. the changing gravitational potential. and the possible effects of matter pressure within in the action. formalism described in Section 3 may well reveal that a different formi of hierarchical scaling pertains in the stronely non-linear regime."," Taking into account the expansion of the Universe, the changing gravitational potential, and the possible effects of matter pressure within in the action formalism described in Section 3 may well reveal that a different form of hierarchical scaling pertains in the strongly non-linear regime."868 One aspect of this. is that the hierarchy of correlation functions that describe a lognormal distribution display Wirkwood (1935) scaling. while it appears from. numerical N-body simulations that cosmological Uuctuations display a dillerent hierarchical form.," One aspect of this is that the hierarchy of correlation functions that describe a lognormal distribution display Kirkwood (1935) scaling, while it appears from numerical $N$ -body simulations that cosmological fluctuations display a different hierarchical form."869 For adiscussion of the relationship between lognormal and hierarchical scaling. see Coles Frenk (1991).," For adiscussion of the relationship between lognormal and hierarchical scaling, see Coles Frenk (1991)."870"GRBs In this respect photoionisation of dust grains can play an important role (Lazzati, Perna Ghisellini 2001; Lazzati, Covino Ghisellini; Draine Hao 2002; Campana et al.","GRBs In this respect photoionisation of dust grains can play an important role (Lazzati, Perna Ghisellini 2001; Lazzati, Covino Ghisellini; Draine Hao 2002; Campana et al."871 2007)., 2007).872" Moreover, the absorbing column densities measured in the optical based on damped Lyman-a absorption are a factor of ~10 lower than those measured in the X-ray band (Campana et al."," Moreover, the absorbing column densities measured in the optical based on damped $\alpha$ absorption are a factor of $\sim 10$ lower than those measured in the X–ray band (Campana et al."873 2010; Fynbo et al., 2010; Fynbo et al.874 2009)., 2009).875 This has been interpreted as due to photoionization of the surrounding medium by GRB photons (Campana et al., This has been interpreted as due to photoionization of the surrounding medium by GRB photons (Campana et al.876" 2006, 2007; Watson et al."," 2006, 2007; Watson et al."877 2007; Campana et al., 2007; Campana et al.878 2010; Schady et al., 2010; Schady et al.879 2011)., 2011).880 The presence of a large amount of material is also testified by the existence of ‘dark’ GRBs., The presence of a large amount of material is also testified by the existence of `dark' GRBs.881 There are several definitions of dark GRBs., There are several definitions of dark GRBs.882 The easiest is that they do not show an optical counterpart (Fynbo et al., The easiest is that they do not show an optical counterpart (Fynbo et al.883 2001)., 2001).884 Since this definition is clearly related to the sensitivity (and availability) of the instruments used for the follow-up a more general definition is needed., Since this definition is clearly related to the sensitivity (and availability) of the instruments used for the follow-up a more general definition is needed.885 Based on the predictions of the fireball model (Mésszárros Rees 1997) one can require that the optical to X-ray spectral index Box (i.e. the slope between the fluxes in the R-band and at 3 keV at 11 hr after the burst) should be lower than 0.5 (Jakobsson et al., Based on the predictions of the fireball model (Mésszárros Rees 1997) one can require that the optical to X–ray spectral index $\beta_{OX}$ (i.e. the slope between the fluxes in the $R$ -band and at 3 keV at 11 hr after the burst) should be lower than 0.5 (Jakobsson et al.886 2004)., 2004).887" This will individuate optically sub-luminous bursts, i.e. fainter than expected from the fireball model."," This will individuate optically sub-luminous bursts, i.e. fainter than expected from the fireball model."888" Alternatively, with the advent ofSwift, X-ray spectral slopes were more easily available and a somewhat different definition was put forward by van der Horst et al. ("," Alternatively, with the advent of, X–ray spectral slopes were more easily available and a somewhat different definition was put forward by van der Horst et al. ("8892009) for which Box is shallower than 6x—0.5.,2009) for which $\beta_{OX}$ is shallower than $\beta_X - 0.5$.890" The darkness of a GRB can have different causes: it can be due to intrinsically optically faint GRBs, it can be due to absorption by intervening material within the host galaxy or it can be due to high redshift GRBs, thus being absorbed by the intergalactic medium."," The darkness of a GRB can have different causes: it can be due to intrinsically optically faint GRBs, it can be due to absorption by intervening material within the host galaxy or it can be due to high redshift GRBs, thus being absorbed by the intergalactic medium."891 Several works have addressed this topic in theSwift era when a number of facilities allowed a quick follow-up of the afterglows., Several works have addressed this topic in the era when a number of facilities allowed a quick follow-up of the afterglows.892 The fraction of dark bursts has been estimated to be ~25—5096 according to Jakobsson's definition (Melandri et al., The fraction of dark bursts has been estimated to be $\sim 25-50\%$ according to Jakobsson's definition (Melandri et al.893 2008; Roming et al., 2008; Roming et al.894 2009; Cenko et al., 2009; Cenko et al.895 2009; Greiner et al., 2009; Greiner et al.896 2011; Melandri et al., 2011; Melandri et al.897 2011)., 2011).898 It is now believed that the faint optical afterglow emission of dark bursts might be due to a moderate intrinsic extinction at moderate redshifts., It is now believed that the faint optical afterglow emission of dark bursts might be due to a moderate intrinsic extinction at moderate redshifts.899 Greiner et al. (, Greiner et al. (9002011) estimated a ~20% contribution from high redshift (zZ4— 5) GRBs to the dark population only.,2011) estimated a $\sim 20\%$ contribution from high redshift $z\gsim 4-5$ ) GRBs to the dark population only.901 Salvaterra et al. (, Salvaterra et al. (902"2011, see also Nava et al.","2011, see also Nava et al."903 2011) selected a complete sample of bright GRBs based on optical observability (Jakobsson et al., 2011) selected a complete sample of bright GRBs based on optical observability (Jakobsson et al.904 2006) andSwift BAT peak flux P>2.6 ph s! ?., 2006) and BAT peak flux $P\ge 2.6$ ph $^{-1}$ $^{-2}$.905 The sample consists of 58 GRBs and it is complete in spectroscopic redshift at 9096 (with 9596 of GRBs having some constraints on the redshift)., The sample consists of 58 GRBs and it is complete in spectroscopic redshift at $90\%$ (with $95\%$ of GRBs having some constraints on the redshift).906 'This sample offers the opportunity to study in an unbiased way the distribution of the X-ray column densities and its relation to GRB darkness., This sample offers the opportunity to study in an unbiased way the distribution of the X–ray column densities and its relation to GRB darkness.907 'The paper is organised as follows., The paper is organised as follows.908 In section 2 we derive the X-ray absorbing column densities for the Salvaterra's sample and briefly describe how the slope Box has been computed for each GRB of the sample., In section 2 we derive the X–ray absorbing column densities for the Salvaterra's sample and briefly describe how the slope $\beta_{OX}$ has been computed for each GRB of the sample.909 In section 3 we discuss our findings and in section 4 we draw our conclusions., In section 3 we discuss our findings and in section 4 we draw our conclusions.910 'The intrinsic column densities were computed using the automated data products provided by the Swift/XRT GRB spectra repository (Evans et al., The intrinsic column densities were computed using the automated data products provided by the /XRT GRB spectra repository (Evans et al.911 2009)., 2009).912 The archive has been recently updated by reprocessing all the on-line GRB data products using the latest software and calibration (Evans 2011)., The archive has been recently updated by reprocessing all the on-line GRB data products using the latest software and calibration (Evans 2011).913 Therefore some of these values overwrite those reported in Campana et al. (, Therefore some of these values overwrite those reported in Campana et al. (9142010).,2010).915 In Table 1 we list the column density value at the host galaxy redshift Nu(z)., In Table 1 we list the column density value at the host galaxy redshift $N_H(z)$.916 These are obtained fitting an absorbed power law model to the data in the specified time interval when there are no strong spectral variations., These are obtained fitting an absorbed power law model to the data in the specified time interval when there are no strong spectral variations.917 The absorption component is modeled with withinXSPEC., The absorption component is modeled with within.918 We consider two components one Galactic (held fixed) and a component at the redshift of the GRB (ZPHABS)., We consider two components one Galactic (held fixed) and a component at the redshift of the GRB ).919 The Galactic column density for each burst is provided by the Leiden/Argentine/Bonn (LAB) Survey of Galactic HI (Kalberla et al., The Galactic column density for each burst is provided by the Leiden/Argentine/Bonn (LAB) Survey of Galactic HI (Kalberla et al.920 2005)., 2005).921" For those GRBs without redshift, we fix the redshift of the free absorption component to zero, so that the resulting value provides a lower limit to the intrinsic column density."," For those GRBs without redshift, we fix the redshift of the free absorption component to zero, so that the resulting value provides a lower limit to the intrinsic column density."922 In the next sections we will also use the Box index., In the next sections we will also use the $\beta_{OX}$ index.923 This index is computed as the spectral index connecting the R-band flux and the (unabsorbed) 3 keV flux at 11 hr from the trigger., This index is computed as the spectral index connecting the $R$ -band flux and the (unabsorbed) 3 keV flux at 11 hr from the trigger.924 The collection of indexes and limits for the burst in our sample can be found in Melandri et al. (, The collection of indexes and limits for the burst in our sample can be found in Melandri et al. (9252011).,2011).926The shear correlation functious expected for each model are shown iu Figure 1.,The shear correlation functions expected for each model are shown in Figure 1.927 Note that our linear predictions would be revised upward for 0«10 if nonlinear evolution were included. |2].., Note that our linear predictions would be revised upward for $\theta \lesssim 10'$ if nonlinear evolution were included \cite{jai97}.928 Ta the absence of leusiug. the fluctuation of C;(0) averaged in au interval of width A. would be 7|C;(0)|= lO). where Nyans(0)c2z(li10)02A02Aloe0. is the nmuber of source pairs in this interval.," In the absence of lensing, the fluctuation of $C_{i}(\theta)$ averaged in an interval of width $\Delta \theta$, would be $\sigma \left[ C_{i}(\theta) \right] = g^{-2}929\sigma_{\epsilon}^{2} N_{\rm pairs}^{-\frac{1}{2}}(\theta)$ , where $N_{\rm pairs}(\theta)\simeq 2 \pi (\ln 10) n^{2} A \theta^{2} \Delta930\log \theta$ is the number of source pairs in this interval."931 As the straight lines in Fieure d demonstrate. we will be able to detect a signal for ο(0) and Co(0) for 0 ranging from 0.2 to 20 deerees.," As the straight lines in Figure 1 demonstrate, we will be able to detect a signal for $C_{1}(\theta)$ and $C_{2}(\theta)$ for $\theta$ ranging from 0.2 to 20 degrees."932 The complete lensing signal can be measured by performing a naxinmuu likelihood analysis for the power spectrum amplitude [3].., The complete lensing signal can be measured by performing a maximum likelihood analysis for the power spectrum amplitude \cite{kam98}.933 The signal-to-noise ratio. SNR(£Z). expected with this method is listed in the last coluun of table 1 and is about 10 for cIluster-normalized models.," The signal-to-noise ratio, $({\cal934L})$, expected with this method is listed in the last column of table 1 and is about 10 for cluster-normalized models."935 Because the weak-leusiug signal is only of the order of Svsteimnatic effects must be carefully accounted for.," Because the weak-lensing signal is only of the order of, systematic effects must be carefully accounted for."936 The following brefiv describes the major, The following briefly describes the major937and A-type stars (Fie. τὸ.,and A-type stars (Fig. \ref{fig7}) ).938" A best fit by eve tothe JAK, observations for the former vields a reddening of II) =0.15+0.02 Ξ0. LEO0.07) arc a distauce modulus of AL;=9.7+O1 (Vy AA=9.54 0.21). corresponding oa distance of d=W7L40.08 kpc. valijos that are reasonably cosistent with those obtained for 10 €‘luster from.CBW photometry."," A best fit by eye tothe $_s$ observations for the former yields a reddening of $= 0.15 \pm0.02$ $= 0.51 \pm0.07$ ) and a distance modulus of $_J = 9.7 \pm0.1$ $_0$ $_V = 9.34 \pm0.24$ ), corresponding to a distance of $d = 0.74 \pm0.08$ kpc, values that are reasonably consistent with those obtained for the cluster from photometry."939 Tl«* model isochrone from Mevuetetal.(1993) tlrat best fits tie observations has logf=9.5. nuovius a clustcY age of ~6 Cir. although the reeL eiauts are isplaced recward of that isochroucs nml ike he case for Berkeley Ll red eian chump stars.," The model isochrone from \citet{me93} that best fits the observations has $\log t = 9.8$, implying a cluster age of $\sim6$ Gyr, although the red giants are displaced redward of that isochrone, much like the case for Berkeley 44 red giant clump stars."940 Conceivably a refined eiipirical caibratiou of 2\ASS intrinsic colors that iucludes a separate relationu for red giant stars could clirate the problen., Conceivably a refined empirical calibration of 2MASS intrinsic colors that includes a separate relation for red giant stars could eliminate the problem.941 There appear to be large nuniys of AL dar* Wine along the line of sight to the cluster., There appear to be large numbers of M dwarfs lying along the line of sight to the cluster.942" The muplied best ft bv eve to the 1Η. observatious for he eroup of reddened B-type stars vields a reddening ofII) =0.30+0.02 =1.02 £0.07) aud a distance modulis of Af,=13.2+0.2 Ty AR=12.1:+ 1.29). corresponding to a distance of οἱ=3.12+0.12 kpc."," The implied best fit by eye to the $_s$ observations for the group of reddened B-type stars yields a reddening of $= 0.30 \pm0.02$ $= 1.02 \pm0.07$ ) and a distance modulus of $_J = 13.2 \pm0.2$ $_0$ $_V = 12.47 \pm0.29$ ), corresponding to a distance of $d = 3.12 \pm0.42$ kpc."943" Similar values were used bv Turner(2010) with an earlier version of the 2MASS calibration to establish very reasonable estinates for he reddening and hnuninosiv of the 68 Cepheid 5 Vulpeculae as a possible cluster member,", Similar values were used by \citet{tu10} with an earlier version of the 2MASS calibration to establish very reasonable estimates for the reddening and luminosity of the $^{\rm d}$ Cepheid S Vulpeculae as a possible cluster member.944 S Vul is represente bv the star πο in Fie. 7.., S Vul is represented by the star symbol in Fig. \ref{fig7}. .945 In thepresent iistance the results imply intrinsic parameters of (4By (Vjjo=UST20.07 and (Mj=G.8N6-0.29 for the Cepheic. close to what would ο predicted. emipirically," In thepresent instance the results imply intrinsic parameters of $(\langle B \rangle - \langle V \rangle)_0 = 0.87 \pm 0.07$ and $\langle M_V \rangle = -6.86 \pm 0.29$ for the Cepheid, close to what would be predicted empirically"946proposed for the S.2-m Subaru Telescope and aimed for a detailed investigation into the nature of dark energy and into galaxy formation anc evolution.,proposed for the 8.2-m Subaru Telescope and aimed for a detailed investigation into the nature of dark energy and into galaxy formation and evolution.947 Similar scientific motivations supported. the proposal of a wide-field fiber-feck spectrograph. the Super Lue Deplovable Experiment (SIDE. ?)). for the LO-m Gran Telescopio Canarias.," Similar scientific motivations supported the proposal of a wide-field fiber-fed spectrograph, the Super Ifu Deployable Experiment (SIDE, \citealt{Prada2008}) ), for the 10-m Gran Telescopio Canarias."948 None of these instruments were finally built but they are excellent. examples of state-of-the-art survey spectrographs aiming to fulfill. next-generation scientific requirements., None of these instruments were finally built but they are excellent examples of state-of-the-art survey spectrographs aiming to fulfill next-generation scientific requirements.949 Several spectrographs have otherwise been accepted. for construction. such as the Fibre Multi-Object Spectrograph (FAIOS. ?)). à near-infrarecl instrument which is already mounted on the Subaru Telescope.," Several spectrographs have otherwise been accepted for construction, such as the Fibre Multi-Object Spectrograph (FMOS, \citealt{Kimura2010}) ), a near-infrared instrument which is already mounted on the Subaru Telescope."950 Already. in the [ast stages of commissioning is also the set of. 16 multi-fiber spectrographs for the five-degree field of view Chinese Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST. 2)).," Already in the last stages of commissioning is also the set of 16 multi-fiber spectrographs for the five-degree field of view Chinese Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST, \citealt{Wang2009}) )."951 LAMOST. was conceived to. carry out several wicde-Lield spectroscopic. surveys focusing on. both the structure of the Milky Way and the large-scale structure of the Universe., LAMOST was conceived to carry out several wide-field spectroscopic surveys focusing on both the structure of the Milky Way and the large-scale structure of the Universe.952 Finally. as an example of next-generation spectroscopic facilities. we will mention the Bie Baryonic Oscillation Spectroscopic Survey (BigBOSS. ?)).," Finally, as an example of next-generation spectroscopic facilities, we will mention the Big Baryonic Oscillation Spectroscopic Survey (BigBOSS, \citealt{Schlegel2009}) )."953 BigBOSS is à proposed. erouncd-hase dark energy. experiment to study barvon acoustic oscillation with an all-sky galaxy. recishift survey. making use of a multi-object. fiber-fed spectrograph on the Mavall 4m telescope at For all fiber-feck spectrographs (as. those. mentioned above) a primordial ancl common technical problem is the positioning of fiber ends. which must match the projected position of objects in the focal plane.," BigBOSS is a proposed ground-base dark energy experiment to study baryon acoustic oscillation with an all-sky galaxy redshift survey, making use of a multi-object fiber-fed spectrograph on the Mayall 4-m telescope at For all fiber-fed spectrographs (as those mentioned above) a primordial and common technical problem is the positioning of fiber ends, which must match the projected position of objects in the focal plane."954 In. order to. solve this dillicultv. the concept. used in most. recentlv-proposed fiber-fed spectrographs (SIDE. LAAIOST. DBigBOSS. etcetera) |consists of an array of fiber positioners covering the entire focal plane which is able to position all. fiber heads simultaneously.," In order to solve this difficulty, the concept used in most recently-proposed fiber-fed spectrographs (SIDE, LAMOST, BigBOSS, etcetera) consists of an array of fiber positioners covering the entire focal plane which is able to position all fiber heads simultaneously."955 This solution reduces drastically the recontiguration time of the svstem as compared. to the most common alternative based on a pick-and-place device., This solution reduces drastically the reconfiguration time of the system as compared to the most common alternative based on a pick-and-place device.956 Important for this work. in a real survey normally a single configuration of the array of positioners is not. enough. to observe all (or even a given required fraction) of the objects in à target field.," Important for this work, in a real survey normally a single configuration of the array of positioners is not enough to observe all (or even a given required fraction) of the objects in a target field."957 Several configurations (or tiles) are needed to reach a given completeness. depending on the typical number of objects per fiber positioner.," Several configurations (or tiles) are needed to reach a given completeness, depending on the typical number of objects per fiber positioner."958 Ehe purpose of this work is to present an optimized wav to assign fibers to objects so that the maximum number of objects is assigned in the first tiles., The purpose of this work is to present an optimized way to assign fibers to objects so that the maximum number of objects is assigned in the first tiles.959 We also discuss on some additional wavs of optimizing the fiber positioning process. depending on the capabilities of the This paper is organized as follows.," We also discuss on some additional ways of optimizing the fiber positioning process, depending on the capabilities of the This paper is organized as follows."960 In Section 2.. we define some important concepts and. provide. the nomenclature that we use throughout this work.," In Section \ref{sec:nom}, we define some important concepts and provide the nomenclature that we use throughout this work."961 In Section 3.. we brielly describe a general svstem consisting of an array of positioners covering the intrument local plane.," In Section \ref{sec:robot}, we briefly describe a general system consisting of an array of positioners covering the intrument focal plane."962 In Section 4.. we present our optimized Liber positioning algorithm. that we call draining algorithm. ancl assess its performance as compared to a random assignment in catalogs of randomly. distributed. objects.," In Section \ref{sec:draining}, we present our optimized fiber positioning algorithm, that we call draining algorithm, and assess its performance as compared to a random assignment in catalogs of randomly distributed objects."963 Section 5 is dedicated: to evaluating further optimizations such as rotation of the focal plane., Section \ref{sec:additional} is dedicated to evaluating further optimizations such as rotation of the focal plane.964 In Section 6... we test. the ellicienev of our optimizations in mock galaxy catalogs crawn from cosmological simulations.," In Section \ref{sec:real}, we test the efficiency of our optimizations in mock galaxy catalogs drawn from cosmological simulations."965 Finally. in Section 7.. we summarize our main results and discuss on their implications.," Finally, in Section \ref{sec:discussion}, we summarize our main results and discuss on their implications."966 In order to facilitate the reacder's comprehension we will first introduce some basic concepts that will be frequently quoted in this work., In order to facilitate the reader's comprehension we will first introduce some basic concepts that will be frequently quoted in this work.967 Namely: Note that the main intention of this work is to present a complete and optimized method for. fiber. assignment., Namely: Note that the main intention of this work is to present a complete and optimized method for fiber assignment.968 We will therefore. and. unless otherwise stated. consider a target field. of approximately the size of the focal plane of the spectrograph.," We will therefore, and unless otherwise stated, consider a target field of approximately the size of the focal plane of the spectrograph."969 Only rotation of the focal plane will be allowed as an additional optimization., Only rotation of the focal plane will be allowed as an additional optimization.970 Lhe process of tiling itself. that involves positioning tiles on a large region of the sky (as compared to the size of a tile). will only be discussed in a qualitative way.," The process of tiling itself, that involves positioning tiles on a large region of the sky (as compared to the size of a tile), will only be discussed in a qualitative way."971 The concept that we outline here follows a standard design that can be extrapolated to most future fiher-Led multi-object spectrographs., The concept that we outline here follows a standard design that can be extrapolated to most future fiber-fed multi-object spectrographs.972 In these instruments. the focal," In these instruments, the focal"973The possible existence of exoplanets in coorbital motion has fascinated planetary scientists for several years.,The possible existence of exoplanets in coorbital motion has fascinated planetary scientists for several years.974 Since the diversity of exoplanetary configurations continue to surprise us. even more than 15 years after the discovery of Peg51b. and it seems almost natural to expect Trojan planets to exist somewhere and the announcement of their discovery to be only a matter of time.," Since the diversity of exoplanetary configurations continue to surprise us, even more than 15 years after the discovery of Peg51b, and it seems almost natural to expect Trojan planets to exist somewhere and the announcement of their discovery to be only a matter of time."975 Probably the first detailed analysis of hypothetical coorbital planets is due to Laughlin and Chambers (2002)., Probably the first detailed analysis of hypothetical coorbital planets is due to Laughlin and Chambers (2002).976 They studied three types of coorbital configurations: tadpole orbits (around £ and L:; equilateral points) horse-shoe configurations and “eccentric resonances”.," They studied three types of coorbital configurations: tadpole orbits (around $L_4$ and $L_5$ equilateral points), horse-shoe configurations and “eccentric resonances”."977 They proposed to distinguish between coorbital and single planet fits from RV data by observing residuals from long-term observations (more than ten orbital periods). because the coorbital configurations have large mutual interactions due to resonant motion.," They proposed to distinguish between coorbital and single planet fits from RV data by observing residuals from long-term observations (more than ten orbital periods), because the coorbital configurations have large mutual interactions due to resonant motion."978 For systems with more than one planet. it is well known that the existence of resonant motion may be possible evidence of a past large-scale planetary migration due to interactions with the gaseous disk.," For systems with more than one planet, it is well known that the existence of resonant motion may be possible evidence of a past large-scale planetary migration due to interactions with the gaseous disk."979 Although their importance is unquestionable. it is still intriguing why some commensurabilities are very populated (e.g. 2/1 MMR) and others that are currently empty (particularly the 1/1 MMR).," Although their importance is unquestionable, it is still intriguing why some commensurabilities are very populated (e.g., 2/1 MMR) and others that are currently empty (particularly the 1/1 MMR)."980 Lagrange (1873) discovered stable solutions for three massive bodies such that at all times their relative positions are located in the vertices of an equilateral triangle of variable size (L4 and £; solutions)., Lagrange (1873) discovered stable solutions for three massive bodies such that at all times their relative positions are located in the vertices of an equilateral triangle of variable size $L_4$ and $L_5$ solutions).981 Linear stability analyses traditionally focused on the restricted three-body problem (where one of the masses vanishes. e.g Morais 2001. Namouni et al.," Linear stability analyses traditionally focused on the restricted three-body problem (where one of the masses vanishes, e.g Morais 2001, Namouni et al."982 1999 and references therein)., 1999 and references therein).983 Recently. Nauenberg (2002) numerically investigated the dynamical stability of general three body problem as a function of the eccentricity of the orbits and the Rouths” mass parameter.," Recently, Nauenberg (2002) numerically investigated the dynamical stability of general three body problem as a function of the eccentricity of the orbits and the Rouths' mass parameter."984 The, The985size of dlrrs) with typical parameters of primordial clouds (Haiman.Rees&Loeb1996).,size of dIrrs) with typical parameters of primordial clouds \citep{hrl96}.986. Furthermore. early type stars as the sources of LW photons are rare in dirrs.," Furthermore, early type stars as the sources of LW photons are rare in dIrrs."987 Therefore. the negative-feedback on further star formation brought about the dissociation by the LW photons may be negligible in dlrrs.," Therefore, the negative-feedback on further star formation brought about the dissociation by the LW photons may be negligible in dIrrs."988 By the way. if is formed by gas-phase reactions (equations 1--4). the formative abundance of H». vg. largely depends on the eabundance. vj. because the formation process through is more effective than the one through H5 (in 322. we discuss that gas-phase formation may dominate grain-catalyzed formation in dlrrs).," By the way, if is formed by gas-phase reactions (equations \ref{hm1}- ), the formative abundance of $\mathrm{H_2}$, $y_\mathrm{H_2}$, largely depends on the abundance, $y_\mathrm{H^-}$, because the formation process through is more effective than the one through $\mathrm{H_2^+}$ (in 2, we discuss that gas-phase formation may dominate grain-catalyzed formation in dIrrs)."989 We expect that in dlrrs is more effectively influenced by the destruction of than by the direct dissociation of due to the LW photons., We expect that in dIrrs is more effectively influenced by the destruction of than by the direct dissociation of due to the LW photons.990 This is because that the typical mean free path of the destroying infrared (IR) photons (its wavelength vt€1.64 jm). Ay. would be sufficiently longer than that of the LW photons: Ag~100kpe C» the typical size of dlrrs) with typical parameters of primordial clouds.," This is because that the typical mean free path of the destroying infrared (IR) photons (its wavelength $\lambda \la 1.64\ \mathrm{\mu991 m}$ ), $l_\mathrm{IR}$, would be sufficiently longer than that of the LW photons; $l_\mathrm{IR}\sim 100\ \mathrm{kpc}$ $\gg$ the typical size of dIrrs) with typical parameters of primordial clouds."992 Therefore. the IR photons can penetrate and affect the whole ISM.," Therefore, the IR photons can penetrate and affect the whole ISM."993 Furthermore. the IR photons are also radiated by low-mass stars as well as early type stars.," Furthermore, the IR photons are also radiated by low-mass stars as well as early type stars."994 Thus. all stars born in the previous starburst phase can be considered as the sources of the destroying photons.," Thus, all stars born in the previous starburst phase can be considered as the sources of the destroying photons."995 If is seriously destroyed by the IR photons of the interstellar radiation field (ISRF) of ας. the star formation activity may become more inactive at almost the whole ISM.," If is seriously destroyed by the IR photons of the interstellar radiation field (ISRF) of dIrrs, the star formation activity may become more inactive at almost the whole ISM."996" With this expectation. we construct the theoretical model to investigate yy,."," With this expectation, we construct the theoretical model to investigate $y_\mathrm{H_2}$."997 In. $22. we compare the rates of gas-phase and grain-catalyzed formation. and show gas-phase formation may dominate in dIrrs.," In 2, we compare the rates of gas-phase and grain-catalyzed formation, and show gas-phase formation may dominate in dIrrs."998 $3 deseribes our model for the star formation process in dirrs and $4. presents our results., 3 describes our model for the star formation process in dIrrs and 4 presents our results.999 Finally. we summarize our study and briefly discuss about the next starburst phase in $5.," Finally, we summarize our study and briefly discuss about the next starburst phase in 5."1000 formation on dust-grain surfaces completely dominates gas-phase one in the local ISM., formation on dust-grain surfaces completely dominates gas-phase one in the local ISM.1001 However. if the gas ratio. D. is lower than a eritical value. D... gas-phase formation dominates grain-catalyzed formation (Kamaya&Hirashita2001:Glover 2003)..," However, if the dust-to-gas ratio, $D$, is lower than a critical value, $D_\mathrm{cr}$, gas-phase formation dominates grain-catalyzed formation \citep{kh01, glover03}. ."1002 Despite the formation rate on grain surfaces is still uncertain. Glover(2003). calculates Din some astrophysical situations by tentatively adopting the rate of Hollenbach&McKee(1979).," Despite the formation rate on grain surfaces is still uncertain, \citet{glover03} calculates in some astrophysical situations by tentatively adopting the rate of \citet{hm79}."1003". As noted in Glover (2003).. the temperature dependence of D,,is very strong: at low temperatures (Z7.€afewx10° K). grain-catalyzed formation is relatively efficient and is very small (D,€107 Daw. where is the dust-to-gas ratio in the local ISM). while at high temperatures. gas-phase formation ts efficient and thus. is large."," As noted in \citet{glover03}, the temperature dependence of is very strong; at low temperatures $T\la \mathrm{a\ few}\times 10^2\dkel$ ), grain-catalyzed formation is relatively efficient and is very small $D_\mathrm{cr}\la 10^{-3}D_\mathrm{MW}$ , where is the dust-to-gas ratio in the local ISM), while at high temperatures, gas-phase formation is efficient and thus, is large."1004 In addition. also depends on the ionisation degree and the density of ISM: both high-ionisation and high-density lead the high efficiency of phase formation and large D.," In addition, also depends on the ionisation degree and the density of ISM; both high-ionisation and high-density lead the high efficiency of gas-phase formation and large $D_\mathrm{cr}$."1005" By the way. we focus on the process that the ISM of dlIrrs once is heated up by stellar-radiation. supernovae and/or other processes, and then cools down to the temperature at which star formation is effective under ISRF."," By the way, we focus on the process that the ISM of dIrrs once is heated up by stellar-radiation, supernovae and/or other processes, and then cools down to the temperature at which star formation is effective under ISRF."1006 Thus. re-calculating (eq. (," Thus, re-calculating (eq. ("100735) of Glover(2003))) by using the physical parameters in which we interested. we have Dy.210-7Dapy at T25000K as shown in the dotted line of figure 1..,"35) of \citet{glover03}) ) by using the physical parameters in which we interested, we have $D_\mathrm{cr} \ga 10^{-2}\dmw$ at $T\ga 5000\dkel$ as shown in the dotted line of figure \ref{fig1}."1008" This critical value ts on the same order of magnitude with the typical value for dlIrrs Dai,~13»107Dyiw. CLisenfeld&Ferrara1998). ", This critical value is on the same order of magnitude with the typical value for dIrrs $D_\mathrm{dIrrs}\sim 1.3\times 10^{-2}\dmw$ \citep{lf98}. .1009At T€35000K. the ISM cools off at a stroke.," At $T\la 5000\dkel$, the ISM cools off at a stroke."1010" This is because D, becomes smaller than Dy... and thus. formation on dust-grain surfaces may dominate: therefore. rapidly increases."," This is because $D_\mathrm{cr}$ becomes smaller than $D_\mathrm{dIrrs}$, and thus, formation on dust-grain surfaces may dominate; therefore, rapidly increases."1011 Furthermore. if the metallicity of dlrrs is higher than a critical value ~107Zc; (Nishi&Tashiro2000) (the same order with the metallicity of the most metal- galaxy. I Zw 18). metal cooling dominates cooling at this temperature range.," Furthermore, if the metallicity of dIrrs is higher than a critical value $\sim 10^{-2}Z_{\sun}$ \citep{nt00} (the same order with the metallicity of the most metal-deficient galaxy, I Zw 18), metal cooling dominates cooling at this temperature range."1012 However. we are interested in the temperature at which the cooling timescale is the longest because global star formation timescale is decided by the slowest physical process.," However, we are interested in the temperature at which the cooling timescale is the longest because global star formation timescale is decided by the slowest physical process."1013 Thus. the interesting temperature is found to be ~5000K. at which gas-phase formation dominates.," Thus, the interesting temperature is found to be $\sim 5000\dkel$, at which gas-phase formation dominates."1014 Therefore. it is meaningful to study the SFHs of dlrs on the assumption that gas-phase formation ts important.," Therefore, it is meaningful to study the SFHs of dIrrs on the assumption that gas-phase formation is important."1015 We calculate the time-dependent. non-chemical equilibrium. ionisation and molecule formation history of a gas system in dlrrs composed of hydrogen and helium.," We calculate the time-dependent, non-chemical equilibrium, ionisation and molecule formation history of a gas system in dIrrs composed of hydrogen and helium."1016 Neglecting the dynamics of the gas system in ISM. we concentrate on the time evolution of the density and temperature in some regions in dIrrs.," Neglecting the dynamics of the gas system in ISM, we concentrate on the time evolution of the density and temperature in some regions in dIrrs."1017 We consider the following 9 chemical species: H.Hs:Hj.Πε.He.e.," We consider the following 9 chemical species; $\mathrm{H,\ H^+,\ H^-,\ H_2,\ H_2^+,\ He,\ He^+,\ He^{++},\ e^-}$."1018 In dlrs. the helium abundance is still maintained almost primordial value because dlrs are still in an early stage of chemical evolution: therefore. it is assumed to be primordial value of hydrogen by mass fraction) in our calculation (Skillmanetal. 1999).," In dIrrs, the helium abundance is still maintained almost primordial value because dIrrs are still in an early stage of chemical evolution; therefore, it is assumed to be primordial value of hydrogen by mass fraction) in our calculation \citep{skillman93, izotov99}."1019". At first. the ISRF in our model. ον. is assumed to have same energy dependence with that of the solar vicinity. Je (seeMathis.Mezger&Panagia1983). and its intensity 15 normalised by that of the solar vicinity; J,=€-TP, In order to investigate the dependence of on the ISRE. we change the ratio & from 0.01 to 100 with the step of one order of magnitude."," At first, the ISRF in our model, $J_{\nu}$, is assumed to have same energy dependence with that of the solar vicinity, $J_{\nu}^{\sun}$ \citep[see][]{mmp83}, and its intensity is normalised by that of the solar vicinity; $J_{\nu} = \varepsilon \cdot J_{\nu}^{\sun}$ In order to investigate the dependence of on the ISRF, we change the ratio $\varepsilon$ from 0.01 to 100 with the step of one order of magnitude."1020" At next.decomposing the ISRF of solar vicinity into four parts. that is. early type stars. two types of disc stars (Tay=7500K..4000 K) and red giant stars (To=3000 K) as in Mathis.Mezger&Panagia (1983)... we investigate which degree eachcomponent affects yy,.Initial. conditions of all calculations are Tin,=1.0κ10°Κ.nin)3.0x107 ο”. and the initial abundances of each chemical species are that in chemical equilibriumat 7."," At next,decomposing the ISRF of solar vicinity into four parts, that is, early type stars, two types of disc stars $\teff =1021 7500\dkel,\ 4000\dkel$ ) and red giant stars $\teff = 3000\dkel$ ) as in \citet{mmp83}, we investigate which degree eachcomponent affects $y_\mathrm{H_2}$ .Initial conditions of all calculations are $T_\mathrm{ini} = 1.0\times 10^6\dkel,\ n_\mathrm{ini}=3.0\times1022 10^{-3}\ \mathrm{cm^{-3}}$ , and the initial abundances of each chemical species are that in chemical equilibriumat $T_\mathrm{ini}$ ."1023"emission, using our 3D reconstructing technique, is that of a double interleaved ring system, one being composed of O-rich material, and the other being composed of shocked ISM knots.","emission, using our 3D reconstructing technique, is that of a double interleaved ring system, one being composed of O-rich material, and the other being composed of shocked ISM knots."1024"The fact that many ISM knots happen to coincide with O-rich knots when viewed from above is probably a coincidence, since these are shocked by the blast wave, not the oxygen-rich material passing through the reverse shock.","The fact that many ISM knots happen to coincide with O-rich knots when viewed from above is probably a coincidence, since these are shocked by the blast wave, not the oxygen-rich material passing through the reverse shock."1025" However, there may be a case to be made for a closer interaction between either the or the clumps and the Lasker's Bowl complex, since their combined shape matches perfectly to the overall shape of the Lasker's Bowl feature, suggesting a direct interaction."," However, there may be a case to be made for a closer interaction between either the or the clumps and the Lasker's Bowl complex, since their combined shape matches perfectly to the overall shape of the Lasker's Bowl feature, suggesting a direct interaction."1026" However, there are two issues arising from this scenario."," However, there are two issues arising from this scenario."1027" First, the and clumps cannot be related to each other, one being blue-shifted, and the other red-shifted, and therefore well-separated in space."," First, the and clumps cannot be related to each other, one being blue-shifted, and the other red-shifted, and therefore well-separated in space."1028" Second, the Lasker's Bowl appears to be blue shifted."," Second, the Lasker's Bowl appears to be blue shifted."1029" This is consistent with it being a foreground object, as suggested by the X-ray shadowing, since the cloud shock within the Lasker's Bowl complex would be propagating through it towards the observer."," This is consistent with it being a foreground object, as suggested by the X-ray shadowing, since the cloud shock within the Lasker's Bowl complex would be propagating through it towards the observer."1030 The clump cannot be hitting it as is moving in the other direction., The clump cannot be hitting it as is moving in the other direction.1031" However, there is still a case to be made that the clump is associated, as it lies in a region of enhanced X-ray emission, possibly associated with the reverse (bow) shock generated when the blast wave over-ran the rear surface of the large ISM cloud."," However, there is still a case to be made that the clump is associated, as it lies in a region of enhanced X-ray emission, possibly associated with the reverse (bow) shock generated when the blast wave over-ran the rear surface of the large ISM cloud."1032"Early-type main sequence stars exhibit. a number of peculiarities usually not encountered in cooler stars: fast rotation, debris disks. enhanced surface metallicities (Am). magnetic fields and rapid oscillations (Ap and roAp stars). ete.","Early-type main sequence stars exhibit a number of peculiarities usually not encountered in cooler stars: fast rotation, debris disks, enhanced surface metallicities (Am), magnetic fields and rapid oscillations (Ap and roAp stars), etc."1033 Although stellar structure and evolutior models are now rather successful in reproducing the observed physical properties of most A-type stars. the observational constraints on these models remain relatively weak. occasionally leading to surprising discoveries.," Although stellar structure and evolution models are now rather successful in reproducing the observed physical properties of most A-type stars, the observational constraints on these models remain relatively weak, occasionally leading to surprising discoveries."1034 An example ts provided by the recent interferometric observations of the AOV benchmark starVega.. that confirmed that Vega. as previously shown by Gulliver. Hill Adelman (1994)). is a pole-on fast rotator near eritical velocity (Aufdenberg et al. 2006)).," An example is provided by the recent interferometric observations of the A0V benchmark star, that confirmed that Vega, as previously shown by Gulliver, Hill Adelman \cite{gulliver94}) ), is a pole-on fast rotator near critical velocity (Aufdenberg et al. \cite{aufdenberg06}) )."1035 The same interferometric observations showed that Vega harbors a hot debris disk within within AAU from the star (Absil et al. 2006)).74956..41913..321.3.. 9278)," The same interferometric observations showed that Vega harbors a hot debris disk within within AU from the star (Absil et al. \cite{absil06}) )., )"1036) is a bright multiple star including at least three identified components. and is among our closest stellar neighbors. with a revised parallax of πμ=40.5x0.4 mmas (van Leeuwen 2007)).," is a bright multiple star including at least three identified components, and is among our closest stellar neighbors, with a revised parallax of $\pi_{\rm Hip} = 40.5 \pm 0.4$ mas (van Leeuwen \cite{vanleeuwen07}) )."1037 This object has many observational peculiarities., This object has many observational peculiarities.1038 Firstly. it was discovered only in 1997 that ὁ Vel hosts one of the brightest of all known eclipsing binaries (Otero et al. 2000)).," Firstly, it was discovered only in 1997 that $\delta$ Vel hosts one of the brightest of all known eclipsing binaries (Otero et al. \cite{otero00}) ),"1039 with a remarkably long orbital period (P.45 ddays)., with a remarkably long orbital period $P \approx 45$ days).1040 This eclipsing binary is also one of the very few that are easily observable with the naked eye ον=2).," This eclipsing binary is also one of the very few that are easily observable with the naked eye $m_V1041\approx 2$ )."1042 The eclipsing pair was first resolved using optical interferometry by Kellerer et al. (2007))., The eclipsing pair was first resolved using optical interferometry by Kellerer et al. \cite{kellerer07}) ).1043 Secondly. 6 VVel is known to have a moderate thermal infrared excess (e.g. Aumann 1985.. Su et al. 2006)).," Secondly, $\delta$ Vel is known to have a moderate thermal infrared excess (e.g. Aumann \cite{aumann85}, Su et al. \cite{su06}) ),"1044 and observations revealed a spectacular bow shock caused by the motion of 6 VVel in a dense interstellar cloud (Gásspárr et al. 2008))., and observations revealed a spectacular bow shock caused by the motion of $\delta$ Vel in a dense interstellar cloud (Gásspárr et al. \cite{gaspar08}) ).1045 The presence of interstellar material was also reported by Hempel Schmitt (2003)). who observed two red-shifted absorbing components in absorption in the Ca II K line. of probable interstellar origin.," The presence of interstellar material was also reported by Hempel Schmitt \cite{hempel03}) ), who observed two red-shifted absorbing components in absorption in the Ca II K line, of probable interstellar origin."1046 In Paper I of the present series. Kervella et al. (2009))," In Paper I of the present series, Kervella et al. \cite{kervella09}) )"1047 confirmed that the infrared excess is essentially emitted by the bow shock. and not warm circumstellar material located close to the stars.," confirmed that the infrared excess is essentially emitted by the bow shock, and not warm circumstellar material located close to the stars."1048 In the framework of a search for resolved emission due to debris disks. Moerchen et al. (2010))," In the framework of a search for resolved emission due to debris disks, Moerchen et al. \cite{moerchen10}) )"1049 obtained thermal infrared images of 0 VVel using the Gemini South telescope and the T- instrument. and detected a marginally resolved emission atul=10.4 um. In Paper IL. Pribulla et al. (2011))," obtained thermal infrared images of $\delta$ Vel using the Gemini South telescope and the T-ReCS instrument, and detected a marginally resolved emission at $\lambda =105010.4\,\mu$ m. In Paper II, Pribulla et al. \cite{pribulla11}) )"1051 used à combination of high-resolution spectroscopy and photometric observations (from the SMEI instrument. attached to the Coriolis satellite) to derive an accurate orbital solution for the eclipsing binary ó Vel A. and estimate the physical parameters of ὁ VVel Aa and Ab.," used a combination of high-resolution spectroscopy and photometric observations (from the SMEI instrument, attached to the Coriolis satellite) to derive an accurate orbital solution for the eclipsing binary $\delta$ Vel A, and estimate the physical parameters of $\delta$ Vel Aa and Ab."1052 They identified that the two eclipsing components are fast rotating stars. with respective masses of 2.53+0.11M. and 2.37+0.10M.. (=4% accuracy). and estimated the mass of 0 Vel B to be =|1.5M...," They identified that the two eclipsing components are fast rotating stars, with respective masses of $2.53 \pm 0.11\,M_\odot$ and $2.37 \pm10530.10\,M_\odot$ $\approx 4\%$ accuracy), and estimated the mass of $\delta$ Vel B to be $\approx1.5\,M_\odot$."1054 In spite of this recent progress. uncertainties remain on the fundamental parameters of the different components of the system. in particular on their exact masses.," In spite of this recent progress, uncertainties remain on the fundamental parameters of the different components of the system, in particular on their exact masses."1055 Taking e=vantage of the availability of NACO astrometry of the ó VVel A-B pair. and new interferometric observations from," Taking advantage of the availability of NACO astrometry of the $\delta$ Vel A-B pair, and new interferometric observations from"1056"gas particle and the center of ErisMC, d;.","gas particle and the center of ErisMC, $d_{i}$."1057" Analogously to equation (4)), we then define a metal mass-weighted source halo mass and distance from ErisMC center as and respectively."," Analogously to equation \ref{eqn:zen}) ), we then define a metal mass-weighted source halo mass and distance from ErisMC center as and respectively."1058 We have separated gas particles into different groups according to their (zen) and plotted in Figure 9 the projected metallicity of each group at redshift 3., We have separated gas particles into different groups according to their $\langle z_{\rm en}\rangle$ and plotted in Figure \ref{fig9} the projected metallicity of each group at redshift 3.1059" Metals within ErisMC’s virial radius are clearly “younger”, i.e. they are characterized by an enrichment redshift between 3 and 3.5."," Metals within ErisMC's virial radius are clearly “younger"", i.e. they are characterized by an enrichment redshift $\langle z_{\rm en}\rangle$ between 3 and 3.5."1060" Because of the long wind propagation(zen) time, “older” metals with (Zen) between 4 and 5 are spread over 100 (physical) kpc perpendicularly to ErisMC’s disk."," Because of the long wind propagation time, “older"" metals with $\langle z_{\rm en}\rangle$ between 4 and 5 are spread over 100 (physical) kpc perpendicularly to ErisMC's disk."1061 Low-metallicity gas in this enrichment redshift range can be seen as far as 200 kpc from the main host center as it is ejected from nearby dwarfs (see also Figs., Low-metallicity gas in this enrichment redshift range can be seen as far as 200 kpc from the main host center as it is ejected from nearby dwarfs (see also Figs.1062 3 and 4))., \ref{fig3} and \ref{fig4}) ).1063 There is little material contaminated by metals at (zen)>5 within ErisMC’s virial radius., There is little material contaminated by metals at $\langle z_{\rm en}\rangle >5$ within ErisMC's virial radius.1064" Late ((Zen)« galactic “superwinds” — the result of recent star formation5) in ErisMC’s main host — are found to account for less than of all the metals observed beyond 2Ryir Figure 10 sheds light ,on the role played by satellites and nearby dwarfs in contaminating ErisMC’s circumgalactic medium."," Late $\langle z_{\rm en}\rangle <5$ ) galactic “superwinds"" -- the result of recent star formation in ErisMC's main host – are found to account for less than of all the metals observed beyond $2\rvir$, Figure \ref{fig10} sheds light on the role played by satellites and nearby dwarfs in contaminating ErisMC's circumgalactic medium."1065 It shows the total mass of heavy elements released by the main host and its satellites as a function of distance from ErisMC’s center at redshift 3., It shows the total mass of heavy elements released by the main host and its satellites as a function of distance from ErisMC's center at redshift 3.1066" About of all the metals within 100 kpc of the center originate from the main host, and the rest from its satellites."," About of all the metals within 100 kpc of the center originate from the main host, and the rest from its satellites."1067" Beyond 100 kpc, nearby dwarfs start dominating the metal budget."," Beyond 100 kpc, nearby dwarfs start dominating the metal budget."1068 Both the host and the satellites contribute to the recent (z< 4) pollution of gas within the virial radius., Both the host and the satellites contribute to the recent $z<4$ ) pollution of gas within the virial radius.1069" Older metals within Ry typically form in satellite progenitors, collect along the filaments into the main host, and are not blown away by galactic outflows."," Older metals within $R_{\rm vir}$ typically form in satellite progenitors, collect along the filaments into the main host, and are not blown away by galactic outflows."1070" Note how, within 150 kpc or so, the distribution of metals from satellites is rather smooth and follows that from the main host, an indication that gas polluted by star formation in satellite progenitors is stirred up and well mixed with ErisMC's galactic outflows."," Note how, within 150 kpc or so, the distribution of metals from satellites is rather smooth and follows that from the main host, an indication that gas polluted by star formation in satellite progenitors is stirred up and well mixed with ErisMC's galactic outflows."1071 Spikes due to individual nearby dwarfs can be seen beyond 85 kpc., Spikes due to individual nearby dwarfs can be seen beyond 85 kpc.1072 It is interesting at this stage to look at the masses of the satellites that contribute to the enrichment of the CGM., It is interesting at this stage to look at the masses of the satellites that contribute to the enrichment of the CGM.1073" Figure 11 shows the metal-weighted mean halo mass, (Men) (defined in eq. 5)),"," Figure \ref{fig11} shows the metal-weighted mean halo mass, $\langle M_{\rm en}\rangle$ (defined in eq. \ref{eqn:Mhalo}) ),"1074 for gas at different physical distances from ErisMC’s center., for gas at different physical distances from ErisMC's center.1075" Most of the satellites’ metals come from systems more massive than 10?Mo, with the peak of the distribution typically around 109°Mo."," Most of the satellites' metals come from systems more massive than $10^9\,\msun$, with the peak of the distribution typically around $10^{9.5}\,\msun$."1076 Satellites smaller than 105?Mo do not cause significant pollution as they are unable to form many stars both because of SN feedback and the suppression of baryonic infall by the UV background.," Satellites smaller than $10^{8.5}\,\msun$ do not cause significant pollution as they are unable to form many stars both because of SN feedback and the suppression of baryonic infall by the UV background."1077" Also, halos smaller than 105Mo are resolved by less than 1,000 particles in our simulation, and the inability"," Also, halos smaller than $10^{8}\,\msun$ are resolved by less than 1,000 particles in our simulation, and the inability"1078"Large scale gravitational torques. such as bars and interactions. are thought to transport eas into the ceutral region of galaxies and. specifically, m the vicinity of active galactic nuclei (Shlostman et al.","Large scale gravitational torques, such as bars and interactions, are thought to transport gas into the central region of galaxies and, specifically, in the vicinity of active galactic nuclei (Shlosman et al."1079 1990)., 1990).1080 Sevfert galaxies are the low hüuiosity subset of AGNs., Seyfert galaxies are the low luminosity subset of AGNs.1081 According fo the accreting supermassive black hole paradieu. the accretion rate inferred for Seyfert nuclei islow (10!10FALyr 3) id. therefore. imuch fuelling from the host ealaxyv is uot required.," According to the accreting supermassive black hole paradigm, the accretion rate inferred for Seyfert nuclei is low $10^{-1}-10^{-2}M_{\odot}1082yr^{-1}$ ) and, therefore, much fuelling from the host galaxy is not required."1083 Indeed. MeLeod Ricke (1995). Ho et al (," Indeed, McLeod Rieke (1995), Ho et al. ("108419972). Mulehaey Regan (1997) show that the occurrence of bars iu Sevtert galaxies is uot lüsher than in normal galaxies.,"1997a), Mulchaey Regan (1997) show that the occurrence of bars in Seyfert galaxies is not higher than in normal galaxies."1085 Yet.t there is both theorefieal aud observational evidence that stellar bars do drive gas into he Seercentraltres] regionveo of galaxies∖ (Athanassonla⊀ 1992. ⋠↽⊓⊲≻⋅Tacconl/— et al," Yet, there is both theoretical and observational evidence that stellar bars do drive gas into the central region of galaxies (Athanassoula 1992, Tacconi et al."1086 1997. Laine et al.," 1997, Laine et al."1087 1998)., 1998).1088" The resulting central cohnccntration of gas might not be relevant for the fuclling process, but can play a role dm the obscuration of the active uucleus. ie. stellar bars could contribute to the obscuration that affects Sevtert 2s."," The resulting central concentration of gas might not be relevant for the fuelling process, but can play a role in the obscuration of the active nucleus, i.e. stellar bars could contribute to the obscuration that affects Seyfert 2s."1089 This connection would xc very duportant for the unified theories (CÀuntonucci 1993)., This connection would be very important for the unified theories (Antonucci 1993).1090 In this letter we tackle this issuc by comparing the degree of obscuration in Sy2s with the strength of the stellar bar iu their lost ealaxy., In this letter we tackle this issue by comparing the degree of obscuration in Sy2s with the strength of the stellar bar in their host galaxy.1091 Tard Acray- spectra ean he regarded as the hest tool to Bieasure directly the absorbing coluuu density iu Sevfert ealaxies., Hard X-ray spectra can be regarded as the best tool to measure directly the absorbing column density in Seyfert galaxies.1092 Recent surveys have sieuificantly chlarecd the salple of Sv2s for which an estimate of Nyy is available. id have also reduced. the bias against heavily obscured objects that plagued former studies (Maiolino et al.," Recent surveys have significantly enlarged the sample of Sy2s for which an estimate of $_H$ is available, and have also reduced the bias against heavily obscured objects that plagued former studies (Maiolino et al."1093 1998a. Dassaui ct al.," 1998a, Bassani et al."1094 1998. Risaliti ct al.," 1998, Risaliti et al."1095 1998)., 1998).1096 We restricted. our study to obscured Sevterts in the Maioling Rieke (1995) sample. completed with 158 additional objects discovered iu the Πο ct al. (," We restricted our study to obscured Seyferts in the Maiolino Rieke (1995) sample, completed with 18 additional objects discovered in the Ho et al. ("109719971) survey.,1997b) survey.1098 These two Sevfert samples are much less biased than others iu terms of bunünositv aud obscuration of the active nucleus and. therefore. can be cousidered representative of the local population of Sevtert galaxies.," These two Seyfert samples are much less biased than others in terms of luminosity and obscuration of the active nucleus and, therefore, can be considered representative of the local population of Seyfert galaxies."1099" For AGNs which are thin to Compton scattering (i.c. Ngcdle 2) along our line of sight the Ny can be derived from the photoclectric cntoff in the 210 keV sycctral range. provided that the sigual to noise is high οποιο],"," For AGNs which are thin to Compton scattering (i.e. $_H < 10^{24}cm^{-2}$ ) along our line of sight the $_H$ can be derived from the photoelectric cutoff in the 2–10 keV spectral range, provided that the signal to noise is high enough."1100 If the source is Compton thick then the direct component in the 210 keV range is completely suppressed and we can οἱ observe the reflected componcut. eenerallv little absorbed.," If the source is Compton thick then the direct component in the 2–10 keV range is completely suppressed and we can only observe the reflected component, generally little absorbed."1101" As a consequence. Compton thick Sy2s are sometimes misidentified as ""low absorption objects” when observed in the 2-10 keV range."," As a consequence, Compton thick Sy2s are sometimes misidentified as “low absorption objects” when observed in the 2-10 keV range."1102" However. (o fact tha the absorbing coluun deusitv is actually diehey[m] (o7d0?ie;g) 2) can be inferred from severalb idieators, such as the equivalent width of the Fe line qnd the spectral slope. aud by comparing. the N-ray- flux «th other isotropic indicators of the intrinsic Iminosity."," However, the fact that the absorbing column density is actually higher $>10^{24}cm^{-2}$ ) can be inferred from several indicators, such as the equivalent width of the Fe line and the spectral slope, and by comparing the X-ray flux with other isotropic indicators of the intrinsic luminosity."1103" 4 yore detailed discussion of this issue is giveu in Maiolino ος al, (", A more detailed discussion of this issue is given in Maiolino et al. (110419984) aud Bassani et al. (,1998a) and Bassani et al. (11051998).,1998).1106 We just mention 4]lat sensitive spectra at higher cuereics. such as those (tained bv BeppoSAX in the 10200 keV baud. cau ieutify column deusities iu the range 1075—Ld?en? (Nfatt et al.," We just mention that sensitive spectra at higher energies, such as those obtained by BeppoSAX in the 10–200 keV band, can identify column densities in the range $10^{24}-10^{25}cm^{-2}$ (Matt et al."1107 1998. Cappi et al.," 1998, Cappi et al."1108 1998) or set a lower limit of ten2 (ALaiolino et al., 1998) or set a lower limit of $10^{25}cm^{-2}$ (Maiolino et al.1109 1998a)., 1998a).1110 Iu Tab., In Tab.1111" 1 we list all the Sevtert 2. 1.9 aud 1.5 galaxies πωο, those showing indication of obscuration) iu the joiut Maiolino Rieke (1995) aud Πο et al. ("," 1 we list all the Seyfert 2, 1.9 and 1.8 galaxies (i.e. those showing indication of obscuration) in the joint Maiolino Rieke (1995) and Ho et al. ("11121997b) samples,1997b) samples1113ssoltware package written at the Lyon Observatory (Rousse 1992).,software package written at the Lyon Observatory (Rousset 1992).1114" ""his included. bias subtraction. pixel-to-pixel. lla iclding. spectral extraction. wavelength. calibration. lla ielding. removal of cosmic ravs. differential atmospheric refraction correction and Hux calibration for all individua exposures."," This included bias subtraction, pixel-to-pixel flat fielding, spectral extraction, wavelength calibration, flat fielding, removal of cosmic rays, differential atmospheric refraction correction and flux calibration for all individual exposures."1115 The resulting data-cubes were then resampled ο à square grid and merged., The resulting data-cubes were then resampled to a square grid and merged.1116 Details about these reduction steps can be found in Imsellem (10996)., Details about these reduction steps can be found in Emsellem (1996).1117 In the nex paragraph. we only mention points specific to the 11993 rean and the NGC 2974 data.," In the next paragraph, we only mention points specific to the 1993 run and the NGC 2974 data."1118 A slehtlv incorrect position angle of the CCD with respect to the lens array led to some unwanted contaminations between adjacent spectra at their edges: this only alfected the cconfiguration. for which spectra were safelv truncated to a wavelength. range of 6570GOGOΑ.," A slightly incorrect position angle of the CCD with respect to the lens array led to some unwanted contaminations between adjacent spectra at their edges: this only affected the configuration, for which spectra were safely truncated to a wavelength range of 6570–6960."1119. The wavelength calibration was found to be accurate to within 0.03. pixel: this was mace possible through the use of a Fabry-Perot etalon which provides regularly spaced: Airy lines., The wavelength calibration was found to be accurate to within 0.03 pixel: this was made possible through the use of a Fabry-Perot etalon which provides regularly spaced Airy lines.1120 The absolute Iux calibration of the sspectra was performed using spectro-photometric standard stars., The absolute flux calibration of the spectra was performed using spectro-photometric standard stars.1121 For the cconfiguration we used an available [ux-calibrated. long-slit spectrum (CGoudfrooij Emsellem 1996)., For the configuration we used an available flux-calibrated long-slit spectrum (Goudfrooij Emsellem 1996).1122 The stellar kinematics were derived from the sspectra via a slightly modified. version of Bender's (1990) Fourier Correlation Quotient (FCX hereafter) method., The stellar kinematics were derived from the spectra via a slightly modified version of Bender's (1990) Fourier Correlation Quotient (FCQ hereafter) method.1123 Line strengths were measured using an empirical correction for the dispersion as in IEmsellem et ((1996)., Line strengths were measured using an empirical correction for the dispersion as in Emsellem et (1996).1124 Since no specific attempt was made to calibrate our data. onto the Lick system. we remind the reader that svstematic olfsets may exist between our line-streneth values ancl other published ones.," Since no specific attempt was made to calibrate our data onto the Lick system, we remind the reader that systematic offsets may exist between our line-strength values and other published ones."1125 “The emission-lines in. the spectra were fitted. by Gaussian profiles using the FIP/SPIECTIVA software written by Arlette Rousset (Lyon Observatory - Rousset 1992)., The emission-lines in the spectra were fitted by Gaussian profiles using the FIT/SPECTRA software written by Arlette Rousset (Lyon Observatory - Rousset 1992).1126 As discussed in Goudfrooi] Emscllem (1996). when ionized gas is present the eemission-line doublet at 5198.5200 (hercalter da55200) can jeopardize the analysis of stellar dynamics and stellar populations of galaxies in the spectral domain around the feature," As discussed in Goudfrooij Emsellem (1996), when ionized gas is present the emission-line doublet at 5198,5200 (hereafter 5200) can jeopardize the analysis of stellar dynamics and stellar populations of galaxies in the spectral domain around the feature."1127 We therefore devised an iterative procedure to climinate .the contribution of da55200 to our sspectra., We therefore devised an iterative procedure to eliminate the contribution of 5200 to our spectra.1128 This method. will be described ancl illustrated in detail in à separate paper. so we only provide an outline ope: Just as described above. we use a library of star and galaxy spectra to remove the stellar continuum in the sspectra.," This method will be described and illustrated in detail in a separate paper, so we only provide an outline here: Just as described above, we use a library of star and galaxy spectra to remove the stellar continuum in the spectra."1129 However. the limited wavelength: coverage and the high equivalent width of the emission. lines in this spectral domain makes this a somewhat dillicult task.," However, the limited wavelength coverage and the high equivalent width of the emission lines in this spectral domain makes this a somewhat difficult task."1130 For that reason. we built an optimal template using the stellar kinematies derived from the sspectra and only including the stellar templates which were used in the fit of the sspectra: this prevents artificial variations of (c.g.) the width of the aabsorption line.," For that reason, we built an optimal template using the stellar kinematics derived from the spectra and only including the stellar templates which were used in the fit of the spectra: this prevents artificial variations of (e.g.) the width of the absorption line."1131 An example of such a fit ancl subtraction is shown in Fig. 2.., An example of such a fit and subtraction is shown in Fig. \ref{fig:fitNII}.1132 The residual ‘pure’ emission-line spectra were then fitted. using the software package (Rousset 1992) assuming Gaussian profiles for cach incliviclual line., The residual `pure' emission-line spectra were then fitted using the software package (Rousset 1992) assuming Gaussian profiles for each individual line.1133maintained.,maintained.1134 Due to the complex topologies of the magnetic field. the magnetic field advected with accretion toward smaller radii. which connects the black hole to the disk. does not have to be balanced by the magnetic field adsyected from larger radii which also connects the black hole to the disk.," Due to the complex topologies of the magnetic field, the magnetic field advected with accretion toward smaller radii, which connects the black hole to the disk, does not have to be balanced by the magnetic field advected from larger radii which also connects the black hole to the disk."1135 However. if the radial velocitw of particles in the disk is much smaller (han their rotational velocity. the inflow time-scale is much larger than the dvnamical time-scale.," However, if the radial velocity of particles in the disk is much smaller than their rotational velocity, the inflow time-scale is much larger than the dynamical time-scale."1136 Then. it is reasonable {ο assume that within one rotation period. the global configuration of the magnetic field is almost unchanged. aud the overall change in a macroscopic «quantity al a given radius in the disk is much smaller than the quantitw itself.," Then, it is reasonable to assume that within one rotation period, the global configuration of the magnetic field is almost unchanged, and the overall change in a macroscopic quantity at a given radius in the disk is much smaller than the quantity itself."1137 When this condition is salislied. we sav that the disk ancl the magnetic field are in a quasi-steady state.," When this condition is satisfied, we say that the disk and the magnetic field are in a quasi-steady state."1138 In a quasi-steady state. a macroscopic quantity al a given radius may change significantly over a long period of time and the magnetic connection between the black hole and the disk may disappear al last. but they are approximately unchanged within one rotation period of the disk.," In a quasi-steady state, a macroscopic quantity at a given radius may change significantly over a long period of time and the magnetic connection between the black hole and the disk may disappear at last, but they are approximately unchanged within one rotation period of the disk."1139 In this section we solve the equations for energy. conservation and angular momentum conservation for such a quasi-sleacly state disk magnetically coupled to a black hole., In this section we solve the equations for energy conservation and angular momentum conservation for such a quasi-steady state disk magnetically coupled to a black hole.1140 For a steady. axisvinmetric. and (hin Weplerian disk around a Ixerr black hole. the eeneral relativistic equations of energv conservation and angular momentum conservation have been investigated in detail by NovikovandThorne(1973):Page(1974): and Thorne(1974).," For a steady, axisymmetric, and thin Keplerian disk around a Kerr black hole, the general relativistic equations of energy conservation and angular momentum conservation have been investigated in detail by \citet{nov73,pag74}; and \citet{tho74}."1141. Assiune the magnetic field is weak so that its influence on the dynamics of disk particles is negligible. then a thin Keplerian disk is a goodapproximation*.," Assume the magnetic field is weak so that its influence on the dynamics of disk particles is negligible, then a thin Keplerian disk is a good."1142. With the magnetic coupling between the black hole and the disk being taken into account. for a quasi-steady state (he conservation of angular momentun is described by where Mp=dAly/dl is the accretion rate of mass (measured by an observer at infinity: we use (he convention Mp>0 [or accretion). £ is the specific angular momentum of a particle in the disk. g is the internal viscous torque of the disk. F is the energy [αν radiated away from the surface of the disk (measured by an observer co-rotating with Che disk). aud ff is the [ιν of angular momentum transfered from the black hole to the disk bv (he magnetic field.," With the magnetic coupling between the black hole and the disk being taken into account, for a quasi-steady state the conservation of angular momentum is described by where $\dot {M}_D \equiv dM_D/dt$ is the accretion rate of mass (measured by an observer at infinity; we use the convention $\dot {M}_D>0$ for accretion), $L^+$ is the specific angular momentum of a particle in the disk, $g$ is the internal viscous torque of the disk, $F$ is the energy flux radiated away from the surface of the disk (measured by an observer co-rotating with the disk), and $H$ is the flux of angular momentum transfered from the black hole to the disk by the magnetic field."1143 The conservation of energy is described by, The conservation of energy is described by1144important above ~10 keV as compared to photoclectric absorption.,important above $\sim10$ keV as compared to photoelectric absorption.1145 Adding the transmitted AGN component given by eq., Adding the transmitted AGN component given by eq.1146 3 to eq. 2..," \ref{eq:tra} to eq. \ref{eq:ref},"1147 we construct the Iransimálled-NCGUN | thermal model as: The photon-index E. the cutoll energy. £e: (fixed. to 200 keV). and the normalization. Avcw. are the same or both the reflection ancl transmitted. components.," we construct the AGN + thermal model as; The photon-index $\Gamma$, the cutoff energy, $E_C$ (fixed to 200 keV), and the normalization, $K_{\rm AGN}$, are the same for both the reflection and transmitted components."1148 The relative intensities between the transmitted component and he reflection component is determined by the solid. angle. HI. which is left free.," The relative intensities between the transmitted component and the reflection component is determined by the solid angle, $R$, which is left free."1149 The metallicity of the elements lighter han Fe and the viewing angle j(=cos are fixed at 1.0 solar and 0.45. respectively.," The metallicity of the elements lighter than Fe and the viewing angle $ \mu = cos \theta $ are fixed at 1.0 solar and 0.45, respectively."1150 As in the previous fits. including the contamination-source Component in the model. we it the four spectra jointly. with this moclel.," As in the previous fits, including the contamination-source component in the model, we fit the four spectra jointly with this model."1151 The Bronsmilied-XOGN. | thermal mocel gives a good fit (Figure S.. Fable 5).," The AGN + thermal model gives a good fit (Figure \ref{fig:reftra}, , Table 5)."1152 The derived. photon index is P= 1.59. (vi. which is consistent with the canonical value of 1.9 (Pounds et al.," The derived photon index is $\Gamma$ = 1.59 $^{+0.42}_{-0.26}$, which is consistent with the canonical value of 1.9 (Pounds et al."1153 1990)., 1990).1154 Phe best-fit solid angle of he reflector. /?=Of2z. is 0.51. and the absorption column density. Igcox is found to be 1.7107! em>.," The best-fit solid angle of the reflector, $R = \Omega/2\pi$ is 0.51, and the absorption column density, $N_{\rm H,AGN}$, is found to be $1.7\times10^{24}$ $^{-2}$."1155 Since R was poorly constrained. the intrinsic luminosity of the AGN as à large error range.," Since $R$ was poorly constrained, the intrinsic luminosity of the AGN has a large error range."1156" Lowe assume that /? does not exceed 1.0. Lx is obtained to be 1.1""1074 ores/s in the range 2. 10 keV. When we leave the viewing angle µ free. the itting parameters as well as the intrinsic luminosity remain essentially the same. if 2?<1.0 (Table 4.3))."," If we assume that $R$ does not exceed 1.0, $L_{\rm X}$ is obtained to be $1.1^{+4.5}_{-0.5}\times10^{44}$ ergs/s in the range 2 – 10 keV. When we leave the viewing angle $\mu$ free, the fitting parameters as well as the intrinsic luminosity remain essentially the same, if $R \leq 1.0$ (Table \ref{tab:5}) )."1157 So far. we assumed that the matter that obscures the AGN is located only on the line of sight.," So far, we assumed that the matter that obscures the AGN is located only on the line of sight."1158 Lo the absorbing matter covers a significant solid angle viewed from the ACN such as in the case of a torus. some of the incoming photons will be scattered. into our line of sight.," If the absorbing matter covers a significant solid angle viewed from the AGN such as in the case of a torus, some of the incoming photons will be scattered into our line of sight."1159 Then the moclel given by eq., Then the model given by eq.1160 3. would. overestimate the ΑΝ. Luminosity., \ref{eq:tra} would overestimate the AGN luminosity.1161 Alatt. Pompilio. Franca (1999) performed a Monte Carlo calculation of the X-ray transmission. through spherically distributed matter lor various column densities.," Matt, Pompilio, Franca (1999) performed a Monte Carlo calculation of the X-ray transmission through spherically distributed matter for various column densities."1162 According to their result. the true AGN luminosity would be smaller by a factor of ~2. if the absorbing matter is distributed in a spherical geometry.," According to their result, the true AGN luminosity would be smaller by a factor of $\sim2$, if the absorbing matter is distributed in a spherical geometry."1163 Consequently. for the same Ilux from the cold reflector. the true value of # should be larger by a factor o£ 2 than that in Table 5.," Consequently, for the same flux from the cold reflector, the true value of $R$ should be larger by a factor of 2 than that in Table 5."1164 Phe column density of the absorbing matter is also subject to a slight overestimation., The column density of the absorbing matter is also subject to a slight overestimation.1165 The case that a heavy absorber exists only on the line of sight is rather unlikely., The case that a heavy absorber exists only on the line of sight is rather unlikely.1166 On the other hand. since the fitting result shows a relatively small absorption for the reflection component. the absorbing matter is probably not covering the entire sphere.," On the other hand, since the fitting result shows a relatively small absorption for the reflection component, the absorbing matter is probably not covering the entire sphere."1167 Phere two cases. a cloud on the line of sight are spherically distributed matter. are considered. to represent (wo extremes.," There two cases, a cloud on the line of sight are spherically distributed matter, are considered to represent two extremes."1168 1n conclusion. the fransmilled-AGN model gives the following AGN parameters: P=1.33.2.02. Lx(2lO0keV) = 5«107. 6«10. orgs/s. I? — OLI. and Ngaos = LO 2.7.1074 7.where the range of parameters represents not only the statistical errors but also the uncertainties due to unknown inclination angle of the," In conclusion, the AGN model gives the following AGN parameters: $\Gamma = 1.33-2.02$, $L_{\rm X}$ (2–10keV) = $5\times10^{43}$ – $6\times10^{44}$ ergs/s, $R$ = 0.1–1, and $N_{\rm H,AGN}$ = 1.0– $\times10^{24}$ $^{-2}$,where the range of parameters represents not only the statistical errors but also the uncertainties due to unknown inclination angle of the"1169which have not expenrieuced star formation iu the past 10 ves will cnt littleBre... but significant FIR radiation.,"which have not experienced star formation in the past $10^7$ yrs will emit little, but significant FIR radiation."1170 A inore quantitative approach is presented iji Fie., A more quantitative approach is presented in Fig.1171 1 where we COMpAre the oserved uuclear properties of NGC 915 with svuthesis nxxlels bx Leitherer et al. (1999))., \ref{fig:sbmod} where we compare the observed nuclear properties of NGC 4945 with synthesis models by Leitherer et al. \cite{leitherer}) ).1172 We have considered twx) extreme cases of star formation history., We have considered two extreme cases of star formation history.1173 The thick solic lue iu the figureC» represeuts au lustantaneous burst with mass 3.5«4I0ML. wrereas the thick dashed liue is a continmous star formation rate of 0.13M.vr.4., The thick solid line in the figure represents an instantaneous burst with mass $3.5\xten{7}\Mo$ whereas the thick dashed line is a continuous star formation rate of $0.13\Mo\YR\1$.1174 In bohn cases a Salpeter initial mass function (.e. XAL 77). upper mass eutotff of aand abundances Z=Z. are chosen.," In both cases a Salpeter initial mass function (i.e. $\propto M^{-2.35}$ ), upper mass cutoff of and abundances $Z=\Zo$ are chosen."1175 Panel 1 shows the evolution of he ioniziug photon rate (Q(IE))) as a fiction of tine after the beginuiug of the burst., Panel 1 shows the evolution of the ionizing photon rate ) as a function of time after the beginning of the burst.1176 The shaded region limits the values compatible with the observations: Ds estimated from the total μις in the NICMOS images (5.6⋅«410153orestem2 3) deredaeued with de= imag aud Ay= 20mae ando convered usus case D. approxiuation for II reconibinatious.," The shaded region limits the values compatible with the observations; is estimated from the total flux in the NICMOS images $5.6\xten{-13}\ERG\S\1\CM\2$ ), dereddened with $A_V=5$ mag and $A_V=20$ mag and converted using case B approximation for H recombinations."1177" Panel 2 eives the οςuvaleut width of Ηλ... the obser""ed value outlined by the shaded area is a lower lnut fx the starburst models acd was derived by rescaling the observed fux and dividing bv the flux observed iu the same aperture with the F222M filter.", Panel 2 gives the equivalent width of $W_\lambda(\BG)$ ); the observed value outlined by the shaded area is a lower limit for the starburst models and was derived by rescaling the observed flux and dividing by the flux observed in the same aperture with the F222M filter.1178 Panel 3 is the evolution of he SuperNova Rate (SNR)., Panel 3 is the evolution of the SuperNova Rate (SNR).1179 Ey.iniaes of SNR from racio observations suggest values >>L3yr| (Koonuncef 1993). h2vrL (Forbes Norris 1998)). down to (Moorwood Oliva 199 133).," Estimates of SNR from radio observations suggest values $>0.3\YR\1$ (Koornneef \cite{koorn}) ), $0.2\YR\1$ (Forbes Norris \cite{forbes}) ), down to (Moorwood Oliva \cite{moorwood94a}) )."1180 The shaded region covers lio range., The shaded region covers the range.1181 Pauel bis the mechanical Iuuinositv ]xodnueed by he Supernovae., Panel 4 is the mechanical luminosity produced by the Supernovae.1182 Finally. paucls 5 aud 6 eive he I-baud aud bolometric Iuninosity. respectively.," Finally, panels 5 and 6 give the K-band and bolometric luminosity, respectively."1183" The alowed ranec or the Is monochromatic huninositv is οἼνοιι w the total observed fux iu a 67<6"" aperture centered on the KK peak where photospheric cussion from supoergiaus ds known ο dominate (€Jliva ct al. 199953).", The allowed range for the K monochromatic luminosity is given by the total observed flux in a $6\arcsec\times 6\arcsec$ aperture centered on the K peak where photospheric emission from supergiants is known to dominate (Oliva et al. \cite{oliva99b}) ).1184 The upper aud lower Πατς represen the values obtained after dendadeuiung by Ay—=3)on nag and Ay= 20mae., The upper and lower limits represent the values obtained after dereddening by $A_V=5$ mag and $A_V=20$ mag.1185 The upper iuit to the volometric huuiuositv is thefofad NCC 1015 Iuninositv derived frou: IRAS observations (Rice et al. 1988))., The upper limit to the bolometric luminosity is the NGC 4945 luminosity derived from IRAS observations (Rice et al. \cite{rice88}) ).1186 In i] cases the hin doted line represents fho tine at which the properties of the instantaneous burst meet the 6oervational constraints., In all cases the thin dotted line represents the time at which the properties of the instantaneous burst meet the observational constraints.1187 The crossed squar' represent the coumbinatio1 of the wo models at ἐξ105yy., The crossed square represent the combination of the two models at $t=\ten{7.4}\YR$.1188 It is clear from the figure that au instautaneous burst Έττοῦvy is capable of iiccti1 all the οἱπαναολα ‘oustraints., It is clear from the figure that an instantaneous burst of $t\sim\ten{6.8}\YR$ is capable of meeting all the observational constraints.1189 It reproduces the correct Supernova rate id WN baud huunmositv aud its bolometric ununositv dominates the total bolometric Wuuinosity of the galaxy., It reproduces the correct supernova rate and K band luminosity and its bolometric luminosity dominates the total bolometric luminosity of the galaxy.1190" Conversely the coutiunous burst fails to rc]xoduce. the SNR and Is ΓΩ,", Conversely the continuous burst fails to reproduce the SNR and K luminosity.1191 Just considering hese two models alone if is tempting to 1ier that the starburst powers the bolometric euission of NCC1915., Just considering these two models alone it is tempting to infer that the starburst powers the bolometric emission of NGC4945.1192 ITowever. the lustautaneous and continuous SFR are two extreme aud sinplistie cases;," However, the instantaneous and continuous SFR are two extreme and simplistic cases."1193 More realistically the SF historv is more complex since bursts have a finite and lianited length or are he coubination of several different events., More realistically the SF history is more complex since bursts have a finite and limited length or are the combination of several different events.1194 As iui cxample we consider tle case of two bursts of star formation talking ace at the same time: oue mstautaueous aid the other continuous., As an example we consider the case of two bursts of star formation taking place at the same time: one instantaneous and the other continuous.1195 Both ie the same characteristics as the παν presened above., Both have the same characteristics as the bursts presented above.1196 The properties of this double nest model at f£=10°!yr are shown iu tie flere Nw he crossed squares., The properties of this double burst model at $t=\ten{7.4}\YR$ are shown in the figure by the crossed squares.1197 The choice of the time is arbitrary ⋜⋯≼↧⋜⋯⋅↖↽∪↑∐↸∖↥⋅↖↽⋜↧↕⋯∖↴⋝↸∖↑∖↖↽↸∖↸∖∐↓∩∣⊳−⋅∏⋅⋜⋯≼↧∩∣⊳⊽↾⋅↖⇁↥⋅∐∐∶↴∙⊾∐↑ ey ↽−↣ ⋅ do., The choice of the time is arbitrary and any other value between $\ten{7.2}\YR$ and $\ten{7.5}\YR$ might do.1198 Evei du this case the starburst model mects all the observational constraints: ls provided for by the continuous burst while SNR aud Is nuimositv come from the 1istantaneous burst., Even in this case the starburst model meets all the observational constraints: is provided for by the continuous burst while SNR and K luminosity come from the instantaneous burst.1199 The nmuportaut difference with respect to the single lustautareous burst is that the bolometric huuimositv of the burst is now ~20% of the total bolometric Iunuinosityv of the galaxy., The important difference with respect to the single instantaneous burst is that the bolometric luminosity of the burst is now $\lesssim 20\%$ of the total bolometric luminosity of the galaxy.1200 The nechanical huninosity injected by the SN in the “Gustantancous” burst Gvlich dominates also in the double burst ukxlel) is ~LOSOeL.. over ~10!yy.," The mechanical luminosity injected by the SN in the ""instantaneous"" burst (which dominates also in the double burst model) is $\sim \ten{8.5}\Lo$ over $\sim \ten{7.4}\YR$."

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