The Halo Occupation Distribution of Active Galactic Nuclei
Suchetana Chatterjee, Colin DeGraf, Jonathan Richardson, Zheng Zheng, Daisuke Nagai, Tiziana Di Matteo
aa r X i v : . [ a s t r o - ph . C O ] S e p Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 19 October 2018 (MN L A TEX style file v2.2)
The Halo Occupation Distribution of Active GalacticNuclei
Suchetana Chatterjee , Colin DeGraf , Jonathan Richardson , , Zheng Zheng , ,Daisuke Nagai , , Tiziana Di Matteo Department of Astronomy, Yale University, New Haven, CT 06520 USA McWilliams Center for Cosmology, Carnegie Mellon University, Pittsburgh, PA 15213 USA Yale Center for Astronomy and Astrophysics, Department of Physics, Yale University, New Haven, CT 06520 USA Department of Physics and Astronomy, University of Utah, 115 South 1400 East, Salt Lake City, UT 84112
19 October 2018
ABSTRACT
Using a fully cosmological hydrodynamic simulation that self-consistently incorporatesthe growth and feedback of supermassive black holes and the physics of galaxy for-mation, we examine the effects of environmental factors (e.g., local gas density, blackhole feedback) on the halo occupation distribution of low luminosity active galacticnuclei (AGN). We decompose the mean occupation function into central and satellitecontribution and compute the conditional luminosity functions (CLF). The CLF of thecentral AGN follows a log-normal distribution with the mean increasing and scatterdecreasing with increasing redshifts. We analyze the light curves of individual AGNand show that the peak luminosity of the AGN has a tighter correlation with halomass compared to instantaneous luminosity. We also compute the CLF of satelliteAGN at a given central AGN luminosity. We do not see any significant correlationbetween the number of satellites with the luminosity of the central AGN at a fixedhalo mass. We also show that for a sample of AGN with luminosity above 10 ergs/sthe mean occupation function can be modeled as a softened step function for centralAGN and a power law for the satellite population. The radial distribution of AGNinside halos follows a power law at all redshifts with a mean index of − . ± . Through recent observations it has been shown thatactive galactic nuclei (AGN) play a significant role inthe evolution of galaxies. The observed correlation be-tween the mass of the central black hole and the velocitydispersion of the bulge of the host galaxy suggests astrong connection between galaxy evolution and black holeactivity (e.g., Gebhardt et al. 2000; Merritt & Ferrarese2001; Tremaine et al. 2002; Graham et al. 2011). Sev-eral theoretical models relating AGN activity or blackhole growth to galaxy evolution have been proposed(e.g., Soltan 1982; Silk & Rees 1998; Salucci et al. 1999;Kauffmann & Haehnelt 2000; Wyithe & Loeb 2003;Marconi et al. 2004; Cattaneo et al. 2006; Croton et al.2006; Di Matteo et al. 2005; Hopkins et al. 2006; Lapi et al.2006; Shankar et al. 2004). Differentiating between thesetheoretical models requires several observational quantities.Measurements of the AGN luminosity function (e.g.,Boyle et al. 2000; Fan et al. 2001) and the number densityof black hole hosts in the present universe can provide anestimate of the duty cycle of black holes. Alternatively, the black hole mass function (e.g., Shankar et al. 2004;Graham & Driver 2007) measured at the current epochcan provide constraints on models of black hole growth.Measurement of AGN clustering provides a unique wayto study the physical characteristics of AGN throughthe connection with their host dark matter halos (e.g.,Croom et al. 2004; Gilli et al. 2005; Myers et al. 2006;Shen et al. 2009; Ross et al. 2009).Theoretically clustering properties of AGN have beenmostly studied with semi-analytic models using the halomodel or the black hole continuity equation approach (e.g.,Shankar et al. 2010a; Bonoli et al. 2009; Lidz et al. 2006).Although semi-analytic models have provided the formal-ism for interpreting quasar clustering, there are certain is-sues that these models cannot approach. In this formalismphysical parameters (e.g.,“quasar duty cycle”) are treatedas free parameters that are constrained from clustering mea-surements (e.g., Martini & Weinberg 2001). There also ex-ist degeneracies between parameters in the models (e.g.,Shankar et al. 2010b). Moreover in most of these modelsblack holes are accreting at a fixed fraction of the Eddington c (cid:13) Chatterjee et al.
Boxsize N p m DM m gas ǫ ( h − Mpc) ( h − M ⊙ ) ( h − M ⊙ ) ( h − kpc)33 .
75 2 × . × . × . Table 1.
The numerical parameters in the simulation. N p , m DM , m gas and ǫ are defined as the total number of particles, mass ofthe dark matter particles, mass of the gas particles, and comovinggravitational softening length respectively. rate, making accretion rate dependent on black hole massonly. In reality, parameters like accretion efficiency and theduty cycle are not fixed and depend strongly on environ-ment (e.g., local gas density, mergers, feedback from AGN).Some recent semi-analytic studies started to consider moregeneral cases of black hole accretion to investigate the cos-mological co-evolution of black holes and the evolution ofAGN luminosity functions (e.g., Marulli et al. 2008, 2009;Malbon et al. 2007; Menci et al. 2008).Hydrodynamic simulations of galaxy formation withblack hole growth can capture the environmental depen-dence of accretion. The growth of black holes is tied withthe full dynamics of dark matter. Also with these sim-ulations we can model the interplay between AGN andgalaxy formation in the form of feedback and self-regulatedgrowth (e.g., Wyithe & Loeb 2003). Thus these simulationsprovide an excellent platform to study the co-evolution ofAGN with large scale structures over cosmological timescales. Studies of AGN clustering using cosmological sim-ulations have been carried out by Thacker et al. (2009) andDegraf et al. (2011a). Degraf et al. (2011a) calculates thecorrelation function of black holes using a smoothed particlehydrodynamics (SPH) cosmological simulation that incorpo-rates galaxy formation physics and self-consistent black holegrowth and feedback (Di Matteo et al. 2008). They showthat the black hole correlation function consists of two dis-tinct components: contributions from intra-halo and inter-halo black hole pairs, i.e., the one-halo and two-halo terms.At small scales the one-halo term still follows a power law,which is different from that of dark matter. This boost insmall scale power is due to galaxies hosting multiple blackholes.Despite their advantages, studies using hydrodynam-ical simulations are limited due to their computationalcosts. For example simulations are limited to small boxes(Di Matteo et al. 2008) restricting the analysis to smallscales and low luminosity AGN. The computational cost ofrunning these simulations to z = 0 limits the possibilityto compare the outputs with observations in the local uni-verse. Also since every modification of the recipies adoptedto describe the ‘sub-grid’ physics requires rerun of the simu-lations, it is not feasible to do systematic parameter studies.Semi-analytic studies are advantageous over hydro simula-tions in this context. We now employ the SPH simulation ofDi Matteo et al. (2008) to investigate the relation betweenAGN and their host halos within the halo occupation dis-tribution (HOD) framework, a useful analytic formalism formodeling and interpreting AGN clustering. In our approach,the expensive hydrodynamic simulation is used to obtain in-sights on a general analytic technique for studying AGN clustering. The HOD (e.g., Ma & Fry 2000; Seljak 2000;Berlind & Weinberg 2002) provides an analytic formalismfor understanding clustering properties of galaxies or, in thiscase, AGN. It is characterized by the probability P ( N | M )that a halo of mass M contains N AGN of a given type,together with their spatial and velocity distribution insidehalos. As long as the HOD at a fixed halo mass is statisti-cally independent of the large scale environments of halos(e.g., Bond et al. 1991), it provides a complete descriptionof the relation between AGN and halos, allowing the calcu-lation of any clustering statistics (e.g., two point correlationfunction, three point correlation function, void probabil-ity distribution, pairwise velocity distribution) at all scales(small, intermediate, large) for a given cosmological model.This implies that if we can constrain the HOD empirically,we will have knowledge of everything that the measuredclustering properties have to tell us about AGN formationand evolution models. The HOD allows to distinguish be-tween the background cosmology and AGN evolution mod-els. The cosmological parameters are encoded in the distri-bution of halos, where as the bias between mass and AGN isfully described in the probability distribution P ( N | M ) (seeBerlind & Weinberg 2002, Zheng & Weinberg 2007 for thestrength of HOD). The HOD formalism has been widely usedin interpreting galaxy clustering (see Zehavi et al. 2005).In this paper we perform a theoretical study on the rela-tion between AGN and dark matter halos using cosmologicalsimulations. We assess the validity of several simplifying as-sumptions in the HOD modeling of AGN and its predictivepower and limitations for modeling AGN clustering data.Our paper is organized as follows: In § § § The numerical code uses a standard ΛCDM cosmologicalmodel with cosmological parameters from the first yearWMAP results (Spergel et al. 2003). The simulation usesan extended version of the parallel cosmological Tree Par-ticle Mesh-SPH code GADGET2 (Springel 2005). Gas dy-namics is modeled with Lagrangian SPH (Monaghan 1992);radiative cooling and heating processes are computed fromthe prescription given by Katz et al. (1996). The relevantphysics of star formation and the associated supernova feed-back have been approximated based on a sub-resolutionmultiphase model for the interstellar medium developedby Springel & Hernquist (2003). The size of the simula-tion box is 33 . h − comoving Mpc with periodic bound-ary conditions. A detailed description of the implementa-tion of black hole accretion and the associated feedbackmodel is given in Di Matteo et al. (2008). Black holes arerepresented as collisionless “sink” particles that can grow inmass by accreting gas or by mergers. The Bondi-Hoyle re-lation (Bondi 1952) is used to model the accretion rate ofgas onto a black hole and capture the environmental depen-dence of black hole accretion. The accretion rate is given c (cid:13) , 000–000 OD modeling for AGN −5 −4 −3 −2 −1 z=5.0 χ z=3.0 M halo [M ⊙ ] z=1.0 Figure 1.
Distribution of accretion rates scaled by the Eddington value ( χ = ˙ M/ ˙ M EDD ) as a function of halo mass at redshift 5 . . . by ˙ M BH = 4 π [ G M ρ ] / ( c s + v ) / , where ρ and c s aredensity and speed of sound of the local gas, v is the velocityof the black hole with respect to the gas, and G is gravi-tational constant. Although the Bondi parameterization as-sumes spherical accretion, observations show that the Bondirelation adequately captures the physical state of the blackhole and the Bondi scaling holds at scales much larger thanthe Bondi radius (e.g., Allen et al. 2006).The bolometric luminosities of the AGN are L Bol = η ˙ M BH c where η = 0 . E f such that ˙ E f = ǫ f L Bol with the feed-back efficiency ǫ f taken to be 5%. Based on previous stud-ies of galaxy mergers, the value of the feedback efficiencyparameter ǫ f is chosen to be 5% in the simulation, a nec-essary fraction to reproduce the normalization of the ob-served M BH − σ relation at z = 0 (Di Matteo et al. 2005).This feedback energy is put directly into the gas smooth-ing kernel at the position of the black hole (Di Matteo et al.2008). The feedback energy is assumed to be distributedisotropically for the sake of simplicity; however the responseof the gas can be anisotropic (e.g., Chatterjee et al. 2008;Di Matteo et al. 2008). The formation mechanism for theseed black holes which evolve into the observed supermassiveblack holes today is not known. The simulation creates seedblack holes in halos that cross a specified mass threshold.At a given redshift, halos are defined by a friends-of-friendsgroup finder algorithm run on the fly. For any halo withmass M ≥ × h − M ⊙ that does not contain a blackhole, the densest gas particle is converted to a black hole ofmass M BH = 5 × h − M ⊙ . The choice of the seed mass inthe present simulation was based on current models of seedblack hole formation in the universe (e.g., Bromm & Loeb2003; Bromm & Larson 2004). The black hole then growsvia the accretion prescription given above and by mergerswith other black holes (Di Matteo et al. 2008). The simula-tion parameters are shown in Table 1.The detailed parameter studies of this simulation,and comparison with several observations have been pre- viously done by Sijacki et al. (2007); Di Matteo et al.(2008); Colberg & Di Matteo (2008); Croft et al. (2009);Degraf et al. (2010). The model has reproduced the ob-served M BH − σ relation, total black hole mass density(Di Matteo et al. 2008), and the AGN luminosity functionsand their evolution in optical, soft and hard X-ray band(Degraf et al. 2010). The black hole mass density from thesimulation matches well with the constraints from the in-tegrated X-ray luminosity function (Shankar et al. 2004;Marconi et al. 2004) and the accretion rate density is con-sistent with the constraints of Hopkins et al. (2007a). Thismodel has been also used in galaxy merger simulations toinvestigate black hole growth and their correlation withhost galaxies (Di Matteo et al. 2005; Robertson et al. 2006;Hopkins et al. 2007b).The model has some intrinsic limitations. It does nottreat the physics of the accretion disc in detail, which isnot feasible in a simulation with cosmological volume. Nev-ertheless, the model is capable of representing some keyaspects of black hole evolution in a cosmological contextand in reproducing many observational results. Althoughthe model has some limitations, it has been fairly success-ful in reproducing some of the key observational results.Several other teams (Booth & Schaye 2009; Johansson et al.2008; Teyssier et al. 2011) have now implemented similarmodeling for black hole accretion and feedback in hydro-dynamic simulations. Booth & Schaye (2009) have indepen-dently explored the parameter space of the fiducial modelof Di Matteo et al. (2008). Teyssier et al. (2011) have im-plemented this prescription in an adaptive mesh refinementcode (different from the SPH formalism) and showed thatAGN feedback can solve the overcooling problem in clus-ters. This large number of previous investigations make thisparticular subgrid model a good choice for studying co-evolution of AGN with their host dark matter halos. Weemphasize that in this work we do not intend to explore theparameter space related to the subgrid modeling of blackholes. Instead we study the relation between AGN and darkmatter halos in one simulation box. The goal of our cur-rent study is to obtain a useful description between AGN c (cid:13) , 000–000 Chatterjee et al. and dark matter to guide the interpretation of observations(e.g., AGN clustering) and to learn about AGN evolutionusing the model of Di Matteo et al. (2008).
For our analysis we consider halos above a mass scale of10 M ⊙ and black holes with masses above 10 M ⊙ . Thischoice of mass scales will minimize the effect of the seed massin our results. We also restricted our analysis to black holeswith Eddington scaled accretion rate χ = ˙ M/ ˙ M EDD ≥ − since we want to study systems with active accretion. Thisselection imposes a luminosity cut of 10 ergs/s in our sam-ple. One of the key goals of this paper is to separate the con-tributions to the occupation distribution from the centraland satellite AGN (as done for galaxy HOD by Zheng et al.(2005)). We consider all the black holes within R (definedas the radius within which the enclosed mean density is 200times the critical density) of a halo to be associated withthe host halo. The most massive black hole within R isassumed to be the central AGN and the rest are designatedas satellites. At z = 1 . , . , and 5 . R respec-tively. We expect the central black hole to be located at thecenter of the main galaxy in the halo since this is the placeof highest gas density and thus maximal black hole growth.The fact that most ‘central AGN’ are found near the groupcenter shows that our technique for identifying the centralAGN is reasonably adequate. Due to the limited volume ofour simulation we could only probe the faint end of the AGNluminosity function (Degraf et al. 2010). For calculating themean occupation we study AGN samples with bolometricluminosities above 10 ergs/s, corresponding to the obser-vational limit of X-ray selected AGN in deep surveys (e.g.,Ueda et al. 2003; Boyle et al. 1993; Cowie et al. 2003). Wealso show the distribution of AGN with luminosities above10 ergs/s and 10 ergs/s for theoretical interests to seethe luminosity dependence of HOD parameters.In a companion paper, Degraf et al. (2011b) (hereafterPaper I), we use the same SPH simulation to characterizethe HOD of black holes as a function of black hole mass.Our present study is fundamentally different from that inPaper I. We aim to study the HOD of AGN in terms ofAGN luminosity. By definition the HOD is always stud-ied based on physical properties of the object. In the caseof galaxy clustering, the galaxy HOD has been extensivelystudied in the literature based on color, luminosity, stellarmass (see Zehavi et al. 2005, Zheng et al. 2007). Black holemass and luminosity (accretion rates) are different param-eters and there does not exist an obvious one-to-one corre-spondence between mass and accretion rates (e.g. Fig. 1).Additional baryonic physics is needed to go from black holemass to accretion rate (and thus luminosity). There is somecorrelation between mass and accretion rates, but the scat-ter is huge and the correlation depends strongly on redshift(Colberg & Di Matteo 2008; Chatterjee et al. 2008).In practice, it is barely possible to have accurate massmeasurement of a large sample of black holes beyond thelocal universe. Therefore, the study in Paper I is mostly oftheoretical interest. By investigating the occupation prop-erties of black holes at the subhalo level, Paper I developsan analytic mechanism to populate dark matter halos with black holes in simulation. On the contrary, AGN luminos-ity is more readily measured observationally and there areexisting and ongoing efforts in measuring AGN/quasar clus-tering as a function of luminosity. Our study in this paperwill provide the necessary ingredient in interpreting theseobservations. Similar to the mass function of black holesand luminosity function of AGN, the black-hole-mass basedHOD and AGN-luminosity based HOD are complementarytools to advance our understanding of black hole evolution.Since the goal of this paper is to provide the HODframework to interpret observations we adopt some tech-nical differences in the definition of dark matter halos andthe choice of our sample from Paper I. In Paper I we dif-ferentiate between central and satellite black holes at thesubhalo level. Black holes residing in the central subgroupare called central black holes and black holes residing insatellite subgroups are called satellite black holes. In thenomenclature in Paper I there can be multiple central blackholes. We emphasize that the model in Paper I will be usefulfor populating halos (N body simulations) with black holesusing semi-analytic approaches and for studying the distri-bution of black holes in cosmological simulations. On theother hand our approach in this paper is to perform a the-oretical study on the relation between AGN (selected basedon luminosity) and dark matter halos and examine the as-sumptions in the HOD for modeling AGN clustering data.Our identification of central (i.e. most massive black holewithin R ) and satellite (rest of the black holes within R ) AGN is equivalent to primary and secondary blackholes in Paper I (see Fig. 2 of Paper I) and is similar to thestandard terminology used for galaxy HOD. We note thatthe friends-of-friends halos were used in Paper I for study-ing black hole occupation. Here we choose R to definethe halo boundary, which is commonly adopted in defininggalaxy clusters. Since the HOD describes bias at the level ofsystems near dynamical equilibrium, traditional virial meth-ods of mass estimation can take advantage of this and pro-vide a direct measurement of the probability distribution P ( N | M ) (Berlind & Weinberg 2002). We have verified thatthe two different halo definitions show a good agreement inassigning black holes to host halos within 10%. In this section we present the distribution of accretion ratesas a function of halo mass and black hole mass. From thiswe calculate the conditional luminosity functions and themean occupation distribution of central and satellite AGN.Finally we show the radial distribution of the satellite AGNand provide the best-fit hod parameters.
Figure 1 shows the distribution of the Eddington scaled ac-cretion rate ( χ = ˙ M/ ˙ M EDD ), as a function of halo massfor three redshifts. The black points are central AGN andthe red open circles represent satellites. The mean rate isroughly independent of halo mass, which is commonly as-sumed in semi-analytic studies. However, the mean value of χ at a given halo mass varies with redshift. AGN at higher c (cid:13) , 000–000 OD modeling for AGN M O • M O • M O • -4 -2
1 0.1 0.3 0.5 z=5.0 10 -4 -2
1 10 -4 -2 Figure 2.
The distribution of Eddington scaled accretion rates ( χ ) for different black hole mass and redshift bins. From left to right,columns correspond to black hole mass bins, 6 . ≤ Log(M BH ) ≤ .
5, 6 . ≤ Log(M BH ) ≤ .
0, and Log(M BH ) ≥ .
0. The top, middle,and bottom panels correspond to redshifts 1 .
0, 3 .
0, and 5 . z = 1 . . . redshifts (left panel of Fig. 1 showing z = 5 .
0) tend to ac-crete at a higher value than their low redshift counterparts(right panel of Fig. 1 showing z = 1 . χ as a function of black hole mass. It isdefined as the conditional probability distribution of χ fora given black hole mass P ( χ | M BH ). The solid and the dot-ted lines denote central and satellite AGN, respectively. Themean rates are again roughly independent of black hole massbut vary substantially with redshift. The central and satel-lite distributions tend to trace each other at all redshifts.In Fig. 3 we present the spatial distribution of the satel-lite AGN. The sizes of the circles are proportional to theblack hole mass (left panel), gas mass (middle panel), andstellar mass (right panel) respectively. The gas and the stel-lar mass are computed within a spherical region of radius10 kpc surrounding the black hole. The green triangles rep-resent black holes with zero stellar mass within 10 kpc. Thetop, middle, and bottom panels are for z = 1 .
0, 3 .
0, and5 . χ at low redshift do not correlate with the mass distributionof the black holes (left panel of Fig. 3). The mass distribu-tion of black holes is not significantly different at different redshifts. At low redshifts the gas mass around black holesdecreases and so do the accretion rates. This is due to theeffect of AGN feedback. Outflow from AGN is responsiblefor expelling gas from the vicinity of the black hole and sup-pressing its own growth. AGN feedback is responsible forshutting down star-formation too. In Fig. 3 we also see theevidence of suppressed stellar mass in the immediate neigh-borhood of the AGN. We see evidence of how a local phe-nomenon (feedback) affects the global distribution of AGN,regardless of the host halo mass (see Fig. 1 for the host halomasses). This picture is consistent with what has been seenin previous studies (e.g., Di Matteo et al. 2008; Sijacki et al.2007) and semi-analytic models (e.g., Wyithe & Loeb 2003) The conditional luminosity function (CLF) (e.g., Yang et al.2003), in this case for AGN, is defined as the luminositydistribution Φ( L | M ) of AGN that reside in halos of a givenmass M . The global luminosity function is given byΦ( L ) = Z dndM Φ( L | M ) dM, (1)where Φ( L ) is the AGN luminosity function and dn/dM is the halo mass function. The CLF constitutes the differ-ential form of the HOD. The CLF provides a tool to ex- c (cid:13) , 000–000 Chatterjee et al. −5 −4 −3 −2 −1 z=1.0 −5 −4 −3 −2 −1 χ z=3.0 −5 −4 −3 −2 −1 Black Hole Mass z=5.0 r/R
Gas Mass 0.01 0.1 1Stellar Mass
Figure 3.
Spatial distribution of the satellite AGN. The size of each circle is proportional to the mass of the black hole (left panel), gasmass (middle panel), and stellar mass (right panel). The gas and the stellar mass are computed within a spherical region of 10 kpc aroundthe black hole. The green triangles represent black holes with no stars within 10 kpc. The top, middle and bottom panels correspond to z = 1 . z = 3 .
0, and z = 5 . M halo ≥ M ⊙ and black hole mass M BH ≥ M ⊙ . The accretion rates do not show any dependence on radius. The accretion rates do not show anypattern with black hole mass either, but there is a correlation with gas mass and stellar mass. In general the accretion rate is higher fora higher gas (stellar) mass. As we go to low redshifts the gas mass and stellar mass around black holes decreases due to the effect ofAGN feedback. AGN feedback is responsible for expelling gas from the vicinity of the black hole and suppressing its own growth. amine the distribution of halo mass for a given luminos-ity and study luminosity dependent clustering. This for-malism has been widely used in modeling galaxy cluster-ing with data from 2dFGRS and DEEP2 redshift surveys(e.g., van den Bosch et al. 2003). The CLF is useful in gen-erating mock catalogs which can then be used to test thecosmological model (e.g., Mo et al. 2004; Yan et al. 2004).Figure 4 shows the CLF in bins of halo mass running fromLog M = 11 . ± .
25 (left most panel) to Log M ≥ . .
0, 3 .
0, and5 .
0, respectively.The luminosity distributions reveal several features.The central AGN luminosity distribution closely traces alog-normal distribution (e.g., Martini & Weinberg 2001).Fig. 5 captures the features we observe in the CLF. Thetop panel of Fig. 5 shows the evolution of the mean log lu-minosity of the central AGN as a function of halo mass. The bottom panel of Fig. 5 shows the 1 σ scatter in the logof the luminosity. The mean luminosity at a given halo massevolves with redshift, with higher mean luminosity at higherredshifts. The scatter in the luminosity distribution of cen-tral AGN increases toward lower redshift, indicating that theluminosities for a given halo mass are more uniform at highredshift than at low redshift. As a result of this, at low red-shifts AGN samples based on luminosity will have a widerrange of host halo masses and hence clustering will dependweakly on luminosity. However at high redshifts luminositydependent clustering will be more prominent. Similar red-shift evolution of luminosity dependent clustering has beenobserved with SDSS quasars (Shen et al. 2009, 2007). Wenote that the clustering properties of AGN will be largelyrelated to their host halo mass. However we find that ac-cretion rates and hence luminosity depends strongly on lo-cal properties particularly at low redshifts (e.g., feedbackdiscussed in § c (cid:13) , 000–000 OD modeling for AGN L Bol [ergs/s] P ( L B o l | M h a l o ) M O • M O • M O • M O • z=1.0z=3.0z=5.0 0.1 0.3 0.5 0.7 Figure 4.
The conditional luminosity functions of the AGN in the simulation. The top, middle and bottom panels show the probabilitydistributions for redshifts 1 .
0, 3 .
0, and 5 .
0, respectively. The halo mass bins range from 10 M ⊙ − . M ⊙ (leftmost), to ≥ . M ⊙ (rightmost). The dashed and dotted lines represent the probability distribution for the central and satellite AGN. The curves arenormalized by the total number of halos in each mass bin. The central AGN traces a log-normal distribution as commonly assumed insemi-analytic studies. The error bars represent the Poisson error bars in each bin. of redshifts (Colberg & Di Matteo 2008). The shape of thesatellite luminosity function cannot be identified definitivelydue to lack of statistics. We note that the lower end of thesatellite luminosity function is affected by the resolution ofthe simulation and the seed black hole mass, which is mani-fested in the cut-off of the luminosity function. The satellitedistribution also shows some variation with halo mass. For agiven halo mass the peak of the satellite distribution tendsto be at a lower luminosity than the central AGN.To examine the effect of the central AGN on the num-ber distribution of satellites within a halo, we compare theconditional luminosity functions of satellite AGN for halosdiffering in central AGN luminosities. This is defined as theconditional distribution of satellite AGN luminosities for afixed M halo and L cenBol . We used a large halo mass bin to in-crease the statistics of our sample. We note that there is acorrelation between central AGN luminosity and halo mass.To eliminate the effect of mass-dependent central AGN lu-minosity, we divide halos according to the central AGN lu-minosity as follows. For each redshift, at each halo mass, wetag halos as ‘high Lcen’ (‘low Lcen’) if their central AGNluminosities are above (below) the mean central AGN lumi-nosity at that mass (Fig.5). Then the conditional luminosityfunctions of satellite AGN are computed for the ‘high Lcen’and ‘low Lcen’ halos, respectively. The results are shownin Fig. 6. The solid lines show the distribution of satellite luminosities for ‘high Lcen’ sample and the dashed lines rep-resent the distribution of satellite luminosities for ‘low Lcen’sample.The two groups of curves are for two halo mass bins. Theopen and the filled black circles connected by the dashed andsolid lines respectively represent the halo mass bin 11 . ≤ Log( M halo ) ≤ .
0. Similarly the blue open triangles and theopen squares connected by the dashed and solid lines respec-tively represent the halo mass bin 12 . ≤ Log( M halo ) ≤ . z = 3 .
0. Our results are similarfor z = 1 . z = 5 .
0. The correlation between central andsatellite AGN luminosity at a fixed halo mass will have im-portant implications on the small scale clustering strength.If there exists a strong large scale feedback effect from thecentral AGN it can possibly alter the local gas distributionaround satellite AGN and suppress the growth of the satel-lite black holes. This in effect will decrease the number ofluminous satellites in a halo with a higher central AGN lu-minosity and we would observe an anti-correlation betweensatellite number and central AGN luminosity.In Fig. 6 we do not see any correlation between thenumber of satellites and the luminosity of the central AGN.It has been shown in Chatterjee et al. (2008) that in groupscale halos (the most massive halos in our simulation) feed- c (cid:13) , 000–000 Chatterjee et al. Dot−dashed: Z=1.0Solid: Z=3.0Dashed: Z=5.0 L B o l ( e r g s / s ) M halo [M ⊙ ] σ l og L Figure 5.
The mean (upper panel) and scatter (lower panel) ofthe central AGN conditional luminosity function as a function ofhalo mass, shown in Figure 4. The scatter is defined as the 1 σ scatter from the mean in Log L Bol . The dot-dashed, solid, anddashed lines denote redshifts 1 .
0, 3 .
0, and 5 .
0, respectively. Fora given halo mass the mean increases with redshifts. The growthof the black holes is possibly suppressed and hence the accretionrate (and the luminosity thereof) is lower at lower redshifts. Thescatter in the distribution is also high at low redshifts since severalfactors (e.g., feedback from black holes) introduce spread in the L Bol − M halo relation. back from the central AGN can extend up to a few hundredkpc and thus can potentially affect the satellite distribu-tion. However in higher mass halos satellite AGN will alsobe residing in more massive subhalos and so they will berelatively unaffected from the feedback effects of the centralAGN. We note that in the self regulatory growth paradigmthe AGN shuts down its own growth by blowing up the gasaround it (as seen in Fig. 3) but the feedback effects do notaffect the gas distribution around neighboring black holes. We see a difference in the mean of the CLF for the cen-tral AGN between z = 1 . z = 3 .
0. To investi-gate this effect we extracted the light curves of the AGN(Colberg & Di Matteo 2008; Degraf et al. 2010) and lookedat their peak luminosities between z = 2 . z = 1 .
0. Theresult is shown in Fig. 7. The peak luminosities (blue stars)of the central AGN show a lower scatter with halo mass andthe best-fit relation is L Bol = 10 (cid:18) M halo . M ⊙ (cid:19) . ± . ergs / s , (2) L Bol (ergs/s) P ( L B o l — M h a l o ) Solid: L cenhigh
Dashed: L cenlow
Figure 6.
Dependence of the conditional luminosity function ofsatellite AGN on central AGN luminosity. The open and the filledblack circles connected by the dashed and solid lines respectivelyrepresent the halo mass bin 11 . ≤ Log( M halo ) ≤ .
0. Similarlythe blue open triangles and the open squares connected by thedashed and solid lines respectively represent the halo mass bin12 . ≤ Log( M halo ) ≤ .
0. The solid and the dashed lines rep-resent the distribution of satellite AGN luminosities for centralAGN with L Bol above (higher) and below (lower) the mean lu-minosity (see Fig. 5) respectively. We do not see any significantcorrelation between central AGN luminosity and the number ofsatellites. The error bars at each bin represent the Poisson errorbars. M halo [M ⊙ ] L B o l ( e r g s / s ) Star:PeakCircles:Instantaneous
Figure 7.
Bolometric luminosity of the central AGN as a functionof halo mass calculated at z = 1 .
0. The blue points show thepeak luminosity between z = 2 . z = 1 .
0, and the red opencircles show the instantaneous luminosity at z = 1 .
0. The peakluminosity tends to correlate more tightly with halo mass thaninstantaneous luminosity. c (cid:13) , 000–000
OD modeling for AGN < N > Z=3.010 L Bol >10 ergs/s M halo [M ⊙ ] L Bol >10 ergs/s L Bol >10 ergs/s Figure 8.
The mean occupation distribution of the AGN as a function of halo mass. The top, middle, and bottom panels correspondto redshifts 1 .
0, 3 .
0, and 5 .
0, respectively. The left, middle and right columns correspond to different luminosity cuts. The black pointsrepresent the mean occupation of all the AGN within R and the red open circles show the contribution from the satellite AGN. Themean occupancy of the central AGN can be idealized as a softened step function while the satellite population can be approximated by apower law (see Eqs. 4 and 5). The black solid, blue dot-dashed, and the red dashed lines are the best-fit models for the total, central, andsatellite occupation respectively. The best-fit HOD parameters are shown in Table 2. The error bars reflect the 1 σ Poisson error bars. where L Bol is the peak bolometric luminosity. We over-plot the instantaneous luminosity at z = 1 . . ± . M BH − σ relation to show that black holes residing inhigher mass halos enter the feedback dominated phase at anearlier time than black holes populating lower mass halos.Thus feedback effects will alter the M halo − L Bol correlationresulting in a wider distribution of host halo masses for agiven AGN luminosity at lower redshift. This result is alsoin agreement with Lidz et al. (2006) who conclude that thepeak luminosity is more correlated with halo mass than theinstantaneous luminosity of AGN and hence a better indi-cator of clustering. However, we cannot measure the peakluminosity of the AGN in practice.
We model the mean occupation function of AGN indark matter halos by decomposing it into a more physi-cally illuminating central and satellite contributions (e.g.,Kravtsov et al. 2004; Zheng et al. 2005; Zehavi et al. 2005) h N ( M ) i = h N cen ( M ) i + h N sat ( M ) i (3)where h N cen ( M ) i represents the mean occupation functionof central AGN and h N sat ( M ) i represents the mean occu-pation function of satellites (see discussions in § h N ( M ) i depends only on halo mass (e.g., Bond et al.1991; Lemson & Kauffmann 1999). h N ( M ) i is shown as afunction of halo mass in Fig. 8. The black filled circles showthe total occupation and the red open circles show the satel-lite occupation. The black solid, blue dot-dashed, and thered dashed lines are the best-fit models for the total, cen-tral, and satellite occupation. The top, middle, and bottompanels show redshifts 1 .
0, 3 .
0, and 5 .
0, respectively, while the c (cid:13) , 000–000 Chatterjee et al. left, middle, and right columns denote luminosity thresholds10 ergs/s, 10 ergs/s, and 10 ergs/s.We see that the central AGN occupation number fol-lows a distribution close to a softened step function and thesatellite occupation follows a power law similar to the galaxyor the dark matter subhalo case (e.g., Kravtsov et al. 2004;Zheng et al. 2005). Our HOD model is defined as follows: h N cen i = 12 (cid:20) (cid:18) Log M − Log M min σ LogM (cid:19)(cid:21) (4) h N sat i = ( M/M ) α exp( − M cut /M ) (5)In this formalism there are four parameters for modeling theHOD: M min , defining the halo mass where the occupation ofcentral AGN of a given type (in the present case we chooseAGN in terms of luminosity type) is 0 . σ LogM the char-acteristic transition width; M , the mass scale at which themean number of satellites above a given luminosity thresholdequals unity; and α , the power law exponent for the satelliteoccupation. However it has been observed that the mean oc-cupation of the satellites drops off faster than a power lawat lower halo mass (e.g., Zheng et al. 2005; Kravtsov et al.2004; Conroy et al. 2006) and we also see this trend in ourcase. We use the parameterization of Tinker et al. (2005) tomodel this drop-off. The parameter M cut is used to modelthe rolling off the power law. So we have a five parame-ter HOD model. The best-fit HOD parameters are shown inTable 2. The change in the luminosity threshold does affectthe mean value of the power law exponent but the valuesare consistent within 1 σ . The power law exponent also showweak evolution (seen in Paper I) with redshift but is consis-tent with no evolution within statistical limits.We compute the distribution of AGN with respect to themean P ( N |h N i ). In Paper I we showed that the distributionof satellite number (without any mass or luminosity cut)follows a Poisson distribution. We have verified that this isalso the case for AGN in any luminosity threshold sample.We further performed a Kolmogorov-Smirnov (KS) test tocheck whether the satellite distribution follows a Poissondistribution in our luminosity selected sample. The meanP-value that we obtain by performing the KS test over allredshifts and over all mass and luminosity bins is 0 .
92. Thisshows that the null hypothesis is strongly accepted and thedistribution of the satellites is close to a Poisson distribution.
Our model of central occupation is slightly different than Pa-per I. In Paper I we do not impose any mass cut and hencethe fraction of halos (above the threshold mass) containingblack holes is always unity (see Eqs. 1 and 2 in Paper I).In this paper the softening of the step function arises fromthe luminosity based selection. We note that at lower lumi-nosities the duty cycle is extremely close to 1 . ergs/s sample(right panel of Fig. 8). In Fig. 9 we show the differences inthe mean occupation function between a mass selected anda luminosity selected sample. The black solid lines show themean occupation function of AGN with bolometric luminosi-ties greater than 10 ergs/s at z = 1 . M halo [M ⊙ ] < N > Z=1.0
Figure 9.
The mean occupation distribution of the AGN for dif-ferent selections. The black solid lines represent the mean occupa-tion function of AGN with bolometric luminosities greater than10 ergs/s at z = 1 . z = 1 . ergs/s. The red dashed lines represent the mean occupationfunctions for the mass selected sample with triangles represent-ing central black holes and open circles representing satellite blackholes. In all cases the error bars are 1 σ Poisson error bars. tion of central AGN and the open circles represent the meanoccupation of satellite AGN. We now use the best-fit rela-tion between black hole mass and AGN luminosity at z = 1 . ergs/s. Thered dashed lines represent the mean occupation functionsfor the mass selected sample with triangles representing cen-tral black holes and open circles representing satellite blackholes.We see a clear difference between the two populations atlower halo masses. For the central AGN (triangles) the solidand the dashed lines converge at a mass scale of 10 . M ⊙ .Also the mass-selected occupation function falls-off verysteeply below this mass scale. This difference arises fromlower mass black holes residing in lower mass halos with highEddington ratios. Also the correspondence between blackhole mass and host halo mass is tighter than luminosity andhence we see this sharp cut-off in the occupation function forthe mass selected sample. Recently Gallo et al. (2010) foundevidence of such low mass high accretion rate black holes inlocal early type galaxies in the AMUSE-Virgo survey. Forthe satellite population (open circles) the lack of conver-gence in the occupation function between the two popula-tion is prominent even at higher halo masses. The minimumhalo mass for hosting satellite black holes (based on mass) ismuch higher than minimum halo mass for hosting satelliteAGN with equivalent luminosity. We thus see that the HODproperties will be significantly different between a mass se- c (cid:13)000
The mean occupation distribution of the AGN for dif-ferent selections. The black solid lines represent the mean occupa-tion function of AGN with bolometric luminosities greater than10 ergs/s at z = 1 . z = 1 . ergs/s. The red dashed lines represent the mean occupationfunctions for the mass selected sample with triangles represent-ing central black holes and open circles representing satellite blackholes. In all cases the error bars are 1 σ Poisson error bars. tion of central AGN and the open circles represent the meanoccupation of satellite AGN. We now use the best-fit rela-tion between black hole mass and AGN luminosity at z = 1 . ergs/s. Thered dashed lines represent the mean occupation functionsfor the mass selected sample with triangles representing cen-tral black holes and open circles representing satellite blackholes.We see a clear difference between the two populations atlower halo masses. For the central AGN (triangles) the solidand the dashed lines converge at a mass scale of 10 . M ⊙ .Also the mass-selected occupation function falls-off verysteeply below this mass scale. This difference arises fromlower mass black holes residing in lower mass halos with highEddington ratios. Also the correspondence between blackhole mass and host halo mass is tighter than luminosity andhence we see this sharp cut-off in the occupation function forthe mass selected sample. Recently Gallo et al. (2010) foundevidence of such low mass high accretion rate black holes inlocal early type galaxies in the AMUSE-Virgo survey. Forthe satellite population (open circles) the lack of conver-gence in the occupation function between the two popula-tion is prominent even at higher halo masses. The minimumhalo mass for hosting satellite black holes (based on mass) ismuch higher than minimum halo mass for hosting satelliteAGN with equivalent luminosity. We thus see that the HODproperties will be significantly different between a mass se- c (cid:13)000 , 000–000 OD modeling for AGN Redshift L Bol (ergs s − ) N centot N sattot Log( M min /M ⊙ ) σ LogM α Log( M /M ⊙ ) Log( M cut /M ⊙ ) ≥ . ± .
15 1 . ± .
21 0 . ± .
05 12 . ± .
63 11 . . ≥
927 226 11 . ± .
11 1 . ± .
20 0 . ± .
08 12 . ± .
32 11 . ≥
56 4 13 . ± .
27 0 . ± .
27 1 . ± .
12 13 . ± .
01 11 . ≥ . ± .
06 0 . ± .
05 0 . ± .
13 11 . ± .
48 11 . . ≥ . ± .
08 0 . ± .
13 0 . ± .
13 11 . ± .
41 11 . ≥
199 42 11 . ± .
05 0 . ± .
06 1 . ± .
32 12 . ± .
12 11 . ≥
410 66 10 . ± .
04 0 . ± .
03 0 . ± .
18 11 . ± .
81 11 . . ≥
407 66 10 . ± .
06 0 . ± .
05 0 . ± .
18 11 . ± .
81 11 . ≥
121 18 11 . ± .
09 0 . ± .
18 1 . ± .
37 12 . ± .
83 11 . Table 2.
AGN HOD parameters for three redshifts corresponding to Eqs. 4 and 5. Columns 3 and 4 show the total number of centraland satellite black holes in each bin. lected sample and a luminosity selected sample. This is be-cause a relatively small halo can host a bright AGN if thereis high density gas. On the other hand, it is difficult to get amassive black hole in a small halo, since that would requiresignificant amounts of dense gas over a long period of time.
Fig. 9 shows the radial distribution of the number density ofsatellite AGN (luminosity greater than 10 ergs/s) withinhost halos of masses 11 . ≤ Log( M halo ) ≤ .
0. The red cir-cles, blue triangles, and the green squares show the profile at z = 1 . z = 3 .
0, and z = 5 . β (power law index of AGN: averaged overall redshifts) and Log( n ) (normalization: averaged over allredshifts) are − . ± .
08 and − . ± .
05 for the sam-ple shown in Fig. 9. The power law index β does not showany significant dependence on halo mass or AGN luminos-ity either. For comparison we also show the profile of darkmatter and galaxies within AGN host halos. The solid andthe dotted lines show the average profiles (averaged over allredshifts) for dark matter and satellite galaxies respectively.The minimum stellar mass that we used for obtaining thegalaxy profile is 10 M ⊙ (roughly 100 times the stellar massresolution). The profiles do not show any variation if wechange the threshold stellar mass for selecting galaxies. Thecurrent choice of stellar mass is an optimization between res-olution elements and statistics. The profiles are normalizedto the mean number density of the corresponding species(satellite AGN/dark matter/ satellite galaxies) within R (e.g., Nagai & Kravtsov 2005).We also fit NFW profile (Navarro et al. 1997) to theAGN radial distribution. We fit the profiles for differentconcentration parameters and calculate the corresponding Pvalues. At all redshifts our data strongly disfavors the nullhypothesis and the NFW profile is ruled out at 3 σ . We notethat the AGN are more centrally concentrated than darkmatter and galaxies. The reason that we see an enhancedpopulation of AGN at the center of the halo compared togalaxies is because of the merging process of black holes. When two galaxies merge there exists a time lag betweenmerging galaxies and the merging of AGN that reside inthem. This time lag is due to the time it takes for the satel-lite AGN to fall in to the halo center where it can merge withthe central AGN. After the two galaxies merge the time thatit takes for the AGN to merge can then be further affected bythe gas content of these galaxies. Lin & Mohr (2007) mea-sure the radial profile of radio sources in clusters and showthat it is consistent with an NFW profile with a concentra-tion of 25. Martini et al. (2007) study the radial distributionof X-ray selected AGN in clusters and find that AGN withX-ray luminosities above 10 ergs/s show stronger centralconcentration than cluster host galaxies. However, a biggersample with L X ≥ ergs/s (closer to our sample of AGN)does not show any stronger evidence of central concentra-tion; different from what we observe in simulation.In Fig. 11 we show the relation between stellar mass andAGN luminosity at z = 1 .
0. The stellar mass is computedwithin a spherical region of radius 30 kpc surrounding theblack hole. We selected different spatial scales to computethe stellar mass. The values converge between radii of 25kpc to 30 kpc and hence we chose 30 kpc to be the relevantradius for computing the stellar mass content in AGN hostgalaxies. The black points represent central AGN and thered open circles show the satellite distribution. In the caseof central AGN the stellar mass for more luminous AGNis generally higher. AGN will have higher luminosity whenthe accretion rate is high, which is more likely when thegas density is high. Also when the gas density is high thecooling rate will be higher and hence there will be morestars. So in general higher density will correspond to highaccretion rates of AGN and higher stellar mass. For satelliteAGN this trend is very weak. But even for satellite AGNif we consider a luminosity selected sample we will system-atically choose AGN with higher stellar mass. Also in Fig.3 we see that AGN with higher stellar mass content tendto reside in the central regions of the halos. This can po-tentially increase the higher concentration of AGN seen inFig. 10 for a luminosity selected sample. To further checkthis we selected AGN based on their stellar mass contentand computed their average radial profile. We find a steepermean slope ( β ∼ − .
7) for the stellar mass selected sam-ple compared to the luminosity selected sample. This againis an indication of enhanced central concentration of AGNwith higher stellar mass content in their host galaxies. c (cid:13) , 000–000 Chatterjee et al. r/R n / n AGN
Circles: z = 1.0Triangles: z = 3.0Squares: z = 5.0Dashed: bestfitSolid: Dark MatterDotted: Galaxies
Figure 10.
The radial profile of satellite AGN. The open circles,triangles, and squares show the profiles at z = 1 . z = 3 .
0, and z = 5 . L Bol > ergs/s and host halo masses between10 − M ⊙ . The radial profiles do not exhibit any significantevolution with redshift. The dashed line shows the average power-law fit over all redshifts. The best-fit value for the slope is − . ± .
08. For comparison we also show the profile of dark matterand galaxies within AGN host halos. The solid and the dottedlines show the average profiles (averaged over all redshifts) fordark matter and satellite galaxies respectively. The error bars arerepresentative of the 1 σ error bars. In this paper, we study the relation between AGN and darkmatter halos using a cosmological SPH simulation that in-corporates black hole and galaxy formation physics. Specifi-cally we have investigated the effect of environmental factors(e.g., feedback, local gas density, host galaxy mass) on theaccretion rates of AGN within dark matter halos and howit affects the occupation distribution of AGN. We examinea number of simplifying assumptions in the HOD modeling(e.g., dependence of AGN luminosity on halo mass, depen-dence of AGN accretion on black hole mass) of AGN andprovide the necessary tools to model AGN clustering data.We have characterized the HOD of faint AGN (the sampleprobed by our simulation box) which can be generalized toincorporate the bright end of the luminosity function.We compute the conditional luminosity functions ofAGN and separate the contributions from the central andsatellite AGN. Our key findings are as follows. (1) The cen-tral AGN luminosities follow a log-normal distribution simi-lar to the assumption in semi-analytic studies. (2) The meanof the CLF for a given halo mass shows a strong dependenceon redshift with higher luminosities at higher redshifts. (3)The scatter in central AGN luminosity is large at low red-shift, but decreases with increasing redshift. This impliesthat the dependence of AGN clustering on luminosity isweak at low redshift, but it can become stronger at highredshift. We analyze the light curves of individual AGN andshow that there exists a tighter correlation between halo mass and peak luminosity rather than instantaneous lumi-nosity. We present the joint distribution of satellite occupa-tion as a function of halo mass and central AGN luminos-ity. We do not see any significant correlation between thesatellite number and the luminosity of the central AGN. Wealso show that the mean occupation function of the centralAGN resembles a softened step function while the satellitepopulation follows a power law with an exponential roll-offat lower mass, similar to what has been observed with thegalaxy HOD. We show that low mass black holes with highEddington ratios residing in low mass halos makes the lumi-nosity based HOD significantly different from the black holemass based HOD.We will now compare our simulation results with semi-analytic models that have been widely used for cluster-ing analysis (e.g., Martini & Weinberg 2001; Shankar et al.2010a). We compare our results with the model describedin Shankar et al. (2010a) who computed the mass functionof black holes at z = 3 . .
52. In our simulation we ob-serve the average slope to be (1 . ± .
06) at z = 3 .
0. Thereis a large scatter from the mean slope and the 1 σ scatter is0 .
44. We note that this relation in our simulation is depen-dent on the AGN model and the ratio of the threshold halomass that can host black holes to the mass of the seed blackholes. Shankar et al. (2010a) assumes the black holes to beaccreting with a constant Eddington fraction. Although themean χ in our simulation is roughly independent of halomass as seen in Figure 1, they do show an evolution withredshift. This has been also noted in Shankar et al. (2010a)where they suggest that the assumption of constant Edding-ton fraction might break down at the faint end. The otherimportant parameter is the scatter in the L Bol − M halo rela-tion. We find a log-normal distribution as assumed in semi-analytic studies. However the scatter strongly depends onredshift with increasing scatter at low redshifts (shown inFigure 5).Observationally the most relevant physical quantity de-scribing an AGN is luminosity. Recently Miyaji et al. (2010)and Starikova et al. (2010) have used X-ray selected AGNto constrain the HOD empirically. We propose to compareour HOD model with observational samples in a follow-uppaper. However an alternative approach would be select-ing black holes based on their mass and measure clusteringstatistics based on black hole mass. Although we do not havereliable observational measurements of black hole masses, wehave also provided the framework for predicting clusteringproperties based on the black hole mass function in PaperI. These two complimentary approaches would impose eventighter constraints on theoretical models of AGN growth andfeedback. Our analysis provides the first step toward com-paring semi-analytic and simulation results on AGN clus-tering and assessing some of the simplifying assumptions inthe present interpretations of AGN clustering observationsand constraining physical parameters. Because of the smallsimulation box, our current study is limited to low luminos-ity AGN, and the results on satellite AGN suffer from smallnumber statistics. A larger simulation box with larger sta-tistical samples spanning both the faint and the bright end c (cid:13) , 000–000 OD modeling for AGN M star [M ⊙ ] L B o l ( e r g s / s ) CentralSatellite
Figure 11.
Relation between stellar mass and AGN luminosity at z = 1 .
0. The stellar mass is computed within a spherical regionof radius 30 kpc surrounding the black hole. The black pointsrepresent central AGN and the red open circles show the satellitedistribution. In the case of central AGN the stellar mass for moreluminous AGN is generally higher. For satellite AGN this trend isvery weak. But even for satellite AGN if we consider a luminosityselected sample we will systematically choose AGN with higherstellar mass. of the luminosity function can provide tighter constraintson AGN HOD. Also, the mass of the seed black hole is de-pendent on the resolution of the simulation, imposing anartificial mass cut in the simulation. Future work on highresolution simulation and more accurate modeling of accre-tion and feedback (e.g., Booth & Schaye 2009) will also beneeded to understand the full implication of gas physics andblack hole accretion on clustering studies. The HOD formal-ism has been successfully incorporated in galaxy evolution.We hope that our work will have the same impact for study-ing the co-evolution of AGN and their hosts and shed lighton the AGN-galaxy connection.
ACKNOWLEDGMENTS
We would like to thank Douglas Rudd, Laurie Shaw, andFrank van den Bosch for some useful discussions whichhelped in the analysis and physical interpretation of someresults. We thank David Weinberg for suggesting the analy-sis for looking at the correlation between central and satel-lite AGN luminosities. We also thank the referee for thecomments which helped in improving the draft. JR wassupported by the Yale College Dean’s Science ResearchFellowship through summer 2010. ZZ gratefully acknowl-edges support from Yale Center for Astronomy and Astro-physics through a YCAA fellowship. DN was supported inpart by the NSF grant AST-1009811, by NASA ATP grantNNX11AE07G, and by Yale University. The work in CMUwas supported by the National Science Foundation, NSFPetapps, OCI-0749212 and NSF AST-1009781. The simula-tions were carried out at the NSF Teragrid Pittsburgh Su-percomputing Center (PSC).
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