Do you see what I see? Exploring the consequences of luminosity limits in black hole-galaxy evolution studies
Mackenzie L. Jones, Ryan C. Hickox, Simon J. Mutch, Darren J. Croton, Andrew F. Ptak, Michael A. DiPompeo
DDraft version September 30, 2018
Preprint typeset using L A TEX style emulateapj v. 12/16/11
DO YOU SEE WHAT I SEE? EXPLORING THE CONSEQUENCES OF LUMINOSITY LIMITS IN BLACKHOLE-GALAXY EVOLUTION STUDIES
Mackenzie L. Jones , Ryan C. Hickox , Simon J. Mutch , Darren J. Croton , Andrew F. Ptak , Michael A.DiPompeo Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia Centre for Astrophysics & Supercomputing, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia and NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771, USA
Draft version September 30, 2018
ABSTRACTIn studies of the connection between active galactic nuclei (AGN) and their host galaxies there iswidespread disagreement on some key aspects stemming largely from a lack of understanding of thenature of the full underlying AGN population. Recent attempts to probe this connection utilizeboth observations and simulations to correct for a missed population, but presently are limited byintrinsic biases and complicated models. We take a simple simulation for galaxy evolution and adda new prescription for AGN activity to connect galaxy growth to dark matter halo properties andAGN activity to star formation. We explicitly model selection effects to produce an “observed”AGN population for comparison with observations and empirically motivated models of the localuniverse. This allows us to bypass the difficulties inherent in many models which attempt to infer theAGN population by inverting selection effects. We investigate the impact of selecting AGN based onthresholds in luminosity or Eddington ratio on the “observed” AGN population. By limiting our modelAGN sample in luminosity, we are able to recreate the observed local AGN luminosity function andspecific star formation-stellar mass distribution, and show that using an Eddington ratio thresholdintroduces less bias into the sample by selecting the full range of growing black holes, despite thechallenge of selecting low mass black holes. We find that selecting AGN using these various thresholdsyield samples with different AGN host galaxy properties.
Keywords: galaxies: active INTRODUCTION
In the past decade there has been significant progressin building a generalized model of the formation and evo-lution of galaxies and their host halos across cosmic time(See Silk & Mamon 2012 for a review). These galaxyformation models have illustrated the impact of stellarand AGN feedback on galaxy growth (e.g., Kauffmannet al. 1993; Springel et al. 2005a; Bower et al. 2006; Cro-ton et al. 2006; Genel et al. 2014; Schaye et al. 2015;Volonteri et al. 2015; Khandai et al. 2015; Feng et al.2016). However, the connection between galaxy growthand black hole growth is not well understood. Thevolume-averaged galaxy-black hole growth rate is consis-tent with the black hole-spheroid mass relationship (e.g.,Heckman et al. 2004) and the masses of supermassiveblack holes (SMBH) are found to be correlated with hoststellar bulge properties (Kormendy & Ho 2013), how-ever the physical processes connecting black holes to theirgalaxies are still uncertain (Alexander & Hickox 2012).One major challenge lies in understanding selection ef-fects (e.g., color selection, obscuration, flux limits, andluminosity limits) in observed AGN samples. Selec-tion effects become apparent as different methods acrosswavelengths intended to probe the same physical phe-nomena yield populations with different AGN and galaxyproperties. It is difficult to correct for selection effects asit is not immediately apparent which effects, or even howmany, are influencing what is observed. For example, thedistribution of the Eddington ratio (the ratio of bolomet-ric luminosity to the Eddington limit) in the X-rays is ob- served to be approximately power-law in shape and spansseveral orders of magnitude, while in the optical, the Ed-dington ratio distribution is observed to vary by galaxyage (Kauffmann & Heckman 2009). This discrepancybetween observed accretion rate distributions, where ac-cretion rate refers to the specific accretion rate, i.e. Ed-dington ratio, can be resolved when selection effects inspectroscopic classification are taken into account (Joneset al. 2016). Additionally, AGN are preferentially foundin the most massive, bulge dominated galaxies across allwavelengths. X-ray selected AGN, in particular, are ob-served to reside in more massive host dark matter ha-los compared to optical AGN (e.g., Hickox et al. 2009;Koutoulidis et al. 2013; Richardson et al. 2013). Further-more, the probability of finding an AGN is tied to thehost galaxy star formation rate: the likelihood of findingan AGN increases for star forming galaxies compared toquiescent galaxies for a given accretion rate (e.g., Azadiet al. 2015). Yet the observation that AGN preferen-tially reside in massive galaxies is likely an effect dueto AGN selection above a certain luminosity threshold.For a given luminosity threshold, it is possible to probelower in Eddington ratio for high mass AGN compared tolow mass AGN, for which only the highest accreting sys-tems would be selected (Aird et al. 2012). The strengthof AGN clustering measurements are also shown to varyacross wavelengths (e.g., Hickox et al. 2009; Mendez et al.2016).In recent years, there has been increased insight intothe physical origin of the black hole accretion rate dis- a r X i v : . [ a s t r o - ph . GA ] J un tribution. This distribution is expected to cover a widedynamic range and has converged on a broad universalshape that may be dependent on star formation (e.g.,Aird et al. 2012; Bongiorno et al. 2012; Chen et al. 2013;Hickox et al. 2014; Azadi et al. 2015). Further evidencefor this broad distribution is presented by Veale et al.(2014) in which a variety of accretion distributions areused to recreate the observed quasar luminosity function(QLF). An individual AGN may vary on short timescaleswithin the dynamic range of this AGN accretion ratedistribution (e.g., Hickox et al. 2014; Schawinski et al.2015), while galaxies vary on longer timescales, on orderof (cid:38)
100 Myr (e.g., Alexander & Hickox 2012). Thisvariability may be due to accretion disk instabilities, orfeedback on the accreting material (e.g., Siemiginowska& Elvis 1997; Hopkins et al. 2005; Janiuk & Czerny 2011;Novak et al. 2011), however, most observational evidenceof this variability is indirect (e.g., Schawinski et al. 2010;Keel et al. 2012; Schirmer et al. 2013; Sartori et al. 2016).Due to this variability (or “flickering”) each observationis a snapshot of that source’s current AGN accretion:an instantaneous value, rather than a description of theaverage black hole activity.Further attempts have been made to understand theinterplay between AGN and their host galaxies throughtheoretical modeling. Hydrodynamical models, in partic-ular, investigate AGN accretion and explicitly spatiallyresolve feedback on the interior halo of the host galaxy.Recent models, such as eagle (Schaye et al. 2015), il-lustris (Vogelsberger et al. 2014; Genel et al. 2014), massiveblack-II (Khandai et al. 2015), and BlueTides(Feng et al. 2016) are built to simultaneously describecomplex physical processes and dark matter halo growthproviding spatial and phase information, although thisusually involves sub-grid modeling and many free param-eters. These hydrodynamical simulations have had suc-cess in modeling a variety of AGN properties (e.g., winds,gas properties, luminosity functions), but number statis-tics are sacrificed for better resolution due to the highcomputational cost. Alternatively, semi-analytic modelsseparate baryonic physics from dark matter halo growthand sacrifice spatial information by averaging over thespatial scale which makes them less computationally ex-pensive than hydrodynamic models. This also usuallyinvolves utilizing many free parameters that are oftendegenerate, such that model predictions are not uniqueand can be difficult to interpret (e.g., Henriques et al.2009; Lu et al. 2011; Mutch et al. 2013a).In order to investigate the impact of selection effects onAGN observations, we have built a simple semi-numericalmodel for galaxy evolution and AGN accretion based onthe observed connections between AGN and their hostgalaxies. In this work we take a “forward” modeling ap-proach in which we simulate an intrinsic full galaxy pop-ulation with a complete knowledge of its physical proper-ties and apply known limits due to selection to compareto observations, rather than modeling unknown selectioneffects in observations. We combine the best character-istics of a semi-analytic simulation, a fast model with alow number of parameters, and the expository power ofa straightforward, intuitive prescription for galaxy andblack hole growth. We discuss our method for forwardmodeling the local AGN population in Section 2. Thisis broken into two subsections that discuss the galaxy formation model (2.1) and AGN prescription (2.2). Inthis paper we focus on the most simple of selection ef-fects, namely luminosity limits that are primarily drivenby the sensitivity limits of X-ray surveys. We compareour simulated AGN population to observations by impos-ing limits on luminosity and Eddington ratio in Section3. A discussion of our results and summary are given inSection 4.We utilize the same assumed cosmology as in Mutchet al. (2013b), in which a 1-year Wilkinson MicrowaveAnisotropy Probe (WMAP1; Spergel et al. 2003) colddark matter (CDM) cosmology with Ω m = 0 .
25, Ω Λ =0 .
75, and Ω b = 0 .
045 is used. Likewise, all results areshown with a Hubble constant of h = 0 .
7, where h ≡ H /
100 km s − Mpc − . METHOD OF SIMULATION
The Semi-Numerical Galaxy Formation Model
The host galaxies of our model AGN sample are builtfrom a simulation of galaxies and dark matter halos us-ing the formation history model of Mutch et al. (2013b).This model begins with a sample of dark matter halosfrom the N-body Dark Matter Millennium Simulation(Springel et al. 2005b), where the baryonic content ofthese halos is determined by the halo growth rate andthe cosmological fraction of baryons compared to darkmatter. The Millennium Simulation uses N = 10 par-ticles in a volume of 714 × ×
714 Mpc and followsgalactic evolution from z = 127 to z = 0 in 64 time stepsof ∼ −
350 Myr.Mutch et al. (2013b) combines two simple functionsto connect galactic growth to the formation history ofthe Millennium Simulation dark matter halos; a bary-onic growth function and a physics function. The bary-onic growth function regulates the availability of bary-onic material to be used by stars, mapping the darkmatter growth history to the star formation rate (SFR).The physics equation represents the combined effects ofinternal and external physical processes (e.g. shock heat-ing, supernova feedback, AGN feedback, galaxy mergers,tidal stripping, etc.) on the star formation rate, actingas an efficiency of baryonic matter consumption.In this model, the conversion efficiency of the baryonsinto stars is based on a simple function (Equation 1)that represents baryon cooling, star formation, and bothstellar and AGN feedback physics as one net compo-nent, rather than treating them individually which canbe computationally costly or can introduce significantuncertainty due to a large number of physical parame-ters: M ∗ /M = E M vir exp (cid:32) − (cid:18) ∆ M vir σ M vir (cid:19) (cid:33) , (1)where E M vir represents the baryonic matter conversionefficiency and M vir is the halo virial mass with stan-dard deviation σ M vir . Treating the baryonic matter inthis way allows for each galaxy’s formation to followthe growth history of its individual halo, capturing thetrue diversity of galaxy formation histories, rather thanadding an artificial scatter as is done with many othermethods. This approach has proven to be accurate for z < vir ) or the instantaneous maximum circularvelocity (V max ), which is more directly tied to the gravi-tational potential. Both M vir and V max provide good fitsand can be used interchangeably, although V max may bemore tightly coupled with the stellar mass growth (Red-dick et al. 2013).The Mutch et al. (2013b) model is able to accuratelyrecreate the local stellar mass function and its evolutionto z ∼
3. It also has the capability to trace the stellarmass function as a function of stellar age, which allowsfor passive and star forming galaxies to be treated sepa-rately. For more information on this model, please referto Mutch et al. (2013b).In the Mutch et al. (2013b) semi-numerical model,galaxies are assigned a star formation rate (SFR) fol-lowing the growth of the dark matter halos and avail-ability of the baryonic material. If the galaxy is notflagged as the central galaxy of a dark matter halo, it isassigned SFR = 0. Since these leftover “satellite” galax-ies are passive with low SFR, they may be treated withthis simplification when investigating the local and globalstellar mass function. However, in this work we are di-rectly comparing to the observed SFR distribution andthis simple assumption of assigning “satellite” galaxies aSFR = 0 is no longer applicable. There are also a frac-tion ∼
59% of central galaxies with SFR = 0 for whichwe calculate a SFR.We have devised a simple prescription for repopulat-ing galaxies with SFR = 0 based on the distributionof specific star formation rate (sSFR; SFR/M*) of oursimulated passive central galaxies. For central galaxieswith SFR = 0, the SFR are smoothed over three redshiftbins in order to limit the number of central galaxies withSFR = 0. Any galaxy with SFR = 0, including centralgalaxies with SFR = 0 after the smooth, are assigned asSFR representative of a passive galaxy. The distribu-tion of sSFR for central galaxies is well fit by two gaus-sians, so we assign an sSFR consistent with the passivegaussian distribution. Using this simple method, we canrepopulate the SFR for our “satellite” and central galax-ies in order to more accurately compare to observations.The repopulated sSFR drawn from the passive centralgalaxy sSFR distribution are low enough that they donot greatly impact the average doubling time for our sim-ulated sample (e.g. for a stellar mass of ∼ M (cid:12) thetypical sSFR assigned is 10 − yr − , corresponding toa doubling time of ∼
100 Gyr, and as such, the corre-sponding increase in the stellar mass at each time stepwould be negligible).
A Simple Prescription for AGN Accretion
Since the Mutch et al. (2013b) galaxy evolutionmodel synthesizes complicated physics down to a one-dimensional function, we are able to add complexity inthe form of an AGN component and limit the num-ber of free parameters, while remaining computation-ally tractable. The foundation of our simple prescriptionfor AGN accretion is motivated by the work of Joneset al. (2016), in which it is assumed the instantaneousobserved AGN luminosity is due to short-term variabil-ity (e.g., Alexander & Hickox 2012; Hickox et al. 2014) and follows an Eddington ratio (L bol / L Edd ) distributiondescribed by a Schechter function, a power law with anexponential cutoff near the Eddington Limit (Hopkinset al. 2009): dtd log L bol = (cid:18) L bol L Edd (cid:19) − α exp ( − L bol / L Edd ) . (2)An Eddington ratio distribution that takes the functionalform of a Schechter function consists of only two freeparameters: the slope of the power law α , and the lowercut off L cut which sets the amplitude of the function suchthat the integral of the curve is one.Our black hole masses are derived from the black hole-bulge relationship of H¨aring & Rix (2004), with totalgalaxy stellar mass from the model galaxies used as aproxy for bulge mass (Kormendy & Ho 2013). We notethat there is significant uncertainty and scatter in therelationship between black hole mass and total stellarmass, with marked differences observed for local ellipti-cals and AGN hosts (e.g., Reines & Volonteri 2015). Weadopt the H¨aring & Rix (2004)relationship as it approx-imately bisects that found for ellipticals and AGN hosts,and broadly represents the correlation observed for thefull galaxy population. Furthermore, we do not includea redshift evolution in our black hole mass calculations.There is widespread disagreement about whether a red-shift evolution is present or if any observed evolution iscaused by a sample selection bias (e.g. Decarli et al.2010; Merloni et al. 2010; Schulze & Wisotzki 2011; Ben-nert et al. 2011; Woo et al. 2013; DeGraf et al. 2015;Shankar et al. 2016). We tested the impact of a moder-ate evolution (Merloni et al. 2010) on our analysis andfound that our simulated luminosity functions for bothan evolving and non-evolving black hole-galaxy relation-ship were consistent within their random scatter for red-shifts up to z ∼ . Edd = 1 . × M BH . We then select aninstantaneous AGN bolometric luminosity from the Ed-dington ratio distribution. Both the galaxy and AGNcomponents are defined in terms of bolometric luminosi-ties; using scaling relationships these can be convertedinto different broad-band luminosities. In this paperwe focus on the hard (2 −
10 keV) X-rays, although wenote that this approach could be equally valuable in the >
10 keV, soft X-rays, infrared, and/or optical regime.Galactic X-ray emission is produced by a combinationof high mass X-ray binaries (HMXB), low mass X-raybinaries (LMXB), and hot gas (e.g., Hornschemeier et al.2005; Lehmer et al. 2010; Fragos et al. 2013). In this workwe ignore hot gas since X-ray binaries dominate the X-ray emission above 1 . x,LMXB ( z ) = α (1 + z ) γ M ∗ , L x,HMXB ( z ) = β (1 + z ) δ SF R, (3)where log α = 29 . ± . γ = 2 . ± .
99, log β =39 . ± . δ = 1 . ± .
22, and the contributionfrom HMXB scales with star formation rate (SFR) whileLMXB scales with stellar mass.The AGN X-ray luminosity is derived from the bolo-metric AGN luminosity using the Lusso et al. (2012) ob-served relationship for Type 1 AGN,log L / L [2 − keV ] = ( m ± dm )L Edd + ( q ± dq ) , (4)where m ± dm = 0 . ± .
035 and q ± dq = 2 . ± . X and theobscured fraction from Merloni et al. 2014 (See theirfigure 9). For AGN that are “unobscured”, we assigna column density of log N H = 20 cm − , while thoseselected to be “obscured” have column densities drawnfrom the NuSTAR-informed N H distribution (Lansburyet al. 2015; Figure 13b). Based on these column den-sities and X-ray spectral models (e.g., Lansbury et al.2014) we then add X-ray absorption to our obscuredsample. We run our simulation both with and withoutthis prescription for obscuration and find that addingobscuration does not significantly alter the results of ouranalysis, other than extending the lower cutoff of theAGN X-ray luminosities from L X = 10 . erg s − toL X = 10 . erg s − (with obscuration) and altering theamplitude of our AGN X-ray luminosity function (seeSection 3.1). There is no change for the highest lumi-nosities (L X > erg s − ). We thus have a simulatedgalaxy and AGN X-ray luminosity for every object in oursample and can investigate the properties of this X-rayemission to compare to observations. COMPARISON OF THE SIMULATED AGN POPULATIONWITH X-RAY OBSERVATIONS
In our simulation we built bolometric AGN and galaxyluminosities which are then scaled into X-ray luminosi-ties. At this point our X-ray sample represents an in-trinsic snapshot of the full AGN population. In orderto compare our simulation to observations we must for-ward model the selection effects we would expect to seein these observed results.In the literature, there are a range of different param-eters used to define an AGN. In the X-ray band, AGNare most often selected based on an observed luminos-ity threshold. This threshold is often set at the transi-tion where AGN emission begins to dominate host galaxyemission (L X ∼ . erg s − ). Despite the ease of thismethod for selecting the brightest AGN, by definition itdoes not select less luminous AGN, especially when theseAGN have luminosities comparable to their host galaxy(e.g., highly star forming galaxies).Alternatively, an AGN may be defined by its accre-tion rate using colors, broad lines, or by the Eddingtonratio. Typically, this threshold is set at an Eddingtonratio of λ (cid:38) .
01 (e.g., Hopkins et al. 2009). Since theEddington ratio is closely linked to the black hole mass,selecting an AGN in this way often relies on accuratemeasurements of the black hole, which may be difficult toacquire for large samples. Additionally, it becomes chal-lenging to separate AGN accretion from other accretionprocesses at low luminosities (e.g., Lehmer et al. 2016).
Figure 1.
Comparison of the X-ray luminosity function (XLF)from our model at z = 0 to results from X-ray observations. TheXLF for the full sample of model galaxies is given as a solid grey linewhile the galaxy and AGN components that make up the total X-ray emission are shown as light grey triple-dot-dash and dash lines,respectively. The turnover of the total X-ray luminosity at L X ∼ erg s − is caused by the minimum contribution from starformation as defined by the mass limit of our model sample. Themodel XLF is then compared to the distributions of the luminosityand Eddington ratio limited model samples: luminosity limit ofL X ∼ . erg s − (green) and Eddington ratio limit of 0.01(magenta). We further compare our limited model samples to theXLF of Aird et al. (2010) at z = 0 (orange). We find that ourluminosity limited sample most closely matches the full theoreticalcurve. While at high luminosities (L X (cid:38) erg s − ) we are ableto match the Aird et al. (2010) XLF with our full sample XLF andboth of our limited sample XLF. An Eddington ratio limit, however, is better for select-ing low-luminosity AGN compared to a luminosity lim-ited sample, as demonstrated by our following analysis.In this work we are able to fully explore this thresholdsince each of our simulated AGN has a known Eddingtonratio drawn from our Schechter function distribution.
The AGN Luminosity Function
We first compare our model AGN population to theobserved AGN X-ray luminosity function (XLF). Thisdistribution is particularly useful for investigating AGNevolution but observations are uncertain at faint lumi-nosities and high redshifts due to poor number statisticsand contamination (e.g., Nandra et al. 2005; Aird et al.2010). To mitigate these problems, luminosity limits arecommonly placed on samples, thereby adding a knownselection effect.
The AGN luminosity function at z = 0 We compare our model initially to the luminosity-dependent density evolution (LDDE) model of the hardX-ray luminosity function from Aird et al. (2010). Weare able to “tune” our model to match the Aird et al.(2010) XLF at z = 0 by varying our model AGN Edding-ton ratio distribution α and lower cutoff parameters. Weapproximately match the distribution with α = 0 . cut = − . bol / L Edd . This Schechter function distri-
Figure 2.
Comparison of the X-ray luminosity function (XLF) evolution from our model to results from X-ray observations. The XLFevaluated near the center of each redshift bin for the full sample of model galaxies is shown as a solid blue line. These model XLF arecompared to the Aird et al. (2010) XLF for these same bins (solid black line) and the best Eddington distribution parameters are chosenby a minimum chi-squared calculation. The Aird et al. (2010) XLF for z = 0 is shown in each bin for comparison. We find good agreementto z ∼ .
2. Deviations at higher redshift are likely due to the simplicity of the model and may be solved by adding additional complexities,such as connecting AGN accretion to the star formation rate. bution deviates from the parameters presented in Joneset al. (2016) ( α = 0 . cut = − .
75 L bol / L Edd ). Weexpect that alpha will be steeper since our distribution isdescribing AGN activity in both the active and quiescentgalaxy population (Gabor & Bournaud 2013), whereas inJones et al. (2016), we focus on the Eddington ratio dis-tribution of star forming galaxies alone. It is worthwhileto note that when comparing these theoretical distribu-tions at z = 0 with observations that are higher redshifts,an exact comparison is difficult due to the evolution ofthe XLF (e.g., Ueda et al. 2014).The luminosity function that we calculate with oursimulated AGN population appears as a double powerlaw with its break at L X ∼ erg s − (solid greyline, Figure 1). This characteristic shape is influencedby the black hole mass function and is consistent withwhat is modeled by Aird et al. (2010, orange, Figure 1).At low luminosities we observe a turnover due to thegalaxy dominating the X-ray emission and the minimumcontribution from star formation as imposed by our blackhole mass limit. Since our simulation relies on the ran-dom selection of the accretion rate from the Eddingtonratio distribution, as well as randomly assigning which galaxies are obscured, we ran a bootstrap resampling todemonstrate the variance of our simulation due to theserandom selections. We show these random assignmentsand limited volume do not introduce a significant uncer-tainty to our model XLF (grey area, Figure 1).We can further examine the effects of selecting AGNbased on two different thresholds on the “observed” XLF.The Eddington ratio limited sample (solid purple line,Figure 1) yields a similar wide distribution in luminosity(39 . (cid:46) log L X (cid:46) .
5) compared to the full model galax-ies (solid grey line, Figure 1). We note that in practice,it is difficult to select AGN below L X ∼ erg s − dueto contamination from other accretion processes (e.g.,Lehmer et al. 2016). Imposing a luminosity limit (solidgreen line, Figure 1), as we would expect, causes the XLFto truncate below L X = 10 . erg s − as it is defined,which is consistent with the LDDE model of Aird et al.(2010). At high luminosities (L X (cid:38) erg s − ), whereall AGN are accreting at high Eddington rates, we findthat our models, including those that have imposed lim-its, are consistent with the Aird et al. (2010) XLF at z = 0. This suggests that our simple prescription forAGN accretion is valid to first order for describing thefull AGN population at z = 0. An evolving AGN luminosity function
We further explore the evolution with redshift of theXLF in our model. AGN X-ray luminosities for galax-ies in earlier (higher-z) snapshots from the Mutch et al.(2013b) simulation are calculated following the z = 0 pre-scription outlined in Section 2.2 (also using an Eddingtonratio distribution given by a Schechter function). We cal-culate the minimum chi-squared fit between our modelXLF and the Aird et al. (2010) AGN XLF for a selectionof nine redshift bins in order to determine our best fitparameters for the Schechter function α , and lower cut-off (Figure 2). Over this redshift range, α varies between0 . .
8, while the lower cutoff varies between − . − .
0. We find that our XLF are qualitatively consis-tent with the Aird et al. (2010) XLF within these redshiftbins to z ∼ . z (cid:46) Host Galaxy SFR and Mass
The Mutch et al. (2013b) simulation tracks the star for-mation rate of our model galaxies, thus we can calculatethe specific star formation rate (sSFR; ratio of the starformation rate to the stellar mass). The full simulateddistribution in sSFR-stellar mass (grey contours, Figure3) is consistent with the shape of the eagle hydrody-namical theoretical distribution for z = 0 (Guo et al.2016) as well as the observed sSFR-stellar mass distribu-tions from Schiminovich et al. (2007) (0 . < z < . . < z < . X =10 . erg s − to select AGN from 0 . < z < .
2. Inorder to more accurately compare these results to ourmodel output at z = 0, we correct the sSFR of thisobserved comparison sample using the Lee et al. (2015)galaxy main sequence evolution (SFR ∝ (1+ z ) . ± . )at z = 0 .
2. We find comparable “observed” distributionsthat are truncated at higher stellar mass compared to ourintrinsic AGN population; we are able to match obser-vations that are different from our intrinsic distributionby using appropriate limits. We see a slight shift of ourluminosity limited model to higher stellar masses com-pared to the Mendez sample as shown by the histograms.Our overestimation of the stellar masses may in partbe due to the connection between AGN accretion andstar formation, such that the AGN fraction decreasesfor passive galaxies (e.g., Chen et al. 2013; Azadi et al.2015). AGN suppression in high mass systems is not yetincluded in this simple model.
Figure 3.
Specific star formation rate versus stellar mass distri-bution for both the full sample of model galaxies (grey-black) com-pared to the distribution for the model luminosity limited samplewith lower limit of L X = 10 . erg s − . We do not include thesSFR-M* distribution of the Eddington limited sample for claritysince our Eddington ratios are tied to the stellar mass such thatthis limit does not change the overall shape of the full distribution.The corrected Mendez et al. (M16, 2016) observed X-ray AGN areshown in orange squares and are consistently distributed with re-spect to the luminosity limited sample. Normalized histograms ofeach axis are shown for clarity. With the addition of the galaxy main sequence evo-lution to the Mendez et al. (2016) sample, our limitedmodel sSFR appears consistent with observations. Usinga straightforward and simple semi-numerical model, weare able to build comparable intrinsic sSFR-stellar massdistributions, as well as broadly match what is observedwith appropriate limits.
The Halo Occupation Distribution of AGN
We further investigate the host dark matter halosof our simulated AGN and compare our simple modelto results from the observational clustering analysis ofRichardson et al. (2013) as well as the simulation of Chat-terjee et al. (2012). We compute the halo occupationdistribution (HOD) for luminosity and Eddington ratiolimited samples with respect to our intrinsic full sam-ple. As shown in the color-mass analysis, our Eddingtonratio limited sample (magenta, Figure 4) follows a distri-bution consistent with the intrinsic sample and thus thedistribution of the ratio appears flat on the HOD. Thissuggests that by selecting AGN based on Eddington ratiowe are capturing the black hole growth across all masslimits.Our luminosity limited sample, however, deviates fromour model intrinsic sample so the HOD takes on a pos-itive slope with a turnover at M ∼ M (cid:12) . We com-pare this shape to the Richardson et al. (2013) distri-bution at z ∼ . z = 1 . Figure 4.
The mean halo occupation distribution (HOD) of boththe luminosity limited, L X > . erg s − , (green) and Edding-ton limited, λ > .
01, (magenta) samples of simulated AGN. Wecompare our modeled samples to the observational HOD analysisof Richardson et al. (2013) at z ∼ . z = 1 . X > erg s − (cyan). While not able to becompared directly, the luminosity limited model HOD at z = 0lies within the overall shape of the Richardson et al. (2013) andChatterjee et al. (2012) HOD. a simple semi-numerical model attains the general shapeof a theoretically motivated HOD as well as the observa-tionally informed HOD. This reinforces the result that asimple prescription can describe the observed AGN pop-ulation to first order and by varying the criteria thatdefine our AGN population, we are selecting AGN withdifferent host galaxy and halo properties. SUMMARY
Our goal has been to build a simulation of the fullAGN population and their host galaxy properties usinga straightforward semi-numerical model, in order to in-vestigate the impact of AGN selection criteria on the“observed” population. We begin with a sample of darkmatter halos from the Millennium N-body simulation(Springel et al. 2005b) and connect galactic growth tothe dark matter halo formation history using the Mutchet al. (2013b) formation history semi-numerical model.Our AGN accretion model is motivated by the resultsof Jones et al. (2016) and is straightforward and com-putationally inexpensive. It treats AGN accretion as aninstantaneous rate selected from an Eddington ratio dis-tribution that takes the functional form of a Schechterfunction. Using a variety of galaxy and AGN scalingrelationships, we convert our simulated bolometric lu-minosities into X-ray luminosities to better compare toobservations. We assign AGN to be obscured or unob-scured following the prescription outlined in Section 2.2.With our simulated full AGN population, we explicitlymodel selection effects by defining our “observed” AGNsamples based on typical observational limits; a luminos-ity threshold of L X > . erg s − and an Eddingtonratio limit of λ (cid:38) .
01. We then compare our intrin-sic AGN population, as well as the two limited samples,to a variety of published relationships. We are able torecreate the Aird et al. (2010) XLF using a Schechter function Eddington ratio distribution with a power-lawslope of α = 0 . cut = − .
0. ThesSFR-M* distribution of our intrinsic AGN populationis broadly consistent with that of the eagle hydro-dynamical simulation at z = 0 (Guo et al. 2016) aswell as the observational distributions of Schiminovichet al. (2007) (0 . < x < .