Philip F. Hopkins et al- The Co-Formation of Spheroids and Quasars Traced in their Clustering

8/3/2019 Philip F. Hopkins et al- The Co-Formation of Spheroids and Quasars Traced in their Clustering

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statistics of the quasar, red galaxy, and merger mass and lu-minosity functions are consistent and can be used to predict oneanother (Hopkins et al. 2007, 2006c, 2006f ).

However, it is by no means clear whether this is, in fact, thedominant mechanism for the triggering of quasars and buildupof early-type populations. For example, the association betweenBH and stellar mass discussed above leads some models to tiequasar activity directly to star formation (e.g., Granato et al. 2004),implying it will evolve in a manner tracing star-forming galax-ies, with this evolution and the corresponding downsizing effectroughly independent of mergers and morphological galaxy seg-regation at redshifts zP2. Others invoke poststarburst activegalactic nucleus (AGN) feedback to suppress star formation onlong timescales and at relatively low accretion rates through, e.g.,radio-mode feedback (Croton et al. 2006). In this specific case,the radio-mode is associated with low-luminosity activity aftera quasar phase builds a massive BH (i.e., quasar relics), but itis possible to construct scenarios (e.g., Ciotti & Ostriker 2001;Binney 2004) in which the same task is accomplished by cyclic, potentially quasar-like (i.e., high Eddington ratio) bursts of ac-tivity, or in which the radio-mode might be directly associated

with an optically luminous quasar mode, either of which wouldimply quasars should trace the established old red galaxy pop-ulation at each redshift. In several models, a distinction betweenhot and cold accretion modes (Birnboim & Dekel 2003;Keres et al. 2005; Dekel & Birnboim 2006), in which new gascannot cool into a galactic disk above a critical dark matter halomass, determines the formation of red galaxy populations, essen-tially independent of quasar triggering (e.g., Cattaneo et al. 2006but see also Binney 2004).

At low luminosities (MBk23, important atzP0:5), mod-els predict that stochastic, high-Eddington ratio Seyfert activitytriggered in gas-rich, disk-dominated systems will contribute in-creasingly to the AGN luminosity function (Hopkins & Hernquist2006), with enhancements to these fueling mechanisms from bar

instabilities and galaxy harassment. Indeed, the morphologicalmakeup of low-luminosity, low-redshift Seyfert galaxies appearsto support this, with increasing dominance of unperturbed disks atlow luminosities seen locally (e.g., Kauffmann et al. 2003b; Dong& De Robertis 2006) and at low redshift z $ 0Y1 (Sanchez et al.2004; Pierce et al. 2006). At high luminosities (even at theseredshifts), however, the quasar populations are increasingly domi-nated by ellipticals and merger remnants, particularly those withyoung stellar populations suggesting recent starburst activity(Kauffmann et al. 2003b; Sanchez et al. 2004; Vanden Berk et al.2006; Best et al. 2005; Dong & De Robertis 2006), and even clearmerger remnants (Sanchez et al. 2004). Still, some models extendthe observed fueling in disk systems to high-redshift quasars, in-voking disk instabilities in very gas-rich high-redshift disks as a

primary triggering mechanism (Kauffmann & Haehnelt 2000).Clearly, observations which can break the degeneracies be-tween these quasar fueling models are of great interest. Unfor-tunately, comparison of the quasar and galaxy or host luminosityfunctions, while important, suffers from a number of degenera-cies and can be tuned in most semianalytic models. Direct ob-servations of host morphologies, while an ideal tool for this study,are difficult at high redshift and highly incomplete, especially forbright quasars that dominate their host galaxylightin all observedwave bands. However, the clustering of these populations may rep-resent a robust test of their potential correlations, which does notdepend sensitively on sample selection. Critically, considering theclustering of quasars and their potential hosts is not highly model-dependent in the way of, e.g., mapping between their luminosity

functions or modeling their triggering rates in an a priori fashion.

In recent years, wide-field surveys such as the Two DegreeField (2dF) QSO Redshift Survey (2QZ; Boyle et al. 2000) andthe Sloan Digital Sky Survey (SDSS; York et al. 2000) have en-abled tight measurements of quasar clustering to redshifts z $ 3,and a detailed breakdown of galaxy clustering as a function ofgalaxy mass, luminosity, color, and morphology (e.g., Norberget al. 2002; Zehavi et al. 2002; Li et al. 2006a). These observa-tions allow us to consider the possible triggering mechanismsof quasars in a robust, empirical manner, and answer several keyquestions. Which local populations have the appropriate cluster-ing to be the descendants of high-redshift quasars? How is thequasar epoch of these populations related to galaxy formation?And, to the extent that quasars are associated with spheroid for-mation, are bright quasar populations dominated by quasars trig-gered in formation events?

In this paper we investigate the link between quasar activityand galaxy formation by comparing the observed clustering ofquasar and galaxy populations as a function of mass, luminosity,color, and redshift. In x 2 we compare the clustering of quasarsand local galaxies to determine which galaxy populations de-scend from high-redshift quasar progenitors. In x 3 we consider

the clustering of quasars as a function of luminosity and redshift,checking the robustness of our results and presenting tests for thedominance of different AGN fueling mechanisms at low luminosi-ties. Section 4 compares the clustering of quasars as a functionof redshift with that of different galaxy populations at the sameredshift, ruling out several classes of fueling models. Section 5further considers the age as a function of stellar and BH mass ofthese galaxy populations, and uses this to predict quasar clus-tering as a function of redshift for different host populations. Inx 6 we use these comparisons to predict quasar clustering athigh redshifts, presenting observational tests to determine the ef-ficiency of high-redshift quasar feedback. Finally, in x 7 we dis-cuss our results and conclusions,and their implications for variousmodels of quasar triggering and BH-spheroid co-evolution.

Throughout, we adopt a WMAP1 (

M;; h; 8; ns) (0:27;0:73; 0:71; 0:84; 0:96) cosmology (Spergel et al. 2003) and

normalize all observations and models shown to this cosmology.Although the exact choice of cosmology may systematicallyshift the inferred bias and halo masses (primarily scaling with8), our comparisons (i.e., relative biases) are unchanged, andrepeating our calculations for a concordance (0.3, 0.7, 0.7, 0.9,1.0) cosmology or the WMAP3 results of Spergel et al. (2007)has little effect on our conclusions. All magnitudes are in theVega system.

2. USING CLUSTERING TO DETERMINE THE PARENTPOPULATION OF QUASARS/ELLIPTICALS

At a given redshift zi, quasars are being triggered in some

parent halo population. These halos, and by consequence thequasars they host, cluster with some bias/amplitude b(zi). Thehalos will subsequently evolve via gravitational clustering, whichin linear theory predicts their subsequent clustering at any laterredshiftzf will be given by

b(zf) 1 D(zi)

D(zf)

hb(zi) 1

i1

(Fry 1996; Mo & White 1996; Croom et al. 2001), where D(z) isthe linear growth factor. Thus, atz 0, the halos that hosted thequasars atzi will have a bias ofb(0) 1 D(zi) b(zi) 1.

The quasar luminosity function at a given redshift has a char-

acteristic luminosity L. Given that quasars (at least those with

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LkL) are typically observed to have high Eddington ratiosk L/LEdd % 0:3Y0:5 (Heckman et al. 2004; Vestergaard 2004;McLure & Dunlop 2004; Kollmeier et al. 2006), this L reflectsthe characteristic mass of active BHs at that redshift, MBH %3:0 k1 ; 108 M (L/10

13 L). Direct observations of quasar

Eddington ratios/BH masses (McLure & Dunlop 2004; Kollmeieret al. 2006), limits from the X-ray background ( Elvis et al. 2002;Cao 2005) and BH mass functions (Soltan 1982; Yu & Tremaine2002; Marconi et al. 2004; Shankar et al. 2004; Hopkins et al.2007), radio luminosity functions ( Merloni 2004; McLureet al. 2004), and relic low-luminosity Eddington ratios (Hopkinset al. 2006d) all rule out the possibility that these BHs subse-quently gain significant mass (k10%Y20% growth) after theirbrief active phase, so the MBH above is equivalent (within itserrors) to the z 0 BH mass of these objects. Since the rela-tionship between BH mass and host luminosity or mass is welldetermined at z 0 (MBH Mgal with % 0:001; Marconi& Hunt 2003; Haring & Rix 2004), knowing MBH(z 0) of apopulation implies, with little uncertainty, its z 0 host mass

Mgal or luminosity.

In Figure1 we consider the clustering of quasars as a functionof redshift, evolved to z 0. At each redshift where the quasarclustering b(z) is measured, we also know the characteristic lu-minosity L. Here we adopt the bolometric L determined in theobservational compilation of Hopkins et al. (2007)

log (L=L) k0 k1 k2 2 k3

3; 2

log1 z

1 zref

zref 2 ; 3

(k0 13:036; k1 0:632; k2 11:76; k3 14:25), but forour purposes this is identical to adopting the B band or X-ray Lfrom Ueda et al.(2003), Croom et al.(2004), Hasinger et al.(2005),or Richards et al. (2006a) and converting it to a bolometric Lwith a typical bolometric correction from Marconi et al. (2004),Richards et al. (2006b), or Hopkins et al. (2007). Given the con-versions above, we consider the implied characteristic BH massand, assuming little subsequent BH growth, the corresponding

z 0 stellar mass or luminosity in a given band (here from the

Fig. 1.Evolved clustering of quasar descendents (colored points) as a function of mass or luminosity, compared to clustering of early type ( filled black circles) andlate type (open black circles) galaxies of the same mass/luminosity. The measured clustering of quasars at a given z(samples as labeled) is evolved in linear theory to thegiven observed redshift, and plotted as of function of the relic host galaxy mass/luminosity. Galaxy clustering is shown at z 0 from (Li et al. (2006a; color andmorphologically selected early types as squares and circles, respectively), Zehavi et al. (2005; color-selected stars, Percival et al. (2007; SDSS LRGs; triangles), and

Norberg et al. (2002; diamonds); atz 0:1Y0:4 from Shepherd et al. (2001; stars) and Brown et al. (2003 and references therein; diamonds); atz 0:4Y0:8 from Meneuxet al. (2006; star), Phleps et al. (2006; circle) andBrown et al. (2003 andreferences therein; diamonds);andatz 0:8Y1:5 from Meneuxet al. (2006;squares) and Coilet al.(2004; circles). Fitted lines showthe best-fit bias of early type galaxies at each zas a function of mass/ luminosity (Norberg et al. 2001; Tegmark et al. 2004; Li et al. 2006a).[See the electronic edition of the Journal for a color version of this figure.]

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MBH-Lhostrelations of Marconi & Hunt 2003). Knowing how the bias of these halos evolves toz 0 (eq. [1]), we plotthe bias as afunction of stellar mass, atz 0, of the evolved quasar parentpopulation. We compare this with observed bias as a function ofstellar mass or luminosity for both early- and late-type galaxies.Note that the lowest and highest redshift bins (z $ 0:5 and z $2:5, respectively) in the Myers et al. (2007a) quasar clusteringmeasurements are significantly affected by catastrophic redshifterrors (owing to their considering all photometrically classifiedquasars, as opposed to just spectroscopically confirmed quasars);we follow their suggestion and decrease (increase) the clusteringamplitude in the lowest ( highest) redshift bin by $20%; excludingthese points entirely, however, has no effect on our conclusions.

For reference, we show the characteristicMBH correspondingto L in the QLF (as defined above) as a function of redshift inFigure 2. Whether we adopt a direct conversion from the ob-served L (eq. [3]) with observed Eddington ratios, as above, orinvoke any of several empirical models for the QLF Eddingtonratio distribution, we obtain a similarMBH. The figureillustratesthe inherent factorP2 systematic uncertainty in the appropriateEddington ratios and bolometric corrections used in our conver-sions. These uncertainties, however, are at most comparable tothe uncertainties in quasar clustering measurements. Because ofthis, our conclusions and comparisons are not sensitive to theexactmethod we use to estimate theMBH corresponding toL at agiven redshift.

The comparison in Figure 1 is possible at any redshift, notsimply z 0. We repeat our methodology above at severalzobs 0 1, evolving the bias to b(zobs ). The agreement withred galaxy clustering observed as a function of mass at each zobsis good, at all zP1. At higher redshifts, small fields in galaxysurveys limit ones ability to measure clustering as a bivariatefunction of luminosity and color/morphology at the highest lu-minosities, where the relics of z $ 2Y3 quasars are expected.

3. CLUSTERING AS FUNCTION OF LUMINOSITYAND DIFFERENT AGN FUELING MECHANISMS

The comparison in Figure 1 has one important caveat. We as-sumed that measurements of quasar clustering at a given redshiftare representative of a characteristic active mass MBH / Lof the QLF. In other words, quasar clustering should be a weakfunction of the exact quasar luminosity, at least nearL. If this

were not true, our comparison would break down on two levels.First, it would be sensitive to the exact luminosity distribution ofobserved quasars. Second, if quasars of slightly different lumi-nosities at the same redshift represented different BH/ host masses(consequently making quasar clustering a strong function of qua-sar luminosity), there would be no well-defined characteristicactive mass at that redshift.

Fortunately, Lidz et al. (2006) considered this question in de-tail, and demonstrated that realistic quasar light-curve and life-time models like those of Hopkins et al. (2006b) indeed predict arelatively flat quasar bias as a function of luminosity, in contrastto more naive models, which assume a one-to-one correlation be-tween observed quasar luminosity, BH mass, and host stellar/halo mass. This appears to be increasingly confirmed by direct

observations, with Adelberger & Steidel (2005a), Croom et al.(2005), Myers et al. (2006, 2007a), Porciani & Norberg (2006),and Coil et al. (2006a) finding no evidence for a significant de-pendence of quasar clustering on luminosity.

Figure 3 explicitly considers the dependence of bias on lumi-nosity and its possible effects on our conclusions. We plot, ateach of several redshifts, the observed bias of quasars as a func-tion of luminosity. For the sake of direct comparison, all observa-tions are converted to a bolometric luminosity with the bolometriccorrections from Hopkins et al. (2007). The QLF break luminos-ity L at each redshift, estimated in Hopkins et al. (2007) is alsoshown. The first thing to note is that the quasar observations withwhich we compare generally sample the QLF very near L, soregardless of the dependence of bias on luminosity, our conclu-

sions are not changed. We have, for example, recalculated the re-sults of x 2 assuming that the characteristic mass of active BHsis given by MEdd(hLobsi), where hLobsi is the mean (or median)observed quasar luminosity in each clustering sample in Figure 1,and find it makes no difference (changing the comparisons byT1 ).

We compare the observations with various theoretical mod-els in Figure 3. The models of Hopkins et al. (2005a) define theconditional quasar lifetime; i.e., time a quasar with a given final(relic) BH mass (or equivalently, peak quasar luminosity) spendsover its lifetime in various luminosity intervals, tQ(L j MBH).Since this is much less than the Hubble time at all redshifts ofinterest, the observed QLF (QL) is given by the convolutionof tQ(L j MBH) with the rate at which quasars of a given relic

mass MBH are triggered or turned on,

Q(L)

ZtQ(LjMBH)(MBH) dlog MBH; 4

where (MBH) is the rate of triggering, i.e., number of quasarsformed or triggered per unit time per unit volume per logarithmicinterval in relic mass. The integrand here defines the relative con-tribution to a given observed luminosity interval from each in-terval in MBH. Given the BH-host mass relation, we can convertthis to the relative contribution fromhosts of different massesMgal[i.e., dQ(L)/dlog Mgal]. In detail, we assume thatP(MBHjMgal)is distributed as a lognormal about the mean correlation, with a

Fig. 2.Characteristic active mass of BHs at a given redshift, i.e., the BHmasscorresponding to (dominant at)L in the QLF. Blacksquares adopt the virialrelation BH mass determinations of Kollmeier et al. (2006). Circles fit the ob-served QLF at each redshift (Hopkins et al. 2007) to quasar light-curve models(Hopkins et al. 2006b). Stars adopt the simplified continuity model from Yu &Tremaine(2002) andMarconi et al.(2004) given theUedaet al.(2003) QLF. Thedashed line ( Merloni 2004) and derives the active mass distribution from theradio and X-ray black hole fundamental plane. The black solid line is a fittedrelation (eqs. [3] and [8]). The active BH mass is well defined. Adopting dif-ferent estimators does not significantly alter our conclusions or comparisons inFigs. 1 and 11. [See the electronic edition of the Journal for a color version of this

figure.]

QUASAR AND ELLIPTICAL CLUSTERING 113No. 1, 2007


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dispersion of 0.3 dex taken from observations (Marconi & Hunt2003; Haring & Rix 2004; Novak et al. 2006 ) and hydrodynam-ical simulations (Di Matteo et al. 2005; Robertson et al. 2006a).Calculating the bias for a given relic MBH orMgal and observedredshift as in x 2, we can integrate over these contributions todetermine the appropriately weighted mean bias as a function ofobserved quasar luminosity,

hbi(L;z) 1

Q(L)

Zb(Mgal;z)

dQ(L)

d log MgaldlogMgal: 5

Although binning by both luminosity and redshift greatly re-duces the size of observed samples and increases their errors,the observations in Figure 3 confirm the predictions of Lidz et al.(2006) to the extent that they currently probe. To contrast, weconstruct an alternative straw-man model. Specifically, wecompare with the naive expectation, if all quasars were at thesame Eddington ratio (so-called light bulb models), i.e., if therewas a one-to-one correlation between observed luminosity andBH mass (and correspondingly, host mass), which produces amuch steeper trend of bias as a function of luminosity and issignificantly disfavored (>4.5 ; although from any individualsample the significance is only $2 ). We also compare the pre-dicted clustering as a function of luminosity from the semiana-

lytic models of Kauffmann & Haehnelt (2002) and Wyithe &

Loeb (2003), which adopt idealized, strongly peaked /decayingexponential quasar light curves [i.e., Eddington-limited growthto a peak luminosity, then subsequentL / exp (t/tQ)] andthere-fore yield similar predictions to the constant Eddington ratiolight bulb model (and are likewise disfavored at >4 ).

Figure 4 highlights the dependence of bias on luminosity inthe observations and models by plotting the relative bias b/b[where b b(L)] near the QLF L, more clearly demonstratingthe observational indication of a weak dependence. Alterna-tively, we can fit each observed sample binned by luminosity ata given redshift to a slope,

b

b 1

d(b=b)

dlog Llog (L=L); 6

the results of which are shown in Figure 5 as a function of red-shift, compared to the slope (evaluated at L) predicted by thevarious models. At all redshifts, the observations are consistentwith no dependence of clustering on luminosity, and stronglydisfavor the light bulb class of models (again, at $4 atz $1:5Y2). This confirms the conclusions of these studies individ-ually, particularly the most recent observations from Myers et al.(2007a) and the largest luminosity baseline observations fromAdelberger & Steidel (2005a).The weak dependence predicted by

the models of Hopkins et al. (2006b); Lidz et al. (2006) provides

Fig. 3. Quasar bias as a function of quasar luminosity at each of several redshifts. The circles show quasar observations from Fig. 1 (same line styles). Open circles addthe local (zP 0:3) observations of Constantin & Vogeley (2006; SDSS LLAGN [LINERS+Seyferts]; squares), Wake et al. (2004; SDSS; star), and Grazian et al. (2004;AERQS; diamond) and the z$ 1 cross-correlation measurements of Coil et al. (2006a; SDSS+DEEP2; circles). The dotted line shows L(z). These are compared tovarious models described in the text (curves, as labeled). Models in black adopt the feedback-regulated quasar light-curve/lifetime models from Hopkins et al. (2006a)

others consider more simplified light bulb model light curves. [ See the electronic edition of the Journal for a color version of this figure.]



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a considerably improved fit, although even it may be marginallytoo steep relative to the observations.

Galaxy clustering (and therefore, presumably, host halo mass)appears to be much more strongly correlated with galaxy lumi-nosity or stellar mass (Fig. 1) than with quasar luminosity (at agiven redshift); i.e., the weak dependence of bias on quasar lu-

minosity appears to be driven by variation in Eddington ratiosat a characteristic active mass. This is also supported by com-parison of quasar luminosity functions and number counts, in asemianalytic context (Volonteri et al. 2006). We note that thisis completely consistent with observations that find similar highEddington ratios for all bright quasars, as these are confined toLkL, (and indeed the Hopkins et al. [2006b] and Lidz et al.[2006] model predictions do, at these highest luminosities, re-produce this and imply a steep trend of bias with luminosity).However, the relatively weak trend in clustering near and belowL makes our conclusions throughout considerably more robust,so long as the observed quasar sample resolves L (true for allplotted points).

Despite the detail of the models involved, the predictions in

Figure 3 are all simplified in that they model only one mecha-

nism for quasar fueling. However, Hopkins & Hernquist (2006)(among others) predict that at low luminosities, contributionsfrom smaller BHs in nonmerging disk bulges, triggered by diskand bar instabilities, stochastic accretion, harassment, or other perturbations, are expected to dominate the Seyfert popu-lation. We therefore repeat our calculation, but allow different

fueling mechanisms in different hosts to contribute to differ-ent quasar luminosities, according to the models of Hopkins &Hernquist (2006) and Lidz et al. (2006). Because the Seyfertsin this particular model (Hopkins & Hernquist 2006) are gen-erally less massive systems at high Eddington ratio in blue, star-forming galaxies, they are less biased than merger remnants ofsimilar observed luminosity.

The inclusion of these populations in Figure 3 does not changeour conclusions nearL $ L. However it does introduce a feature,generally a sharp decrease in observed bias, at the luminositywhere these secular fueling mechanisms begin to dominate theAGN population. This luminosity is typically quite low, L $1011Y1012 L (corresponding roughly to luminosities belowthe classical Seyfert-quasar division of MB 23). The only

redshift at which the clustering of such very low-luminosity

Fig. 4.Same as Fig. 3, but showing the relative quasar bias b/b [b b(L)] as a function of luminosity nearL for the models and most well-constrained ( Myerset al. 2007a) and largest luminosity baseline (Adelberger & Steidel 2005a) observations, to highlight the luminosity dependence and differences between the models. [Seethe electronic edition of the Journal for a colorversion of this figure.]



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AGN has been measured iszP 0:2, by which point massive, gas-rich mergers are sufficiently rare that the predicted Seyfertpopulation from Hopkins & Hernquist (2006) dominates themerger-triggered quasar population at all luminosities, erasingthe feature indicative of a change in the characteristic host popu-lation. However, it is possible that deeper clustering observa-

tions atz $ 1Y2 will eventually probe these luminosities, and testthis prediction.

Realistically, the luminosities of interest are sufficiently lowthat X-ray surveys present the most viable current probe, butwith the small P1 deg 2 field sizes typical of most surveys, thequasar autocorrelation function cannot be constrained to the nec-essary accuracy to distinguish the models. However, as proposedin Kauffmann & Haehnelt(2002) the AGN-galaxy cross-correlationpresents a possible solution. For example, there are sufficientgalaxies atz $ 1 in the fields of surveys like e.g., DEEP2 orCOMBO-17 (with field sizes of $3.5 and $0.8 deg 2, respec-tively) that the accuracy of cross-correlation measurements islimited by the number of AGN; considering the hard X-ray-selected AGN samples in the CDF-N or CDF-S (with field sizes$0.010.5 deg 2 ) from z $ 0:8Y1:6 would represent a factor$2Y3 increase in the number density of AGN over the Coil et al.(2006a) sample in Figure 3, while extending the AGN luminos-ities to a depth of $3 ; 109 L ($10

42 ergs s1 cm2). The mea-surement of the cross-correlation between observed galaxies inthese fields and deep X-ray-selected faint AGN at zk 0:5 does,therefore, present a realistic means to test the differences in these

models at lowluminosities.The observationof a feature as shownin Figure 3 should correspond to a characteristic transition in thequasar host/fueling populations.

4. CLUSTERING OF DIFFERENT POPULATIONS

In Figure 6 we compare the observed quasar bias and corre-lation length as a function of redshift with the expected clustering

Fig. 5.Best-fit dependence of quasar bias on luminosity d(b/b/dlogL)from the observations in Figs. 3 and 4 (circles), compared to the dependenceexpected from the models (calculated at L). The observations favor little or nodependence of clusteringon luminosity. [See the electronic edition of the Journal

for a colorversion of this figure.]

Fig. 6.Clusteringof quasars as a functionof redshift (coloredcirclesin left panels, black in otherpanels; as in Fig. 1),compared to different modelsof possible hostpopulations.The topand bottom panels plotbias and comovingcorrelationlength,respectively. The solidline inverts the comparison in Fig.1, i.e.,uses the estimatedlocalclustering of red galaxies to predict the quasar clustering, assuming that quasars are the progenitors of present ellipticals ( long-dashed lines show $1 range fromuncertaintiesin local biasand observedbright quasar Eddington ratios). The dotted lines correspond to halos of constantmass (as labeled). Thecenter panel compares thiswith the observed clustering of early-type galaxies (at the characteristic red galaxy M orL atzP1; at higher redshiftb(M) is not longer well determined, so various

passive galaxy surveys are considered). The right panels compare with late-type galaxies. [See the electronic edition of the Journal for a colorversion of this fig

ure.]



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of quasar hosts, i.e., evolving the observed bias of BH (quasarrelic) hosts up from z 0. A z 0 elliptical galaxy or spher-oidof stellar massMgal has a bias b(M; z 0) shown in Figure1,and a BHof massMBH % 0:001 Mgal. For convenience, we adoptthe analytic fit to b(Mgal; z 0) in Li et al. (2006a)

b(Mgal; z 0)=b 0:896 0:097(Mgal=M); 7

where here M 1:02 ; 1011 M is the Schechter functionbreak mass (Bell et al. 2003) and b 1:2 for red galaxies(Zehavi et al. 2005; Li et al. 2006a). The progenitors of thesesystems therefore represent the characteristic active systemswhen the QLF characteristic luminosityL(z) isgivenbyL(z) %k LEdd(0:001 Mgal), i.e., when these BHs dominated the $Lquasar population and assembled most of their mass. Evolvingthe local observed bias of thez 0 spheroids, b(Mgal; z 0), tothis redshift with equation (1) yields the expected bias that thequasar hosts (and therefore quasars themselves) at this redshiftshould have, bQ(z). For future comparison, this is approximatelygiven by

bQ(z) % 1 0:014 D(z)1

; 105:70x2:30x 23:35x 3

; 8

where x log (1 z) and D(z) is again the linear growth fac-tor. This expectation is plotted, with the $1 combined un-certainties from errors in the measured QLF L and local biasb(Mgal; z 0), comparable to the inherent factorP2 systematicuncertainty in the appropriate Eddington ratios and bolometriccorrections. We also plot the corresponding correlation length r0;because measurementsof thisquantity are covariant withthe fittedcorrelation function slope , we renormalize the models and ob-servations to

r

0

0 8 h

1

Mpc

r0;Bt

8 h1 Mpc

=1:8

: 9

This is similar to the nonlinearNL8 parameter (standard devia-tion of galaxy count fluctuations in a sphere of radius 8 h1 Mpc,i.e., 8 measured for an evolved density field; see Peebles 1980),and effectively compares the amplitude of clustering at 8 h1 Mpcwith a fiducial model with 1:8, minimizing the covariance.

The expectation agrees well with observed quasar clusteringas a function of redshift (2/ 29:6/32, with no free param-eters). For comparison, we plot the expected clustering of halosof a fixed mass, Mhalo $ 4 ; 10

11Y1013 h1 M, determined in

the context of linear collapse theory following Mo & White(1996) modified according to Sheth et al. (2001) and with the

power spectrum calculated following Eisenstein & Hu (1999)for our adopted cosmology. As noted in most previous studies(e.g., Porciani et al. 2004; Croom et al. 2005), a constant hosthalomass of a few 1012 h1Mprovides a surprisingly good fitto the trend with redshift. This empirical fit, is comparable toour expectation from elliptical populations (best-fit halo mass3:86 ; 1012 h1 M with

2/ 28:9/31; of course, the exactbest-fit mass depends systematically on cosmology, but this con-clusion is robust). There is at most a marginal trend for the halomass to increase with redshift [forMhalo / (1 z)

k, the best-fitk 0:41 0:45; corresponding to a $50% increase over theobserved redshift range].

Note that the measurements shown are not all statistically in-dependent, and the significance of this comparison will diminish

if we consider any single quasar clustering measurement. Figure 7

demonstrates the same comparison, highlighting individual quasarbias measurements separately. However, the previous agreementand our conclusions are similar in all cases. As discussed by theauthors, Porciani & Norberg (2006) find a somewhat higher clus-tering amplitude in their highest redshift (z$ 2) bin than Croomet al. (2005) studying the same sample (and higher than Myers

et al. (2006) and Adelberger & Steidel (2005a) who study inde-pendent samples), but the significance of the Porciani & Norberg(2006) result is P2 .

That a constant halo mass fits the data as well as observedsuggests that there may be a physical driver or triggering mech-anism associated with these halos. It is suggestive that this cor-responds to the group scale; i.e., minimum halo mass of smallgalaxy groups, in which galaxy-galaxy mergers are expectedto proceed most efficiently. However, the redshift evolution ofthis threshold is not well determined (but see Coil et al. 2006c,who find a similar group scale halo mass atz 1), nor is therate or behavior of merging within such halos. An a priori theo-retical model for the prevalence of quasars in halos of this massis therefore outside the scope of this paper, but remains an impor-

tant topic for future work.

Fig. 7.Same as Fig. 6 (top left), but showing only single quasar clusteringmeasurements to highlight the significance of these comparisons from any indi-vidualsurvey. The two 2dF results are not independent, but use different methodsto derivethe quasar bias. [Seethe electronic edition of theJournalfor a colorver-

sion of this figure.]



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Since it is also established, as discussed in x 2, that the char-acteristic mass of active BHs increases with redshift, this impliessubstantial evolution in the ratio of BH to host halo mass toz $ 2. It is unclear how much of this may owe toevolutionin theratio of BH to host stellar mass: observational estimates implysome such evolution (e.g., Shields et al. 2006; Peng et al. 2006;Woo et al. 2006), but upper limits from evolution in stellar massdensities (Hopkins et al. 2006e) allow only a factor

$2 evolution

by z 2. Therefore, there might also be at least some increasewith redshift in the characteristic ratio of stellar to halo mass.Future constraints from halo occupation models or galaxy clus-tering at high redshifts will be valuable in breaking this degen-eracy, and potentially provide important clues to galaxy assemblyhistories.

We contrast these predictions with two extremely simple mod-els. In the first, quasar activity is an unbiased tracer of dark mat-ter, i.e., b(z) 1. This does, after all, appear true atz 0 (Wakeet al. 2004; Grazian et al. 2004; Constantin & Vogeley 2006).This is immediately strongly ruled out: there is an unambig-uous trend that higher redshift quasars are more strongly bi-ased (as noted in essentially all observed quasar correlation

functions).Next, we consider the possibility that quasars live in thesamehalos at all redshifts. This is equivalent to some classicalinterpretations of pure luminosity evolution in the QLF (e.g.,Mathez 1976); i.e., that quasars are cosmologically long-lived(although other observations demand a lifetime P107 yr; e.g.,Martini 2004 and references therein), and dim from z 2 to thepresent. It is also equivalent to saying that quasars are triggered,even for a short time, in the same objects over time (e.g., stochas-tically or by some cyclic mechanism). In this case, the quasarlifetime can still be short (with a low duty cycle $ 103),although Eddington ratios must still tend to increase with red-shift. Then, the halo bias evolves as equation (1), from az 0value b(0) $ 1:0Y1:2 (Norberg et al. 2002). Although this model

is qualitatively consistent with some quasar observations, it isnot nearly sufficient to explain the evolution of clustering ampli-tude with redshift and is ruled out at very high (>10 ) signifi-cance. As noted in previous studies of quasar clustering (Croomet al. 2005), quasars at different redshifts must reside in differentparent halo populations; quasars cannot, as a rule, be long livedor recurring/episodic/cyclic (although this does notapply to verylow-accretion rate activity, perhaps associated with radio modes;see, e.g., Hopkins et al. 2006d).

Rather than a uniform population of halos at all redshifts, whatif quasars uniformly sample observed galaxy populations? It is,for example, easy to modify the above scenario slightly: quasarsare cosmologically long-lived or uniformly cyclic/episodic, butonly represent the present/extant population of BHs (equivalently,

the present population of spheroids). In this case, quasar correla-tion functions should uniformly trace early-type correlations at allredshifts.

Figure 6 compares observed early-type/red galaxy clusteringas a function of redshift with that measured for quasar popula-tions. At low redshiftszP 1, both mass functions and clusteringas a function of mass/ luminosity are reasonably well determined,so we plot clustering at the characteristic early-type (Schechterfunction) M or L. At higher redshift, caution should be used,since this characteristic mass/luminosity is not well determined,and so we can only plot clustering of observed massive red gal-axies (which, given the observed dependence of clustering am-plitude on mass/luminosity and color, may bias these estimatesto high b(z) if surveys are not sufficiently deep to resolve M or

L). There is also the additional possibility that the poorly known

redshift distribution of these objects may introduce artificial scat-ter in their clustering estimates. Bearing these caveats in mind,the clustering of quasars and red galaxies are inconsistent at high(>6 ) significance. Quasars do not uniformly trace the popu-lations of spheroids/BHs which are in place at a given red-shift. Note, however, that in this comparison the systematic errorsalmost certainly dominate the formal statistical uncertainties, sothe real significance may be considerably lower.

An alternative possibility is that BH growth might uniformlytrace star formation. In this case, quasar clustering should tracethe star-forming galaxy population. Figure 6 compares observedlate-type/blue/star-forming galaxy clustering as a function of red-

shift with that observed for quasar populations. Again, at zP

1we plot clustering at the characteristic M or L. At higherredshift we can only plot combined clustering of observedstar-forming populations (generally selected as Lyman breakgalaxies); again caution is warranted given the known depen-dence of clustering on galaxy mass/luminosity (for LBGs, seeAllen et al. 2005). In any case, the clustering is again inconsis-tent at high (>10 ) significance. Quasars do notuniformly tracestar-forming galaxies. This appears to be contrary to some pre-vious claims (e.g., Adelberger & Steidel 2005a); however, inmost cases where quasars have been seen to cluster similarly toblue galaxies, eitherfaintAGN populations (not$L quasars)or bright (3L) blue galaxies were considered. Indeed, qua-sars do cluster in a manner similar to the brightestblue galax-

ies observed at several redshifts (e.g., Coil et al. 2006b; Allenet al. 2005 at z $ 1 and zk2, respectively). This should notbe surprising; since quasars require some cold gas supply fortheir fueling, they cannot be significantly more clustered thanthe most highly clustered (most luminous) population of gal-axies with that cold gas. Again, this highlights the fact thatthe real systematic issues in this comparison probably makethe significance considerably less than the formal $10 seenhere.

We would also like to compare quasar clustering directly tothe clustering of gas-rich ( luminous) mergers. Figure 8 attemptsto do so, using available clustering measurementsfor likely major-merger populations. At low redshifts, Blake et al. (2004) havemeasured the clustering of a large, uniformly selected sample

of poststarburst (E+A or K+A) elliptical galaxies in the SDSS,

Fig. 8.Same as Fig. 6, but comparing observed quasar clustering (gray cir-cles) as a function of redshift to that various populations usually associated withgalaxy mergers (black circles): poststarburst (E+A/K+A) galaxies, close galaxy

pairs, and submillimeter galaxies. [ See the electronic edition of the Journal for acolorversion of this figure.]



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which from their colors, structural properties, and fading mor-phological disturbances (e.g., Goto 2005 and references therein)are believed to be recent major merger remnants. Infante et al.(2002) have also measured the large-scale clustering of closegalaxy pairs selected from the SDSS at low redshift. At highredshift, no such samples exist, but Blain et al. (2004) have es-timated the clustering of a moderately large sample of spec-troscopically identified submillimeter galaxies at z

$2Y3, for

which the similarity to local ULIRGs in high star formation rates,dust content, line profiles, and disturbed morphologies suggeststhat they are systems undergoing major, gas-rich mergers (e.g.,Pope et al. 2005, 2006; Chakrabarti et al. 2006 and referencestherein). The clustering of these populations is consistent at eachredshift with observed quasar clustering (see also Hopkins et al.2007). This is contrary to the conclusions of Blain et al. (2004)but they compared their SMG clustering measurement with ear-lier quasar clustering data (Croom et al. 2002) below their me-dian redshiftz$ 2:5. Figure 8 demonstrates that the dependenceof quasar clustering on redshift is such that at the same redshifts,the two agree very well. However, given the very limited natureof the data, and the lack of a uniform selection criteria for on-

going or recent mergers at different redshifts, we cannot drawany strong conclusions from the direct merger-quasar clusteringcomparison alone.

Although quasars do not appear to trace star-forming galaxies,Adelberger et al. (2005 and references therein) have shown thatthe star formation rates, clustering properties, and number den-sities of high-redshift LBGs suggest that they are the progenitorsof present-day ellipticals. To the extent that quasars are alsothe progenitors of ellipticals (but with a larger clustering ampli-tude at a given redshift compared to LBGs), this suggests acrude straw-man outline of an evolutionary sequence withtime, from LBG to quasar to remnant elliptical galaxy. Knowinghowthe clustering properties of halos hosting LBGs with a givenobserved bias at some redshift zLBG will subsequently evolve,

we can determine the redshiftzQ at which this matches observedquasar clustering properties. This offset, if LBGs and quasars areindeed subsequent progenitor phases in the sequence of evo-lution to present day ellipticals, defines the duration of theLBG phase or time between LBG and quasar stages.

Figure 9 considers this in detail. We show the observed clus-tering of quasars and LBGs from Figure 6, with curves illustrat-ing the subsequent clustering evolution of the LBG host halosobserved at z 1, z 2, and z 3. These correspond to thecharacteristic observed quasar clustering at z 0:4, z 1:0,and z 1:3, respectively. Thus, halos of the characteristic LBGhost halo mass atz 3 will grow to the characteristic quasar hostmass atz 1:3, and so on. We also show the physical time cor-responding to this offset, calculated from the observed LBG clus-

tering at various redshifts and the best-fit estimate of the LBGhost mass $4 ; 1011 h1 M, and this time divided by the Hub-ble time (age of the universe) at the quasar epoch zQ. Interest-ingly, this implies that objects characteristically spend $3Y4 Gyr($1/2tH at the redshifts of interest) in the LBG phase. Thismay reflect the time for dark matter halos to grow from the char-acteristic LBG mass, at which star formation and the conversionof mass to light appears to be most efficient (e.g., White & Rees1978) to the typical quasar host mass; but it is also possible thatassociated physical processes related to quasar fueling or the ter-mination of star formation set this timescale. If quasars are trig-gered in major mergers, this rather large time offset (as opposedto the typical $100 Myr delay between starburst and quasar inmajor merger simulations, Di Matteo et al. 2005) implies that

LBGs are themselves not primarily driven in major mergers. Asimilar conclusion was recently reached by Law et al. (2007)from direct analysis of LBG morphologies atz $ 2Y3. This con-clusion and the LBG clustering in Figure 9 (Wechsler et al. 2001)are broadly consistent withthe expectations of semianalytic models

Fig. 9.Top: Clustering of quasarsand star-forminggalaxies, as in Fig.6. Thesolid lines show the subsequent evolution of the clustering of the star-forminggalaxy halos fromz 1; 2; 3. Middle: The time delay between the star-formingor LBGphase andquasar epoch,definedas thetimeafterthe observed redshift

of each LBG population at which its evolved clustering will match that of theobserved quasar population. The circles are as in the top panel, with data fromOuchiet al.(2004; invertedtriangles) added atz> 4.The dashedanddotted linesshow time for halos of mass $4 ; 1011 h1 M (the typical LBG host mass) ateach redshift to reach $4 ; 1012 h1 M (dotted line) or the (weakly redshift-dependent) halo mass defined by our best-fit trend in the top panel ( solid line).

Bottom: Same as the middle panel, but the time shown is as a fraction of theHubbletime at the quasar epoch. [See the electroniceditionof the Journal for acolorversion of this figure.]



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(Somerville et al. 2001), which argue that LBGs are driven largelyby collisional minor merging.

We can also use this approach to determine the time betweenthe quasar and red/elliptical phases in this evolutionary se-quence. Figure 10 shows this, in the style of Figure 9, where theredshift shown in the middle and lower panels refers to the red-shift of the observed quasar population, and the time to the de-lay at which their evolved clustering matches that measured forthe red galaxy population. Note that the continuous curves cal-culated in the middle and lower panels assume that the red gal-

axy clustering is well fitted by the plotted (top panel) constant

halo mass $1:6 ; 1013 h1 M curve; this is, in fact, not a verygood approximation at low redshifts, hence these curves divergebelowz $ 1Y2 from the times calculated from the actual red gal-axy clustering measurements.

In the lower panels, we also plot the time for burst-quenchedstar formation history models adapted from Harker et al. (2006b)to redden to a typical constant red galaxy threshold rest-framecolor U

B>

0:35. These model star formation histories as-

sume a constant star formation rate until 1 Gyrbefore the quasarepoch, then a factor 5 enhanced star formation rate for this1 Gyr, at which point star formation ceases. Essentially, thisyields a useful toy model for quenching, if indeed the trig-gering of quasars is associated with the formation of ellipticalsor termination of star formation (the prequenching enhancementbeing an approximation to, e.g., merger-induced star forma-tion enhancements), which Harker et al. (2006b) demonstrateyields a reasonable approximation to the observed mean color,number density, and Balmer HF absorption strength evolu-tion of red galaxies. The predicted time for such quenched starformation histories to redden to typical red galaxy colors agreeswell with the time estimated from clustering here at all redshifts;

i.e., the color and halo mass evolution of these systems are con-sistent with reasonable star formation histories in which quasaractivity is associated with quenching or the termination of starformation.

We have estimated the time offsets in Figures 9 and 10 from adirect comparison of the observed clustering. Instead, one mightimagine adopting the implied halo mass ($4 ; 1011 h1M) atthe star-forming phase and using extended Press-Schechter(EPS) theory to calculate the average time for a typical pro-genitor halo of this mass at each observed redshift to growto the implied quasar host halo mass ($4 ; 1012 h1 M). Wediscuss this in greater detail in x 5, and show that it has no ef-fect on our conclusions. For the purposes here, adopting thismethodology (specifically, calculating the evolution of the main

branch progenitor halo mass with redshift following Neisteinet al. (2006) in our adopted cosmology) systematically increasesthe inferred time delays (circles) in Figure 9 by $1Y2 Gyr andthose in Figure 10 by $0.5Y1 Gyr, but does not significantlychange the plotted trends or comparisons.

So, this leaves us with the following suggested empiricalpicture of galaxy evolution. Galaxies form and experience atypical star-forming or LBG epoch, with maximal efficiencyaround a characteristic halo mass of a few $1011 h1M. Growthcontinues, presumably via normal accretion, minor mergers, andstar formation, for roughly half a Hubble time, until systemshave growth to a characteristic halo mass $4 ; 1012 h1M. Atthis point, some mechanism (for example, a major merger, as thismay be the characteristic scale at which the host halo grows large

enough to host multiple large star-forming systems) triggers ashort-lived quasar phase, drives a morphological transforma-tion from disk to spheroid, and terminates star formation. About$1Y2 Gyr after this, the host halos have grown to $1013 h1Mand the spheroids have reddened sufficiently to join the typicalred galaxy population. They then passively evolve (althoughthey may experience some gas-poor or dry mergers) to z 0,satisfying observed correlations between BH and spheroid prop-erties. Although individual BHs can, in principle, gain signifi-cant mass from dry mergers (see, e.g., Malbon et al. 2006),this cannot (by definition) add to the total mass budget of BHs,which must be built up via accretion. Note that this is only arough conception outline of an average across populationsand should not be taken too literally. Different systems will

undergo these processes at different times, and ( possibly) via

Fig. 10.Same as Fig. 9, butinstead showing thetime from thequasar phaseto the red galaxy phase implied by the observed clustering of both populations.The long-dashed lines in the middle and bottom panels show the time required forthe burst-quenched star formation history models from Harker et al. (2006b)(which yield a good empirical approximation to the buildup and mean color evo-lution of red galaxies) to redden to a threshold U B > 0:35. [See the electronicedition of the Journal for a colorversion of this figure.]



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different mechanisms. Still, this provides a potentially usefulframework in which to interpret these observations.

5. AGE-MASS RELATIONS AND CLUSTERING

In Figure 11 we compare the mean age of BHs of a givenz 0 mass with that of the stellar population of their hosts. At

a given redshift, the characteristic QLF luminosity L(z) andcorresponding characteristic active mass MBH from Figure 2define the epoch of growth of BHs of that mass. The typicalage of BHs of that mass will be the time since this epoch. Indetail, equation (4)relates the observed QLFto the rate at whichBHs of a given relic mass are formed as a function of redshift.We adopt the fits to this equation given in Hopkins et al. (2007),which use the model quasar light curves determined in Hopkinset al. (2006a, 2006b) to calculate the time-averaged rate of for-mation of individual BHs as a function of mass and redshift, toestimate the median age (peak in rate of formation/creation ofsuch BHs as a function of time) and 25%Y75% interquartilerange in formation times. This introduces some model depen-dence, but as discussed in x 2 a similar result is obtained using

very different methodologies, including purely empirical, sim-

plified models (Yu & Tremaine 2002; Merloni 2004; Marconiet al. 2004; Shankar et al. 2004), or direct calculation from ob-served Eddington ratio distributions ( Vestergaard 2004; McLure& Dunlop 2004; Kollmeier et al. 2006).

In any case, we recover the well-known trend that the moremassive BHs are formed at characteristically earlier times (Salucci

et al. 1999; Yu & Tremaine2002; Ueda et al. 2003; Heckman et al.2004; Hasinger et al. 2005; Merloni 2004; Marconi et al. 2004;Shankar et al. 2004; McLure & Dunlop 2004; Kollmeier et al.2006). This is not surprising, as most massive BHs must be inplace by z$ 2 to power the brightest quasars, and these objectsare generally dead by low redshift (with lower mass objectsdominating the local QLF, e.g., Heckman et al. 2004).

Given a BH mass, we can compare with the observationallydetermined age of the typical host galaxy (with MBH Mgal).First, we consider early-type hosts, specifically the stellar agesof host spheroids of BHs at each mass MBH. The mean ages (anddispersion about that mean) of ellipticals as a function of stellarmass have been estimated in a number of studies, recently forexample by Gallazzi et al. (2005, 2006), who fit SDSS spec-

tra ( line indices) and photometry for$175,000 local galaxies

Fig. 11.Left: The toppanel shows the meanz 0 age (look-back timeto themean formation epoch) of BHs as a function of mass (black solid line; the dashedlinesshow 25%75% quartile ranges), compared to the stellar population age of their hosts. Ages of spheroids as a function of mass (with MBH Mgal) are shown (circles)from Nelan et al. (2005; NFPS; squares), Gallazzi et al. (2006; SDSS; stars), Thomas et al. (2005; field subsample; circles). Errors show the dispersion in ages at a givenmass. The bottom panel uses this age to predict quasar clustering as a function of redshift; i.e., assuming the quasar epoch of spheroids of a given mass is associated with

the termination of star formation (the black lines are as labeled; the circles show observed quasar clustering as in Fig. 6). Center: Same, for ages of host disks; ages from-model fits of Bell & de Jong (2000; ) and Gavazzi et al. (2002; ); the offset between them owes to the choice of initial time in the -model. The solid and dotted lines as-sume MBH / Mbulge and MBH / (Mdisk Mbulge), respectively. The dashed lines recalculate the age for a single-burst SFH. The bottom panel again uses this age to predictquasarclustering as a function of redshift (asin theleft panels) assumingthat quasaractivityis associatedwiththe starformation epoch (aslabeled).Right: Thesolidlineshowsthe all progenitor age (DM; downsizing from Neistein et al. 2006); the dashed line shows the age of the main progenitor halo, and the dotted line shows the time whenhalo crossed the quenching mass from Dekel & Birnboim (2006). The bottom panel again uses this age to predict clustering (as in the left and middle panels), assumingquasar age is equal to the halo age as labeled. [See the electronic edition of the Journal for a color version of this figure.]



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to various realistic star formation histories, including a mix ofcontinuous and/or starbursting histories while allowing mass,total metallicity, and abundance ratios to freely vary. Theyquote r-band light-weighted ages, which for our purposes areeffectively equivalent to the ages determined by fitting a singlestellar population (SSP) or single-burst model to observedspectra, and indeed agree very well with best-fit SSP ages fromsimilar SDSS samples (Clemens et al. 2006; Bernardi et al.2006) and previous studies (Jrgensen 1999; Trager et al. 2000;Kuntschner et al. 2001; Caldwell et al. 2003; Bernardi et al.2005; Nelan et al. 2005; Thomas et al. 2005; Collobert et al.2006; see Renzini 2006 for a review) as a function of ellipticalstellar mass. A similar result is also obtained independently byTreu et al. (2005) and di Serego Alighieri et al. (2006) fromstudies of the fundamental plane evolution of early-type galax-ies. Note that the error bars shown are the measured dispersionsin the population about the mean age at a given mass, not the un-certainties in the mean ages themselves (which are smaller;$0.2 Gyr statistical, $1 Gyr systematic; see Nelan et al. 2005).The agreement between BH and host stellar ages is good at allmasses; both the trend and dispersion (interquartile or 1

range) about it are similar (

2

/$ 8/17 for a direct comparison).If the age of its stellar populations is indicative of when thequasar epoch occurred in a given host, then, without makingany assumptions about the masses of black holes or quasarEddington ratios, we can use the mean age of stellar popula-tions to predict quasar clustering. In this scenario, ellipticals ofmass M, with mean age thost, would represent the populationlighting up as quasars at a look-back time of thost, and so thequasar bias at that look-back time should be the local bias ofellipticals of mass M(eq. [7]), evolved to the appropriate look-back time thost with eq. [1]). Figure 11 compares this expecta-tion with the observed quasar bias as a function of redshift.Despite the very simple nature of this model, which ignores boththe range of ages at a given Mand, similarly, the range in host

masses at a given time, the agreement is reasonable. Includingthe dispersion in ages, i.e., modeling the age distribution at eachMBH as a Gaussian with the observed scatter, improves the agree-ment and yields a nearly identical prediction of bias as a func-tion of redshift to that in Figure 6 (solid black line).

We can of course repeat these exercises for other possiblehost populations. We next consider correlations with the starformation histories of late-type or star-forming host galaxiesi.e., the possibility that quasar activity is generically associatedwith star formation. The observed star formation histories aresimilarly estimated, generally by fitting to exponentially declin-ing models (-models; star formation rate M/ exp (t ti)/since an initial cosmic time ti). Specifically, we consider the fitsof late-type ages as a function of stellar mass from Bell & de Jong

(2000) and Gavazzi et al. (2002) (consistent with Jansen et al.2000; Bell et al. 2000; Boselli et al. 2001; Kauffmann et al.2003a; Perez-Gonzalez et al. 2003; Brinchmann et al. 2004;MacArthur et al. 2004; Gallazzi et al. 2005). The mass-weightedage is calculated from the model SFR (see Bell & de Jong 2000,eq. [3]). Bell & de Jong (2000) and Gavazzi et al. (2002) tech-nically quote the age and metallicity as a function of K- andH-band absolute magnitudes, respectively, but given their quotedbest-fit stellar population models at each luminosity, it is straight-forward to calculate the corresponding mass-to-light ratios (M/LKand M/LH) and convert the observed luminosities to total stellarmasses. To convert to a corresponding BH mass, we considerfirst a uniform application of the local BH-host mass relation,i.e., assuming that BH mass is correlated with totalstellar mass,

and second determining the mean bulge-to-disk ratio for a given

total late-type stellar mass or luminosity (see Fukugita et al.1998; Aller & Richstone 2002; Hunt et al. 2004 for the appro-priate mean B/Tfor different masses/luminosities) and assum-ing that BH mass is correlated with the bulge mass only. Becausethe trend of age as a function of stellar mass is weak, consideringthe total mass or bulge mass makes little difference in our com-parison, and we subsequently consider the observationally pre-ferred correlation between BH and bulge mass.

The mean age of a given population derived from differentmodel star formation histories will, of course, be weighted dif-ferently. To show the systematic effects of such a choice, weroughly estimate the equivalent age from a single burst or SSPmodel. We calculate the z 0 observed (B V) color at eachmass from the mean best-fit models, and then calculate thecorresponding age for the same (B V) of a single burstmodel(of the same metallicity as a function of mass) from the modelsof Bruzual & Charlot (2003) with a Salpeter (1955) IMF. Al-though most of the observations above find this SSP approxi-mation is not good for star-forming galaxies, it illustrates animportant point. The SSP ages are weighted toward the youn-gest, bluest stellar populationsessentially functioning as an

indicator of the most recent epoch of significant star formation,and are therefore quite young (P2 Gyr; similar to the typical timesince recent low-level starbursting activity found in late-typeswith the more realistic star formation histories in Kauffmannet al. 2003a). However, the trend as a function of mass is un-changed and the overall agreement is worse. Therefore, whilethe systematic effects here are substantially larger than the mea-surement errors in mean age as a function of mass, they cannotremedy the poor agreement with the ages of BH populations.

We again use this age as a function of total/bulge mass, andthe observed clustering of late-type galaxies from Figure 1 atz 0, to estimate what the quasar bias as a function of redshiftshould be, if these systems were the hosts of quasars and theirquasar epoch were associated with the age of their stellar pop-

ulations. The predictions are inconsistent with the observationsat high significance (>4.5 ), regardless of the exact age adopted(-model or SSP). In fact, the predicted clustering as a functionof redshift is highly unphysical (owing to the fact that there isrelatively little difference in ages, but strong difference in clus-tering amplitudes from the least to most massive disks). Ulti-mately, this demonstrates that the hypothesis that quasar activitygenerically traces star formation is unphysical. This is also sup-ported by the fact that the integrated global star formation rateand quasar luminosity density evolve in a similar, but not iden-tical manner from z $ 0Y6 (e.g., Merloni et al. 2004).

We next consider the possibility that quasar activity traces pure dark matter assembly processesi.e., that the buildupof BHs in quasar phases purely traces the formation of their

host halos. Given the local BH-host stellar mass relation fromMarconi & Hunt (2003) and the typical halo mass as a functionof early-type hosted galaxy mass calibrated from weak lensingstudies by Mandelbaum et al. (2006) we obtain the mean hosthalo mass as a function of BH mass (meanMhalo $ 4 ; 10

4 MBH;although the relation is weakly nonlinear). For our adopted cos-mology, we then calculate the mean age (defined as the time atwhich half the present mass is assembled) of the main progenitorhalo for z 0 halos of this mass. Error bars are taken from anensemble of random EPS merger trees following Neistein et al.(2006). Knowing the mass of a halo at a given redshift, we cal-culate its clustering following Mo & White (1996) as in x 4, anduse this combined with the mean ages to estimate the expectedquasar clustering as a function of redshift if quasars were asso-

ciated with this formation/assembly of the main progenitor halo.



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Although the exact age will depend on cosmology andthe adoptedthreshold mass fraction at which we define halo age, theresult is the same, namely, we recover the well-known hierarchicaltrend in which the most massive objects are youngest, in contra-diction with quasar/ BH ages.

However, Neistein et al. (2006) have pointed out that themean assembly time, considering allprogenitor halos, can ex-hibit so-called downsizing behavior. We therefore follow theircalculation of the mean age of all progenitors as a function ofz 0 halo (and corresponding BH) mass, and also use this toestimate quasar clustering as a function of redshift. Again, al-though the systematic normalization depends somewhat on ourdefinitions, it is clear that the recovered downsizing trend is,as the authors note, a subtle effect, and not nearly strong enough(inconsistent at >10 ) to explain the downsizing of BH growth.Again, the absolute value of the age obtained can be systemati-cally shifted by changing our definition of halo assembly time, but the trend is not changed and significance of the disagreementwith BH formation times is still high.

Certain feedback-regulated models predict that black hole massshould be correlated with halo circular velocity (as MBH / v

5c or

/v

4

c ; Silk & Rees 1998; Wyithe & Loeb 2003), rather than halomass. To consider this, we have recalculated the all progenitorand main progenitor ages, but instead adopted the time atwhich the appropriate power of the circular velocity (v5c orv

4c )

reaches half the z 0 value. Because, for a given halo mass, vcis larger at higher redshift, this systematically shifts both agesto higher values, but the trends are similar. In each case the re-sulting ages disagree with the quasar/BH ages at even highersignificance.

Alternatively, some models (Birnboim & Dekel 2003; Binney2004; Keres et al. 2005; Dekel & Birnboim 2006) suggest thata qualitative change in halo properties occurs at a characteristicmass, above which gas is shock-heated and cannot cool efficiently,forming a quasi-static hotaccretion mode in which quasar feed-

back can act efficiently. Although there is no necessary reasonwhy quasar activity should be triggered by such a transition, itsposited association with quasar feedback leads us to consider thispossibility.

Knowing the mean z 0 halo mass for a given MBH, we plotthe age at which the main progenitor halo mass surpassed thecritical quenching mass defined as a function of redshift inDekel & Birnboim (2006). Since this amounts to a nearly con-stant characteristic halo mass $;1011Y1012 M, the expectedquasar clustering as a function of redshift is not unreasonable(see Fig. 6; there is a systematic offset, but this is sensitive to theadopted cosmology). However, this model actually predicts toosteep a trend of age with mass (inconsistent at >6 ). The agesof the most massive systems are reasonable (which, in compar-

ison to the ages of ellipticals, has been widely discussed; Dekel& Birnboim 2006; Croton et al. 2006; De Lucia & Blaizot 2007),but the host halo of a typical $108 M BH (i.e., Schechter i)crosses the threshold halo mass a mere $5 Gyr ago, predicting,in this simple model, that these BHs should have been the char-acteristic active systems atz $ 0:5 instead of the observed z $1:2Y1:5. At lower masses, the mean z 0 halos are only justat, or are still below, this critical halo mass. Given the scatter inthe BH-host mass relations, there will be some BHs of thesesmaller masses living in larger halos which have already crossedthe quenching mass, but the age distribution will still be one-sided and weighted to very young ages. To match the observedage trend, there must, in short, be some process which can trig-ger quasar activity at other halo masses before they cross the

quenching threshold.

Finally, we note that in evolving the clustering of local sys-tems up in redshift in the lower panels of Figure 11, theremight be some ambiguity (if, for example, a given z 0 halois assembled from many progenitor high-redshift halos with sig-nificantly different properties). The simple evolution predictedby equation (1) is derived from pure gravitational motions, andtherefore as applied moving backward in time represents aneffective mean bias of the progenitors of thez

0 system (see

Fry 1996). To the extent, however, that there is a dominant pro-genitor halo at a given redshift and many smaller halos which willbeaccreted by the main halo,it is theproperties of the main pro-genitor which are of interest here.

We therefore consider a completely independent approach toempirically compare the clustering measurements shown, whichattempts to capture these subtleties. Given a z 0 population,we can estimate its characteristic host halo mass either directlyfrom the measurements of Mandelbaum et al. (2006) or indi-rectly by matching the observed bias [with bias as a function ofhalo mass calculated for the adopted cosmology following Mo& White (1996) and Sheth et al. (2001) as in x 4]. FollowingNeistein et al. (2006) we then calculate the mass of the main

progenitor halos of thisz 0 mass, as a function of redshift (i.e.,the highest-mass branch of the EPS merger tree at each red-shift). At the redshift of interest (e.g., appropriate look-back time,for the comparisons in the lower panels of Fig. 11), we then cal-culate the expected bias for halos of this main progenitor mass.

Figure 12 reproduces the lower left comparison in Figure 11(the expected clustering of elliptical progenitors at the times de-termined by their stellar population ages), using both our pre-viously adopted methodology and this revised estimation. Thelatter method has the advantage, as noted above, of accountingfor the difference between the main progenitor and smaller, ac-creted systems. The approach, however, suffers from certain in-herent ambiguities in Press-Schechter theory. For example, thecalculated evolution is not necessarily time-reversible, and the

clustering properties are assumed to be a function of halo massalone, which recent high-resolution numerical simulations sug-gest may not be correct (e.g., Gao & White 2007; Harker et al.2006a; Wechsler et al. 2006). In particular, if quasars are trig-gered in mergers (i.e., have particularly recent halo assemblytimes for their postmerger halo masses), then they may repre-sent especially biased regions of the density distribution. Unfor-tunately, it is notclearhow to treat this in detail, as there remainsconsiderable disagreement in the literature as to whether or not asignificant merger bias exists (see, e.g., Kauffmann & Haehnelt2002; Percival et al. 2003; Furlanetto & Kamionkowski 2006).Furthermore the distinction between galaxy-galaxy and halo-halo mergers (with the considerably longer timescale for mostgalaxy mergers) means that it is not even clear whether or not,

after the galaxy merger, there would be a significant age bias. Inany case, most studies suggest that the effect is quite small: usingthe fitting formulae from Wechsler et al. (2002); Wechsler et al.(2006) we find that even in extreme cases (e.g., a M3Mvir halomerging atz 0 as opposed to an average assembly redshiftzf % 6) the result is that the standard EPS formalism under-estimates the bias by %30%. For the estimated quasar host halomasses and redshifts of interest here, the maximal effect isP10%at all z 0Y3, much smaller than other systematic effects wehave considered. This is consistent with Gao & White (2007)andCroton et al. (2007), who find that assembly bias is only im-portant ( beyond the 10% level) for the most extreme halos orgalaxies in their simulations.

In practice, Figure 12 demonstrates that, for the halo masses

of interest here, the two methods yield very similar results. This



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is reassuring, and owes to the fact that the differences from thechoice of methodology discussed above are important only atvery high or very low halo masses, where for example the clus-tering of small halos which are destined to be accreted as sub-structure in clusters (k1015 h1 M) will be very different fromthe clustering of similar-mass halos in field or void environments.Alternatively, one can think of the EPS approach as attempting

to account for the possibility that bias is a nonmonotonic func-tion of mass (e.g., rising galaxy bias at very low luminosities(Norberg et al. 2002 and references therein), which Figure 1demonstrates is important only at masses well below those ofinterest here. To the extent that any merger bias is permanentor long-lived (as expected if the excess clustering is correlatedwith halo concentration or formation time), our standard meth-odology should account for it, as we simply evolve the clusteringof the present hosts of quasar relics to earlier times accordingto gravitational motions. That the different seen is small providesa further reassurance that the effects of merger bias are prob-ably not dramatic. Ultimately, we have recalculated all the resultsherein adopting the more sophisticated (but more model-dependentand potentially more uncertain) EPS approach, and find that it

marginally improves the significance of our conclusions but leavesthem qualitatively unchanged.

6. IMPLICATIONS FOR HIGH-REDSHIFT CLUSTERING

At zk2Y3, comparing quasar and early-type clustering be-comes more ambiguous. Above z $ 2, the QLF turns over,and the density of brightquasars declines. Specifically, it appearsthat the characteristic quasar luminosity L declines (Hopkinset al. 2007 and references therein), at least from z $ 2 to z$ 4:5above which the break L can no longer be determined. Onepossible interpretation of this is an extension of our analysis forzP2; i.e., one could assume that each quasar episode heresignals the end of a BHs growth, which will evolve passivelyto z 0. At z 0, the tightness of the local BH-host relations

means the hosts must have the appropriate mass and lie within

the appropriate halos, to within a factor$2 of the observed scat-ter. Therefore, we can adopt the same approach as in x 4 to usethe local observed clustering as a function of host properties toevolve back in time and predict quasar clustering as a function ofredshift.

Figure 13 shows the bias and correlation length predicted bythis approach, an extension of the model (eq. [8]) we have con-

sidered atzP

2. Figure 14 also shows the typical host halo masscorresponding to the predicted clustering as a function of red-shift (for our adopted cosmology); in this simple extension ofthe zP3 case, the observed decline in the QLF L traces a de-cline in the characteristic (although not most massive) quasar-hosting halo mass.

However, at high redshifts, flux limits may severely bias clus-tering measurements. Although atL < L, quasar clustering doesnot strongly depend on the quasar luminosity (see x 3), implying awell-defined characteristic active mass that we can adopt (see alsoLidz et al. 2006), this is not necessarily true for L > L. In fact,Figure 3 shows (and observations may begin to see; e.g., Porciani& Norberg 2006) a steepening of bias versus luminosity at L >L, reflecting the uniformly high observed quasar Eddington

ratios (Vestergaard 2004; McLure & Dunlop 2004; Kollmeieret al. 2006) at high luminosities, which imply the bright end ofthe QLF (L3L) becomes predominantly a sequence in activeBH mass. To the extent that BH mass traces host mass, then,these systems reside in more massive hosts and will be morestrongly biased.

In order to estimate how this will change the observed clus-tering, we roughly approximate this effect as follows. For a givenflux limit at a given redshift there is a reasonably well-definedsurvey depth, to a minimum luminosityLmin. If this is sufficientlydeep to resolve the QLF break, i.e., Lmin < L, then the weakobserved dependence of clustering on luminosity means the ob-served clustering will trace that characteristic of $L quasarscorresponding to characteristic MBH active BHs and Mgal %

MBH/ hosts (our fiducial model, and the case for all observations

Fig. 12.Observed clustering of quasars, compared to that inferred from their z 0 early-type hosts if the termination of star formation is coincident with quasaractivity (as in the bottom left panel in Fig. 11). Left: Our standard methodology is used to empirically evolve the clustering of local systems (black circles) to the redshiftsshown.Right: Instead,using the full EPS formalismand estimated b(Mhalo;z) to evolvethe clustering of local systems.Differences owing to thechoice of methodologyaresmall at the halo masses of interest. [See the electronic edition of the Journal for a colorversion of this figure.]



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plotted in Fig. 13). However, if the flux limit or redshift is suffi-ciently high such thatLmin > L, then the survey will not samplethese characteristic host masses. In this case, we consider the biasas a function of luminosity plotted in Figure 3 from the models ofHopkins et al. (2006b); Lidz et al. (2006) evaluated at Lmin at thegiven redshift. Qualitatively, for the nearly constant Eddingtonratios observedatL > L,L / MBH / Mgal, weexpectLmin > Lto correspond to an approximate minimum observed host mass,Mmin $ Mgal(L)(Lmin/L) $ MEdd(Lmin)/. Since the QLF slopeis steep at L > L, objects nearLmin orMmin will dominate the

observed sample, and so this amounts to calculating the clus-tering for this mass, instead of Mgal(L), at the given redshift.We caution that this is a rough approximation to more realisticselection effects, but should give us some idea how flux limitswill bias the observed clustering.

We consider several representative flux limits, in observed-frame i-band, typical of optical quasar surveys (e.g., the SDSS),in addition to the case with effectively infinite depth (mi < 30).We calculate L at the appropriate rest-frame wavelengths asa function of redshift using the fits to L from Hopkins et al.(2007) spanning z $ 0Y6 and spanning the relevant rest-framewavelength intervals. At the limits of most current optical sur-veys, mi < 20:2, the QLF breakL is only marginally resolvedat z $ 2Y3, and so above this redshift surveys are systemati-

cally biased to more massive L > L BHs and higher clustering

Fig. 13.Using the model in Figs. 1 and 6 to predict the observable clustering of quasars at high redshifts zk 3. Observed clustering is shown (circles) as in Fig. 1.Different lines show the effect of different observed-frame i-band flux limits, as labeled (note i 20:2 corresponds to the SDSS DR3 completeness limit; Richards et al.2006a). Left panels assume efficient feedback at high redshifts; i.e., that BH growth shuts down after each quasar episode. The center panels assume that all z> 2 BHsgrow with the observed QLF to the characteristic peak luminosities atz$ 2, then shut down (inefficient feedback). The right panels assume quasar growth tracks hosthalo growth, even after a quasar episode, until z 2 (maximal growth). Future observations at z$ 4 with moderately improved flux limits mi < 22 should be able to

break the degeneracies between these models. [See the electronic edition of the Journal for a colorversion of this figure.]

Fig. 14.Characteristic inferred quasar-hosting halo mass corresponding tothe model clustering as a function of redshift shown in Fig. 13, for our adoptedcosmology. Dotted, dashed, and dot-dashed lines are for the appropriate fluxlimits as in Fig. 13. The black, blue, and red lines show the left, center, and rightmodels (efficient feedback, growth to typical z$ 2 quasars, and maximalgrowth, respectively) from Fig. 13 with effectively infinitely deep flux limits(i < 30); allare identicalbelowz $ 2:6. [Seethe electronic edition of theJournal

for a colorversion of this figure.]



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amplitudes. However, a relatively modest improvement in depthto mi < 22 would allow unbiased clustering estimates to be ex-tended to z $ 4.

We have so far assumed that BHs effectively shut downafter their quasar epochi.e., efficient feedback even at highredshifts. Although the various observations discussed above(Eddington ratio distributions, quasar host measurements, HODmodels, black hole mass functions, and our clustering compari-son) demand this be true atzP2

Y3, there are no such constraints

atzk3. In other words, it is possible that the increase in the QLFfrom z $ 6 to z $ 3 traces the growth of the same populations ofBHs, not the subsequent triggering and shutdown of differentpopulations. If BHs atz $ 6 continue to grow to z $ 2Y3 beforeshutting down, they must live in more massive z 0 hostgalaxies (to preserve the tight observed BH-host mass relation),and thus should have stronger clustering amplitudes. We there-fore consider two representative simple models which bracketthe range of possibilities for this growth and present simple testsfor future clustering measurements to break the degeneracy be-tween these models.

First, we assume that quasars grow with the QLF to z $ 2

before shutting down (i.e., inefficient feedback). In sucha case, z $ 6 quasars grow either continuously or episodicallywith their host systems until the epoch where downsizingbegins, and the QLF at all redshifts z> 2 represents the samesystems building up hierarchically. The z 0 relic masses (andtherefore z 0 characteristic host masses, from which we cal-culate the parent halo clustering as a function of redshift) arethen the same at all z ! 2. This is also equivalent to a pure den-sity evolution model for the high-redshift QLF, as in Fan et al.(2001) in which the QLF break luminosity L remains constantabove z $ 2Y3 while the number density/normalization uni-formly declines. Such a model is marginally disfavored by cur-rent measurements (Hopkins et al. 2007), but constraints onL athigh redshifts are sufficiently weak that it remains a possibility.

The clustering as a function of redshift in this model behavesvery differently from the previous model at high redshifts. Ifobjects cannot grow after their quasar epoch even at high red-shifts, then the subsequent decline of the QLF L traces a declinein characteristic active masses, and the bias of active systemsturns over; however, if all grow to the characteristic L atz $ 2, then these high-redshift systems all represent similarz 0 masses by the time they shut down, and must be in-creasingly biased at higher redshifts.

Next, we consider a maximal growth model, in which weassume not only that the buildup of the QLF represents the con-tinued growth of BHs until z$ 2, but also that this growthproportionally tracks the typical growth of dark matter halosover this redshift range. We very crudely estimate the typical

growth with the growth of an average high-redshift quasarhost halo. Based on their space density and BH mass, Fanet al. (2001; 2003) estimate that typical z$ 5Y6 SDSS quasarsrepresent $6 overdensities. We therefore assume that qua-sars at a given redshiftz> 2, with a typical L and correspond-ing MBH at that redshift, will grow by the same proportionalamount as a halo which represents a 6 fluctuation (charac-teristic of halos hosting observed z $ 6 quasars, Y. Li et al.2006b) from the observed redshift to z 2, after which growthshuts down. This then yields the z 0 BH mass, corre-sponding host mass, and evolved clustering. Note that, althoughsimilar, this is not the same as assuming quasars track 6 over-densities atz> 2, because to the extent that the QLF L does notgrow by the same proportionality, this model effectively allows

new or different BHs/host halos to dominate the QLF at differ-

ent redshifts. It simply mandates that they all grow at this rapidrate. For example, an observedz $ 6 B H o f $108M is assumedto reach a mass of 2 ; 109 M atz 2 (and then shuts down, sothat this is also the mass at z 0), and a $108 M observedquasar atz 4 will grow to $5 ; 108 M. The choice of rate isarbitrary, we choose it as a reasonable upper limit. In any case,the predicted evolution of the bias as a function of redshift isextremely steep, so the exact values will be very sensitive tothe growth model and adopted cosmology. The point we wishto illustrate is that this model generically predicts a steep biasevolution atz> 2, which regardless of the details will be dis-tinguishable if future quasar clustering measurements at z 3Y4 can be extended to a depth ofmi < 22.

Note that extending the depth of quasar surveys to mi < 22will move further down the QLF and increase the density ofquasars observed, meaning a smaller survey can be used to con-strain the clustering to comparable accuracy as the SDSS or 2dF.Using the Hopkins et al. (2007) QLF to estimate the relevantspace density of quasars above the flux limit as a function of red-shift and assuming the errors in clustering amplitude relative tothosein Croom et al. (2005) scale asN1/2qso , we estimate that for the

redshift interval 3:5 < z< 4:5 (3:75 < z< 4:25) a field size of$25 deg 2 (50 deg2) would be sufficient to distinguish betweenthe first two models (efficient high-redshift feedback and all high-redshift quasars growing to z $ 2 luminosities) at $2.53 .The last model (maximal evolution) predicts an even more ex-treme departure in clustering properties, and could be distin-guished or ruled out at$2.5Y3 by clustering observations from2:75 < z< 3:25 in just a$815 deg2 field.

7. DISCUSSION/CONCLUSIONS

We compare the clustering of quasars and different galaxypopulations as a function of morphology, mass, luminosity, andredshift, and demonstrate that these comparisons can be used torobustly rule out several classes of models for quasar triggering

and the association between quasar and galaxy growth. In eachcase, the observations favor a model which associates quasarswith the formation event of ellipticals, a strong prediction oftheoretical models which argue that major, gas-rich mergers formellipticals and trigger quasar activity (Hopkins et al. 2006b).

The predicted bias as a function of mass/luminosity for sys-tems which once hosted quasars agrees well at all masses andluminosities with that observed for early-type populations. Inother words, the clustering of an Mgal elliptical galaxy is exactlywhat we would expect if these galaxies, which typically containMBH Mgal ( $ 0:001 Magorrian et al. 1998; Marconi &Hunt 2003; Haring & Rix 2004) BHs, represented the dominanthosts of the quasar population for a brief period, setting L atthat redshift with an Eddington-limitedL LEdd(MBH) epoch

of activity. In the most basic sense, this is a confirmation that el-lipticals today were indeed the host population of high-redshiftquasars (see also Porciani et al. 2004; Croom et al. 2005), withthe appropriate corresponding BH masses. This should not besurprising, since the Soltan (1982) argument demonstrates thatmost BH mass must have been accumulated in bright, near-Eddington quasar epochs, and the tightness of the localBH-host mass relation (and similar BH mass-host property rela-tions, see Novak et al. 2006) argues that BH growth must betightly coupled to the host properties. However, there are ad-ditional nontrivial implications.

First, this implies that there really is a characteristic host andBH mass active at a given epoch, traced by the QLF L. Thisis an important prediction of certain theoretical models for qua-

sar light curves (Hopkins et al. 2005b, 2005c), and supported



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by other lines of observation above. Furthermore, this impliesthat the formation epoch for BHs of a given mass must berelatively short in time, as continually adding BHs of a givenmass (at lower Eddington ratio or in radiatively inefficient states)to the population would dilute the agreement in Figure 1. Qua-sars are active in characteristically different parent halo popula-tions at different redshiftsi.e., most systems cannot undergomultiple separate periods of quasar activity, at least at zP 2.We find further support for this by considering observed quasarclustering as a function of luminosity, which favors the pre-dictions of Lidz et al. (2006); namely, a relatively weak trendof bias as a function of luminosity. In fact, the combination ofquasar clustering measurements as a function of luminosityand redshift supports at high significance previ

Philip F. Hopkins et al- The Co-Formation of Spheroids and Quasars Traced in their Clustering

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Transcript of Philip F. Hopkins et al- The Co-Formation of Spheroids and Quasars Traced in their Clustering