BH Accretion in Low-Mass Galaxies Since z~1
Yong Shi, George Rieke, Jennifer Donley, Michael Cooper, Christopher Willmer, Evan Kirby
aa r X i v : . [ a s t r o - ph ] O c t Draft version October 19, 2018
Preprint typeset using L A TEX style emulateapj v. 11/26/04
BH ACCRETION IN LOW-MASS GALAXIES SINCE Z ∼ Yong Shi , George Rieke , Jennifer Donley , Michael Cooper , Christopher Willmer , Evan Kirby Draft version October 19, 2018
ABSTRACTWe have selected a sample of X-ray-emitting active galactic nuclei (AGNs) in low-mass host galaxies( ∼ × - 2 × M ⊙ ) out to z ∼
1. By comparing to AGNs in more massive hosts, we have foundthat the AGN spatial number density and the fraction of galaxies hosting AGNs depends strongly onthe host mass, with the AGN host mass function peaking at intermediate mass and with the AGNfraction increasing with host mass. AGNs in low-mass hosts show strong cosmic evolution in comovingnumber density, the fraction of such galaxies hosting active nuclei and the comoving X-ray energydensity. The integrated X-ray luminosity function is used to estimate the amount of the accretedblack hole mass in these AGNs and places a strong lower limit of 12% to the fraction of local low-massgalaxies hosting black holes, although a more likely value is probably much higher ( > Subject headings: galaxies: nuclei – galaxies: active – X-rays: galaxies INTRODUCTION
Active galactic nuclei (AGNs), the manifestationof accretion onto massive black holes (MBHs), havebeen recognized as a critical ingredient in galaxy for-mation and evolution. The demography of localgalaxies suggests that most – perhaps all – massivegalaxies host MBHs at their centers and that MBHmasses are correlated with the galaxy bulge prop-erties (Kormendy & Richstone 1995; Magorrian et al.1998; Gebhardt et al. 2000; Ferrarese & Merritt 2000;H¨aring & Rix 2004), implying the coevolution of thegalaxy and MBH. The good match between thelocal BH mass density and the mass density ofAGN relics further suggests that all massive galaxieshave experienced an AGN phase during their evolu-tion (e.g. Aller & Richstone 2002; Shankar et al. 2004;Marconi et al. 2004). Energy feedback from AGNs totheir host galaxies is invoked to explain different as-pects of massive galaxy evolution. AGNs may serve asthe heating sources for cooling flows in clusters (e.g.McNamara & Nulsen 2007). They may suppress starformation in their host galaxies and cause them to mi-grate from the blue cloud to the red-sequence in thecolor-magnitude plot (Croton et al. 2006; Nandra et al.2007; Georgakakis et al. 2008) and they may account for“down-sizing” galaxy evolution (e.g. Cowie et al. 1996).As the most abundant population in the universe, low-mass (defined as stellar mass M ∗ < × M ⊙ throughthis paper) galaxies act as the building blocks of massivegalaxies. However, the current understanding of MBHs’role in low-mass galaxy evolution is limited, leaving uswith some basic questions: Is the existence of BHs in low-mass galaxies as common as it is in massive galaxies? Arethere two types of low-mass galaxy populations (i.e. oneswith BHs vs. ones without BHs)? How many low-massgalaxies experience an AGN phase? All of these ques- Steward Observatory, University of Arizona, 933 N CherryAve, Tucson, AZ 85721, USA UCO/Lick Observatory, Department of Astronomy and Astro-physics, University of California, Santa Cruz, CA 95064 Spitzer Fellow tions are related to a more basic astrophysical problem:what is the black hole occupation function (BHOF; thefraction of galaxies hosting either active or quiet BHs) inlow-mass galaxies?Searching for BHs in low-mass systems offers an uniqueopportunity to extend the MBH- σ correlation for mas-sive galaxies, which not only tests the universality of therelation but also is required to understand the originof the relation. Although the MBH- σ relationship hasbeen confirmed for low-mass systems in the local universe(Barth et al. 2005), some works suggest that the MBH- σ relationship may be replaced at low mass by a similar re-lation involving compact stellar nuclei (Wehner & Harris2006; Ferrarese et al. 2006; Rossa et al. 2006).A better understanding of primordial MBH seedgrowth in the early universe may also benefit from thestudy of BHs in low-mass galaxies, as such work couldreveal aspects of the accretion mode in a low gravita-tional potential and low metallicity environment and ofthe relative importance of mass growth through accre-tion and merging processes. For example, in low-massgalaxies, the impulsive kick from anisotropic gravita-tional emission during BH-BH mergers is thought to bestrong enough to eject central BHs (Favata et al. 2004;Merritt et al. 2004). Understanding AGN activity inlow-mass galaxies can further constrain MBH seed for-mation theories. In a cold dark matter universe, theprimordial MBH seeds form as remnants of PopulationIII stars (e.g. Madau & Rees 2001) or through the directcollapse of pre-galactic gas disks (Lodato & Natarajan2006). The efficiencies in different formation scenariospredict a wide range in the local BHOF in low-massgalaxies which can vary from zero to unity, while theprediction of the BHOF in massive galaxies is invariablyunity as constrained by observations (Volonteri et al.2008).The current study of BHs in low mass galaxiesis mostly limited to low redshift ( z < Chandra and
XMM-Newton
X-ray surveys, wehave searched for X-ray emitting AGNs in low-mass hostgalaxies out to z ∼
1. In this paper, we first describethe identification of AGNs in low-mass galaxies (see § § V max method to correctfor incompleteness in § §
5. In §
6, wediscuss the local BHOF in low-mass galaxies constrainedby our study of high redshift AGNs in such galaxies. Ourconclusions are presented in §
7. Throughout this paper,“low-mass” refers to normal galaxies or AGN host galax-ies with stellar mass M ∗ < × M ⊙ and “massive”indicates those with stellar mass M ∗ > × M ⊙ . Weadopt a cosmology with H =70 km s − Mpc − , Ω m =0.3and Ω Λ =0.7. All magnitudes are defined in the AB sys-tem. DATA: X-RAY SURVEY FIELDS
We have searched for AGNs in low-mass host galax-ies in five
Chandra and
XMM-Newton fields, includ-ing the All-Wavelength Extended Groth Strip Interna-tional Survey (AEGIS), the
Chandra
Deep Field-NorthSurvey (CDF-N), the
Chandra
Deep Field-South Survey(CDF-S), the
Chandra
Large-Area Synoptic X-Ray Sur-vey (CLASXS) and the
XMM-Newton
Large Scale Struc-ture Survey (XMMLSS). Table 1 lists the properties ofthese five fields, including the area, the limiting hard X-ray flux, the available optical/near-IR photometry, thedefinition of secure (multiple-line) spectroscopic redshiftsand the associated references.All the X-ray fields are fully covered by optical/near-IR photometry. For the CDF-N, CDF-S and CLASXSfields, spectroscopic observations have been obtained forX-ray sources, while the redshifts of X-ray objects in theremaining two fields are obtained by matching X-ray cat-alogs to galaxy redshift survey catalogs. Table 2 summa-rizes the total number of X-ray sources and of spectro-scopic targets. The search radii for optical counterpartsto the X-ray sources are 2.0 ′′ and 2.5 ′′ for the Chandra and
XMM-Newton fields, respectively. The optical coun-terparts are identified using R -band catalogs, which gen- erally provide the deepest observations. If multiple opti-cal objects within a search aperture are present, the clos-est one is defined as the optical counterpart. The fractionof X-ray objects with multiple optical sources within asingle aperture is only ∼ §
3) and thus the majority of the optical counterpartsare brighter than 24 in the R -band. At R <
24, the sur-face density of galaxies and stars is about 16.6 arcmin − (Capak et al. 2004). The probability for chance superpo-sition between X-ray and optical sources is 6% and 10%for the Chandra and
XMM-Newton fields, respectively.Given a total of 32 low-mass AGN hosts in the
Chandra fields and zero in the
XMM-Newton field, we have esti-mated that only two objects are expected to have spuri-ous optical counterparts. Our sample only includes theX-ray sources with detected hard X-ray fluxes, definedin the energy range of 2-8 keV. The published 2-10 keVfluxes in the AEGIS and XMMLSS fields have been cor-rected to 2-8 keV on the assumption of a power-law pho-ton index of 1.0, which is the average of hard-X-ray se-lected objects based on the hardness ratio (Nandra et al.2005).All optical type 1 AGNs are excluded as their nuclearradiation contaminates the host optical/near-IR lightseverely. Due to lack of access to the observed spectra,the definition of optical type 1 AGNs is not completelyuniversal over all the fields. In the CLASXS field, type1 objects are defined by having an emission line FWHM > − , while FWHM > − is adoptedfor the CDF-N and CDF-S fields. For the AEGIS andXMMLSS field, we have downloaded the spectra andclassified type 1 objects using FWHM > − . Inthe AEGIS field, some fraction of type 1 objects is stillincluded in the sample as the DEEP2 spectral coveragemisses the permitted lines (H α , H β and MgII2800˚ A ) incertain redshift windows ( ∼ ∼ SELECTION OF AGNS IN LOW-MASS HOST GALAXIES
Objects are identified as active low-mass galaxies ifthey satisfy the following two criteria: 1.) stellar mass M ∗ < × M ⊙ , our definition of low-mass galaxiesand 2.) hard X-ray luminosity L − > erg s − ,indicating an active nucleus.We have measured stellar masses by comparing the ob-served SEDs (i.e., the photometric data included in Ta-ble 1) to 102168 stellar synthesis models produced byBruzual & Charlot (2003)’s code. As listed in Table 3,the stellar models span a wide range of parameter space,including metallicity, extinction, characteristic timescaleof exponential star formation history, fraction of ejectedgas being recycled and galaxy age. To account for thepossible existence of low metallicity and young galaxies,we have included all six available metallicities and galaxyages starting at 10 yrs. The fit algorithm is similar tothat of Bundy et al. (2006) who have used a Bayesian Fig. 1.—
Examples of the best-fit SEDs and the probability dis-tribution of the stellar mass of AGNs in low-mass galaxies in eachfield, where the solid line is the median stellar mass and two dottedlines indicate the 16 % and 84 % probability tails, respectively. technique as described in Kauffmann et al. (2003c). Insummary, for an individual object, the best-fit stellarmass is obtained for each model that corresponds to anage younger than the cosmic age at the redshift of theobject. The associated χ gives the probability (exp(- χ /2)) that this model represents the observed SED.The final probability distribution of the stellar mass isobtained by summing all probabilities within a certainmass bin. We adopted a bin width of 0.01 in log M ∗ ,which on average contains 300 models. The median valueof the stellar mass probability distribution is adopted asthe final mass of a galaxy. Compared to the minimum χ derived stellar mass, the mass obtained by this techniquesuffers much less from model degeneracies. The 68% un-certainty range of the derived stellar mass is defined byexcluding the 16% tail at each end of the probabilitydistribution. Note that this uncertainty mainly reflectsthe photometric errors. For the objects in the CDF-Nand CLASXS fields, there are no published photomet-ric errors. We have adopted universally an uncertaintyof 0.07 magnitude, which is roughly the sky noise for a m R =24 object in these two fields. A small fraction of ob-jects in AEGIS, CDF-S and XMMLSS with very smallphotometric errors show large minimum reduced χ , in-dicating our stellar models are not able to produce theobserved SEDs accurately. To estimate the uncertaintyfor these objects, we increased their photometric errorsto 0.02 magnitude, which gives a reasonable minimum χ ( <
10) and larger uncertainty.We do not include other systematic errors for ourmeasured stellar masses, such as the accuracy of theBruzual & Charlot (2003) code itself and possible alter-native choices for the initial mass function. Our sampleonly includes narrow-line AGNs and thus AGN light con-tamination to the host emission should be small. For ob-scured AGNs, the scattered nuclear light may be strong(Zakamska et al. 2006). However, such scattered emis-sion may affect the host light importantly only in the UV band. To avoid the dust emission from AGN dustytori, we have not used photometry in the mid-IR. Fig. 1shows examples of the observed SED superposed withthe minimum- χ stellar model and the probability dis-tribution of the stellar mass for each field.A mass cut of < × M ⊙ is adopted to define thesample of low-mass host galaxies. Selecting the sample atthis mass threshold is of interest because the properties ofgalaxies and BHs may transition around this mass. Stud-ies of low-redshift galaxies have shown that galaxy prop-erties (star formation history, size and internal structure)show significant differences at the dividing stellar massof 3 × M ⊙ (Kauffmann et al. 2003b). In addition,galaxies with stellar mass < ∼ M ⊙ often harbor com-pact stellar nuclei at their centers, which follow the MBHmass-bulge relationships, but which are rare in moremassive galaxies (Carollo et al. 1998; Laine et al. 2003;Wehner & Harris 2006; Ferrarese et al. 2006). Thesestellar nuclei may be replacements for MBHs in low-masssystems where the gravitational potential is not suffi-ciently deep to form a BH. Furthermore, the fraction ofgalaxies hosting active BHs depends on the galaxy stel-lar mass (Kauffmann et al. 2003a; Heckman et al. 2004;Greene & Ho 2007b). In the most complete local AGNsample, the AGN fraction in galaxies fainter than M B = -20 ( ∼ M ⊙ ) is on average half of the fraction inbrighter ones (Ho et al. 1997).The L − > erg s − AGN selection criterion ismainly based on the energy budget argument that star-forming galaxies rarely produce such high hard X-ray lu-minosities (e.g. Zezas et al. 1998). The resulting sampleof AGNs in low-mass hosts contains 32 objects as listedin Table 4. Each object is labeled by the field namefollowed by the sequence number in the X-ray catalog ofeach field (see Table 1 for references). Fig. 2 shows distri-butions of low-mass AGN properties, including redshift,host stellar mass, 2-8 keV rest-frame luminosity and X-ray to R -band flux ratio.Best et al. (2005) have measured average ratios of BHmasses to the galaxy stellar mass as a function of stel-lar masses for the SDSS galaxy and AGN samples (seetheir Fig.1), where the BH mass is measured throughthe stellar veloclity dispersion and the MBH- σ relation.By assuming that our X-ray selected AGN sample hasthe same BH-to-galaxy mass ratio as the SDSS AGN,we can estimate the Eddington ratio for galaxies with M ∗ = 2 × M ⊙ and L − =10 erg s − . By assum-ing the L bol /L − = 17( L − / erg s − ) . (Shankar et al. 2004) and L − /L − =0.86 (as-suming a power law photon index of 1.0), we have anEddington ratio of 0.007. As shown in §
4, although wecan detect galaxies with stellar masses down to around10 M ⊙ , our sample is complete down to stellar mass of10 . M ⊙ out to redshift of 0.7. For this stellar mass,the black hole mass is on average 3 × M ⊙ (Best et al.2005) and the corresponding Eddington ratio is 0.02 for L − =10 erg s − . As a comparison to those locallow-mass AGNs, our sample may be not deep enoughto include the local classical low-mass Seyfert galaxiessimilar to NGC 4395 or POX 52, but should includegalaxies similar to some low-mass SDSS AGNs found byGreene & Ho (2004, 2007c).To better understand the role of AGNs in low-massgalaxy evolution, we will compare the sample of low-mass Shi et al. Fig. 2.—
Distributions of properties of AGNs in low-mass galax-ies: (a)– redshift distribution; (b) – distribution of host stellarmasses where the dotted line indicates the completeness cut of10 . M ⊙ ; (c) – distributions of the rest-frame 2-8 keV X-ray lu-minosity; (d) – distribution of X-ray to R -band flux ratio. To becomplete, our number density and X-ray luminosity function forAGNs in low-mass hosts are measured for those at 0.1 < z < . M ⊙ < M ∗ < . M ⊙ and L rest2 − > erg s − . host AGNs to a sample of AGNs in massive host galaxies.The comparison sample is defined as stellar mass M ∗ > × M ⊙ and L − > erg s − . INCOMPLETENESS CORRECTIONS AND WEIGHTS
The 1/ V max method The spatial number density of AGNs as a function ofAGN host mass and the X-ray luminosity function ofAGNs in low-mass hosts was calculated using the 1/ V max method (Schmidt 1968). This calculation used those ob-jects with R < L rest2 − > erg s − and M ∗ > × M ⊙ and in two redshift intervals of 0.1 < z < < z < L rest2 − is the rest-frame 2-8 keV fluxassuming a photon index of 1.0 but not correcting for ex-tinction. The maximum volume over which an object isincluded in the sample is given by V max = Z z high z low Ω dVdz dz, (1)where [ z low , z high ] is the redshift range of interest and Ωis the solid angle covered by the X-ray survey at the fluxlevel of the object. While z low is always fixed to the lowend of a redshift interval, the maximum redshift, z high isdefined as: z high = min( z highbin , z limitxray , z limit R ) , (2)where z highbin is the high end of a redshift interval, z limitxray is the limiting redshift at which the observed X-ray fluxreaches the limiting flux in a given field where the K-correction is determined by assuming a power law spec-trum with photon index of 1.0 and z limit R is the limitingredshift where the observed R -band magnitude reaches m limitR =24. To determine the K-correction in the R -band,we have redshifted the minimum reduced χ spectrummodel produced in our stellar mass calculations to mea-sure the R -band magnitude at different distances. Fig. 3.—
The effective solid angle as a function of the hard X-rayflux for objects in AEGIS, CDF-N, CDF-S and CLASXS fields.
As the sensitivity of the X-ray telescope shows energyand positional dependence (for details, see Yang et al.2004), to obtain a simple estimate of the solid angle ata given hard X-ray flux, we have followed Barger et al.(2005) by comparing the observed number of X-ray ob-jects at different hard X-ray fluxes with the average X-raynumber counts from Cowie et al. (2002) and Yang et al.(2004). The sample for comparing number counts is com-posed of all spectroscopically observed (not only thosewith secure redshifts) X-ray objects in the field of CDF-N, CDF-S and CLASXS and all X-ray sources in theAEGIS field. Table 2 lists the number of X-ray objectsand the number of spectroscopic targets in all the fields.The spectroscopic targets are randomly selected for theCDF-S and CLASXS fields. Although the target selec-tion in the CDF-N field has a little bias, the majority ofsources (439 out of 503) have been included in the spec-troscopic sample, making the effect of this bias on thesolid angle measurement negligible (Barger et al. 2005).Note that we have used the Alexander et al. (2003) X-ray catalog in the CDF-S due to its high X-ray positionalaccuracy so that our catalog contains ∼
30 less objectsthan in Barger et al. (2005). The AEGIS field contains1318 objects and the redshift is obtained by matching theX-ray catalog to the DEEP2/AEGIS catalog whose tar-get selection depends on apparent magnitude and color.Therefore, for the objects in the AEGIS field, we haveapplied weights as shown below. Fig. 3 shows the ef-fective solid angle as a function of the hard X-ray flux.At the flux of 10 − erg s − cm − , it is dominated bythe CLASXS (0.4 square degree) and AEGIS fields (0.67square degree).We have followed the method in Willmer et al. (2006)to determine the galaxy weights, ω , for the X-ray objectsin the AEGIS field. These weights are used to account forthe under-sampling of the photometric catalog (i.e. thefraction of objects with spectroscopic observations) andthe redshift success rate of the spectroscopic catalog (i.e.the fraction of spectroscopic targets with secure redshift)of the DEEP2 observations. Briefly, we define a X-ray-optical photometric catalog as all AEGIS X-ray objectsthat have optical counterparts in Coil et al. (2004). Herewe assume that AEGIS X-ray objects without opticalcounterparts (about 25% of the whole X-ray sample) arenot of interest for our study of low-mass systems at z < Fig. 4.—
The broad line AGN fraction in two redshift intervalsof 0 < z < < z < . M ⊙ ). To demonstratethis, we found that 15% of the X-ray objects without op-tical counterparts have L x > erg s − at z=0.7, i.e.satisfy the AGN definition. However, none of these ob-jects have absolute R -band magnitude for m R = 24.75 atz=0.7 brighter than any of the observed low-mass AGNhosts with 9.7 < Log( M ∗ /M ⊙ ) < m R = 24.75is the completeness cut of the DEEP2 photometry cata-log (Coil et al. 2004). For each AEGIS X-ray object witha secure spectroscopic redshift and probability of beinga galaxy P gal > R -( B - R )-( R - I )) space is defined. Then a proba-bility for being within the permitted redshift limit [0.1,1.4] is calculated for each object in the X-ray optical pho-tometric catalog within this data cube. The sum of allthese probabilities within the data cube divided by thenumber of successful redshifts gives the weight ω , whichis further corrected for the probability of being placed inthe slit mask.As discussed in §
2, type 1 AGNs are excluded from thesample and thus a weight is applied to correct for theiromission. The fraction of type 1 AGNs as a functionof the X-ray luminosity is constructed in both redshiftintervals as shown in Fig. 4, which is almost the same asthe result obtained by Barger et al. (2005). The weight iscalculated for each object based on the X-ray luminosity.As shown in Fig. 4, the corrections are small, as our AGNsample does not extend toward high X-ray luminositywhere the broad line fraction is large. Therefore, ourresults throughout the paper do not change significantlyif the broad-line AGN fraction does not apply.Finally, the mass function and X-ray luminosity func-tion are determined as:Φ( X ) dX = X ω/V max dX, (3)where X is the stellar mass or X-ray luminosity, respec-tively, ω is the galaxy weight, and V max is the maximum Fig. 5.—
The number distribution of all spectroscopic targets(open) and objects with secure spectroscopic redshift (hatched). volume for its detection.
Incompleteness
Our AGN sample where the 1/ V max method applies areobjects with secure spectroscopic redshifts, R < M ∗ > × M ⊙ , and L rest2 − > erg s − . The criteriaof secure spectroscopic redshifts does not introduce anysignificant incompleteness. Fig. 5 shows the distributionof R-band magnitude for the spectroscopically observedX-ray objects (open histogram) and the objects with se-cure spectroscopic redshifts (filled histogram). The red-shift success rate is 76% and 68% for spectroscopicallyobserved objects at R <
24 and 22 < R <
24, respectively.Most of the spectroscopically failed objects have 22 < R<
24. Barger et al. (2005) have shown that most objectswith failed spectroscopic redshifts have photometric red-shifts larger than ∼
1. A similar result is found in DEEP2(Willmer et al. 2006). A rough estimate shows that allthe spectroscopically failed objects contain roughly onlytwo low-mass AGN hosts at z < ∼ < R < < R <
24 areof low mass.The limiting R -band magnitude of 24 is deep enough tosample most low-mass galaxies with M ∗ > × M ⊙ out to a redshift of 0.7, the upperlimit where the spa-tial number density is measured. This is because 80%of AGNs with host M ∗ > × are detectable beyonda redshift of 0.7. The omission of a small fraction oflow-mass hosts should not affect the comoving numberdensity as they have been accounted for in the 1/ V max method. To further demonstrate that the R <
24 limitdoes not introduce any significant incompleteness evenin the high redshift interval (0.4 < z < < z < V max method can re-produce the intrinsic spa-tial density, regardless of the loss of a small fraction offaint R-band sources. Briefly, we randomly populatedthe volume with AGNs to a total number similar to thatobserved for 0.4 < z < < z < R -band magnitude of 24 should detect all low-mass galaxies with M ∗ > × M ⊙ . This is because Shi et al. Fig. 6.—
The stellar mass function of AGN hosts with L rest2 − keV > erg s − in the two redshift intervals of 0.1 < z < < z < z < < z < § the Bruzual & Charlot (2003) oldest simple stellar pop-ulations with solar metallicity and M ∗ = 5 × M ⊙ have m R =24 at z=0.4. Younger or lower metallicity galaxieswill emit higher luminosities. We then applied the mea-sured z limit R to the simulated galaxies and measured the1/ V max -based spatial number density. A thousand simu-lations show that there is no systematic difference in ourestimate of the spatial density. For the incompletenessdue to the X-ray detection threshold, since all AGNs (de-fined as L rest2 − > erg s − ) in low-mass hosts with M ∗ > × have z limitXray > V max method shouldrecover the real spatial number density. RESULTS
Comoving Number Density and AGN Fraction
Fig. 6 shows the spatial number density of AGNs with L rest2 − > erg s − as a function of AGN host massin the two redshift intervals of 0.1 < z < < z< ∼ ∼
20 objects per mass bin in high redshiftinterval. However, the peak around a stellar mass of10 . - 10 . M ⊙ is quite possibly real. For example,Greene & Ho (2007b) have measured the local BH massfunction of type 1 SDSS AGNs at z < M ⊙ , which corresponds on average to a hoststellar mass of 10 . M ⊙ (Best et al. 2005). The sta-tistical significance for the low-redshift AGN host massfunction peaking in the second mass bin was estimatedusing a Monte-Carlo simulation. Basically, we perturbedthe mass function at each mass bin ten thousand timesassuming a normal distribution with the 1- σ deviationequal to the measured error. The probabilities for thepeak at first, second and third bins are 10%, 80% and10%, respectively, which indicates that the low-redshiftAGN host mass function most likely peaks in the secondmass bin.To further demonstrate that the AGN host mass func-tion peaks at a higher mass in our high redshift inter-val, the solid line in the upper panel of Fig. 6 showsthe SDSS AGN result at z < < z < z < M ⊙ , deepenough for our purpose. The normalization of the AGNfraction of Kauffmann et al. (2003a) has been decreasedby a factor of 8 to match our normalization (a discus-sion about the difference between the SDSS and our low-redshift samples can be found in § . M ⊙ . We thencarried out a simulation by assuming the 0.4 < z < z< < z < to 10 . M ⊙ . We also assumed that the totalprobability in this mass range is equal to 1. Combiningthe simulated stellar mass and the observed z limitxray and z limit R measured in §
4, we can construct the AGN massfunction at 0.4 < z < < z < < M ⊙ ), while the observations at 0.4 < z < > M ⊙ ). This resultindicates that the tendency for the AGN mass functionin the high redshift interval to peak at higher mass issignificant (99.6%).The simulations shown above test the pure numberstatistics. In order to account for the possible selectionbias that the low-mass galaxies harbor faint AGNs dueto the mild correlation between the galaxy stellar massand the central BH mass coupled with a given Eddingtonratio distribution, we first created a set of stellar masseswith the relative probability following the galaxy stellarmass function from P´erez-Gonz´alez et al. (2008). Thesestellar masses were then converted to the BH mass dis-tribution using the average ratios of BH masses to galaxy Fig. 7.—
The fraction of galaxies hosting active nuclei as afunction of host stellar mass in the two redshift intervals of 0.1
3, the limit-ing Eddington ratio is 0.02 for our lowest stellar massof 10 . M ⊙ . For a galaxy with stellar mass of 10 M ⊙ , the limiting Eddington ratio is 0.001. To have asense of the missed fraction of AGNs with lower Ed-dington ratios, we used the currently most complete lo-cal AGN sample from Ho et al. (1995) as a comparison.Our sample of AGNs should miss a significant fractionof high-ionization Seyfert galaxies, as local Seyferts havea median Eddington ratio of 1.3 × − (Ho 2008). Wemay miss all low-ionization nuclear emission-line regions(LINERs), as none of the local LINERs has an Edding-ton ratio > L rest2 − > erg s − . Identifying these additional AGNs is dif-ficult because of the overlap of their X-ray luminosities Shi et al. Fig. 8.—
The rest-frame 2-8 KeV X-ray luminosity functionof AGNs in low-mass hosts, and of all AGNs in the two redshiftintervals of 0.1 < z < < z < with those resulting from star formation (Ranalli et al.2003). However, it is still important to understand thefraction of galaxies hosting AGNs with relatively highEddington ratios and their trends with host masses, asthese AGNs may be in the phase when feedback fromMBHs is most important and also the main stage of BHgrowth through accretion.
X-ray Luminosity Function of AGNs in Low-MassHosts
Fig. 8 shows the X-ray luminosity functions of AGNsin low-mass hosts (diamonds) and all AGNs (asterisks)in the two redshift intervals of 0.1 < z < R < 24 closely match their results for the higher redshiftinterval. In the low redshift interval, there is about a fac-tor of two difference in the highest luminosity bin. Thisis most likely caused by the cosmic variance due to thesmall comoving volume at low redshift.The total X-ray energy density of AGNs in low-mass hosts can be measured by integrating the XLFwhere there are data points. The measurements give(2.2 ± × and (1.4 ± × erg s − Mpc − at0.1 < z < < z < ± ± Fig. 9.— The redshift evolution of AGNs with host stellar mass9.7 < log M ∗ /M ⊙ < Redshift Evolution of AGNs in Low-Mass Hosts As shown in Fig. 9, AGNs in low-mass hosts showstrong redshift evolution. The number density increaseswith redshift following Φ DAGN = 10 − . ± . (1+ z ) . ± . Mpc − log(M ⊙ ) − , the fraction of low-mass galaxies withAGNs evolves as f AGN = 10 − . ± . (1 + z ) . ± . and theenergy density follows ρ DAGN = 10 . ± . (1+ z ) . ± . erg s − Mpc − in the redshift range of 0 100 (Shi et al. 2008,in preparation) have shown that only ∼ 10% of theseAGNs have N HI > cm − . Heckman et al. (2005)did show that the emission-line-selected AGN sample ismore complete than the X-ray-selected one at low red-shift and that the SDSS AGN spatial density is aboutthree times higher than X-ray-selected AGNs. Althoughat low redshift optical emission line diagnostics are morecomplete, X-ray selection identifies more AGNs at highredshift. X-ray selection also provides more uniform se-lection criteria (e.g., less affected by dilution by the hostgalaxy extended emission). As a summary, the predictionat low-redshift based on our result of cosmic evolution ofAGNs in low-mass galaxies is generally consistent withthe SDSS result, with an offset caused by different selec-tion biases between X-ray-emission-selected AGNs andoptical-emission-line-selected ones. DISCUSSION: BLACK HOLE OCCUPATION FRACTIONIN LOW-MASS GALAXIES Fraction of Galaxies Hosting AGNs § § f AGN = f BHOF γt AGN (4)where f BHOF is the black hole occupation function, i.e.,the fraction of galaxies hosting MBHs at their centers, γ is the fractional AGN trigger rate, i.e., the fractionof MBHs becomes active per unit time, and t AGN is theduration of a nuclear activity episode with L X > ergs − . The trend of AGN fractions with host mass can becaused by the host mass dependence of any one of thethree factors, f BHOF , γ and t AGN . Different models forMBH seed formation in the early universe predict differ-ent mass dependences of f BHOF (Volonteri et al. 2008). t AGN is most likely mass dependent, as the lower masssystems require larger Eddington ratios to be brighterthan L X =10 erg s − .To get some idea of f BHOF of low-mass galaxies, wemake a simple assumption that each major merger trig-gers one-time nuclear activity and thus γ = the merging rate. Although the measurement of the merging rate issubject to various uncertainties (e.g. Cassata et al. 2005;Shi et al. 2006; Lotz et al. 2008), it should be around 0.1-0.2 Gyr − for massive galaxies. Simply assuming γ = 0.1Gyr − for low-mass galaxies, we have : f BHOF = 0 . t AGN . γ ; (0 . < z < . 4) (5) f BHOF = 0 . t AGN . γ ; (0 . < z < . 7) (6)In this simplified case, as long as the duration of oneepisodic nuclear active phase is not long ( < all low-mass galaxies with 9.8 < log M ∗ < z < ∼ Accreted BH Mass by AGNs in Low-Mass Galaxies The amount of BH mass accreted by AGNs in low-mass galaxies since z = 1 can be measured by inte-grating the cosmic evolution of the X-ray energy den-sity of these AGNs obtained in § L bol /L − = 17( L − / erg s − ) . (Shankar et al. 2004), L − /L − =0.86 and themean X-ray luminosity of 7 × erg s − . Assumingthe mass-to-radiation conversion efficiency ε =0.1, thetotal accreted black hole mass in galaxies with 9.7 < log( M ∗ / M ⊙ ) < z = 1 is 3.9( ± × M ⊙ Mpc − .This accreted BH mass must be hosted in local low-mass galaxies. The corresponding total galaxy mass canbe estimated using the bulge-BH relation and bulge-to-disk ratio. The lower limit to the local BHOF is then theratio of the total mass of galaxies hosting the accretedBHs to the total local mass in low-mass galaxies. Inpractice, we can alternatively assume all local low-massgalaxies host BHs. The lower limit of the BHOF is thenthe ratio of the accreted BH mass to the assumed totalBH mass hosted by all local low-mass galaxies.The BH mass function can be determined from thegalaxy velocity dispersion function using the relationshipbetween the velocity dispersion and BH mass ( M BH - σ ).However, it is relatively difficult to measure the veloc-ity dispersion, resulting in incompleteness of the BHmass function at the low mass end. Alternatively, itcan be derived from the bulge luminosity function us-ing the relationship between the bulge luminosity andthe BH mass ( L Bulge - M BH ). In this case, the bulge-to-disk ratios of galaxies with different morphologies arerequired to derive the bulge luminosity function fromthe galaxy total luminosity function. In practice, thetwo methods are actually employed at the same time tocomplement each other. Different studies produce a rel-atively consistent result for the total local BH mass den-sity, which is around 4.5 × M ⊙ Mpc − with uncer-tainty < × M ⊙ Mpc − (Aller & Richstone 2002;Shankar et al. 2004; Marconi et al. 2004). Therefore, theaccreted BH mass by AGNs in low-mass hosts since z =1 is only a small fraction (0.8%) of the total local BHmass density.To estimate the BHOF in local low-mass galaxiesusing the accreted BH mass during their AGN phase0 Shi et al.since z = 1, we first need to determine the localsuccessor of our low-mass AGN hosts. Given the cosmicevolution of the stellar mass density of galaxies with dif-ferent stellar masses provided by P´erez-Gonz´alez et al.(2008), the 9.7 < log( M ∗ / M ⊙ ) < z = 0.5 corresponds roughly to9.85 < log( M ∗ / M ⊙ ) < z = 0. To estimatethe total BH mass associated with local galaxies with9.85 < log( M ∗ / M ⊙ ) < f earlybulge = 0.85 ± f latebulge = 0.30 ± M BH /M ⊙ )= (8.20 ± ± M bulge /10 M ⊙ )(H¨aring & Rix 2004), early and late type galaxieswith 9.85 < log( M ∗ /M ⊙ ) < < log( M BH /M ⊙ ) < < log( M BH /M ⊙ ) < ∗ BH ( M BH M ∗ BH ) α +1 exp[ − ( M BH M BH ∗ ) β ] , (7)we obtained Φ ∗ BH = 5 . ± . × − Mpc − , M ∗ BH =8 . ± . × M ⊙ , α = -0.47( ± β =0.39( ± ∗ BH =1 . ± . × − Mpc − , M ∗ BH = 3 . ± . × M ⊙ , α = -0.57( ± β = 0.34( ± < log( M ∗ / M ⊙ ) < × and 1.2 × M ⊙ Mpc − , respectively. Therefore, the ac-creted BH mass by AGNs in low-mass hosts from z = 1contributes 12% of the local BH mass hosted in galaxieswith 9.85 < log( M ∗ / M ⊙ ) < < z < 1. The current assumptionis that it follows the trend at z < z > z = 1. In this case, the local counterpartshave 10.1 < log( M ∗ / M ⊙ ) < L X > erg s − and (2) the struc- ture of the circumnuclear material may vary with theluminosity in a way that causes lower luminosity objectsto be more obscured, as implied by the decrease in thefraction of type 2 objects with increasing luminosity (e.g.Barger et al. 2005). We calculated the degree of under-estimation in two ways. First, we measured the accretedBH mass of 3.4 × M ⊙ Mpc − by all X-ray-detectedAGNs from z = 1 by integrating the X-ray energy den-sity evolution of all AGNs (see § ∼ × M ⊙ Mpc − accreted by all AGNs from z = 1 with a correction forobscuration and accounting for missing Compton-thickobjects. Therefore, the accreted BH mass by AGNs inlow-mass galaxies is underestimated by a factor of 4, byassuming that the obscuration of these AGNs is simi-lar to that of all AGNs. The second way is to comparethe distribution of the HI column density of observedAGNs to the intrinsic distribution to estimate the frac-tion of missing AGNs. Our X-ray spectral fits of AGNsin low-mass galaxies with X-ray counts > 100 (Shi et al.2008, in preparation) have shown that only 10% of suchAGNs have HI column density N HI > cm − . Thestudy of local Seyfert galaxies shows that 75% of Seyfert2 galaxies have N HI > cm − (Risaliti et al. 1999). IfAGNs in low-mass galaxies have structures of circumnu-clear material similar to those in Seyfert galaxies, 75% ofthe low-mass galaxies should be missed and the accretedBH mass by all such AGNs is underestimated by a factorof 4, similar to the value estimated by the first method.Therefore, the accreted BH mass by all AGNs in low-mass hosts including missed heavily-obscured ones from z = 1, probably contribute ∼ 50% of the local BH masshosted in galaxies with 9.85 < log( M ∗ / M ⊙ ) < < log( M ∗ / M ⊙ ) < < log( M ∗ / M ⊙ ) < z > § L X > erg s − )at z < CONCLUSIONS We have studied a sample of X-ray AGNs in low-masshost galaxies with stellar mass of 5 × M ⊙ < M ∗ < × M ⊙ out to z ∼ 1. Our main conclusions are:(1) By including AGNs in more massive host galaxies,we have constructed the stellar mass function of AGNhost galaxies extending down to the low-mass regime intwo redshift intervals of 0.1 < z < < z < < z< L X > erg s − isnot long ( < < z < < z < ∼ 10% of the X-ray energy density of allthe AGNs in 0 < z < 1, indicating that such AGNs makean energetically significant contribution to the cosmic X-ray background.(4) AGNs in low-mass hosts show strong redshift evo-lution in their comoving number density, the fraction of such galaxies with active nuclei and the comoving radia-tion energy density. By integrating the X-ray luminosityfunction of these AGNs over the redshift range of 0 < z< 1, the accreted black hole mass in galaxies with 5 × M ⊙ < M ∗ < × M ⊙ is (3.9 ± × M ⊙ Mpc − .This number gives a strong lower limit of 12% to thefraction of local low-mass galaxies harboring black holes,which may be much higher ( > REFERENCESAlexander, D. 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J. 1998, MNRAS,301, 915 TABLE 1X-ray Fields FIELD Area F limitXray Ref Optical photometry Ref Secure redshift Refdeg erg s − cm − (1) (2) (3) (4) (5) (6) (7) (8)AEGIS 0.67 5.0 × − s × − z without label ′ s ′ 6, 7CDF-S 0.11 2.8 × − × − 11 B, V, R, I, z ′ 12 all listed z are secure 12XMMLSS 1 5.8 × − 13 B, V, R, I, J, K 14,15,16,17 q − z=3, 4, 13, 14, 23, 24 18 Note . — Col.(1): The field name. Col.(2): The area of the field size in square degree. Col.(3): The limiting X-rayflux in 2-8 keV. Col.(4): The reference for the X-ray data. Col.(5): The available optical/near-IR photometry. Col.(6):The reference for the optical/near-IR photometry. Col.(7): The definition of the secure spectroscopic redshift in eachfield. Col.(8): The reference for the spectroscopic redshift.References – (1) Nandra et al. (2005); Laird et al. (2008); (2) Coil et al. (2004); (3) Bundy et al. (2006); (4) Davis et al.(2003, 2007); (5) Alexander et al. (2003); (6) Barger et al. (2003); (7) Barger et al. (2002); (8) Alexander et al.(2003); (9) Wolf et al. (2004) ; (10) Szokoly et al. (2004); (11) Yang et al. (2004); (12) Steffen et al. (2004); (13)Chiappetti et al. (2005); (14) Le F`evre et al. (2004); (15) McCracken et al. (2003); (16) Radovich et al. (2004); (17)Iovino et al. (2005); (18) Le F`evre et al. (2005) TABLE 2The number of X-ray objects in all fields FIELD CDF-N CDF-S CLASXS AEGIS XMMLSSTotal 503 326 525 1318 286Spec-Observed 439 210 422 357 23