Supermassive Black Hole Mass Function Research Articles

Little Red Dots: An Abundant Population of Faint Active Galactic Nuclei at z ∼ 5 Revealed by the EIGER and FRESCO JWST Surveys

Characterizing the prevalence and properties of faint active galactic nuclei (AGNs) in the early Universe is key for understanding the formation of supermassive black holes (SMBHs) and determining their role in cosmic reionization. We perform a spectroscopic search for broad Hα emitters at z ≈ 4–6 using deep JWST/NIRCam imaging and wide field slitless spectroscopy from the EIGER and FRESCO surveys. We identify 20 Hα lines at z = 4.2–5.5 that have broad components with line widths from ∼1200–3700 km s−1, contributing ∼30%–90% of the total line flux. We interpret these broad components as being powered by accretion onto SMBHs with implied masses ∼107–8 M ⊙. In the UV luminosity range M UV,AGN+host = −21 to −18, we measure number densities of ≈10−5 cMpc−3. This is an order of magnitude higher than expected from extrapolating quasar UV luminosity functions (LFs). Yet, such AGN are found in only <1% of star-forming galaxies at z ∼ 5. The number density discrepancy is much lower when compared to the broad Hα LF. The SMBH mass function agrees with large cosmological simulations. In two objects, we detect complex Hα profiles that we tentatively interpret as caused by absorption signatures from dense gas fueling SMBH growth and outflows. We may be witnessing early AGN feedback that will clear dust-free pathways through which more massive blue quasars are seen. We uncover a strong correlation between reddening and the fraction of total galaxy luminosity arising from faint AGN. This implies that early SMBH growth is highly obscured and that faint AGN are only minor contributors to cosmic reionization.

Exploring Proxies for the Supermassive Black Hole Mass Function: Implications for Pulsar Timing Arrays

Supermassive black holes (SMBHs) reside at the center of every massive galaxy in the local universe with masses that closely correlate with observations of their host galaxy, implying a connected evolutionary history. The population of binary SMBHs, which form following galaxy mergers, is expected to produce a gravitational-wave background (GWB) detectable by pulsar timing arrays (PTAs). PTAs are starting to see hints of what may be a GWB, and the amplitude of the emerging signal is toward the higher end of model predictions. Simulated populations of binary SMBHs can be constructed from observations of galaxies and are used to make predictions about the nature of the GWB. The greatest source of uncertainty in these observation-based models comes from the inference of the SMBH mass function, which is derived from observed host galaxy properties. In this paper, I undertake a new approach for inferring the SMBH mass function, starting from a velocity dispersion function rather than a galaxy stellar mass function. I argue that this method allows for a more direct inference by relying on a larger suite of individual galaxy observations as well as relying on a more “fundamental” SMBH mass relation. I find that the resulting binary SMBH population contains more massive systems at higher redshifts than previous models. Additionally, I explore the implications for the detection of individually resolvable sources in PTA data.

The Luminosity Function of Tidal Disruption Events from Fallback-powered Emission: Implications for the Black Hole Mass Function

Tidal disruption events (TDEs), in which a star is destroyed by the gravitational field of a supermassive black hole (SMBH), are being observed at a high rate owing to the advanced state of survey science. One of the properties of TDEs that is measured with increasing statistical reliability is the TDE luminosity function, , which is the TDE rate per luminosity (i.e., how many TDEs are within a given luminosity range). Here we show that if the luminous emission from a TDE is directly coupled to the rate of return of tidally destroyed debris to the SMBH, then the TDE luminosity function is in good agreement with observations and scales as ∝L −2.5 for high luminosities, provided that the SMBH mass function —the number of SMBHs (N •) per SMBH mass (M •)—is approximately flat in the mass range over which we observe TDEs. We also show that there is a cutoff in the luminosity function at low luminosities that is a result of direct captures, and this cutoff has been tentatively observed. If is flat, which is in agreement with some observational campaigns, these results suggest that the fallback rate feeds the accretion rate in TDEs. Contrarily, if is flat, which has been found theoretically and is suggested by other observational investigations, then the emission from TDEs is likely powered by another mechanism. Future observations and more TDE statistics, provided by the Rubin Observatory/LSST, will provide additional evidence as to the reality of this tension.

Climbing out of the shadows: Building the distance ladder with black hole images

In the era of precision cosmology it has became crucial to find new and competitive probes to estimate cosmological parameters, in an effort of finding answers to the current cosmological tensions/discrepancies. In this work, we show the possibility of using observations of Super Massive Black Hole (SMBH) shadows as an anchor for the distance ladder, substituting the sources usually exploited for such purpose, such as Cepheid variable stars. Compared to the standard approaches, the use of SMBH has the advantage of not needing to be anchored with distance calibrators outside the Hubble flow since the shadows physical size can be estimated knowing the mass of the SMBH. Furthermore, SMBH are supposed to inhabit the center of all galaxies which, in principle, means that we can measure the size of the shadows in any Supernova type Ia host galaxy. Under the assumption that the mass of the SMBH can be accurately and reliably estimated, we find that the Hubble constant can be constrained with a $\approx10\%$ precision even considering current experimental design of ground-based interferometers. By constructing a SMBH catalogue based on a specific choice of the SMBH Mass Function (BHMF), we forecast the constraints on the Hubble constant, finding that a precision of $\approx4\%$ may be within reach of future interferometers.

Predicting Supermassive Black Hole Mass with Machine Learning Methods

It is crucial to measure the mass of supermassive black holes (SMBHs) in understanding the co-evolution between the SMBHs and their host galaxies. Previous methods usually require spectral data which are expensive to obtain. We use the AGN catalog from the Sloan Digital Sky Survey project Data Release 7 (DR7) to investigate the correlations between SMBH mass and their host galaxy properties. We apply the machine learning algorithms, such as Lasso regression, to establish the correlation between the SMBH mass and various photometric properties of their host galaxies. We find an empirical formula that can predict the SMBH mass according to galaxy luminosity, colors, surface brightness, and concentration. The root-mean-square error is 0.5 dex, comparable to the intrinsic scatter in SMBH mass measurements. The 1σ scatter in the relation between the SMBH mass and the combined galaxy properties relation is 0.48 dex, smaller than the scatter in the SMBH mass versus galaxy stellar mass relation. This relation could be used to study the SMBH mass function and the AGN duty cycles in the future.

Climbing Out of the Shadows:\\ Building the Distance Ladder with Black Hole Images

In the era of precision cosmology it has became crucial to find new and competitive probes to estimate cosmological parameters, in an effort of finding answers to the current cosmological tensions/discrepancies. In this work, we show the possibility of using observations of Super Massive Black Hole (SMBH) shadows as an anchor for the distance ladder, substituting the sources usually exploited for such purpose, such as Cepheid variable stars. Compared to the standard approaches, the use of SMBH has the advantage of not needing to be anchored with distance calibrators outside the Hubble flow since the shadows physical size can be estimated knowing the mass of the SMBH. Furthermore, SMBH are supposed to inhabit the center of all galaxies which, in principle, means that we can measure the size of the shadows in any Supernova type Ia host galaxy. Under the assumption that the mass of the SMBH can be accurately and reliably estimated, we find that the Hubble constant can be constrained with a $\approx10\%$ precision even considering current experimental design of ground-based interferometers. By constructing a SMBH catalogue based on a specific choice of the SMBH Mass Function (BHMF), we forecast the constraints on the Hubble constant, finding that a precision of $\approx4\%$ may be within reach of future interferometers.

WISDOM project – VI. Exploring the relation between supermassive black hole mass and galaxy rotation with molecular gas

ABSTRACT Empirical correlations between the masses of supermassive black holes (SMBHs) and properties of their host galaxies are well established. Among these is the correlation with the flat rotation velocity of each galaxy measured either at a large radius in its rotation curve or via a spatially integrated emission-line width. We propose here the use of the deprojected integrated CO emission-line width as an alternative tracer of this rotation velocity, which has already been shown useful for the Tully–Fisher (luminosity–rotation velocity) relation. We investigate the correlation between CO line widths and SMBH masses for two samples of galaxies with dynamical SMBH mass measurements, with spatially resolved and unresolved CO observations, respectively. The tightest correlation is found using the resolved sample of 25 galaxies as $\log (M_\mathrm{BH}/\mathrm{M_\odot })=(7.5\pm 0.1)+(8.5\pm 0.9)[\log (W_\mathrm{50}/\sin i \, \mathrm{km\, s}^{-1})-2.7]$, where MBH is the central SMBH mass, W50 is the full width at half-maximum of a double-horned emission-line profile, and i is the inclination of the CO disc. This relation has a total scatter of $0.6\,$ dex, comparable to those of other SMBH mass correlations, and dominated by the intrinsic scatter of $0.5\,$ dex. A tight correlation is also found between the deprojected CO line widths and the stellar velocity dispersions averaged within one effective radius. We apply our correlation to the COLD GASS sample to estimate the local SMBH mass function.

The Mass Function of Supermassive Black Holes in the Direct Collapse Scenario

Abstract One of the ideas to explain the existence of supermassive black holes (SMBH) in place by z ∼ 7 is a phase of rapid accretion onto direct collapse black holes (DCBH) that started their lives with masses ∼104–5 M ⊙ . Considering the DCBH scenario, we show that the SMBH mass function has two characteristic features: 1. a power-law at intermediate masses whose index is the dimensionless ratio α ≡ λ/γ, where λ is the growth rate of the number of DCBH and γ is the growth rate of DCBH masses, both during the DCBH growth era; 2. a break in the power law profile set by β ≡ γ T, where T is the duration of the DCBH growth era. The observed quasar luminosity function can be described with this tapered power-law function.

The galaxy population within the virial radius of the Perseus cluster

Context. The Perseus cluster is one of the most massive nearby galaxy clusters and is fascinating in various respects. Though the galaxies in the central cluster region have been intensively investigated, an analysis of the galaxy population in a larger field is still outstanding. Aims. This paper investigates the galaxies that are brighter than B ≈ 20 within a field corresponding to the Abell radius of the Perseus cluster. Our first aim is to compile a new catalogue in a wide field around the centre of the Perseus cluster. The second aim of this study is to employ this catalogue for a systematic study of the cluster galaxy population with an emphasis on morphology and activity. Methods. We selected the galaxies in a 10 square degrees field of the Perseus cluster on Schmidt CCD images in B and Hα in combination with SDSS images. Morphological information was obtained both from the “eyeball” inspection and the surface brightness profile analysis. We obtained low-resolution spectra for 82 galaxies and exploited the spectra archive of SDSS and redshift data from the literature. Results. We present a catalogue of 1294 galaxies with morphological information for 90% of the galaxies and spectroscopic redshifts for 24% of them. We selected a heterogeneous sample of 313 spectroscopically confirmed cluster members and two different magnitude-limited samples with incomplete redshift data. These galaxy samples were used to derive such properties as the projected radial velocity dispersion profile, projected radial density profile, galaxy luminosity function, supermassive black hole mass function, total stellar mass, virial mass, and virial radius, to search for indications of substructure, to select active galaxies, and to study the relation between morphology, activity, density, and position. In addition, we present brief individual descriptions of 18 cluster galaxies with conspicuous morphological peculiarities.

On the Diversity of Fallback Rates from Tidal Disruption Events with Accurate Stellar Structure

Abstract The tidal disruption of stars by supermassive black holes (SMBHs) can be used to probe the SMBH mass function, the properties of individual stars, and stellar dynamics in galactic nuclei. Upcoming missions will detect thousands of tidal disruption events (TDEs), and accurate theoretical modeling is required to interpret the data with precision. Here we analyze the influence of more realistic stellar structure on the outcome of TDEs; in particular, we compare the fallback rates—being the rate at which tidally disrupted debris returns to the black hole—from progenitors generated with the stellar evolution code mesa to and γ = 5/3 polytropes. We find that mesa-generated density profiles yield qualitatively different fallback rates as compared to polytropic approximations, and that only the fallback curves from low-mass (1 M ⊙ or less), zero-age main-sequence stars are well fit by either a or 5/3 polytrope. Stellar age has a strong affect on the shape of the fallback curve, and can produce characteristic timescales (e.g., the time to the peak of the fallback rate) that greatly differ from the polytropic values. We use these differences to assess the degree to which the inferred black hole mass from the observed light curve can deviate from the true value, and find that the discrepancy can be at the order of magnitude level. Accurate stellar structure also leads to a substantial variation in the critical impact parameter at which the star is fully disrupted, and can increase the susceptibility of the debris stream to fragmentation under its own self-gravity. These results suggest that detailed modeling is required to accurately interpret observed light curves of TDEs.

The Mass Function of Supermassive Black Holes in the Direct-collapse Scenario

Abstract One of the ideas that explains the existence of supermassive black holes (SMBHs) that are in place by z ∼ 7 is that there was an earlier phase of very rapid accretion onto direct-collapse black holes (DCBHs) that started their lives with masses ∼104–5 . Working in this scenario, we show that the mass function of SMBHs after such a limited time period, with growing formation rate paired with super-Eddington accretion, can be described as a broken power law with two characteristic features. There is a power law at intermediate masses whose index is the dimensionless ratio α ≡ λ/γ, where λ is the growth rate of the number of DCBHs during their formation era, and γ is the growth rate of DCBH masses by super-Eddington accretion during the DCBH growth era. A second feature is a break in the power-law profile at high masses, above which the mass function declines rapidly. The location of the break is related to the dimensionless number β = γ T, where T is the duration of the period of DCBH growth. If the SMBHs continue to grow at later times at an Eddington-limited accretion rate, then the observed quasar luminosity function can be directly related to the tapered power-law function derived in this Letter.

Constraining supermassive black hole evolution through the continuity equation

The population of supermassive black holes (SMBHs) is composed by quiescent SMBHs, such as those seen in local galaxies including the Milky Way's, and active ones, resulting in quasars and active galactic nuclei (AGN). Outside our neighbourhood, all the information we have on SMBHs is derived from quasars and AGN, giving us a partial view. We study the evolution of the SMBH population, total and active, by the continuity equation, backwards in time from z=0 to z=4. Type-1 and type-2 AGN are differentiated in the model on the basis of the Eddington ratio distribution, chosen on the basis of observational estimates. The duty cycle is obtained by matching the luminosity function of quasars, and the average radiative efficiency is the only free parameter in the model. For higher radiative efficiencies (>~0.07) a large fraction of the SMBH population, most of them quiescent, must already be in place by z=4. For lower radiative efficiencies (~0.05), the duty cycle increases with the redshift and the SMBH population evolves dramatically since z=4. The mass function of active SMBHs does not depend on the choice of the radiative efficiency or of the local SMBH mass function, but it is mainly determined by the quasar luminosity function, once the Eddington ratio distribution is fixed. Only a direct measurement of the total BHMF at redshifts z>~2 could break these degeneracies giving important constraints on the average radiative efficiency. Focusing on type-1 AGN, for which observational estimates of the mass function and Eddington ratio distribution exist at various redshift, models with lower radiative efficiencies reproduce better the high-mass end of the mass function at high-z, but they tend to over-predict it at low-z, and vice-versa for models with higher radiative efficiencies.

THE LOCAL BLACK HOLE MASS FUNCTION DERIVED FROM THE MBH–P AND THE MBH–n RELATIONS

ABSTRACT We present a determination of the supermassive black hole (SMBH) mass function for early- and late-type galaxies in the nearby universe (z &lt; 0.0057), established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern hemisphere. The sample is defined by limiting luminosity (redshift-independent) distance, D L = 25.4 Mpc, and a limiting absolute B-band magnitude, . These limits define a sample of 140 spiral, 30 elliptical (E), and 38 lenticular (S0) galaxies. We established the Sérsic index distribution for early-type (E/S0) galaxies in our sample. Davis et al. established the pitch angle distribution for their sample, which is identical to our late-type (spiral) galaxy sample. We then used the pitch angle and the Sérsic index distributions in order to estimate the SMBH mass function for our volume-limited sample. The observational simplicity of our approach relies on the empirical relation between the mass of the central SMBH and the Sérsic index for an early-type galaxy or the logarithmic spiral-arm pitch angle for a spiral galaxy. Our SMBH mass function agrees well at the high-mass end with previous values in the literature. At the low-mass end, although inconsistencies exist in previous works that still need to be resolved, our work is more in line with expectations based on modeling of black hole evolution.

Hard X-ray luminosity function of tidal disruption events: First results from the MAXI extragalactic survey

Abstract We derive the first hard X-ray luminosity function (XLF) of stellar tidal disruption events (TDEs) by supermassive black holes (SMBHs), which gives an occurrence rate of TDEs per unit volume as a function of peak luminosity and redshift, utilizing an unbiased sample observed by the Monitor of All-sky X-ray Image (MAXI). On the basis of the light curves characterized by a power-law decay with an index of −5/3, a systematic search using the MAXI data detected four TDEs in the first 37 months of observations, all of which have been found in the literature. To formulate the TDE XLF, we consider the mass function of SMBHs, that of disrupted stars, the specific TDE rate as a function of SMBH mass, and the fraction of TDEs with relativistic jets. We perform an unbinned maximum likelihood fit to the MAXI TDE list and check the consistency with the observed TDE rate in the ROSAT all-sky survey. The results suggest that the intrinsic fraction of the jet-accompanying events is 0.0007%–34%. We confirm that at z ≲ 1.5 the contamination of the hard X-ray luminosity functions of active galactic nuclei by TDEs is not significant and hence that their contribution to the growth of SMBHs is negligible at the redshifts.

Rates of stellar tidal disruption as probes of the supermassive black hole mass function

Rates of stellar tidal disruption events (TDEs) by supermassive black holes (SMBHs) due to two-body relaxation are calculated using a large galaxy sample (N=146) in order to explore the sensitivity of the TDE rates to observational uncertainties, such as the parametrization of galaxy light profiles and the stellar mass function. The largest uncertainty arises due to the poorly constrained occupation fraction of SMBHs in low-mass galaxies, which otherwise dominate the total TDE rate. The detection rate of TDE flares by optical surveys is calculated as a function of SMBH mass and other observables for several physically-motivated models of TDE emission. We also quantify the fraction of galaxies that produce deeply penetrating disruption events. If the majority of the detected events are characterized by super-Eddington luminosities (such as disk winds, or synchrotron radiation from an off-axis relativistic jet), then the measured SMBH mass distribution will tightly constrain the low-end SMBH occupation fraction. If Eddington-limited emission channels dominate, however, then the occupation fraction sensitivity is much less pronounced in a flux-limited survey (although still present in a volume-complete event sample). The SMBH mass distribution of the current sample of TDEs, though highly inhomogeneous and encumbered by selection effects, already suggests that Eddington-limited emission channels dominate. Even our most conservative rate estimates appear to be in tension with much lower observationally inferred TDE rates, and we discuss several possible resolutions to this discrepancy.

BLACK HOLE AND GALAXY COEVOLUTION FROM CONTINUITY EQUATION AND ABUNDANCE MATCHING

[abridged] We investigate the coevolution of galaxies and hosted supermassive black holes throughout the history of the Universe by a statistical approach based on the continuity equation and the abundance matching technique. Specifically, we present analytical solutions of the continuity equation without source term to reconstruct the supermassive black hole (BH) mass function from the AGN luminosity functions. Such an approach includes physically-motivated AGN lightcurves tested on independent datasets, which describe the evolution of the Eddington ratio and radiative efficiency from slim- to thin-disc conditions. We nicely reproduce the local estimates of the BH mass function, the AGN duty cycle as a function of mass and redshift, along with the Eddington ratio function and the fraction of galaxies with given stellar mass hosting an AGN with given Eddington ratio. We exploit the same approach to reconstruct the observed stellar mass function at different redshift from the UV and far-IR luminosity functions associated to star formation in galaxies. These results imply that the buildup of stars and BHs in galaxies occurs via in-situ processes, with dry mergers playing a marginal role at least for stellar masses < 3 10^11 M_sun and BH masses < 10^9 M_sun, where the statistical data are more secure and less biased by systematic errors. In addition, we develop an improved abundance matching technique to link the stellar and BH content of galaxies to the gravitationally dominant dark matter component. The resulting relationships constitute a testbed for galaxy evolution models, highlighting the complementary role of stellar and AGN feedback in the star formation process. Finally, the clustering properties of BHs and galaxies are found to be in full agreement with current observations, so further validating our results from the continuity equation.

THE BLACK HOLE MASS FUNCTION DERIVED FROM LOCAL SPIRAL GALAXIES

We present our determination of the nuclear supermassive black hole (SMBH) mass function for spiral galaxies in the Local Universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the Southern Hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of SMBH evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of SMBHs since the epoch of maximum quasar activity. A luminosity distance $\leq$ 25.4 $Mpc$ and an absolute B-band magnitude $\leq$ -19.12 define the sample. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time $\leq$ 82.1 $h_{67.77}^{-1}$ $Myr$ and contained within a comoving volume of 3.37 $\times$ $10^4$ $h_{67.77}^{-3}$ $Mpc^3$. We estimate the density of SMBHs residing in spiral galaxies in the Local Universe is $5.54_{-2.73}^{+6.55}$ $\times$ $10^4$ $h_{67.77}^3$ $M_{\odot}$ $Mpc^{-3}$. Thus, our derived cosmological SMBH mass density for spiral galaxies is $\Omega_{BH} = 4.35_{-2.15}^{+5.14}$ $\times$ $10^{-7}$ $h_{67.77}$.

X-ray emission from high-redshift miniquasars: self-regulating the population of massive black holes through global warming

Observations of high-redshift quasars at z>6 imply that supermassive black holes (SMBHs) with masses over a billion solar masses were in place less than 1 Gyr after the Big Bang. If these SMBHs assembled from "seed" BHs left behind by the first stars, then they must have accreted gas at close to the Eddington limit during a large fraction (>50%) of the time. A generic problem with this scenario, however, is that the mass density in million-solar-mass SMBHs at z=6 already exceeds the locally observed SMBH mass density by several orders of magnitude; in order to avoid this overproduction, BH seed formation and growth must become significantly less efficient in less massive protogalaxies, while proceeding uninterrupted in the most massive galaxies that formed first. Using Monte-Carlo realizations of the merger and growth history of BHs, we show that X-rays from the earliest accreting BHs can provide such a feedback mechanism. Our calculations paint a self-consistent picture of black-hole-made climate change, in which the first miniquasars---among them the ancestors of the z>6 quasar SMBHs---globally warm the IGM and suppress the formation and growth of subsequent generations of BHs. We present two specific models with global miniquasar feedback that provide excellent agreement with recent estimates of the z=6 SMBH mass function. For each of these models, we estimate the rate of BH mergers at z>6 that could be detected by the proposed gravitational-wave observatory eLISA/NGO.

COSMOLOGICAL EVOLUTION OF SUPERMASSIVE BLACK HOLES. II. EVIDENCE FOR DOWNSIZING OF SPIN EVOLUTION

The spin is an important but poorly constrained parameter for describing supermassive black holes (SMBHs). Using the continuity equation of SMBH number density, we explicitly obtain the mass-dependent cosmological evolution of the radiative efficiency for accretion, which serves as a proxy for SMBH spin. Our calculations make use of the SMBH mass function of active and inactive galaxies (derived in the first paper of this series), the bolometric luminosity function of active galactic nuclei (AGNs), corrected for the contribution from Compton-thick sources, and the observed Eddington ratio distribution. We find that the radiative efficiency generally increases with increasing black hole mass at high redshifts (z>~1), roughly as \eta \propto M_bh^0.5, while the trend reverses at lower redshifts, such that the highest efficiencies are attained by the lowest mass black holes. Black holes with M_bh>~10^8.5M_sun maintain radiative efficiencies as high as \eta~0.3-0.4 at high redshifts, near the maximum for rapidly spinning systems, but their efficiencies drop dramatically (by an order of magnitude) by z~0. The pattern for lower mass holes is somewhat more complicated but qualitatively similar. Assuming that the standard accretion disk model applies, we suggest that the accretion history of SMBHs and their accompanying spins evolve in two distinct regimes: an early phase of prolonged accretion, plausibly driven by major mergers, during which the black hole spins up, then switching to a period of random, episodic accretion, governed by minor mergers and internal secular processes, during which the hole spins down. The transition epoch depends on mass, mirroring other evidence for "cosmic downsizing" in the AGN population; it occurs at z~2 for high-mass black holes, and somewhat later, at z~1, for lower-mass systems.

COSMOLOGICAL EVOLUTION OF SUPERMASSIVE BLACK HOLES. I. MASS FUNCTION AT 0 < z {approx}< 2

We present the mass function of supermassive black holes (SMBHs) over the redshift range z = 0-2, using the latest deep luminosity and mass functions of field galaxies to constrain the masses of their spheroids, which we relate to SMBH mass through the empirical correlation between SMBH and spheroid mass (the M{sub .}-M{sub sph} relation). In addition to luminosity fading of the stellar content of the spheroids, we carefully consider the variation of the bulge-to-total luminosity ratio of the galaxy populations and the M{sub .}/M{sub sph} ratio, which, according to numerous recent studies, evolves rapidly with redshift. The SMBH mass functions derived from the galaxy luminosity and mass functions show very good agreement, both in shape and in normalization. The resultant SMBH mass function and integrated mass density for the local epoch (z Almost-Equal-To 0) match well those derived independently by other studies. Consistent with other evidence for cosmic downsizing, the upper end of the mass function remains roughly constant since z Almost-Equal-To 2, while the space density of lower mass black holes undergoes strong evolution. We carefully assess the impact of various sources of uncertainties on our calculations. A companion paper uses the mass function derived in this workmore » to determine the radiative efficiency of black hole accretion and constraints that can be imposed on the cosmological evolution of black hole spin.« less