Black Hole Mass Function Research Articles

Monte Carlo Markov Chain parameter estimation in semi-analytic models of galaxy formation

[abridged] We present a statistical exploration of the parameter space of the De Lucia and Blaizot version of the Munich semi-analytic model built upon the millennium dark matter simulation. This is achieved by applying a Monte Carlo Markov Chain method to constrain the 6 free parameters that define the stellar and black-hole mass functions at redshift zero. The model is tested against three different observational data sets, including the galaxy K-band luminosity function, B-V colours, and the black hole-bulge mass relation, separately and combined, to obtain mean values, confidence limits and likelihood contours for the best fit model. Using each observational data set independently, we discuss how the SA model parameters affect each galaxy property and to what extent the correlations between them can lead to improved understandings of the physics of galaxy formation. When all the observations are combined, we find reasonable agreement between the majority of the previously published parameter values and our confidence limits. However, the need to suppress dwarf galaxy formation requires the strength of the supernova feedback to be significantly higher in our best-fit solution than in previous work. To balance this, we require the feedback to become ineffective in halos of lower circular velocity than before, so as to permit the formation of sufficient high-luminosity galaxies: unfortunately, this leads to an excess of galaxies around L*. Although the best-fit is formally consistent with the data, there is no region of parameter space that reproduces the shape of galaxy luminosity function across the whole magnitude-range. We discuss modifications to the semi-analytic model that might simultaneously improve the fit to the observed luminosity function and reduce the reliance on excessive supernova feedback in small halos.

Feast and Famine: regulation of black hole growth in low-redshift galaxies

We analyze the observed distribution of Eddington ratios as a function of supermassive black hole mass for a large sample of nearby galaxies drawn from the Sloan Digital Sky Survey. We demonstrate that there are two distinct regimes of black hole growth in nearby galaxies. The first is associated with galaxies with significant star formation in their central kiloparsec regions, and is characterized by a broad log-normal distribution of accretion rates peaked at about one percent of the Eddington limit. In this regime, the Eddington ratio distribution is independent of the mass of the black hole and shows no further dependence on the central stellar population of the galaxy. The second regime is associated with galaxies with old central stellar populations, and is characterized by a power-law distribution function of Eddington ratios. In this regime, the time-averaged mass accretion rate onto black holes is proportional to the mass of stars in the galaxy bulge, with a constant of proportionality that depends on the mean stellar age of the stars. This result is once again independent of black hole mass. We show that both the slope of the power-law and the decrease in the accretion rate onto black holes in old galaxies are consistent with population synthesis model predictions of the decline in stellar mass loss rates as a function of mean stellar age. Our results lead to a very simple picture of black hole growth in the local Universe. If the supply of cold gas in a galaxy bulge is plentiful, the black hole regulates its own growth at a rate that does not further depend on the properties of the interstellar medium. Once the gas runs out, black hole growth is regulated by the rate at which evolved stars lose their mass.

THE EVOLUTION OF THEMBH-σ RELATION INFERRED FROM THE AGE DISTRIBUTION OF LOCAL EARLY-TYPE GALAXIES AND ACTIVE GALACTIC NUCLEI EVOLUTION

We utilize the local velocity dispersion function (VDF) of spheroids, together with their inferred age--distributions, to predict the VDF at higher redshifts (0<z<6), under the assumption that (i) most of the stars in each nearby spheroid formed in a single episode, and (ii) the velocity dispersion sigma remained nearly constant afterward. We assume further that a supermassive black hole (BH) forms concurrently with the stars, and within ~1 Gyr of the formation of the potential well of the spheroid, and that the relation between the mass of the BH and host velocity dispersion maintains the form M_BH ~ sigma^{beta} with beta~4, but with the normalization allowed to evolve with redshift as ~(1+z)^{alpha}. We compute the BH mass function associated with the VDF at each redshift, and compare the accumulated total BH mass density with that inferred from the integrated quasar luminosity function (LF; the so--called Soltan argument). This comparison is insensitive to the assumed duty cycle or Eddington ratio of quasar activity, and we find that the match between the two BH mass densities favors a relatively mild redshift evolution, with alpha ~ 0.26, with a positive evolution as strong as alpha>1.3 excluded at the 99% confidence level. A direct match between the characteristic BH mass in the VDF--based and quasar LF--based BH mass functions also yields a mean Eddington ratio of lambda ~ 0.5-1 that is roughly constant within 0<z<3. A strong positive evolution in the M_BH-sigma relation is still allowed by the data if galaxies increase, on average, their velocity dispersions since the moment of formation, due to dissipative processes. If we assume that the mean velocity dispersion of the host galaxies evolves as sigma(z)=sigma(0)*(1+z)^{-gamma}, we find a lower limit of gamma>0.23 for alpha>1.5. abridged

DETERMINING QUASAR BLACK HOLE MASS FUNCTIONS FROM THEIR BROAD EMISSION LINES: APPLICATION TO THE BRIGHT QUASAR SURVEY

We describe a Bayesian approach to estimating quasar black hole mass functions (BHMF) using the broad emission lines to estimate black hole mass. We show how using the broad-line mass estimates in combination with statistical techniques developed for luminosity function estimation (e.g., the 1/Va correction) leads to statistically biased results. We derive the likelihood function for the BHMF based on the broad-line mass estimates, and derive the posterior distribution for the BHMF, given the observed data. We develop our statistical approach for a flexible model where the BHMF is modeled as a mixture of Gaussian functions. Statistical inference is performed using Markov chain Monte Carlo (MCMC) methods, and we describe a Metropolis–Hastings algorithm to perform the MCMC. The MCMC simulates random draws from the probability distribution of the BHMF parameters, given the data, and we use a simulated data set to show how these random draws may be used to estimate the probability distribution for the BHMF. In addition, we show how the MCMC output may be used to estimate the probability distribution of any quantities derived from the BHMF, such as the peak in the space density of quasars. Our method has the advantage that it is able to constrain the BHMF even beyond the survey detection limits at the adopted confidence level, accounts for measurement errors and the intrinsic uncertainty in broad-line mass estimates, and provides a natural way of estimating the probability distribution of any quantities derived from the BHMF. We conclude by using our method to estimate the local active BHMF using the z < 0.5 Bright Quasar Survey sources. At z ∼ 0.2, the quasar BHMF falls off approximately as a power law with slope ∼2 for MBH ≳ 108 M☉. Our analysis implies that at a given MBH, z < 0.5 broad-line quasars have a typical Eddington ratio of ∼0.4 and a dispersion in Eddington ratio of ≲0.5 dex.

Is there an upper limit to black hole masses?

We make a case for the existence for ultra-massive black holes (UMBHs) in the Universe, but argue that there exists a likely upper limit to black hole masses of the order of $M \sim 10^{10} \msun$. We show that there are three strong lines of argument that predicate the existence of UMBHs: (i) expected as a natural extension of the observed black hole mass bulge luminosity relation, when extrapolated to the bulge luminosities of bright central galaxies in clusters; (ii) new predictions for the mass function of seed black holes at high redshifts predict that growth via accretion or merger-induced accretion inevitably leads to the existence of rare UMBHs at late times; (iii) the local mass function of black holes computed from the observed X-ray luminosity functions of active galactic nuclei predict the existence of a high mass tail in the black hole mass function at $z = 0$. Consistency between the optical and X-ray census of the local black hole mass function requires an upper limit to black hole masses. This consistent picture also predicts that the slope of the $M_{\rm bh}$-$\sigma$ relation will evolve with redshift at the high mass end. Models of self-regulation that explain the co-evolution of the stellar component and nuclear black holes naturally provide such an upper limit. The combination of multi-wavelength constraints predicts the existence of UMBHs and simultaneously provides an upper limit to their masses. The typical hosts for these local UMBHs are likely the bright, central cluster galaxies in the nearby Universe.

RADIO PROPERTIES OF LOW-REDSHIFT BROAD LINE ACTIVE GALACTIC NUCLEI

The question as to whether the distribution of radio-loudness in active galactic nuclei (AGN) is actually bimodal has been discussed extensively in the literature. Futhermore, there have been claims that radio-loudness depends on black hole mass and Eddington ratio. We investigate these claims using the low redshift broad line AGN sample of Greene & Ho (2007), which consists of 8434 objects at z 10) and radio-quiet (RQ, R < 10) objects, but instead fill in a more radio-intermediate population in a continuous fashion for all subsamples. We find that 4.7% of the AGN in the flux-limited subsample are RL based on core radio emission alone. We calculate the radio-loud fraction (RLF) as both a function of black hole mass and Eddington ratio. The RLF decreases (from 13% to 2%) as Eddington ratio increases over 2.5 order of magnitude. The RLF is nearly constant (~5%) over 4 decades in black hole mass, except for an increase at masses greater than 10^8 solar masses. We find for the FIRST detected subsample that 367 of the RL AGN have black hole masses less than 10^8 solar masses, a large enough number to indicate that RL AGN are not a product of only the most massive black holes in the local universe.

SELF-CONSISTENT MODELS OF THE AGN AND BLACK HOLE POPULATIONS: DUTY CYCLES, ACCRETION RATES, AND THE MEAN RADIATIVE EFFICIENCY

We construct evolutionary models of the populations of AGN and supermassive black holes, in which the black hole mass function grows at the rate implied by the observed luminosity function, given assumptions about the radiative efficiency and the Eddington ratio. We draw on a variety of recent X-ray and optical measurements to estimate the bolometric AGN luminosity function and compare to X-ray background data and the independent estimate of Hopkins et al. (2007) to assess remaining systematic uncertainties. The integrated AGN emissivity closely tracks the cosmic star formation history, suggesting that star formation and black hole growth are closely linked at all redshifts. Observational uncertainties in the local black hole mass function remain substantial, with estimates of the integrated black hole mass density \rho_BH spanning the range 3-5.5x10^5 Msun/Mpc^3. We find good agreement with estimates of the local mass function for a reference model where all active black holes have efficiency \eps=0.065 and L_bol/L_Edd~0.4. In this model, the duty cycle of 10^9 Msun black holes declines from 0.07 at z=3 to 0.004 at z=1 and 0.0001 at z=0. The decline is shallower for less massive black holes, a signature of "downsizing" evolution in which more massive black holes build their mass earlier. The predicted duty cycles and AGN clustering bias in this model are in reasonable accord with observational estimates. If the typical Eddington ratio declines at z<2, then the "downsizing" of black hole growth is less pronounced. Matching the integrated AGN emissivity to the local black hole mass density implies \eps=0.075 (\rho_BH/4.5x10^5 Msun/Mpc^3)^{-1} for our standard luminosity function estimate (25% higher for Hopkins et al.'s), lower than the values \eps=0.16-0.20 predicted by MHD simulations of disk accretion.

Observing white dwarfs orbiting massive black holes in the gravitational wave and electro-magnetic window

We consider a potentially new class of gravitational wave sources consisting of a white dwarf coalescing into a massive black hole in the mass range � 10 4 10 5 M⊙. These sources are of particular interest because the gravitational wave signal produced during the inspiral phase can be detected by the Laser Interferometer Space Antenna (LISA) and is promptly followed, in an extended portion of the black hole and white dwarf mass parameter space, by an electro-magnetic signal generated by the tidal disruption of the star, detectable with X-ray, optical and UV telescopes. This class of sources could therefore yield a considerable number of scientific payoffs, that include precise cosmography at low redshift, demographics of black holes in the mass range � 10 4 10 5 M⊙, insights into dynamical interactions and populations of white dwarfs in the cores of dwarf galaxies, as well as a new probe into the structure and equation of state of white dwarfs. By modelling the gravitational and electromagnetic radiation produced by these events, we find them detectable in both observational windows at a distance � 200 Mpc, and possibly beyond for selected regions of the parameter space. We also estimate the detection rate for a number of model assumptions about black hole and white dwarf mass functions and dynamical interactions: the rate is (not surprisingly) highly uncertain, ranging from � 0.01yr −1 to � 100yr −1 . This is due to the current limited theoretical understanding and minimal observational constraints for these objects and processes. However, capture rate scaling arguments favor the high end of the above range, making likely the detection of several events during the LISA lifetime.

Jet Power Extracted from ADAF and the Applications to X‐Ray Binaries and the Radio Galaxy FR Dichotomy

We calculate the jet power of the classical Blandford-Znajek (BZ) model and hybrid model developed by Meier based on the global solutions of advection-dominated accretion flows (ADAFs) surrounding Kerr black holes. We find that the jet power of the hybrid model is larger than that of the pure BZ model. The jet power will dominate over the accretion power, and the objects will enter into jet-power-dominated advective systems,'' when the accretion rate is less than a critical value m(c) = M-c/M-Edd, where 3 x 10(-4) less than or similar to m(c) less than or similar to 5 x 10(-3) is a function of black hole spin parameter. The accretion power will be dominant when m greater than or similar to m(c), and the objects will enter into accretion-power-dominated advective systems.'' This is roughly consistent with that constrained from the low/hard-state black hole X-ray binaries (e. g., Fender et al.). We calculate the maximal jet power as a function of black hole mass with the hybrid jet formation model, and find it can roughly reproduce the dividing line of the Ledlow-Owen relation for FR I/FR II dichotomy in jet the power-black hole (BH) mass plane (Q(jet)-M-BH) if the dimensionless accretion rate m similar to 0.01 and BH spin parameter j similar to 0.9-0.99 are adopted. This accretion rate m similar to 0.01 is consistent with that of the critical accretion rate for the accretion mode transition of a standard disk to an ADAF constrained from the state transition of X-ray binaries. Our results imply that most FR I galaxies may be in the ADAF accretion mode similar to the low/hard-state XRBs.

Rapidly spinning massive black holes in active galactic nuclei: evidence from the black hole mass function

The comparison of the black hole mass function (BHMF) of active galactic nuclei (AGN) relics with the measured mass function of the massive black holes in galaxies provides strong evidence for the growth of massive black holes being dominated by mass accretion. We derive the Eddington ratio distributions as functions of black hole mass and redshift from a large AGN sample with measured Eddington ratios given by Kollmeier et al. We find that, even at the low mass end, most black holes are accreting at Eddington ratio ~0.2, which implies that the objects accreting at extremely high rates should be rare or such phases are very short. Using the derived Eddington ratios, we explore the cosmological evolution of massive black holes with an AGN bolometric luminosity function (LF). It is found that the resulted BHMF of AGN relics is unable to match the measured local BHMF of galaxies for any value of (constant) radiative efficiency. Motivated by Volonteri, Sikora & Lasota's study on the spin evolution of massive black holes, we assume the radiative efficiency to be dependent of black hole mass, i.e., it is low for M 10^8 solar masses. We find that the BHMF of AGN relics can roughly reproduce the local BHMF of galaxies if the radiative efficiency ~0.08 for the black holes with 10^9 solar masses, which implies that most massive black holes (>10^9 solar masses) are spinning very rapidly.

A synthesis model for AGN evolution: supermassive black holes growth and feedback modes

We present a comprehensive synthesis model for the active galactic nuclei (AGN) evolution and the growth of supermassive black hole (SMBH) in the Universe. We assume that black holes accrete in just three distinct physical states, or 'modes': at low Eddington ratio, only a radiatively inefficient, kinetically dominated mode is allowed [low kinetic (LK)]; at high Eddington ratio, instead, AGN may display both a purely radiative [radio quiet, high radiative (HR)] and a kinetic [radio loud, high kinetic (HK)] mode. We solve the continuity equation for the black hole mass function using the locally determined one as a boundary condition, and the hard X-ray luminosity function as tracer of the AGN growth rate distribution, supplemented with a luminosity-dependent bolometric correction and an absorbing column distribution. Differently from most previous semi-analytic and numerical models for black hole growth, we do not assume any specific distribution of Eddington ratios, rather we determine it empirically by coupling the mass and luminosity functions and a set of fundamental relations between observables in the three accretion modes. SMBH always show a very broad accretion rate distribution, and we discuss the profound consequences of this fact for our understanding of observed AGN fractions in galaxies, as well as for the empirical determination of SMBH mass functions with large surveys. We confirm previous results and clearly demonstrate that, at least for z≤ 1.5, SMBH mass function evolves antihierarchically, i.e. the most massive holes grew earlier and faster than less massive ones. For the first time, we find hints of a reversal of such a downsizing behaviour at redshifts above the peak of the black hole accretion rate density (z ≈2). We also derive tight constraints on the (mass-weighted) average radiative efficiency of AGN: under the simplifying assumption that the mass density of both high redshift (z ∼5) and 'wandering' black holes ejected from galactic nuclei after merger events are negligible compared to the local mass density, we find that 0.065 0.07, where ξ 0 is the local SMBH mass density in units of 4.3 x 10 5 M ⊙ Mpc -3 . We trace the cosmological evolution of the kinetic luminosity function of AGN, and find that the overall efficiency of SMBH in converting accreted rest mass energy into kinetic power, e kin , ranges between e kin ≃ (3-5) x 10 -3 , depending on the choice of the radio core luminosity function. Such a 'kinetic efficiency' varies however strongly with SMBH mass and redshift, being maximal for very massive holes at late times, as required for the AGN feedback by many galaxy formation models in cosmological contexts.

Mass Functions of the Active Black Holes in Distant Quasars from the Sloan Digital Sky Survey Data Release 3

We present the mass functions of actively accreting supermassive black holes over the redshift range 0.3 <= z <= 5 for a well-defined, homogeneous sample of 15,180 quasars from the Sloan Digital Sky Survey Data Release 3 (SDSS DR3) within an effective area of 1644 square degrees. This sample is the most uniform statistically significant subset available for the DR3 quasar sample. It was used for the DR3 quasar luminosity function, presented by Richards et al., and is the only sample suitable for the determination of the SDSS quasar black hole mass function. The sample extends from i = 15 to i = 19.1 at z less than about 3 and to i = 20.2 for z greater than about 3. The mass functions display a rise and fall in the space density distribution of active black holes at all epochs. Within the uncertainties the high-mass decline is consistent with a constant slope of beta of about -3.3 at all epochs. This slope is similar to the bright end slope of the luminosity function for epochs below z = 4. Our tests suggest that the down-turn toward lower mass values is due to incompleteness of the quasar sample with respect to black hole mass. Further details and analysis of these mass functions will be presented in forthcoming papers.

High-frequency X-ray variability as a mass estimator of stellar and supermassive black holes

There is increasing evidence that supermassive black holes in active galactic nuclei (AGN) are scaled-up versions of Galactic black holes. We show that the amplitude of high-frequency X-ray variability in the hard spectral state is inversely proportional to the black hole mass over eight orders of magnitude. We have analysed all available hard-state data from RXTE of seven Galactic black holes. Their power density spectra change dramatically from observation to observation, except for the high-frequency (≥ 10 Hz) tail, which seems to have a universal shape, roughly represented by a power law of index -2. The amplitude of the tail, C M (extrapolated to 1 Hz), remains approximately constant for a given source, regardless of the luminosity, unlike the break or quasi-periodic oscillation frequencies, which are usually strongly correlated with luminosity. Comparison with a moderate-luminosity sample of AGN shows that the amplitude of the tail is a simple function of black hole mass, C M = C/M, where C ≈ 1.25 M ⊙ Hz -1 . This makes C M a robust estimator of the black hole mass which is easy to apply to low-to moderate-luminosity supermassive black holes. The high-frequency tail with its universal shape is an invariant feature of a black hole and, possibly, an imprint of the last stable orbit.

The evolution of massive black hole seeds

We investigate the evolution of high redshift seed black hole masses at late times and their observational signatures. The massive black hole seeds studied here form at extremely high redshifts from the direct collapse of pre-galactic gas discs. Populating dark matter halos with seeds formed in this way, we follow the mass assembly of these black holes to the present time using a Monte-Carlo merger tree. Using this machinery we predict the black hole mass function at high redshifts and at the present time; the integrated mass density of black holes and the luminosity function of accreting black holes as a function of redshift. These predictions are made for a set of three seed models with varying black hole formation efficiency. Given the accuracy of current observational constraints, all 3 models can be adequately fit. Discrimination between the models appears predominantly at the low mass end of the present day black hole mass function which is not observationally well constrained. However, all our models predict that low surface brightness, bulgeless galaxies with large discs are least likely to be sites for the formation of massive seed black holes at high redshifts. The efficiency of seed formation at high redshifts has a direct influence on the black hole occupation fraction in galaxies at z=0. This effect is more pronounced for low mass galaxies. This is the key discriminant between the models studied here and the Population III remnant seed model. We find that there exists a population of low mass galaxies that do not host nuclear black holes. Our prediction of the shape of the black hole mass - velocity dispersion relation at the low mass end is in agreement with the recent observational determination from the census of low mass galaxies in the Virgo cluster.

Modelling the cosmological co-evolution of supermassive black holes and galaxies – I. BH scaling relations and the AGN luminosity function

We model the cosmological co-evolution of galaxies and their central supermassive black holes (BHs) within a semi-analytical framework developed on the outputs of the Millennium Simulation. This model, described in detail by Croton et al. and De Lucia and Blaizot, introduces a ‘radio mode’ feedback from active galactic nuclei (AGN) at the centre of X-ray emitting atmospheres in galaxy groups and clusters. Thanks to this mechanism, the model can simultaneously explain: (i) the low observed mass dropout rate in cooling flows; (ii) the exponential cut-off in the bright end of the galaxy luminosity function and (iii) the bulge-dominated morphologies and old stellar ages of the most massive galaxies in clusters. This paper is the first of a series in which we investigate how well this model can also reproduce the physical properties of BHs and AGN. Here we analyse the scaling relations, the fundamental plane and the mass function of BHs, and compare them with the most recent observational data. Moreover, we extend the semi-analytic model to follow the evolution of the BH mass accretion and its conversion into radiation, and compare the derived AGN bolometric luminosity function with the observed one. While we find for the most part a very good agreement between predicted and observed BH properties, the semi-analytic model underestimates the number density of luminous AGN at high redshifts, independently of the adopted Eddington factor and accretion efficiency. However, an agreement with the observations is possible within the framework of our model, provided it is assumed that the cold gas fraction accreted by BHs at high redshifts is larger than at low redshifts.

The Most Massive Black Holes in the Universe: Effects of Mergers in Massive Galaxy Clusters

Recent observations support the idea that nuclear black holes grew by gas accretion while shining as luminous quasars at high redshift, and they establish a relation of the black hole mass with the host galaxy's spheroidal stellar system. We develop an analytic model to calculate the expected impact of mergers on the masses of black holes in massive clusters of galaxies. We use the extended Press-Schechter formalism to generate Monte Carlo merger histories of halos with a mass 1015 h-1 M☉. We assume that the black hole mass function at z = 2 is similar to that inferred from observations at z = 0 (since quasar activity declines markedly at z < 2), and we assign black holes to the progenitor halos assuming a monotonic relation between halo mass and black hole mass. We follow the dynamical evolution of subhalos within larger halos, allowing for tidal stripping, the loss of orbital energy by dynamical friction, and random orbital perturbations in gravitational encounters with subhalos, and we assume that most black holes will efficiently merge after their host galaxies (represented as the nuclei of subhalos in our model) merge. Our analytic model reproduces numerical estimates of the subhalo mass function. We find that mergers can increase the mass of the most massive black holes in massive clusters typically by a factor ~2, after gas accretion has stopped. In our 10 realizations of 1015 h-1 M☉ clusters, the highest initial (z = 2) black hole masses are 5-7 × 109 M☉, but four of the clusters contain black holes in the range 1-1.5 × 1010 M☉ at z = 0. Satellite galaxies may host black holes whose mass is comparable to, or even greater than, that of the central galaxy. Thus, black hole mergers can significantly extend the very high end of the black hole mass function.

The Mass Function of Active Black Holes in the Local Universe

We present the first measurement of the BH mass function for broad-line active galaxies in the local universe. Using the ~8500 broad-line active galaxies from SDSS DR4, we construct a broad-line luminosity function that agrees very well with the local soft X-ray luminosity function. Using standard virial relations, we then convert observed broad-line luminosities and widths into BH masses. A mass function constructed in this way has the unique capability to probe the mass region <106 M☉, which, while insignificant in terms of total BH mass density, nevertheless may place important constraints on the mass distribution of seed BHs in the early universe. The characteristic local active BH has a mass of ~107 M☉ radiating at 10% of the Eddington rate. The active fraction is a strong function of BH mass; at both higher and lower masses the active mass function falls more steeply than one would infer from the distribution of bulge luminosity. The deficit of local massive radiating BHs is a well-known phenomenon, while we present the first robust measurement of a decline in the space density of active BHs at low mass.

Distribution of the Very First Population III Stars and Their Relation to Brightz ≈ 6 Quasars

We discuss the link between dark matter halos hosting the first Population III stars and the rare, massive halos that are generally considered to host bright quasars at high redshift (z ≈ 6). The main question that we intend to answer is whether the supermassive black holes powering these QSOs grew out from the seeds planted by the first intermediate-mass black holes created in the universe. This question involves a dynamical range of 1013 in mass, and we address it by combining N-body simulations of structure formation to identify the most massive halos at z ≈ 6 with a Monte Carlo method based on linear theory to obtain the location and formation times of the first-light halos within the whole simulation box. We show that the descendants of the first ≈106 M☉ virialized halos do not, on average, end in the most massive halos at z ≈ 6, but rather live in a large variety of environments. The oldest Population III progenitors of the most massive halos at z ≈ 6 form instead from density peaks that are on average 1.5 σ more common than the first Population III star formed in the volume occupied by one bright high-z QSO. The intermediate-mass black hole seeds planted by the very first Population III stars at z 40 can easily grow to masses mBH > 109.5 M☉ by z = 6 assuming Eddington accretion with radiative efficiency 0.1. Quenching of the black hole accretion is therefore crucial to avoid an overabundance of supermassive black holes at lower redshift. This can be obtained if the mass accretion is limited to a fraction η ≈ 6 × 10-3 of the total baryon mass of the halo hosting the black hole. The resulting high-end slope of the black hole mass function at z = 6 is α ≈ -3.7, a value within the 1 σ error bar for the bright-end slope of the observed quasar luminosity function at z = 6.

Unveiling Obscured Accretion in the Chandra Deep Field–South

A large population of heavily obscured, Compton Thick AGNs is predicted by models of galaxy formation, models of Cosmic X-ray Background and by the ``relic'' super-massive black-hole mass function measured from local bulges. However, so far only a handful of Compton thick AGNs have been possibly detected using even the deepest Chandra and XMM surveys. Compton-thick AGNs can be recovered thanks to the reprocessing of the AGN UV emission in the infrared by selecting sources with AGN luminosity's in the mid-infrared and faint near-infrared and optical emission. To this purpose, we make use of deep HST, VLT, Spitzer and Chandra data on the Chandra Deep Field South to constrain the number of Compton thick AGN in this field. We show that sources with high 24$\mu$m to optical flux ratios and red colors form a distinct source population, and that their infrared luminosity is dominated by AGN emission. Analysis of the X-ray properties of these extreme sources shows that most of them (80$\pm15%$) are indeed likely to be highly obscured, Compton thick AGNs. The number of infrared selected, Compton thick AGNs with 5.8$\mu$m luminosity higher than $10^{44.2}$ erg s$^{-1}$ turns out to be similar to that of X-ray selected, unobscured and moderately obscured AGNs with 2-10 keV luminosity higher than $10^{43}$ erg s$^{-1}$ in the redshift bin 1.2-2.6. This ``factor of 2'' source population is exactly what it is needed to solve the discrepancies between model predictions and X-ray AGN selection.

On the Inconsistency between the Black Hole Mass Function Inferred fromM•‐σ andM•‐LCorrelations

Black hole masses are tightly correlated with the stellar velocity dispersions of the bulges which surround them and slightly less well correlated with the bulge luminosity. It is common to use these correlations to estimate the expected abundance of massive black holes. This is usually done by starting from an observed distribution of velocity dispersions or luminosities and then changing variables. This procedure neglects the fact that there is intrinsic scatter in these black hole mass-observable correlations. Accounting for this scatter results in estimates of black hole abundances which are larger by almost an order of magnitude at masses >109 M☉. Including this scatter is particularly important for models which seek to infer quasar lifetimes and duty cycles from the local black hole mass function. However, even when scatter has been accounted for, the M•-σ relation predicts fewer massive black holes than does the M•-L relation. This is because the σ-L relation in the black hole samples currently available is inconsistent with that in the SDSS sample from which the distributions of L or σ are based: the black hole samples have smaller L for a given σ, or larger σ for a given L. The σ-L relation in the black hole samples is similarly discrepant with that in other samples of nearby early-type galaxies. This suggests that current black hole samples are biased: if this is a selection rather than a physical effect, then the M•-σ and M•-L relations currently in the literature are also biased from their true values.