Black Hole Mass Density Research Articles

Birth of Rapidly Spinning, Overmassive Black Holes in the Early Universe

The James Webb Space Telescope (JWST) has unveiled numerous massive black holes (BHs) in faint, broad-line active galactic nuclei (AGNs). The discovery highlights the presence of dust-reddened AGN populations, referred to as “little red dots (LRDs),” more abundant than X-ray-selected AGNs, which are less influenced by obscuration. This finding indicates that the cosmic growth rate of BHs within this population does not decrease but rather increases at higher redshifts beyond z ∼ 6. The BH accretion rate density deduced from their luminosity function is remarkably higher than that from other AGN surveys in X-ray and infrared bands. To align the cumulative mass density accreted to BHs with the observed BH mass density at z ≃ 4–5, as derived from the integration of the BH mass function, the radiative efficiency must be doubled from the canonical 10% value, achieving significance beyond the >3σ confidence level. This suggests the presence of rapid spins with 96% of the maximum limit among these BHs under the thin-disk approximation, maintained by prolonged mass accretion instead of chaotic accretion with randomly oriented inflows. Moreover, we derive an upper bound for the stellar mass of galaxies hosting these LRDs, ensuring consistency with galaxy formation in the standard cosmological model, where the host stellar mass is limited by the available baryonic reservoir. Our analysis gives a lower bound for the BH-to-galaxy mass ratio that exceeds the typical value known in the nearby universe and aligns with that for JWST-detected unobscured AGNs. Accordingly, we propose a hypothesis that the dense, dust-rich environments within LRDs facilitate the emergence of rapidly spinning and overmassive BH populations during the epoch of reionization. This scenario predicts a potential association between relativistic jets and other high-energy phenomena with overmassive BHs in the early universe.

The Mass Density of Merging Binary Black Holes over Cosmic Time

The connection between the binary black hole (BBH) mergers observed by LIGO-Virgo-KAGRA and their stellar progenitors remains uncertain. Specifically, the fraction ϵ of stellar mass that ends up in BBH mergers and the delay time τ between star formation and merger carry information about the astrophysical processes that produce merging BBHs. We model the merger rate in terms of cosmic star formation, coupled with a metallicity-dependent efficiency ϵ and a distribution of delay times τ, and infer these parameters with data from the Third Gravitational-Wave Transient Catalog. The progenitors to merging BBHs preferentially form in low-metallicity environments with a low-metallicity efficiency of log10ϵ<Zt=−3.99−0.87+0.68 and a high-metallicity efficiency of log10ϵ<Zt=−4.60−0.34+0.30 at 90% credibility. The data also prefer short delay times. For a power-law distribution p(τ) ∝ τ α , we find τmin<1.9Gyr and α < −1.32 at 90% credibility. Our model allows us to extrapolate the mass density in BBHs to high redshifts. We cumulatively integrate our density rate over time to get the total density of merging stellar-mass BBHs as a function of redshift. Today, BBH mergers are only ∼0.01% of the total stellar-mass density created by >10 M ⊙ progenitors. However, because massive stars are short lived, there may be more mass in merging BBHs than in living massive stars as early as ∼2.5 Gyr ago. We also compare to the mass in supermassive black holes, finding that the densities were comparable ∼12.5 Gyr ago, but their densities quickly increased to ∼75 times the density in merging stellar-mass BBHs by z ∼ 1.

The impact of black hole scaling relation assumptions on the mass density of black holes

ABSTRACT We examine the effect of supermassive black hole (SMBH) mass scaling relation choice on the inferred SMBH mass population since redshift z ∼ 3. To make robust predictions for the gravitational wave background (GWB), we must have a solid understanding of the underlying SMBH demographics. Using the SDSS and 3D-HST + CANDELS surveys for 0 &amp;lt; z &amp;lt; 3, we evaluate the inferred SMBH masses from two SMBH–galaxy scaling relations: MBH–Mbulge and MBH–σ. Our SMBH mass functions come directly from stellar mass measurements for MBH–Mbulge, and indirectly from stellar mass and galaxy radius measurements along with the galaxy mass fundamental plane for MBH–σ. We find that there is a substantial difference in predictions especially for z &amp;gt; 1, and this difference increases out to z = 3. In particular, we find that using velocity dispersion predicts a greater number of SMBHs with masses greater than 109 M⊙. The GWB that pulsar timing arrays find evidence for is higher in amplitude than expected from GWB predictions which rely on high-redshift extrapolations of local SMBH mass–galaxy scaling relations. The difference in SMBH demographics resulting from different scaling relations may be the origin for the mismatch between the signal amplitude and predictions. Generally, our results suggest that a deeper understanding of the potential redshift evolution of these relations is needed if we are to draw significant insight from their predictions at z &amp;gt; 1.

The ASTRID simulation: the evolution of supermassive black holes

ABSTRACTWe present the evolution of black holes (BHs) and their relationship with their host galaxies in Astrid, a large-volume cosmological hydrodynamical simulation with box size 250 h−1Mpc containing 2 × 55003 particles evolved to z = 3. Astrid statistically models BH gas accretion and active galactic nucleus (AGN) feedback to their environments, applies a power-law distribution for BH seed mass $\, M_{\rm sd}$, uses a dynamical friction model for BH dynamics, and executes a physical treatment of BH mergers. The BH population is broadly consistent with empirical constraints on the BH mass function, the bright end of the luminosity functions, and the time evolution of BH mass and accretion rate density. The BH mass and accretion exhibit a tight correlation with host stellar mass and star formation rate. We trace BHs seeded before z &amp;gt; 10 down to z = 3, finding that BHs carry virtually no imprint of the initial $\, M_{\rm sd}$ except those with the smallest $\, M_{\rm sd}$, where less than 50 per cent of them have doubled in mass. Gas accretion is the dominant channel for BH growth compared to BH mergers. With dynamical friction, Astrid predicts a significant delay for BH mergers after the first encounter of a BH pair, with a typical elapse time of about 200 Myr. There are in total 4.5 × 105 BH mergers in Astrid at z &amp;gt; 3, ∼103 of which have X-ray detectable EM counterparts: a bright $\, {\rm kpc}$ scale dual AGN with LX &amp;gt; 1043 erg s−1. BHs with $\, M_{\rm BH}\sim 10^{7\!-\!8} \, M_{\odot }$ experience the most frequent mergers. Galaxies that host BH mergers are unbiased tracers of the overall $\, M_{\rm BH}\!-\! M_*$ relation. Massive ($\gt 10^{11}\, M_{\odot }$) galaxies have a high occupation number (≳10) of BHs, and hence host the majority of BH mergers.

Accretion History of AGNs. III. Radiative Efficiency and AGN Contribution to Reionization

Abstract The cosmic history of supermassive black hole (SMBH) growth is important for understanding galaxy evolution, reionization, and the physics of accretion. Recent NuSTAR, Swift-BAT, and Chandra hard X-ray surveys have provided new constraints on the space density of heavily obscured active galactic nuclei (AGNs). Using the new X-ray luminosity function derived from these data, we here estimate the accretion efficiency of SMBHs and their contribution to reionization. We calculate the total ionizing radiation from AGNs as a function of redshift, based on the X radiation and distribution of obscuring column density, converted to ultraviolet (UV) wavelengths. Limiting the luminosity function to unobscured AGNs only, our results agree with current UV luminosity functions of unobscured AGNs. For realistic assumptions about the escape fraction, the contribution of all AGNs to cosmic reionization is ∼4 times lower than the galaxy contribution (23% at z ∼ 6). Our results also offer an observationally constrained prescription that can be used in simulations or models of galaxy evolution. To estimate the average efficiency with which SMBHs convert mass to light, we compare the total radiated energy, converted from X-ray light using a bolometric correction, with the most recent local black hole mass density. The most likely value, η ∼ 0.3–0.34, approaches the theoretical limit for a maximally rotating Kerr black hole, η = 0.42, implying that on average growing SMBHs are spinning rapidly.

On the Absence of High-redshift AGNs: Little Growth in the Supermassive Black Hole Population at High Redshifts

Abstract We search for high-redshift (z &gt; 4.5) X-ray active galactic nuclei (AGNs) in the deep central (off-axis angle &lt; 5.′7) region of the 7 Ms Chandra Deep Field-South X-ray image. We compile an initial candidate sample from direct X-ray detections. We then probe more deeply in the X-ray data by using preselected samples with high spatial resolution near-infrared (NIR)/mid-infrared (MIR) (Hubble Space Telescope (HST) 1.6 μm and Spitzer 4.5 μm) and submillimeter (ALMA 850 μm) observations. The combination of the NIR/MIR and submillimeter preselections allows us to find X-ray sources with a wide range of dust properties and spectral energy distributions (SEDs). We use the SEDs from the optical to the submillimeter to determine if previous photometric redshifts were plausible. Only five possible z &gt; 5 X-ray AGNs are found, all of which might also lie at lower redshifts. If they do lie at high redshifts, then two are Compton-thick AGNs. Three of the five are ALMA 850 μm sources, including the two Compton-thick AGN candidates. We find that (i) the number density of X-ray AGN drops rapidly at high redshifts, (ii) the detected AGNs do not contribute significantly to photoionization at z &gt; 5, and (iii) the measured X-ray light density over z = 5–10 implies a very low black hole accretion density with very little growth in the black hole mass density in this redshift range.

Constraining black hole–galaxy scaling relations and radiative efficiency from galaxy clustering

The masses of supermassive black holes are observed to increase with either the total mass or the mean (random) velocity of the stars in their host galaxies. The origin of these correlations remains elusive due to observational systematics and biases that severely limit our knowledge of the local demography of supermassive black holes. Here, we show that the large-scale spatial distribution of local active galactic nuclei (AGN) can constrain the shape and normalization of the black hole–stellar mass relation, thus bypassing resolution-related observational biases. In turn, our results can set more stringent constraints on the AGN radiative efficiency, e. For currently accepted values of the AGN obscured fractions and bolometric corrections, our estimated local supermassive black hole mass density favours mean e values of ~10–20%, suggesting that the vast majority of supermassive black holes are spinning moderately to rapidly. With large-scale AGN surveys coming online, our methodology will enable even tighter constraints on the fundamental parameters that regulate the growth of supermassive black holes. The large-scale spatial distribution of local active galactic nuclei can constrain the black hole–stellar mass relation and their mean radiative efficiency to 10–20%, suggesting moderate to high spins for the vast majority of supermassive black holes.

The clustering of undetected high-redshift black holes and their signatures in cosmic backgrounds

ABSTRACT There exist hitherto unexplained fluctuations in the cosmic infrared background on arcminute scales and larger. These have been shown to cross-correlate with the cosmic X-ray background, leading several authors to attribute the excess to a high-redshift growing black hole population. In order to investigate potential sources that could explain this excess, in this paper, we develop a new framework to compute the power spectrum of undetected sources that do not have constant flux as a function of halo mass. In this formulation, we combine a semi-analytic model for black hole growth and their simulated spectra from hydrodynamical simulations. Revisiting the possible contribution of a high-redshift black hole population, we find that too much black hole growth is required at early epochs for z &amp;gt; 6 accretion to explain these fluctuations. Examining a population of accreting black holes at more moderate redshifts, z ∼ 2–3, we find that such models produce a poor fit to the observed fluctuations while simultaneously overproducing the local black hole mass density. Additionally, we rule out the hypothesis of a missing Galactic foreground of warm dust that produces coherent fluctuations in the X-ray via reflection of Galactic X-ray binary emission. Although we firmly rule out accreting massive black holes as the source of these missing fluctuations, additional studies will be required to determine their origin.

The cosmic evolution of massive black holes in the Horizon-AGN simulation

We analyse the demographics of black holes (BHs) in the large-volume cosmological hydrodynamical simulation Horizon-AGN. This simulation statistically models how much gas is accreted onto BHs, traces the energy deposited into their environment and, consequently, the back-reaction of the ambient medium on BH growth. The synthetic BHs reproduce a variety of observational constraints such as the redshift evolution of the BH mass density and the mass function. Strong self-regulation via AGN feedback, weak supernova feedback, and unresolved internal processes result in a tight BH-galaxy mass correlation. Starting at z~2, tidal stripping creates a small population of BHs over-massive with respect to the halo. The fraction of galaxies hosting a central BH or an AGN increases with stellar mass. The AGN fraction agrees better with multi-wavelength studies, than single-wavelength ones, unless obscuration is taken into account. The most massive halos present BH multiplicity, with additional BHs gained by ongoing or past mergers. In some cases, both a central and an off-centre AGN shine concurrently, producing a dual AGN. This dual AGN population dwindles with decreasing redshift, as found in observations. Specific accretion rate and Eddington ratio distributions are in good agreement with observational estimates. The BH population is dominated in turn by fast, slow, and very slow accretors, with transitions occurring at z=3 and z=2 respectively.

The Illustris simulation: the evolving population of black holes across cosmic time

We study the properties of black holes and their host galaxies across cosmic time in the Illustris simulation. Illustris is a large scale cosmological hydrodynamical simulation which resolves a (106.5 Mpc)^3 volume with more than 12 billion resolution elements and includes state-of-the-art physical models relevant for galaxy formation. We find that the black hole mass density for redshifts z = 0 - 5 and the black hole mass function at z = 0 predicted by Illustris are in very good agreement with the most recent observational constraints. We show that the bolometric and hard X-ray luminosity functions of AGN at z = 0 and 1 reproduce observational data very well over the full dynamic range probed. Unless the bolometric corrections are largely underestimated, this requires radiative efficiencies to be on average low, epsilon_r <= 0.1, noting however that in our model radiative efficiencies are degenerate with black hole feedback efficiencies. Cosmic downsizing of the AGN population is in broad agreement with the findings from X-ray surveys, but we predict a larger number density of faint AGN at high redshifts than currently inferred. We also study black hole -- host galaxy scaling relations as a function of galaxy morphology, colour and specific star formation rate. We find that black holes and galaxies co-evolve at the massive end, but for low mass, blue and star-forming galaxies there is no tight relation with either their central black hole masses or the nuclear AGN activity.

THESPITZERMID-INFRARED AGN SURVEY. II. THE DEMOGRAPHICS AND COSMIC EVOLUTION OF THE AGN POPULATION

We present luminosity functions derived from a spectroscopic survey of AGN selected from Spitzer Space Telescope imaging surveys. Selection in the mid-infrared is significantly less affected by dust obscuration. We can thus compare the luminosity functions of the obscured and unobscured AGN in a more reliable fashion than by using optical or X-ray data alone. We find that the AGN luminosity function can be well described by a broken power-law model in which the break luminosity decreases with redshift. At high redshifts ($z>1.6$), we find significantly more AGN at a given bolometric luminosity than found by either optical quasar surveys or hard X-ray surveys. The fraction of obscured AGN decreases rapidly with increasing AGN luminosity, but, at least at high redshifts, appears to remain at $\approx 50$\% even at bolometric luminosities $\sim 10^{14}L_{\odot}$. The data support a picture in which the obscured and unobscured populations evolve differently, with some evidence that high luminosity obscured quasars peak in space density at a higher redshift than their unobscured counterparts. The amount of accretion energy in the Universe estimated from this work suggests that AGN contribute about 12\% to the total radiation intensity of the Universe, and a high radiative accretion efficiency $\approx 0.18^{+0.12}_{-0.07}$ is required to match current estimates of the local mass density in black holes.

Mass without radiation: Heavily obscured AGNs, the X-ray background, and the black hole mass density

A recent revision of black hole scaling relations (Kormendy & Ho 2013), indicates that the local mass density in black holes should be increased by up to a factor of five with respect to previously determined values. The local black hole mass density is connected to the mean radiative efficiency of accretion through the time integral of the AGN volume density and a significant increase of the local black holes mass density would have interesting consequences on AGN accretion properties and demography. One possibility to explain a large black hole mass density is that most of the Black Hole growth is via radiatively inefficient channels such as super Eddington accretion, however, given the intrinsic degeneracies in the Soltan argument, this solution is not unique. Here we show how it is possible to accommodate a larger fraction of heavily buried, Compton thick AGN, without violating the limit imposed by the hard X-ray and mid-infrared backgrounds spectral energy density.

Tracing the cosmic growth of supermassive black holes to z ∼ 3 with Herschel★

We study a sample of Herschel-PACS selected galaxies within the GOODS-South and the COSMOS fields in the framework of the PACS Evolutionary Probe (PEP) project. Starting from the rich multi-wavelength photometric data-sets available in both fields, we perform a broad-band Spectral Energy Distribution (SED) decomposition to disentangle the possible active galactic nucleus (AGN) contribution from that related to the host galaxy. We find that 37 per cent of the Herschel-selected sample shows signatures of nuclear activity at the 99 per cent confidence level. The probability to reveal AGN activity increases for bright ($L_{\rm 1-1000} > 10^{11} \rm L_{\odot}$) star-forming galaxies at $z>0.3$, becoming about 80 per cent for the brightest ($L_{\rm 1-1000} > 10^{12} \rm L_{\odot}$) infrared (IR) galaxies at $z \geq 1$. Finally, we reconstruct the AGN bolometric luminosity function and the super-massive black hole growth rate across cosmic time up to $z \sim 3$ from a Far-Infrared (FIR) perspective. This work shows general agreement with most of the panchromatic estimates from the literature, with the global black hole growth peaking at $z \sim 2$ and reproducing the observed local black hole mass density with consistent values of the radiative efficiency $\epsilon_{\rm rad}$ ($\sim$0.07).

NEW OBSERVATIONAL CONSTRAINTS ON THE GROWTH OF THE FIRST SUPERMASSIVE BLACK HOLES

We constrain the total accreted mass density in supermassive black holes at z>6, inferred via the upper limit derived from the integrated X-ray emission from a sample of photometrically selected galaxy candidates. Studying galaxies obtained from the deepest Hubble Space Telescope images combined with the Chandra 4 Msec observations of the Chandra Deep Field South, we achieve the most restrictive constraints on total black hole growth in the early Universe. We estimate an accreted mass density <1000Mo Mpc^-3 at z~6, significantly lower than the previous predictions from some existing models of early black hole growth and earlier prior observations. These results place interesting constraints on early black growth and mass assembly by accretion and imply one or more of the following: (1) only a fraction of the luminous galaxies at this epoch contain active black holes; (2) most black hole growth at early epochs happens in dusty and/or less massive - as yet undetected - host galaxies; (3) there is a significant fraction of low-z interlopers in the galaxy sample; (4) early black hole growth is radiatively inefficient, heavily obscured and/or is due to black hole mergers as opposed to accretion or (5) the bulk of the black hole growth occurs at late times. All of these possibilities have important implications for our understanding of high redshift seed formation models.

The Multiwavelength AGN Population and the X-ray Background

AbstractIn order to fully understand galaxy formation we need to know when in the cosmic history are supermassive black holes (SMBHs) growing more intensively, in what type of galaxies this growth is happening and what fraction of these sources are invisible at most wavelengths due to obscuration. Active Galactic Nuclei (AGN) population synthesis models that can explain the spectral shape and intensity of the cosmic X-ray background (CXRB) indicate that most of the SMBH growth occurs in moderate-luminosity (LX~ 1044 erg/s) sources (Seyfert-type AGN), at z~ 0.5−1 and in heavily obscured but Compton-thin, NH~ 1023cm−2, systems. However, this is not the complete history, as a large fraction of black hole growth does not emit significantly in X-rays either due to obscuration, intrinsic low luminosities or large distances. The integrated intensity at high energies indicates that a significant fraction of the total black hole growth, 22%, occurs in heavily-obscured systems that are not individually detected in even the deepest X-ray observations. We further investigate the AGN triggering mechanism as a function of bolometric luminosity, finding evidence for a strong connection between significant black hole growth events and major galaxy mergers from z~ 0 to z~ 3, while less spectacular but longer accretion episodes are most likely due to other (stochastic) processes. AGN activity triggered by major galaxies is responsible for ~60% of the total black hole growth. Finally, we constrain the total accreted mass density in supermassive black holes at z &gt; 6, inferred via the upper limit derived from the integrated X-ray emission from a sample of photometrically selected galaxy candidates. We estimate an accreted mass density &lt;1000 M⊙Mpc−3 at z~ 6, significantly lower than the previous predictions from some existing models of early black hole growth and earlier prior observations.

A solution of the coincidence problem based on the recent galactic core black hole mass density increase

A mechanism capable to provide a natural solution to two major cosmological problems, i.e. the cosmic acceleration and the coincidence problem, is proposed. A specific brane-bulk energy exchange mechanism produces a total dark pressure, arising when adding all normal to the brane negative pressures in the interior of galactic core black holes. This astrophysically produced negative dark pressure explains cosmic acceleration and why the dark energy today is of the same order to the matter density for a wide range of the involved parameters. An exciting result of the analysis is that the recent rise of the galactic core black hole mass density causes the recent passage from cosmic deceleration to acceleration. Finally, it is worth mentioning that this work corrects a wide spread fallacy among brane cosmologists, i.e. that escaping gravitons result to positive dark pressure.

Black hole universe: Construction and analysis of initial data

We numerically construct an one-parameter family of initial data of an expanding inhomogeneous universe model which is composed of regularly aligned black holes with an identical mass. They are initial data for vacuum solutions of the Einstein equations. We call this universe model the "black hole universe" and analyze the structure of these initial data. We study the relation between the mean expansion rate of the 3-space, which corresponds to the Hubble parameter, and the mass density of black holes. The result implies that the same relation as that of the Einstein-de Sitter universe is realized in the limit of the large separation between neighboring black holes. The applicability of the cosmological Newtonian $N$-body simulation to the dark matter composed of black holes is also discussed. The deviation of the spatial metric of the cosmological Newtonian $N$-body system from that of the black hole universe is found to be smaller than about 1% in a region distant from the particles, if the separation length between neighboring particles is 20 times larger than their gravitational radius. By contrast, the deviation of the square of the Hubble parameter of the cosmological Newtonian $N$-body system from that of the black hole universe is about 20% for the same separation length.

Supermassive black holes: connecting the growth to the cosmic star formation rate

ABSTRACT We present a model connecting the cosmic star formation rate (CSFR) to the growth of supermassive black holes. Considering that the evolution of the massive black hole is dominated by accretion (Soltan’s argument) and that the accretion process can be described by a probabilistic function directly regulated by the CSFR, we obtain the evolution of the black hole mass density. Then, using the quasar luminosity function, we determine both the functional form of the radiative efficiency and the evolution of the quasar duty cycle as functions of the redshift. We analyse four different CSFRs showing that the quasar duty cycle, δ(z), peaks at z∼ 8.5–11 and so within the window associated with the reionization of the Universe. In particular, δmax∼ 0.09–0.22 depending on the CSFR. The mean radiative efficiency, , peaks at z∼ 0.1–1.3 with depending on the specific CSFR used. Our results also show that it is not necessary for a supercritical Eddington accretion regime to produce the growth of the black hole seeds. The present scenario is consistent with the formation of black hole seeds ∼103 M⊙ at z∼ 20.

EVOLUTION OF SUPERMASSIVE BLACK HOLES FROM COSMOLOGICAL SIMULATIONS

The correlations between the mass of supermassive black holes and the properties of their host galaxies are investigated through cosmological simulations. Black holes grow from seeds of 100 M⊙ are inserted into density peaks presented in the redshift range 12–15. Seeds grow essentially by accreting matter from a nuclear disk and also by coalescences resulting from merger episodes. At z = 0, our simulations reproduce the black hole mass function and the correlations of the black hole mass, both with stellar velocity dispersion and host dark halo mass. Moreover, the evolution of the black hole mass density derived from the present simulations agrees with that derived from the bolometric luminosity of quasars, indicating that the average accretion history of seeds is adequately reproduced. However, our simulations are unable to form black holes with masses above 109 M⊙ at z ~ 6, whose existence is inferred from the bright quasars detected by the Sloan survey in this redshift range.

GROWTH OF MASSIVE BLACK HOLES AT THEIR LATE STAGE

We derive the black hole mass density as a function of redshift with the bolometric luminosity function of AGN assuming that massive black holes grew via accreting the circumnuclear gases, in which the derived black hole mass density is required to match the measured local black hole mass density at z=0. ADAFs are supposed to present in low luminosity AGNs/normal galaxies, which are very hot and radiate mostly in the hard X-ray band. Most of the XRB is contributed by bright AGNs, and a variety of AGN population synthesis models were developed to model the observed XRB in the last two decades. Based on our derived black hole mass density, we calculate the contribution to the XRB from the ADAFs in faint AGNs/normal galaxies with a given Eddington ratio distribution, which is mostly in hard X-ray energy band with an energy peak at ~200 keV. The growth of massive black holes during ADAF phase can therefore be constrained with the observed XRB. Combining an AGN population synthesis model with our results, we find that the fitting on the observed XRB, especially at hard X-ray energy band with \ga 100 keV, is improved provided the contribution of the ADAFs in low luminosity AGNs/normal galaxies is properly included. It is found that less than ~15 per cent of local massive black hole mass density was accreted during ADAF phases. We suggest that more accurate measurements of the XRB in the energy band with \ga 100 keV in the future may help constrain the growth of massive black holes at their late stage. We also calculate their contribution to the extragalactic gamma-ray background, and find that less than ~1% of the observed EGRB is contributed by the ADAFs in these faint sources.