Eddington Ratio Distribution Function Research Articles

Constraining the Low-mass End of the Black Hole Mass Function and the Active Fraction of the Intermediate-mass Black Holes

We investigate the black hole mass function (BHMF) and the Eddington ratio distribution function (ERDF), focusing on the intermediate-mass black holes (IMBHs) with masses down to M • ∼ 104 M ⊙. Based on the active galactic nuclei (AGNs) with a detected broad Hα emission line, we construct a sample of 14,242 AGNs at redshift z < 0.35, including 243 IMBHs with M • < 106 M ⊙. By jointly modeling the BHMF and ERDF via the maximum posterior estimation, we find that the BHMF peaks at ∼106 M ⊙ and exhibits a relatively constant value of 10−4 Mpc−3 dex−1 at the low-mass end. By comparing the derived BHMF of type 1 AGNs with the galaxy mass function based on the updated black hole mass–host galaxy stellar mass relation, we derive the active fraction. We also determine the active fraction for all AGNs using the upper and lower limit of the type 1 fraction. The active fraction decreases from 15%–40% for massive galaxies (M ⋆ > 1010 M ⊙) to lower than ∼2% for dwarf galaxies with M ⋆ ∼ 108 M ⊙. These results suggest that the black hole occupation fraction is expected to be ∼50% for low-mass galaxies (M ⋆ ∼ 108.5–109 M ⊙) if the duty cycle is similar between IMBHs and supermassive black holes.

Black Hole Mass and Eddington-ratio Distributions of Less-luminous Quasars at z ∼ 4 in the Subaru Hyper Suprime-Cam Wide Field

We investigate the black hole mass function (BHMF) and Eddington-ratio distribution function (ERDF) of broad-line active galactic nuclei (AGNs) at z = 4, based on a sample of 52 quasars with i < 23.2 at 3.50 ≤ z ≤ 4.25 from the Hyper Suprime-Cam Subaru Strategic Program S16A-Wide2 data set, and 1462 quasars with i < 20.2 in the same redshift range from the Sloan Digital Sky Survey data release 7 quasar catalog. Virial black hole (BH) masses of quasars are estimated using the width of the CIV 1549 Å line and the continuum luminosity at 1350 Å. To obtain the intrinsic broad-line AGN BHMF and ERDF, we correct for the incompleteness in the low-mass and/or low-Eddington-ratio ranges caused by the flux-limited selection. The resulting BHMF is constrained down to logMBH/M⊙∼7.5 . In comparison with broad-line AGN BHMFs at z ∼ 2 in the literature, we find that the number density of massive SMBHs peaks at higher redshifts, consistent with the downsizing evolutionary scenario. Additionally, the resulting ERDF shows a negative dependence on BH mass, suggesting more massive SMBHs tend to accrete at lower-Eddington ratios at z = 4. With the derived intrinsic broad-line AGN BHMF, we also evaluate the active fraction of broad-line AGNs among the entire SMBH population at z = 4. The resulting active fraction may suggest a positive dependence on BH mass. Finally, we examine the time evolution of broad-line AGN BHMF between z = 4 and 6 through solving the continuity equation. The results suggest that the broad-line AGN BHMFs at z = 4–6 only show evolution in their normalization, but with no significant changes in their shape.

The Assembly of Black Hole Mass and Luminosity Functions of High-redshift Quasars via Multiple Accretion Episodes

The early evolution of the quasar luminosity function (QLF) and black hole mass function (BHMF) encodes key information on the physics determining the radiative and accretion processes of supermassive black holes (BHs) in high-z quasars. Although the QLF shape has been constrained by recent observations, it remains challenging to develop a theoretical model that explains its redshift evolution associated with BH growth self-consistently. In this study, based on a semianalytical model for the BH formation and growth, we construct the QLF and BHMF of the early BH population that experiences multiple accretion bursts, in each of which a constant Eddington ratio is assigned following a Schechter distribution function. Our best-fit model to reproduce the observed QLF and BHMF at z ≃ 6 suggests that several episodes of moderate super-Eddington accretion occur and each of them lasts for τ ≃ 20–30 Myr. The average duty cycle in super-Eddington phases is ≃15% for massive BHs that reach ≳108 M ⊙ by z ≃ 6, which is nearly twice that of the entire population. We find that the observed Eddington ratio distribution function is skewed to a lognormal shape owing to detection limits of quasar surveys. The predicted redshift evolution of the QLF and BHMF suggests a rapid decay of their number and mass density in a cosmic volume toward z ≳ 6. These results will be unveiled by future deep and wide surveys with the James Webb Space Telescope, Roman Space Telescope, and Euclid.

Constraints From Dwarf Galaxies on Black Hole Seeding and Growth Models With Current and Future Surveys

Dwarf galaxies are promising test beds for constraining models of supermassive and intermediate-mass black holes (MBHs) via their BH occupation fraction (BHOF). Disentangling seeding from the confounding effects of mass assembly over a Hubble time is a challenging problem that we tackle in this study with a suite of semianalytical models (SAMs). We show how the measured BHOF depends on the lowest BH mass or active galactic nucleus (AGN) luminosity achieved by a survey. To tell seeding models apart, we need to detect or model all AGNs brighter than 1037 erg s−1 in galaxies of M * ∼ 108−10 M ⊙. Shallower surveys, like eRASS, cannot distinguish between seed models even with the compensation of a much larger survey volume. We show that the AMUSE survey, with its inference of the MBH population underlying the observed AGNs, strongly favors heavy seed models, growing with either a power-law Eddington ratio distribution function or one in which BH accretion is tied to the star formation rate (i.e., the AGN-main sequence, AGN-MS, model). These two growth channels can then be distinguished by the AGN luminosity function at >1040 erg s−1, with the AGN-MS model requiring more accretion than observed at z ∼ 0. Thus, current X-ray observations favor heavy seeds whose Eddington ratios follow a power-law distribution. The different models also predict different radio scaling relations, which we quantify using the fundamental plane of BH activity. We close with recommendations for the design of upcoming multiwavelength campaigns that can optimally detect MBHs in dwarf galaxies.

Probing the Structure and Evolution of BASS Active Galactic Nuclei through Eddington Ratios

We constrain the intrinsic Eddington ratio (λ Edd) distribution function for local active galactic nuclei (AGN) in bins of low and high obscuration and ], using the Swift Burst Alert Telescope 70 month/BASS DR2 survey. We interpret the fraction of obscured AGN in terms of circumnuclear geometry and temporal evolution. Specifically, at low Eddington ratios (−2), obscured AGN outnumber unobscured ones by a factor of ∼4, reflecting the covering factor of the circumnuclear material (0.8, or a torus opening angle of ∼34°). At high Eddington ratios (−1), the trend is reversed, with <30% of AGN having , which we suggest is mainly due to the small fraction of time spent in a highly obscured state. Considering the Eddington ratio distribution function of narrow-line and broad-line AGN from our prior work, we see a qualitatively similar picture. To disentangle temporal and geometric effects at high λ Edd, we explore plausible clearing scenarios such that the time-weighted covering factors agree with the observed population ratio. We find that the low fraction of obscured AGN at high λ Edd is primarily due to the fact that the covering factor drops very rapidly, with more than half the time spent with <10% covering factor. We also find that nearly all obscured AGN at high-λ Edd exhibit some broad lines. We suggest that this is because the height of the depleted torus falls below the height of the broad-line region, making the latter visible from all lines of sight.

BASS XXXVII: The Role of Radiative Feedback in the Growth and Obscuration Properties of Nearby Supermassive Black Holes

We study the relation between obscuration and supermassive black hole (SMBH) accretion using a large sample of hard X-ray selected active galactic nuclei (AGNs). We find a strong decrease in the fraction of obscured sources above the Eddington limit for dusty gas () confirming earlier results, and consistent with the radiation-regulated unification model. This also explains the difference in the Eddington ratio distribution functions (ERDFs) of type 1 and type 2 AGNs obtained by a recent study. The break in the ERDF of nearby AGNs is at . This corresponds to the λ Edd where AGNs transition from having most of their sky covered by obscuring material to being mostly devoid of absorbing material. A similar trend is observed for the luminosity function, which implies that most of the SMBH growth in the local universe happens when the AGN is covered by a large reservoir of gas and dust. These results could be explained with a radiation-regulated growth model, in which AGNs move in the N H–λ Edd plane during their life cycle. The growth episode starts with the AGN mostly unobscured and accreting at low λ Edd. As the SMBH is further fueled, λ Edd, N H and the covering factor increase, leading the AGN to be preferentially observed as obscured. Once λ Edd reaches the Eddington limit for dusty gas, the covering factor and N H rapidly decrease, leading the AGN to be typically observed as unobscured. As the remaining fuel is depleted, the SMBH goes back into a quiescent phase.

BASS. XXX. Distribution Functions of DR2 Eddington Ratios, Black Hole Masses, and X-Ray Luminosities

We determine the low-redshift X-ray luminosity function, active black hole mass function (BHMF), and Eddington ratio distribution function (ERDF) for both unobscured (Type 1) and obscured (Type 2) active galactic nuclei (AGNs), using the unprecedented spectroscopic completeness of the BAT AGN Spectroscopic Survey (BASS) data release 2. In addition to a straightforward 1/V max approach, we also compute the intrinsic distributions, accounting for sample truncation by employing a forward-modeling approach to recover the observed BHMF and ERDF. As previous BHMFs and ERDFs have been robustly determined only for samples of bright, broad-line (Type 1) AGNs and/or quasars, ours are the first directly observationally constrained BHMF and ERDF of Type 2 AGNs. We find that after accounting for all observational biases, the intrinsic ERDF of Type 2 AGNs is significantly more skewed toward lower Eddington ratios than the intrinsic ERDF of Type 1 AGNs. This result supports the radiation-regulated unification scenario, in which radiation pressure dictates the geometry of the dusty obscuring structure around an AGN. Calculating the ERDFs in two separate mass bins, we verify that the derived shape is consistent, validating the assumption that the ERDF (shape) is mass-independent. We report the local AGN duty cycle as a function of mass and Eddington ratio, by comparing the BASS active BHMF with the local mass function for all supermassive black holes. We also present the logN−logS of the Swift/BAT 70 month sources.

Extracting the Possible Intrinsic Relation between the Radiative Efficiency and Mass of QSOs: A Maximum Likelihood Method and its Application to the SDSS DR7 QSOs

Abstract Radiative efficiencies of QSOs and their distribution encode rich information on the evolution of both masses and spins of massive black holes (MBHs) across cosmic time. In this paper, we develop a maximum likelihood method to statistically extract the intrinsic relation between radiative efficiency (ϵ) and mass (M •) of QSOs from their distribution on the luminosity–(empirically estimated virial) mass plane. By using mock samples, we find that strong constraint can be put on the ϵ–M • relation at redshift z ≲ 0.4 from uniform QSO samples similar to those in the Sloan Digital Sky Survey (SDSS) and from QSO samples at z ∼ 0.6 (or ≲1.0) if the magnitude limit of the survey can be ∼1–2 (or 2–3) magnitude deeper. Applying this method to the SDSS DR7 QSOs with z ≲ 0.7, we find (or ) correlation for QSOs with the masses obtained according to the H β (or Mg ii) empirical mass estimator. These contradictory results may be due to the unknown systematic errors in the two mass estimators, preventing an accurate constraint on the ϵ–M • relation by using current available QSO samples. We find that both the estimates of MBH mass and Eddington ratio distribution functions can be affected by the ϵ– relation, suggesting that the determination of this relation is important for understanding the accretion and growth history of MBHs. In the future, the intrinsic ϵ–M • relation is expected to be strongly constrained by using QSO samples obtained from surveys deeper than the SDSS if the host galaxy contamination and systematic errors of the mass estimator(s) can be well modeled or removed.

A Forward Modeling Approach to AGN Variability--Method Description and Early Applications

Abstract We present a numerical framework for the variability of active galactic nuclei (AGNs), which links the variability of AGNs over a broad range of timescales and luminosities to the observed properties of the AGN population as a whole, and particularly the Eddington ratio distribution function. We implemented our framework on GPU architecture, relying on previously published time-series-generating algorithms. After extensive tests that characterize several intrinsic and numerical aspects of the simulations, we describe some applications used for current and future time-domain surveys and for the study of extremely variable sources (e.g., “changing-look” or flaring AGNs). Specifically, we define a simulation setup that reproduces the AGN variability observed in the (intermediate) Palomar Transient Factory survey and use it to forward model longer light curves of the kind that may be observed within the Large Synoptic Survey Telescope (LSST) main survey. Thanks to our efficient implementations, these simulations are able to cover, for example, over 1 Myr with a roughly weekly cadence. We envision that this framework will become highly valuable to prepare for, and best exploit, data from upcoming time-domain surveys, such as, for example, LSST.

Slowing down of cosmic growth of supermassive black holes: theoretical prediction of the Eddington ratio distribution

We show the Eddington ratio distributions of supermassive black holes at a wide redshift range (0 < z < 8) obtained with a semi-analytic model of galaxy formation. The distribution is broadly consistent with observational estimates at low redshift. We find that the growth rate of black holes at higher redshift is more likely to exceed the Eddington limit because the typical gas fraction of the host galaxies is higher at higher redshift. We also find that the super-Eddington growth is more common for less massive supermassive black holes, supporting an idea that supermassive black holes have been formed via super-Eddington accretion. These results indicate the ‘slowing down' of cosmic growth of supermassive black holes: the growth of supermassive black holes with a higher Eddington ratio peaks at higher redshift. We also show the effect of the sample selection on the shape of the Eddington ratio distribution functions and find that shallower observations will miss active galactic nuclei with not only the smaller but also higher Eddington ratios.

The fraction of AGNs in major merger galaxies and its luminosity dependence

We use a phenomenological model which connects the galaxy and AGN populations to investigate the process of AGN triggering through major galaxy mergers at z~0. The model uses stellar mass functions as input and allows the prediction of AGN luminosity functions based on assumed Eddington ratio distribution functions (ERDFs). We show that the number of AGN hosted by merger galaxies relative to the total number of AGN increases as a function of AGN luminosity. This is due to more massive galaxies being more likely to undergo a merger and does not require the assumption that mergers lead to higher Eddington ratios than secular processes. Our qualitative analysis also shows that to match the observations, the probability of a merger galaxy hosting an AGN and accreting at a given Eddington value has to be increased by a factor ~10 relative to the general AGN population. An additional significant increase of the fraction of high Eddington ratio AGN among merger host galaxies leads to inconsistency with the observed X-ray luminosity function. Physically our results imply that, compared to the general galaxy population, the AGN fraction among merger galaxies is ~10 times higher. On average, merger triggering does however not lead to significantly higher Eddington ratios.

AGNs and Their Host Galaxies in the Local Universe: Two Mass-independent Eddington Ratio Distribution Functions Characterize Black Hole Growth

Abstract We use a phenomenological model to show that black hole growth in the local universe ( ) can be described by two separate, mass-independent Eddington ratio distribution functions (ERDFs). We assume that black holes can be divided into two independent groups: those with radiatively efficient accretion, primarily hosted by optically blue and green galaxies, and those with radiatively inefficient accretion, which are mainly found in red galaxies. With observed galaxy stellar mass functions as input, we show that the observed active galactic nucleus (AGN) luminosity functions can be reproduced by using mass-independent, broken power-law-shaped ERDFs. We use the observed hard X-ray and 1.4 GHz radio luminosity functions to constrain the ERDF for radiatively efficient and inefficient AGNs, respectively. We also test alternative ERDF shapes and mass-dependent models. Our results are consistent with a mass-independent AGN fraction and AGN hosts being randomly drawn from the galaxy population. We argue that the ERDF is not shaped by galaxy-scale effects, but by how efficiently material can be transported from the inner few parsecs to the accretion disc. Our results are incompatible with the simplest form of mass quenching where massive galaxies host higher accretion rate AGNs. Furthermore, if reaching a certain Eddington ratio is a sufficient condition for maintenance mode, it can occur in all red galaxies, not just the most massive ones.

The cosmic growth of the active black hole population at 1 &lt;z &lt;2 in zCOSMOS, VVDS and SDSS

We present a census of the active black hole population at 1<z<2, by constructing the bivariate distribution function of black hole mass and Eddington ratio, employing a maximum likelihood fitting technique. The study of the active black hole mass function (BHMF) and the Eddington ratio distribution function (ERDF) allows us to clearly disentangle the active galactic nuclei (AGN) downsizing phenomenon, present in the AGN luminosity function, into its physical processes of black hole mass downsizing and accretion rate evolution. We are utilizing type-1 AGN samples from three optical surveys (VVDS, zCOSMOS and SDSS), that cover a wide range of 3 dex in luminosity over our redshift interval of interest. We investigate the cosmic evolution of the AGN population as a function of AGN luminosity, black hole mass and accretion rate. Compared to z = 0, we find a distinct change in the shape of the BHMF and the ERDF, consistent with downsizing in black hole mass. The active fraction or duty cycle of type-1 AGN at z~1.5 is almost flat as a function of black hole mass, while it shows a strong decrease with increasing mass at z=0. We are witnessing a phase of intense black hole growth, which is largely driven by the onset of AGN activity in massive black holes towards z=2. We finally compare our results to numerical simulations and semi-empirical models and while we find reasonable agreement over certain parameter ranges, we highlight the need to refine these models in order to match our observations.

BLACK HOLE MASS AND EDDINGTON RATIO DISTRIBUTION FUNCTIONS OF X-RAY-SELECTED BROAD-LINE AGNs ATz∼ 1.4 IN THE SUBARUXMM-NEWTONDEEP FIELD

In order to investigate the growth of super-massive black holes (SMBHs), we construct the black hole mass function (BHMF) and Eddington ratio distribution function (ERDF) of X-ray-selected broad-line AGNs at z~1.4 in the Subaru XMM-Newton Deep Survey field. In this redshift range, a significant part of the accretion growth of SMBHs is thought to be taking place. Black hole masses of X-ray-selected broad-line AGNs are estimated using the width of the broad MgII line and the 3000A monochromatic luminosity. We supplement the MgII FWHM values with the Ha FWHM obtained from our NIR spectroscopic survey. Using the black hole masses of broad-line AGNs at redshifts between 1.18 and 1.68, the binned broad-line AGN BHMF and ERDF are calculated using the Vmax method. To properly account for selection effects that impact the binned estimates, we derive the corrected broad-line AGN BHMF and ERDF by applying the Maximum Likelihood method, assuming that the ERDF is constant regardless of the black hole mass. We do not correct for the non-negligible uncertainties in virial BH mass estimates. If we compare the corrected broad-line AGN BHMF with that in the local Universe, the corrected BHMF at z~1.4 has a higher number density above 10^8 Msolar but a lower number density below that mass range. The evolution may be indicative of a down-sizing trend of accretion activity among the SMBH population. The evolution of broad-line AGN ERDF from z=1.4 to 0 indicates that the fraction of broad-line AGNs with accretion rate close to the Eddington-limit is higher at higher redshifts.

Low redshift AGN in the Hamburg/ESO Survey

We estimated black hole masses and Eddington ratios for a well defined sample of local (z<0.3) broad line AGN from the Hamburg/ESO Survey (HES), based on the Hbeta line and standard recipes assuming virial equilibrium for the broad line region. The sample represents the low-redshift AGN population over a wide range of luminosities, from Seyfert 1 galaxies to luminous quasars. From the distribution of black hole masses we derived the active black hole mass function (BHMF) and the Eddington ratio distribution function (ERDF) in the local universe, exploiting the fact that the HES has a well-defined selection function. While the directly determined ERDF turns over around L/L_Edd ~ 0.1, similar to what has been seen in previous analyses, we argue that this is an artefact of the sample selection. We employed a maximum likelihood approach to estimate the intrinsic distribution functions of black hole masses and Eddington ratios simultaneously in an unbiased way, taking the sample selection function fully into account. The resulting ERDF is well described by a Schechter function, with evidence for a steady increase towards lower Eddington ratios, qualitatively similar to what has been found for type~2 AGN from the SDSS. Comparing our best-fit active BHMF with the mass function of inactive black holes we obtained an estimate of the fraction of active black holes, i.e. an estimate of the AGN duty cycle. The active fraction decreases strongly with increasing black hole mass. A comparison with the BHMF at higher redshifts also indicates that, at the high mass end, black holes are now in a less active stage than at earlier cosmic epochs. Our results support the notion of anti-hierarchical growth of black holes, and are consistent with a picture where the most massive black holes grew at early cosmic times, whereas at present mainly smaller mass black holes accrete at a significant rate.