Black hole growth in hierarchical galaxy formation

We incorporate a model for black hole growth during galaxy mergers into the semi-analytical galaxy formation model based on ΛCDM proposed by Baugh et al. Our black hole model has one free parameter, which we set by matching the observed zero-point of the local correlation between black hole mass and bulge luminosity. We present predictions for the evolution with redshift of the relationships between black hole mass and bulge properties. Our simulations reproduce the evolution of the optical luminosity function of quasars. We study the demographics of the black hole population and address the issue of how black holes acquire their mass. We find that the direct accretion of cold gas during starbursts is an important growth mechanism for lower mass black holes and at high redshift. On the other hand, the re-assembly of pre-existing black hole mass into larger units via merging dominates the growth of more massive black holes at low redshift. This prediction could be tested by future gravitational wave experiments. As redshift decreases, progressively less massive black holes have the highest fractional growth rates, in line with recent claims of 'downsizing' in quasar activity.     

Modelling the cosmological co-evolution of supermassive black holes and galaxies – II. The clustering of quasars and their dark environment

We use semi-analytic modelling on top of the Millennium simulation to study the joint formation of galaxies and their embedded supermassive black holes. Our goal is to test scenarios in which black hole accretion and quasar activity are triggered by galaxy mergers, and to constrain different models for the light curves associated with individual quasar events. In the present work, we focus on studying the spatial distribution of simulated quasars. At all luminosities, we find that the simulated quasar two-point correlation function is fit well by a single power law in the range  0.5 ≲ r ≲ 20  h ⁻¹ Mpc  , but its normalization is a strong function of redshift. When we select only quasars with luminosities within the range typically accessible by today's quasar surveys, their clustering strength depends only weakly on luminosity, in agreement with observations. This holds independently of the assumed light-curve model, since bright quasars are black holes accreting close to the Eddington limit, and are hosted by dark matter haloes with a narrow mass range of a few  10¹²  h ⁻¹ M_⊙  . Therefore, the clustering of bright quasars cannot be used to disentangle light-curve models, but such a discrimination would become possible if the observational samples can be pushed to significantly fainter limits. Overall, our clustering results for the simulated quasar population agree rather well with observations, lending support to the conjecture that galaxy mergers could be the main physical process responsible for triggering black hole accretion and quasar activity.     

The dependence of quasar variability on black hole mass

In order to investigate the dependence of quasar variability on fundamental physical parameters like black hole mass, we have matched quasars from the Quasar Equatorial Survey Team, Phase 1 (QUEST1) variability survey with broad-lined objects from the Sloan Digital Sky Survey. The matched sample contains ≈100 quasars, and the Sloan spectra are used to estimate black hole masses and bolometric luminosities. Variability amplitudes are measured from the QUEST1 light curves. We find that black hole mass correlates with several measures of the variability amplitude at the 99 per cent significance level or better. The correlation does not appear to be caused by obvious selection effects inherent to flux-limited quasar samples, host galaxy contamination or other well-known correlations between quasar variability and luminosity/redshift. We evaluate variability as a function of rest-frame time lag using structure functions and find further support for the variability–black hole mass correlation. The correlation is strongest for time lags of the order of a few months up to the QUEST1 maximum temporal resolution of ≈2 yr, and may provide important clues for understanding the long-standing problem of the origin of quasar optical variability. We discuss whether our result is a manifestation of a relation between characteristic variability time-scale and black hole mass, where the variability time-scale is typical for accretion disc thermal time-scales, but find little support for this. Our favoured explanation is that more massive black holes have larger variability amplitudes, and we highlight the need for larger samples with more complete temporal sampling to test the robustness of this result.     

A unified model for the evolution of galaxies and quasars

We incorporate a simple scheme for the growth of supermassive black holes into semi-analytic models that follow the formation and evolution of galaxies in a cold dark matter-dominated Universe. We assume that supermassive black holes are formed and fuelled during major mergers. If two galaxies of comparable mass merge, their central black holes coalesce and a few per cent of the gas in the merger remnant is accreted by the new black hole over a time-scale of a few times 10⁷ yr. With these simple assumptions, our model not only fits many aspects of the observed evolution of galaxies, but also reproduces quantitatively the observed relation between bulge luminosity and black hole mass in nearby galaxies, the strong evolution of the quasar population with redshift, and the relation between the luminosities of nearby quasars and those of their host galaxies. The strong decline in the number density of quasars from z ∼2 to z =0 is a result of the combination of three effects: (i) a decrease in the merging rate; (ii) a decrease in the amount of cold gas available to fuel black holes, and (iii) an increase in the time-scale for gas accretion. The predicted decline in the total content of cold gas in galaxies is consistent with that inferred from observations of damped Ly α systems. Our results strongly suggest that the evolution of supermassive black holes, quasars and starburst galaxies is inextricably linked to the hierarchical build-up of galaxies.     

A Study of the Black Hole Mass and Accretion Rate Distributions of AGNs

The redshift, central black hole mass and accretion rate are important parameters when studying the AGN evolution. The central black hole masses for 172 quasars and Seyfert galaxies are calculated in this paper using the reverberation mapping method. The distributions of central black hole masses, redshifts and the Eddington accretion rates are analyzed, to verify the transition from the quasar to the Seyfert galaxy in the course of evolution.     

A Semi-analytical Model of Quasar Formation

On the basis of Kang et al.’s semi-analytical model of galaxy formation and evolution, the joint formation and evolution of galaxies and their central massive black holes are studied. It is assumed that the activity of quasars is caused by merging of galaxies. Via the introduction of the mass accretion rate of black holes, the bolometric luminosity function of quasars with the redshifts in the region of 0 < z < 4.5 is ascertained. With the respective limitations of the three factors, i.e., the Eddington ratio, black-hole mass function and two-point correlation function, the luminosity function predicted by the model may coincide with observations in the entire range of luminosity. This result reveals that the constant Eddington ratio cannot well describe the accretion of black holes, so the Eddington ratio has to be increased with the redshift in a certain range of redshift. The major merging of galaxies is the effective mechanism of triggering the quasar activity, while the minor merging can merely affect the quasars with low and intermediate luminosities. Its effect on the high-luminosity quasars is very small. At the place of z=1, the quasars with extremely high luminosities possess more intense properties of clustering than other quasars.     

The distribution of supermassive black holes in the nuclei of nearby galaxies

The growth of supermassive black holes by merging and accretion in hierarchical models of galaxy formation is studied by means of Monte Carlo simulations. A tight linear relation between masses of black holes and masses of bulges arises if the mass accreted by supermassive black holes scales linearly with the mass-forming stars and if the redshift evolution of mass accretion tracks closely that of star formation. Differences in redshift evolution between black hole accretion and star formation introduce a considerable scatter in this relation. A non-linear relation between black hole accretion and star formation results in a non-linear relation between masses of remnant black holes and masses of bulges. The relation of black hole mass to bulge luminosity observed in nearby galaxies and its scatter are reproduced reasonably well by models in which black hole accretion and star formation are linearly related but do not track each other in redshift. This suggests that a common mechanism determines the efficiency for black hole accretion and the efficiency for star formation, especially for bright bulges.     

On the spin paradigm and the radio dichotomy of quasars

We investigate whether models based on the assumption that jets in quasars are powered by rotating black holes can explain the observed radio dichotomy of quasars. We show that in terms of the 'spin paradigm' models, radio-loud quasars could be objects in which the rotation rate of the black hole corresponds to an equilibrium between spin-up by accretion and spin-down by the Blandford–Znajek mechanism. Radio-quiet quasars could be hosting black holes with an average spin much smaller than the equilibrium one. We discuss possible accretion scenarios which can lead to such a bimodal distribution of black hole spins.     

A simple model for the evolution of supermassive black holes and the quasar population

An empirically motivated model is presented for accretion-dominated growth of supermassive black holes (SMBH) in galaxies, and the implications are studied for the evolution of the quasar population in the Universe. We investigate the core aspects of the quasar population, including space density evolution, evolution of the characteristic luminosity, plausible minimum masses of quasars, the mass function of SMBH and their formation epoch distribution. Our model suggests that the characteristic luminosity in the quasar luminosity function arises primarily as a consequence of a characteristic mass scale above which there is a systematic separation between the black hole and the halo merging rates. At lower mass scales, black hole merging closely tracks the merging of dark haloes. When combined with a declining efficiency of black hole formation with redshift, the model can reproduce the quasar luminosity function over a wide range of redshifts. The observed space density evolution of quasars is well described by formation rates of SMBH above  ∼10⁸  M_⊙  . The inferred mass density of SMBH agrees with that found independently from estimates of the SMBH mass function derived empirically from the quasar luminosity function.     

The far-infrared–submillimetre spectral energy distribution of high-redshift quasars

We combine photometric observations of high-redshift     quasars, obtained at submillimetre to millimetre wavelengths, to obtain a mean far-infrared (rest-frame) spectral energy distribution (SED) of the thermal emission from dust, parametrized by a single temperature ( T ) and power-law emissivity index ( β ). The best-fitting values are     and     . Our method exploits the redshift spread of this set of quasars, which allows us to sample the SED at a larger number of rest wavelengths than is possible for a single object: the wavelength range extends down to ∼60 μm, and therefore samples the turnover in the greybody curve for these temperatures. This parametrization is of use to any studies that extrapolate from a flux at a single wavelength, for example to infer dust masses and far-infrared luminosities.
We interpret the cool, submillimetre component as arising from dust heated by star formation in the host galaxy of the quasar, although we do not exclude the presence of dust heated directly by the active galactic nucleus (AGN). Applying the mean SED to the data, we derive consistent star formation rates ∼1000 M_⊙ yr⁻¹ and dust masses ∼10⁹ M_⊙, and investigate a simple scheme of AGN and host galaxy co-evolution to account for these quantities. The time-scale for formation of the host galaxy is     , and the luminous quasar phase occurs towards the end of this period, just before the reservoir of cold gas is depleted. Given the youth of the Universe at     (1.6 Gyr), the coexistence of a massive black hole and a luminous starburst at high redshifts is a powerful constraint on models of quasar host galaxy formation.     

The growth history of supermassive black holes and the origin of the radio-loud–radio-quiet dichotomy

Monte Carlo simulations of the growth of supermassive black holes in semi-analytic models of galaxy formation are used to reconstruct characteristic merging and accretion histories. This paper shows that the growth pattern depends on the environment. In field galaxies black holes acquire most of their mass in a single accretion event. Refuellings and mergers with other black holes become important in groups and clusters. I also investigate whether the assumption that radio jets are powered by rotating black holes can explain the observed radio-loud–radio-quiet dichotomy. Wilson & Colbert speculated that rapidly rotating black holes are the natural product of major mergers, while normal accretion through a disc may not give rapidly spinning black holes if the conversion of rotational energy into electromagnetic energy is very efficient. Here I derive predictions for this model including the fraction of radio-loud quasars as a function of redshift and luminosity and compare these predictions with those of alternative proposals.     

Can gas dynamics in centres of galaxies reveal orbiting massive black holes?

If supermassive black holes in centres of galaxies form by merging of black hole remnants of massive Population III stars, then there should be a few black holes of mass one or two orders of magnitude smaller than that of the central ones, orbiting around the centre of a typical galaxy. These black holes constitute a weak perturbation in the gravitational potential, which can generate wave phenomena in gas within a disc close to the centre of the galaxy. Here, we show that a single orbiting black hole generates a three-arm spiral pattern in the central gaseous disc. The density excess in the spiral arms in the disc reaches values of 3–12 per cent when the orbiting black hole is about 10 times less massive than the central black hole. Therefore, the observed density pattern in gas can be used as a signature in detecting the most massive orbiting black holes.     

The obscured growth of massive black holes

The mass density of massive black holes observed locally is consistent with the hard X-ray background provided that most of the radiation produced during their growth was absorbed by surrounding gas. A simple model is proposed here for the formation of galaxy bulges and central black holes in which young spheroidal galaxies have a significant distributed component of cold dusty clouds, which accounts for the absorption. The central accreting black hole is assumed to emit both a quasar-like spectrum, which is absorbed by the surrounding gas, and a slow wind. The power in both is less than the Eddington limit for the black hole. The wind, however, exerts the most force on the gas and, as earlier suggested by Silk & Rees, when the black hole reaches a critical mass it is powerful enough to eject the cold gas from the galaxy, so terminating the growth of both black hole and galaxy. In the present model this point occurs when the Thomson depth in the surrounding gas has dropped to about unity and results in the mass of the black hole being proportional to the mass of the spheroid, with the normalization agreeing with that found for local galaxies by Magorrian et al. for reasonable wind parameters. The model predicts a new population of hard X-ray and submm sources at redshifts above 1, which are powered by black holes in their main growth phase.     

Massive black holes in nuclei of galaxies and quasars

In the first part of the paper the known results on the gravitational interaction of a massive black hole with the surrounding stars in a galactic nucleus are discussed. The tidal disruption of stars in close encounters with a black hole is reviewed. Expressions for the flux of stars on a black hole are given, taking into account energy and angular momentum diffusion of stellar orbits. The scenario of star disruption and accretion of the released stellar matter is depicted. The growth of a black hole in a typical galactic nucleus on account of gas accretion from disrupted stars is discussed. A comparison with the upper limit to the luminosity of the nucleus of our Galaxy puts rather severe constraints on the mass of a hypothetical black hole at the galactic centre. Possible mechanisms preventing the formation and growth of black holes in normal galactic nuclei are discussed.The second part of the paper (Section 8) deals with the hypothesis that massive black holes are the primary energy sources in active galaxies and quasars. The luminosity requirements of bright quasars and weak Seyferts can probably be accounted for in such a model, but there are difficulties in explaining the intermediate range. Mass ejection from Seyferts and quasars is not a severe problem. The same applies to the spectrum. A much more serious objection is the observed periodic and quasi-periodic variability. Another unsatisfactory feature of this hypothesis is that one needs two different evolutionary tracks for quasars and active galaxies, and for normal galaxies.     

Radiative feedback from quasars and the growth of massive black holes in stellar spheroids

We discuss the importance of feedback via photoionization and Compton heating on the co-evolution of massive black holes (MBHs) at the centre of spheroidal galaxies, and their stellar and gaseous components. We first assess the energetics of the radiative feedback from a typical quasar on the ambient interstellar medium (ISM). We then demonstrate that the observed   M _BH–σ  relation could be established following the conversion of most of the gas of an elliptical progenitor into stars, specifically when the gas-to-stars mass ratio in the central regions has dropped to a low level  ∼0.01  or less, so that gas cooling is no longer able to keep up with the radiative heating by the growing central massive black hole (MBH). A considerable amount of the remaining gas will be expelled and both MBH accretion and star formation will proceed at significantly reduced rates thereafter, in agreement with observations of present-day ellipticals. We find further support for this scenario by evolving over an equivalent Hubble time a simple, physically based toy model that additionally takes into account the mass and energy return for the spheroid evolving stellar population, a physical ingredient often neglected in similar approaches.     

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 haloes 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 present observational constraints, all three models can be adequately fitted. 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 exist a population of low-mass galaxies that do not host nuclear black holes. Our prediction of the shape of the M _BH–σ 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.     

Black hole spin and radio loudness in a Λ cold dark matter universe

We use a combination of a cosmological N -body simulation of the concordance Λ cold dark matter paradigm and a semi-analytic model of galaxy formation to investigate the spin development of central supermassive black holes (BHs) and its relation to the BH host galaxy properties. In order to compute BH spins, we use the α model of Shakura & Sunyaev and consider the King et al. warped disc alignment criterion. The orientation of the accretion disc is inferred from the angular momentum of the source of accreted material, which bears a close relationship to the large-scale structure in the simulation. We find that the final BH spin depends almost exclusively on the accretion history and only weakly on the warped disc alignment. The main mechanisms of BH spin-up are found to be gas cooling processes and disc instabilities, a result that is only partially compatible with Monte Carlo models where the main spin-up mechanisms are major mergers and disc instabilities; the latter results are reproduced when implementing randomly oriented accretion discs in our model. Regarding the BH population, we find that more massive BHs, which are hosted by massive ellipticals, have higher spin values than less massive BHs, hosted by spiral galaxies. We analyse whether gas accretion rates and BH spins can be used as tracers of the radio loudness of active galactic nuclei (AGN). We find that the current observational indications of an increasing trend of radio-loud AGN fractions with stellar and BH mass can be easily obtained when placing lower limits on the BH spin, with a minimum influence from limits on the accretion rates; a model with random accretion disc orientations is unable to reproduce this trend. Our results favour a scenario where the BH spin is a key parameter to separate the radio-loud and radio-quiet galaxy populations.     

A Research on the Gravitational Wave Radiation of OJ 287

The research on quasar OJ 287 has lasted over 100 years. OJ 287 exhibits the phenomenon of periodic two-peak outbursts with the eruptive period of 12 years. Observations are rather well interpreted with the black hole binary model. In this model, the secondary black hole moves around the primary black hole and crashes against the accretion disk of the primary black hole, causing outbursts. This model reasonably explains the light curves of OJ 287 and correctly predicts the time of future outbursts. These indirectly justify the precessional effect of general relativity and the existence of gravitational waves. The massive black hole in the center of galaxy is an important kind of gravitational wave source. However, the number of the galaxies with precisely determined kinematical equations of inner components is quite small. The precise kinematic orbits of black holes are provided by the black hole binary model, so the radiation of gravitational waves can be studied on the basis of these kinematic orbits. Based on the existing work, the evolutionary relations of the radiation power and waveform of gravitational waves with time are first derived by using the post-Newtonian approximation method. According to the current progress of the detection equipment of gravitational waves, i.e., IPTA (International Pulsar Timing Array), the direct detection of gravitational waves from OJ 287 may be possible within the future decade.