Evolution of massive binary black holes

Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). In this paper we study the evolution of massive BBHs in realistic galaxy models, using a generalization of techniques used to study tidal disruption rates around massive BHs. The evolution of BBHs depends on BH mass ratio and host galaxy type. BBHs with very low mass ratios (say, ≲0.001) are hardly ever formed by mergers of galaxies, because the dynamical friction time-scale is too long for the smaller BH to sink into the galactic centre within a Hubble time. BBHs with moderate mass ratios are most likely to form and survive in spherical or nearly spherical galaxies and in high-luminosity or high-dispersion galaxies; they are most likely to have merged in low-dispersion galaxies (line-of-sight velocity dispersion ≲90 km s⁻¹) or in highly flattened or triaxial galaxies.
The semimajor axes and orbital periods of surviving BBHs are generally in the range  10^-3–10 pc  and  10–10⁵ yr;  they are also larger in high-dispersion galaxies than in low-dispersion galaxies, larger in nearly spherical galaxies than in highly flattened or triaxial galaxies, and larger for BBHs with equal masses than for BBHs with unequal masses. The orbital velocities of surviving BBHs are generally in the range  10²–10⁴ km s^-1  . The methods of detecting surviving BBHs are also discussed.
If no evidence of BBHs is found in AGNs, this may be either because gas plays a major role in BBH orbital decay or because nuclear activity switches on soon after a galaxy merger, and ends before the smaller BH has had time to spiral to the centre of the galaxy.     

Rates of tidal disruption of stars by massive central black holes

There is strong evidence for some kind of massive dark object in the centres of many galaxy bulges. The detection of flares from tidally disrupted stars could confirm that these objects are black holes (BHs). Here we present calculations of the stellar disruption rates in detailed dynamical models of real galaxies, taking into account the refilling of the loss cone of stars on disruptable orbits by two-body relaxation and tidal forces in non-spherical galaxies. The highest disruption rates (one star per 10⁴ yr) occur in faint ( L ≲10¹⁰ L_⊙) galaxies, which have steep central density cusps. More luminous galaxies are less dense and have much longer relaxation times and more massive BHs. Dwarf stars in such galaxies are swallowed whole by the BH and hence do not emit flares; giant stars could produce flares as often as every 10⁵ yr, although the rate depends sensitively on the shape of the stellar distribution function. We discuss the possibility of detecting disruption flares in current supernova searches. The total mass of stars consumed over the lifetime of the galaxy is of the order of 10⁶ M_⊙, independent of galaxy luminosity; thus, disrupted stars may contribute significantly to the present BH mass in galaxies fainter than ∼10⁹ L_⊙.     

The temperatures of dust-enshrouded active galactic nuclei

A high density of massive dark objects (MDOs), probably supermassive black holes, in the centres of nearby galaxies has been inferred from recent observations. There are various indications that much of the accretion responsible for producing these objects took place in dust-enshrouded active galactic nuclei (AGNs). If so, then measurements of the intensity of background radiation and the source counts in the far-infrared and submillimetre wavebands constrain the temperature of dust in these AGNs. An additional constraint comes from the hard X-ray background, if this is produced by accretion. One possibility is that the dust shrouds surrounding the accreting AGNs are cold, about 30 K. In this event, the dusty AGNs could be some subset of the population of luminous distant sources discovered at 850 μm using the SCUBA array on the James Clerk Maxwell Telescope, as proposed by Almaini, Lawrence & Boyle. An alternative is that the dust shrouds surrounding the accreting AGNs are much hotter (>60 K). These values are closer to the dust temperatures of a number of well-studied low-redshift ultraluminous galaxies that are thought to derive their power from accretion. If the local MDO density is close to the maximum permitted, then cold sources cannot produce this density without the submillimetre background being overproduced if they accrete at high radiative efficiency, and thus a hot population is required. If the dust-enshrouded accretion occurred at similar redshifts to that taking place in unobscured optical quasars, then a significant fraction of the far-infrared background radiation measured by COBE at 140 μm, but very little of the submillimetre background at 850 μm, may have been produced by hot dust-enshrouded AGNs which may have already been seen in recent Chandra X-ray surveys.     

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.     

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 (BH) masses of the order of   M ∼ 10¹⁰ M_⊙  . 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 BH 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 BHs 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 BHs computed from the observed X-ray luminosity functions of active galactic nuclei predict the existence of a high-mass tail in the BH mass function at   z = 0  . Consistency between the optical and X-ray census of the local BH mass function requires an upper limit to BH masses. This consistent picture also predicts that the slope of the   M _bh–σ  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 BHs naturally provide such an upper limit. The combination of multiwavelength 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.     

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.     

The census of nuclear activity of late-type galaxies in the Virgo cluster

The first spectroscopic census of active galactic nuclei (AGNs) associated with late-type galaxies in the Virgo cluster was carried out by observing 213 out of a complete set of 237 galaxies more massive than   M _dyn > 10^8.5 M_⊙  . Among them, 77 are classified as AGNs [including 21 transition objects, 47 low-ionization nuclear emission regions (LINERs) and nine Seyferts] and comprise 32 per cent of the late-type galaxies in Virgo. Due to spectroscopic incompleteness, at most 21 AGNs are missed in the survey, so that the fraction would increase up to 41 per cent. Using corollary near-infrared observations that enable us to estimate galaxy dynamical masses, it is found that AGNs are hosted exclusively in massive galaxies, i.e.   M _dyn≳ 10¹⁰ M_⊙  . Their frequency increases steeply with the dynamical mass from zero at   M _dyn≈ 10^9.5 M_⊙  to virtually 1 at   M _dyn > 10^11.5 M_⊙  . These frequencies are consistent with those of low-luminosity AGNs found in the general field by the Sloan Digital Sky Survey. Massive galaxies that harbour AGNs commonly show conspicuous r -band star-like nuclear enhancements. Conversely, they often, but not necessarily, contain massive bulges. A few well-known AGNs (e.g. M61, M100, NGC 4535) are found in massive Sc galaxies with little or no bulge. The AGN fraction seems to be only marginally sensitive to galaxy environment. We infer the black hole masses using the known scaling relations of quiescent black holes. No black holes lighter than  ∼10⁶ M_⊙  are found active in our sample.     

The growth of central and satellite galaxies in cosmological smoothed particle hydrodynamics simulations

We examine the accretion and merger histories of central and satellite galaxies in a smoothed particle hydrodynamics (SPH) cosmological simulation that resolves galaxies down to  7 × 10⁹ M_⊙  . Most friends-of-friends haloes in the simulation have a distinct central galaxy, typically 2–5 times more massive than the most massive satellite. As expected, satellites have systematically higher assembly redshifts than central galaxies of the same baryonic mass, and satellites in more massive haloes form earlier. However, contrary to the simplest expectations, satellite galaxies continue to accrete gas and convert it to stars; the gas accretion declines steadily over a period of 0.5–1 Gyr after the satellite halo merges with a larger parent halo. Satellites in a cluster mass halo eventually begin to lose baryonic mass. Typically, satellites in our simulation are 0.1–0.2 mag bluer than in models that assume no gas accretion on to satellites after a halo merger. Since   z = 1  , 27 per cent of central galaxies (above  3 × 10¹⁰ M_⊙  ) and 22 per cent of present-day satellite galaxies have merged with a smaller system above a 1:4 mass ratio; about half of the satellite mergers occurred after the galaxy became a satellite and half before. In effect, satellite galaxies can remain 'central' objects of halo substructures, with continuing accretion and mergers, making the transition in assembly histories and physical properties a gradual one. Implementing such a gradual transformation in semi-analytic models would improve their agreement with observed colour distributions of satellite galaxies in groups and with the observed colour dependence of galaxy clustering.     

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

We analyse the observed distribution of Eddington ratios  ( L / L _Edd)  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 [   M _*/star formation rate (SFR) ∼  a Hubble time] in their central kiloparsec regions, and is characterized by a broad lognormal distribution of accretion rates peaked at a few per cent of the Eddington limit. In this regime, the Eddington ratio distribution is independent of the mass of the black hole and shows little dependence on the central stellar population of the galaxy. The second regime is associated with galaxies with old central stellar populations (   M _*/SFR ≫  a Hubble time), and is characterized by a power-law distribution function of Eddington ratios. In this regime, the time-averaged mass accretion rate on to 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 on to 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.     

An application of the Kerr black hole fly-wheel model to statistical properties of QSOs/AGNs

The aim of this work is to demonstrate the properties of the magnetospheric model around Kerr black holes (BHs), the so-called fly-wheel (rotation driven) model. The fly-wheel engine of the BH–accretion disc system is applied to the statistics of QSOs/AGNs. In the model, the central BH is assumed to be formed at z ∼10² and obtains nearly maximum but finite rotation energy (∼extreme Kerr BH) at the formation stage. The inherently obtained rotation energy of the Kerr BH is released through a magnetohydrodynamic process. This model naturally leads to a finite lifetime of AGN activity.
Nitta, Takahashi & Tomimatsu clarified the individual evolution of the Kerr BH fly-wheel engine, which is parametrized by BH mass, initial Kerr parameter, magnetic field near the horizon and a dimensionless small parameter. We impose a statistical model for the initial mass function (IMF) of an ensemble of BHs using the Press–Schechter formalism. With the help of additional assumptions, we can discuss the evolution of the luminosity function and the spatial number density of QSOs/AGNs.
By comparing with observations , it is found that a somewhat flat IMF and weak dependence of the magnetic field on the BH mass are preferred. The result explains well the decrease of very bright QSOs and decrease of population after z ∼2.     

Compact massive objects in Virgo galaxies: the black hole population

We investigate the distribution of massive black holes (MBHs) in the Virgo cluster. Observations suggest that active galactic nuclei activity is widespread in massive galaxies ( M _*≳ 10¹⁰ M_⊙), while at lower galaxy masses star clusters are more abundant, which might imply a limited presence of central black holes in these galaxy-mass regimes. We explore if this possible threshold in MBH hosting is linked to nature , nurture or a mixture of both. The nature scenario arises naturally in hierarchical cosmologies, as MBH formation mechanisms typically are efficient in biased systems, which would later evolve into massive galaxies. Nurture , in the guise of MBH ejections following MBH mergers, provides an additional mechanism that is more effective for low mass, satellite galaxies. The combination of inefficient formation, and lower retention of MBHs, leads to the natural explanation of the distribution of compact massive objects in Virgo galaxies. If MBHs arrive to the correlation with the host mass and velocity dispersion during merger-triggered accretion episodes, sustained tidal stripping of the host galaxies creates a population of MBHs which lie above the expected scaling between the holes and their host mass, suggesting a possible environmental dependence.     

The Difference between the α-disks of Seyfert 1 Galaxiesand Quasars

In a previous paper, it was suggested that contamination of the nuclear luminosity by the host galaxy plays an important role in determining the parameters of the standard a disk of AGNs. Using the nuclear absolute B band magnitude instead of the total absolute B band magnitude, we have recalculated the central black hole masses, accretion rates and disk inclinations for 20 Seyfert 1 galaxies and 17 Palomar-Green (PG) quasars. It is found that a small value of a is needed for the Seyfert 1 galaxies than for the PG quasars. This difference in a possibly leads to the different properties of Seyfert 1 galaxies and quasars. Furthermore, we find most of the objects in this sample are not accreting at super-Eddington rates if we adopt the nuclear optical luminosity in our calculation.     

X-rays from cusps of compact remnants near galactic centres

Compact remnants – stellar mass black holes and neutron stars formed in the inner few parsec of galactic centres are predicted to sink into the central parsec due to dynamical friction on low-mass stars, forming a high concentration cusp. Same physical region may also contain very high-density molecular clouds and accretion discs that are needed to fuel supermassive black hole (SMBH) activity. Here we estimate gas capture rates on to the cusp of stellar remnants, and the resulting X-ray luminosity, as a function of the accretion disc mass. At low disc masses, most compact objects are too dim to be observable, whereas in the high disc case most of them are accreting at their Eddington rates. We find that for low accretion disc masses, compact remnant cusps may be more luminous than the central SMBHs. This 'diffuse' emission may be of importance for local moderately bright active galactic nuclei (AGNs), especially low-luminosity AGNs. We also briefly discuss how this expected emission can be used to put constraints on the black hole cusp near our Galactic Centre.     

Gravitational waves from scattering of stellar-mass black holes in galactic nuclei

Stellar-mass black holes (BHs) are expected to segregate and form a steep density cusp around supermassive black holes (SMBHs) in galactic nuclei. We follow the evolution of a multimass system of BHs and stars by numerically integrating the Fokker–Planck energy diffusion equations for a variety of BH mass distributions. We find that the BHs 'self-segregate', and that the rarest, most massive BHs dominate the scattering rate closest to the SMBH  (≲10⁻¹ pc)  . BH–BH binaries form out of gravitational wave emission during BH encounters. We find that the expected rate of BH coalescence events detectable by Advanced LIGO is  ∼1–10² yr⁻¹  , depending on the initial mass function of stars in galactic nuclei and the mass of the most massive BHs. We find that the actual merger rate is likely ∼10 times larger than this due to the intrinsic scatter of stellar densities in many different galaxies. The BH binaries that form this way in galactic nuclei have significant eccentricities as they enter the LIGO band (90 per cent with   e > 0.9  ), and are therefore distinguishable from other binaries, which circularize before becoming detectable. We also show that eccentric mergers can be detected to larger distances and greater BH masses than circular mergers, up to  ∼700 M_⊙  . Future ground-based gravitational wave observatories will be able to constrain both the mass function of BHs and stars in galactic nuclei.     

Supermassive Black Holes in Early-Type Galaxies: Relationship with Radio Emission and Constraints on the Black Hole Mass Function

Using recently published estimates — based on high spatial resolution spectroscopy — of the mass M _BH of nuclear black holes for a sample of nearby galaxies, we explore the dependence of galaxy nucleus emissivity at various wavelengths on M _BH. We confirm an almost linear scaling of the black hole mass with the baryonic mass of the host spheroidal galaxy. A remarkably tight relationship is also found with both nuclear and total radio centimetric flux, with a very steep dependence of the radio flux on M _BH ( P  ∝  M ^2.5_BH). The high-frequency radio power is thus a very good tracer of a supermassive black hole, and a good estimator of its mass. This, together with the lack of significant correlations with the low-energy X-ray and far-IR flux, supports the view that advection-dominated accretion is ruling the energy output in the low accretion rate regime. Using the tight dependence of total radio power on M _BH and the rich statistics of radio emission of galaxies, we derive an estimate of the mass function of remnants in the nearby Universe. This is compared with current models of quasar and active galactic nucleus (AGN) activity and of the origin of the hard X-ray background (HXRB). As for the former, continuous long-lived AGN activity is excluded by the present data with high significance, whereas the assumption of a short-lived, possibly recurrent, activity pattern gives remarkable agreement. The presently estimated black hole mass function also implies that the HXRB has been produced by a numerous population (∼ 10⁻² Mpc⁻³) of moderately massive ( M _BH ∼ 10⁷ M⊙) black holes.     

The masses of black holes in the nuclei of spirals

We use the innermost kinematics of spirals to investigate whether these galaxies could host the massive black hole remnants that once powered the quasi-stellar object (QSO) phenomenon. Hundreds of rotation curves of early- and late-type spirals are used to place upper limits on the central black hole (BH) masses. We find that (i) in late-type spirals, the central massive dark objects (MDOs) are about 10–100 times smaller than the MDOs detected in ellipticals, and (ii) in early-type spirals, the central bodies are likely to be in the same mass range as the elliptical MDOs. As a consequence, the contribution to the QSO/active galactic nuclei (AGN) phenomenon by the BH remnants eventually hosted in spirals is negligible: ρ _BH(Sb–Im)<6×10⁴ M_⊙ Mpc⁻³ . We find several hints that the MDO mass versus bulge mass relationship is significantly steeper in spirals than in ellipticals, although the very issue of the existence of such a relation for late Hubble type objects remains open. The upper limits on the masses of the BHs resident in late-type spirals are stringent: M _BH10⁶–10⁷ M_⊙, indicating that only low-luminosity activity could possibly have occurred in these objects .     

The relationship between X-ray variability and the central black hole mass

We assembled a sample of Seyfert 1 galaxies, quasi-stellar objects (QSOs) and low-luminosity active galactic nuclei (LLAGNs) observed by ASCA , the central black hole masses of which have been measured. We found that the X-ray variability (which is quantified by the 'excess variance' σ _rms²) is significantly anti-correlated with the central black hole mass, and it is likely that a linear relationship of σ _rms²∝ M _bh⁻¹ exists. It can be interpreted that the short time-scale X-ray variability is caused by some global coherent variations in the X-ray emission region, which is scaled by the size of the central black hole. Hence the central black hole mass is the driving parameter of the previously established relation between X-ray variability and luminosity. Our findings favour the hypothesis that the narrow-line Seyfert 1 galaxies and QSOs harbour smaller black holes than the broad-line objects, and can also easily explain the observational fact that high-redshift QSOs have greater variability than local AGNs at a given luminosity. Further investigations are needed to confirm our findings, and a large sample X-ray variability investigation can give constraints on the physical mechanisms and evolution of AGNs.     

X-ray emission from accretion disks in active galactic nuclei

We constructed a grid of relativistic models for standard high-relative-luminosity accretion α-disks around supermassive Kerr black holes (BHs) and computed X-ray spectra for their hot, effectively optically thin inner parts by taking into account general-relativity effects. They are known to be heated to high (～10⁶–10⁹ K) temperatures and to cool down through the Comptonization of intrinsic thermal radiation. Their spectra are power laws with an exponential cutoff at high energies; i.e., they have the same shape as those observed in active galactic nuclei (AGNs). Fitting the observed X-ray spectra of AGNs with computed spectra allowed us to estimate the fundamental parameters of BHs (their mass and Kerr parameter) and accretion disks (luminosity and inclination to the line of sight) in 28 AGNs. We show that the Kerr parameter for BHs in AGNs is close to unity and that the disk inclination correlates with the Seyfert type of AGN, in accordance with the unification model of activity. The estimated BH masses M_x are compared with the masses M_rev determined by the reverberation mapping technique. For AGNs with luminosities close to the Eddington limit, these masses agree and the model under consideration may be valid for them. For low-relative-luminosity AGNs, the differences in masses increase with decreasing relative luminosity and their X-ray emission cannot be explained by this model.     

Strong size evolution of the most massive galaxies since z∼ 2

Using the combined capabilities of the large near-infrared Palomar/DEEP-2 survey, and the superb resolution of the Advanced Camera for Surveys HST camera, we explore the size evolution of 831 very massive galaxies  ( M _⋆≥ 10¹¹ h ⁻²₇₀ M_⊙)  since   z ∼ 2  . We split our sample according to their light concentration using the Sérsic index n . At a given stellar mass, both low  ( n < 2.5)  and high  ( n > 2.5)  concentrated objects were much smaller in the past than their local massive counterparts. This evolution is particularly strong for the highly concentrated (spheroid like) objects. At   z ∼ 1.5  , massive spheroid-like objects were a factor of 4 (±0.4) smaller (i.e. almost two orders of magnitudes denser) than those we see today. These small sized, high-mass galaxies do not exist in the nearby Universe, suggesting that this population merged with other galaxies over several billion years to form the largest galaxies we see today.