The black hole mass–stellar velocity dispersion correlation: bulges versus pseudo-bulges

We investigate the correlation between the supermassive black holes (SMBHs) mass ( M _bh) and the stellar velocity dispersion  (σ_*)  in two types of host galaxies: the early-type bulges (disc galaxies with classical bulges or elliptical galaxies) and pseudo-bulges. In the form  log ( M _bh/M_⊙) =α+β log (σ_*/200 km s⁻¹)  , the best-fitting results for the 39 early-type bulges are the slope  β= 4.06 ± 0.28  and the normalization  α= 8.28 ± 0.05  ; the best-fitting results for the nine pseudo-bulges are  β= 4.5 ± 1.3  and  α= 7.50 ± 0.18  . Both relations have intrinsic scatter in  log  M _bh  of ≲0.27 dex. The   M _bh–σ_*  relation for pseudo-bulges is different from the relation in the early-type bulges over the 3σ significance level. The contrasting relations indicate the formation and growth histories of SMBHs depend on their host type. The discrepancy between the slope of the   M _bh–σ_*  relations using different definition of velocity dispersion vanishes in our sample, a uniform slope will constrain the coevolution theories of the SMBHs and their host galaxies more effectively. We also find the slope for the 'core' elliptical galaxies at the high-mass range of the relation appears steeper  (β≃ 5–6)  , which may be the imprint of their origin of dissipationless mergers.     

On the evolution of the black hole: spheroid mass ratio

We present the results of a study which uses the 3C RR sample of radio-loud active galactic nuclei to investigate the evolution of the black hole:spheroid mass ratio in the most massive early-type galaxies from  0 < z < 2  . Radio-loud unification is exploited to obtain virial (linewidth) black hole mass estimates from the 3C RR quasars, and stellar mass estimates from the 3C RR radio galaxies, thereby providing black hole and stellar mass estimates for a single population of early-type galaxies. At low redshift  ( z ≲ 1)  , the 3C RR sample is consistent with a black hole:spheroid mass ratio of   M _bh/ M _sph≃ 0.002  , in good agreement with that observed locally for quiescent galaxies of similar stellar mass  ( M _sph≃ 5 × 10¹¹ M_⊙)  . However, over the redshift interval  0 < z < 2  the 3C RR black hole:spheroid mass ratio is found to evolve as   M _bh/ M _sph∝ (1 + z )^2.07±0.76  , reaching   M _bh/ M _sph≃ 0.008  by redshift   z ≃ 2  . This evolution is found to be inconsistent with the local black hole:spheroid mass ratio remaining constant at a moderately significant level (98 per cent). If confirmed, the detection of evolution in the 3C RR black hole:spheroid mass ratio further strengthens the evidence that, at least for massive early-type galaxies, the growth of the central supermassive black hole may be completed before that of the host spheroid.     

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.     

High-redshift galaxies, their active nuclei and central black holes

We demonstrate that the luminosity function of the recently detected population of actively star-forming galaxies at redshift z  = 3 and the B -band luminosity function of quasi-stellar objects (QSOs) at the same redshift can both be matched with the mass function of dark matter haloes predicted by standard variants of hierarchical cosmogonies for lifetimes of optically bright QSOs anywhere in the range 10⁶ to 10⁸ yr. There is a strong correlation between the lifetime and the required degree of non-linearity in the relation between black hole and halo mass. We suggest that the mass of supermassive black holes may be limited by the back-reaction of the emitted energy on the accretion flow in a self-gravitating disc. This would imply a relation of black hole to halo mass of the form M _bh ∝  v ⁵_halo ∝  M ^5/3_halo and a typical duration of the optically bright QSO phase of a few times 10⁷ yr. The high integrated mass density of black holes inferred from recent black hole mass estimates in nearby galaxies may indicate that the overall efficiency of supermassive black holes for producing blue light is smaller than previously assumed. We discuss three possible accretion modes with low optical emission efficiency: (i) accretion at far above the Eddington rate, (ii) accretion obscured by dust, and (iii) accretion below the critical rate leading to an advection-dominated accretion flow lasting for a Hubble time. We further argue that accretion with low optical efficiency might be closely related to the origin of the hard X-ray background and that the ionizing background might be progressively dominated by stars rather than QSOs at higher redshift.     

The black hole mass – spheroid luminosity relation

The differing   M _bh– L   relations presented in McLure & Dunlop, Marconi & Hunt and Erwin et al. have been investigated. A number of issues have been identified and addressed in each of these studies, including but not limited to the removal of a dependency on the Hubble constant, a correction for dust attenuation in the bulges of disc galaxies, the identification of lenticular galaxies previously treated as elliptical galaxies and the application of the same ( Y ∣ X ) regression analysis. These adjustments result in relations which now predict similar black hole masses. The optimal K -band relation is  log( M _bh/M_⊙) =−0.37(±0.04)( M _K + 24) + 8.29(±0.08)  , with a total (not intrinsic) scatter in log M _bh equal to 0.33 dex. This level of scatter is similar to the value of 0.34 dex from the     relation of Tremaine et al. and compares favourably with the value of 0.31 dex from the   M _bh– n   relation of Graham & Driver. Using different photometric data, consistent relations in the B and R band are also provided, although we do note that the small  ( N = 13)  R -band sample used by Erwin et al. is found here to have a slope of −0.30 ± 0.06. Performing a symmetrical regression on the larger K -band sample gives a slope of ∼−0.40, implying M _bh∝ L ^1.00. Implications for galaxy–black hole co-evolution, in terms of dry mergers, are briefly discussed, as are the predictions for intermediate mass black holes. Finally, as noted by others, a potential bias in the galaxy sample used to define the   M _bh– L   relations is shown and a corrective formula provided.     

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.     

The relation between black hole masses and Lorentz factors of the jet components in blazars

We explore the relationship between black hole mass (MBH) and the motion of the jet components for a sample of blazars. The Very Long Baseline Array (VLBA) 2cm Survey and its continuation: Monitoring of Jets in active galactic nuclei (AGNs) with VLBA Experiments (MOJAVE) have observed 278 radio-loud AGNs, of which 146 blazars have reliable measurements of their apparent velocities of the jet components. We calculate the minimal Lorentz factors for these sources from their measured apparent velocities, and their black hole masses ate estimated with their broad-line widths. A sig-nificant intrinsic correlation is found between black hole masses and the minimal Lorentz factors of the jet components. The Eddington ratio is only weakly correlated with the min-imal Lorentz factor, which may imply that the Blandford-Znajek (BZ) mechanism may dominate over the Blandford-Payne (BP) mechanism for the jet acceleration (at least) in blazars.     

The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power-law cusp. We show that the bulk of stars with a small angular-momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so-called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement.
Our results show that for a primary black hole mass of  ∼10⁶–10⁷ M_⊙  , the black hole mass-ratio   q > 10⁻²  , cusp size ∼1 pc, the tidal disruption rate can be as large as  ∼10⁻²–1 M_⊙ yr⁻¹  . This is at least 10²–10⁴ times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical-friction time-scale, and it is rather short: ∼10⁵ yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.     

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.