The black hole mass–galaxy age relation

We present evidence that there is a significant correlation between the fraction of the mass of a galaxy that lies in its central black hole and the age of the galactic stellar population. Since the absorption-line indices that are used to estimate the age are luminosity-weighted, they essentially measure the time since the last significant episode of star formation in the galaxy. The existence of this correlation is consistent with several theories of galaxy formation, including the currently favoured hierarchical picture of galaxy evolution, which predicts just such a relation between the black hole mass and the time since the last burst of merger-induced star formation. It is not consistent with models in which the massive black hole is primordial, and hence uncoupled from the stellar properties of the galaxy.     

Mass and spin co-evolution during the alignment of a black hole in a warped accretion disc

In this paper, we explore the gravitomagnetic interaction of a black hole (BH) with a misaligned accretion disc to study BH spin precession and alignment jointly with BH mass M _BH and spin parameter a evolution, under the assumption that the disc is continually fed, in its outer region, by matter with angular momentum fixed on a given direction     . We develop an iterative scheme based on the adiabatic approximation to study the BH–disc co-evolution: in this approach, the accretion disc transits through a sequence of quasi-steady warped states (Bardeen–Petterson effect) and interacts with the BH until the spin   J _BH  aligns with     . For a BH aligning with a corotating disc, the fractional increase in mass is typically less than a few per cent, while the spin modulus can increase up to a few tens of per cent. The alignment time-scale     is of  ∼10⁵–10⁶ yr  for a maximally rotating BH accreting at the Eddington rate. BH–disc alignment from an initially counter-rotating disc tends to be more efficient compared to the specular corotating case due to the asymmetry seeded in the Kerr metric: counter-rotating matter carries a larger and opposite angular momentum when crossing the innermost stable orbit, so that the spin modulus decreases faster and so the relative inclination angle.     

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.     

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.     

Quasi-stars: accreting black holes inside massive envelopes

We study the structure and evolution of 'quasi-stars', accreting black holes embedded within massive hydrostatic gaseous envelopes. These configurations may model the early growth of supermassive black hole seeds. The accretion rate on to the black hole adjusts so that the luminosity carried by the convective envelope equals the Eddington limit for the total mass,   M _*+ M _BH≈ M _*  . This greatly exceeds the Eddington limit for the black hole mass alone, leading to rapid growth of the black hole. We use analytic models and numerical stellar structure calculations to study the structure and evolution of quasi-stars. We show that the photospheric temperature of the envelope scales as   T _ph∝ M ^−2/5_BH M ^7/20_*  , and decreases with time while the black hole mass increases. Once   T _ph < 10⁴ K  , the photospheric opacity drops precipitously and T _ph hits a limiting value, analogous to the Hayashi track for red giants and protostars, below which no hydrostatic solution for the convective envelope exists. For metal-free (Population III) opacities, this limiting temperature is approximately 4000 K. After a quasi-star reaches this limiting temperature, it is rapidly dispersed by radiation pressure. We find that black hole seeds with masses between 10³ and  10⁴ M_⊙  could form via this mechanism in less than a few Myr.     

The evolution of misaligned accretion discs and spinning black holes

In this paper, we consider the process of alignment of a spinning black hole and a surrounding misaligned accretion disc. We use a simplified set of equations, that describe the evolution of the system in the case where the propagation of warping disturbances in the accretion disc occurs diffusively, a situation likely to be common in the thin discs in active galactic nuclei (AGN). We also allow the direction of the hole spin to move under the action of the disc torques. In such a way, the evolution of the hole–disc system is computed self-consistently. We consider a number of different situations and we explore the relevant parameter range, by varying the location of the warp radius R _w and the propagation speed of the warp. We find that the dissipation associated with the twisting of the disc results in a large increase in the accretion rate through the disc, so that AGN accreting from a misaligned disc are likely to be significantly more luminous than those accreting from a flat disc. We compute explicitly the time-scales for the warping of the disc and for the alignment process and compare our results with earlier estimates based on simplified steady-state solutions. We also confirm earlier predictions that, under appropriate circumstances, accretion can proceed in a counter-aligned fashion, so that the accreted material will spin-down the hole, rather than spinning it up. Our results have implication in a number of different observational features of AGN such as the orientation and shape of jets, the shape of X-ray iron lines and the possibility of obscuration and absorption of X-ray by the outer disc as well as the general issue of the spin history of black holes during their growth.     

Computation of mass outflow rate from relativistic quasi-spherical accretion on to black holes

We compute the mass outflow rate R _m˙ from relativistic matter that is accreting quasi-spherically on to the Schwarzschild black holes. Taking the pair-plasma pressure-mediated shock surface as the effective boundary layer (of the black hole) from where the bulk of the outflow is assumed to be generated, computation of this rate is done using combinations of exact transonic inflow and outflow solutions. We find that R _m˙ depends on the initial parameters of the flow, the polytropic index of matter, the degree of compression of matter near the shock surface and the location of the shock surface itself. We thus not only study the variation of the mass outflow rate as a function of various physical parameters governing the problem, but also provide a sufficiently plausible estimation of this rate.     

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.     

M BH–σ relation in Sloan Digital Sky Survey flat-spectrum radio quasars

The relationship between the black hole mass and velocity dispersion indicated with [O  iii ] linewidth is investigated for a sample of 87 flat-spectrum radio quasars selected from the Sloan Digital Sky Survey Data Release 3 quasar catalogue. We found that the   M _BH−σ_[O III]  relation is different from the Tremaine et al. relation for nearby inactive galaxies, with a larger black hole mass at given velocity dispersion. There is no strong evidence of cosmology evolution in the   M _BH−σ_[O III]  relation up to   z ∼ 0.8  . A significant correlation between the [O  iii ] luminosity and broad-line region (BLR) luminosity is found. When transferring the [O  iii ] luminosity to narrow-line region (NLR) luminosity, the BLR luminosity is, on average, larger than the NLR one by about one order of magnitude. We found a strong correlation between the synchrotron peak luminosity and NLR luminosity, which implies a tight relation between the jet physics and accretion process.