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.     

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.     

Hydrodynamic simulations of propagating warps and bending waves in accretion discs

We present the results of a study of propagating warp or bending waves in accretion discs. Three-dimensional hydrodynamic simulations were performed using smoothed particle hydrodynamics (SPH), and the results are compared with calculations based on the linear theory of warped discs.
We examine the response of a gaseous disc to an initially imposed warping disturbance under a variety of physical conditions. We consider primarily the physical regime in which the dimensionless viscosity parameter α < H r , where H r is the disc aspect ratio, so that bending waves are expected to propagate. We also performed calculations for disc models in which α > H r , where the warps are expected to evolve diffusively. Small-amplitude (linear) perturbations are studied in both Keplerian and slightly non-Keplerian discs, and we find that the results of the SPH calculations can be reasonably well fitted by those of the linear theory. The main results of these calculations are: (i) the warp in Keplerian discs when α < H r propagates with little dispersion, and damps at a rate expected from estimates of the code viscosity; (ii) warps evolve diffusively when α > H r ; (iii) the slightly non-Keplerian discs lead to a substantially more dispersive behaviour of the warps, which damp at a similar rate to the Keplerian case, when α < H r .
Initially imposed higher amplitude, non-linear warping disturbances were studied in Keplerian discs. The results indicate that non-linear warps can lead to the formation of shocks, and that the evolution of the warp becomes less wave-like and more diffusive in character.
This work is relevant to the study of the warped accretion discs that may occur around Kerr black holes or in misaligned binary systems, and is mainly concerned with discs in which α < H r . The results indicate that SPH can model the hydrodynamics of warped discs, even when using rather modest numbers of particles.