辐射效率对黑洞质量增长的影响

考虑了在黑洞质量增长过程中,辐射效率的变化对黑洞质量增长的影响．随着吸积的进行,黑洞的角动量会发生变化,辐射效率也会随之发生变化,从而影响了质量增长．对于黑洞的指数增长模型,给出了考虑辐射效率对黑洞质量增长影响下的黑洞质量增长方程,用数值方法进行求解,并得到了黑洞质量随时间变化的曲线．与假定辐射效率为常数的模型对比,结果表明辐射效率的变化对黑洞质量的增长有较明显的影响,使黑洞的增长延迟．这个模型可以定量地说明最近的观测结果．     

Mini-discs around spinning black holes

Accretion on to black holes in wind-fed binaries and in collapsars forms small rotating discs with peculiar properties. Such 'mini-discs' accrete on the free-fall time without the help of viscosity and nevertheless can have a high radiative efficiency. The inviscid mini-disc model was previously constructed for a non-rotating black hole. We extend the model to the case of a spinning black hole, calculate the structure and radiative efficiency of the disc and find their dependence on the black hole spin. If the angular momenta of the disc and the black hole are anti-aligned, a hydrodynamic analogue of Penrose process takes place.     

Heating of the intergalactic medium by primordial miniquasars

A simple analytical model is used to calculate the X-ray heating of the intergalactic medium (IGM) for a range of black hole masses. This process is efficient enough to decouple the spin temperature of the IGM from the cosmic microwave background (CMB) temperature and produce a differential brightness temperature of the order of ∼ 5–20 mK out to distances as large as a few comoving Mpc, depending on the redshift, black hole mass and lifetime. We explore the influence of two types of black holes, those with and without ionizing ultraviolet radiation. The results of the simple analytical model are compared to those of a full spherically symmetric radiative transfer code. Two simple scenarios are proposed for the formation and evolution of black hole mass density in the Universe. The first considers an intermediate mass black hole that form as an end-product of pop III stars, whereas the second considers supermassive black holes that form directly through the collapse of massive haloes with low spin parameter. These scenarios are shown not to violate any of the observational constraints, yet produce enough X-ray photons to decouple the spin temperature from that of the CMB. This is an important issue for future high-redshift 21-cm observations.     

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.     

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.     

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.     

Spectral properties of the accretion discs around rotating black holes

We study the radiation properties of an accretion disc around a rotating black hole. We solve the hydrodynamic equations and calculate the transonic solutions of accretion disc in the presence of shocks. Then we use these solutions to generate the radiation spectrum in the presence of radiative heating and cooling processes. We present the effect of spin parameter of the black hole on the emitted radiation spectrum. In addition, attention has also been paid to the variation in energy spectral index with Kerr parameter and accretion rate. We find that spectral index becomes harder as the spin parameter changes from negative (accretion disc is counter-rotating with respect to the black hole spin) to a positive value. Finally, we compute and compare the spectral characteristics due to a free-fall flow and a transonic flow. We notice significant differences in high energy contributions from these two solutions.     

Optical and infrared signatures of ultra-luminous X-ray sources

We have constructed a model to describe the optical emission from ultra-luminous X-ray sources (ULXs). We assume a binary model with a black hole accreting matter from a Roche lobe filling companion star. We consider the effects of radiative transport and radiative equilibrium in the irradiated surfaces of both the star and a thin accretion disc. We have developed this model as a tool with which to positively identify the optical counterparts of ULXs, and subsequently derive parameters such as the black hole mass and the luminosity class and spectral type of the counterpart. We examine the dependence of the optical emission on these and other variables. We extend our model to examine the magnitude variation at infrared wavelengths, and we find that observations at these wavelengths may have more diagnostic power than in the optical. We apply our model to existing HST observations of the candidates for the optical counterpart of ULX X-7 in NGC 4559. All candidates could be consistent with an irradiated star alone, but we find that a number of them are too faint to fit with an irradiated star and disc together. Were one of these the optical counterpart to X-7, it would display a significant temporal variation.     

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.     

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.     

Jet-driven disk accretion in low luminosity AGN?

We explore an accretion model for low luminosity AGN (LLAGN) that attributes the low radiative output to a low mass accretion rate, , rather than a low radiative efficiency. In this model, electrons are assumed to drain energy from the ions as a result of collisionless plasma microinstabilities. Consequently, the accreting gas collapses to form a geometrically thin disk at small radii and is able to cool before reaching the black hole. The accretion disk is not a standard disk, however, because the radial disk structure is modified by a magnetic torque which drives a jet and which is primarily responsible for angular momentum transport. We also include relativistic effects. We apply this model to the well known LLAGN M87 and calculate the combined disk-jet steady-state broadband spectrum. A comparison between predicted and observed spectra indicates that M87 may be a maximally spinning black hole accreting at a rate of ∼10⁻³ M _⊙ yr⁻¹. This is about 6 orders of magnitude below the Eddington rate for the same radiative efficiency. Furthermore, the total jet power inferred by our model is in remarkably good agreement with the value independently deduced from observations of the M87 jet on kiloparsec scales.     

Cooling flows as a calorimeter of active galactic nucleus mechanical power

The assumption that radiative cooling of gas in the centres of galaxy clusters is approximately balanced by energy input from a central supermassive black hole implies that the observed X-ray luminosity of the cooling flow region sets a lower limit on active galactic nucleus (AGN) mechanical power. The conversion efficiency of the mechanical power of the AGN into gas heating is uncertain, but we argue that it can be high even in the absence of strong shocks. These arguments inevitably lead to the conclusion that the time-averaged mechanical power of AGNs in cooling flows is much higher than the bolometric luminosity of these objects observed currently.
The energy balance between cooling losses and AGN mechanical power requires some feedback mechanism. We consider a toy model in which the accretion rate on to a black hole is set by the classic Bondi formula. Application of this model to the best studied case of M87 suggests that accretion proceeds at approximately the Bondi rate down to a few gravitational radii with most of the power (at the level of a few per cent of the rest mass) being carried away by an outflow.     

Radiation drag driven mass accretion in a clumpy interstellar medium: implications for the supermassive black hole-to-bulge relation

We quantitatively scrutinize the effects of the radiation drag arising from the radiation fields in a galactic bulge in order to examine the possibility that the radiation drag could be an effective mechanism to extract angular momentum in a spheroidal system like a bulge and allow plenty of gas to accrete on to the galactic centre. For this purpose, we numerically solve the relativistic radiation hydrodynamical equation coupled with accurate radiative transfer, and quantitatively assess the radiation drag efficiency. As a result, we find that in an optically thick regime the radiation drag efficiency is sensitively dependent on the density distributions of the interstellar medium (ISM). The efficiency drops according to     in an optically thick uniform ISM, where τ _T is the total optical depth of the dusty ISM , whereas the efficiency remains almost constant at a high level if the ISM is clumpy . Hence, if bulge formation begins with a star formation event in a clumpy ISM, the radiation drag will effectively work to remove the angular momentum and the accreted gas may form a supermassive black hole. As a natural consequence, this mechanism reproduces a putative linear relation between the mass of a supermassive black hole and the mass of a galactic bulge, although further detailed modelling for stellar evolution is required for a more precise prediction.     

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.     

Observational effects of the Kerr metric

Strong gravity effects should have crucial impact on structure and radiative properties of an accretion flow surrounding a black hole. We discuss several observational consequences of such effects. (i) We note that the hard X-ray spectra of Seyfert galaxies, which appear to be intrinsically harder when observed at higher inclination angles, may be most naturally explained by radiative properties of plasmas in the Kerr metric. (ii) We indicate bending of photon trajectories to the equatorial plane, which is a distinct property of rapidly rotating black holes, as the most feasible effect underlying reduced variability of the Fe Kα line observed in several objects. (iii) Both the extreme Fe line profile and the variability pattern (observed, e.g., in a Seyfert galaxy MCG–6-30-15) independently indicate that a primary hard X-ray source must be located within a few gravitational radii from the Kerr black hole. We indicate a hot inner corona as the most likely model of such a source.     

黑洞吸积理论的新进展(Ⅰ):ADAF吸积理论

黑洞的吸积是天体物理学中最重要的基础理论之一。近年来该理论取得了引人瞩目的重大进展,具体表现在两个方面。其一是根据黑洞吸积必定跨声速这一特性,提出在一定条件下吸积流中会出现激波,这可称为含激波的吸积理论;其二是基于对一种局域致冷机制-贮导（advection）致冷的作用的重新认识而建立的,称为ADAF理论。在吸积盘的光学厚度很小或很大两种情况下,粘滞产生的大部分热量没有像在标准薄盘模型中那样辐射出去,而是贮存在流体中随流体的径向运动进入黑洞。与标准薄盘模型相比,贮导吸积盘具有高得多的温度和大得多的径向速度,但角动量小于开普勒角动量,吸积致能的效率要低得多。     

Jet-driven disk accretion in low luminosity AGN?*

We explore an accretion model for low luminosity AGN (LLAGN) that attributes the low radiative output to a low mass accretion rate, , rather than a low radiative efficiency. In this model, electrons are assumed to drain energy from the ions as a result of collisionless plasma microinstabilities. Consequently, the accreting gas collapses to form a geometrically thin disk at small radii and is able to cool before reaching the black hole. The accretion disk is not a standard disk, however, because the radial disk structure is modified by a magnetic torque which drives a jet and which is primarily responsible for angular momentum transport. We also include relativistic effects. We apply this model to the well known LLAGN M87 and calculate the combined disk-jet steady-state broadband spectrum. A comparison between predicted and observed spectra indicates that M87 may be a maximally spinning black hole accreting at a rate of ∼10⁻³  M _⊙ yr⁻¹. This is about 6 orders of magnitude below the Eddington rate for the same radiative efficiency. Furthermore, the total jet power inferred by our model is in remarkably good agreement with the value independently deduced from observations of the M87 jet on kiloparsec scales. ^* This paper has previously been published in Astrophysics and Space Science, vol. 310:3–4.     

A radio-emitting outflow in the quiescent state of A0620−00: implications for modelling low-luminosity black hole binaries

Deep observations with the Very Large Array of A0620–00, performed in 2005 August, resulted in the first detection of radio emission from a black hole binary at X-ray luminosities as low as 10^−8.5 times the Eddington limit. The measured radio flux density, of  51 ± 7 μJy  at 8.5 GHz, is the lowest reported for an X-ray binary system so far, and is interpreted in terms of partially self-absorbed synchrotron emission from outflowing plasma. Making use of the estimated outer accretion rate of A0620−00 in quiescence, we demonstrate that the outflow kinetic power must be energetically comparable to the total accretion power associated with such rate, if it was to reach the black hole with the standard radiative efficiency of 10 per cent. This favours a model for quiescence in which a radiatively inefficient outflow accounts for a sizable fraction of the missing energy, and, in turn, substantially affects the overall dynamics of the accretion flow. Simultaneous observations in the X-ray band, with Chandra , confirm the validity of a non-linear radio/X-ray correlation for hard state black hole binaries down to low quiescent luminosities, thereby contradicting some theoretical expectations. Taking the mass term into account, the A0620−00 data lie on the extrapolation of the so-called Fundamental Plane of black hole activity, which has thus been extended by more than two orders of magnitude in radio and X-ray luminosity. With the addition of the A0620−00 point, the plane relation provides an empirical proof for the scale invariance of the jet-accretion coupling in accreting black holes over the entire parameter space observable with current instrumentation.     

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.     

Accretion of holographic dark energy: dependency only upon horizon radius of expanding universe

In this paper we deal with accretion of dark energy in the holographic dark energy model for a general non-rotating static spherically symmetric black hole. The mass of the black hole increases or decreases depending on the nature of the holographic dark energy (quintessence or phantom) as well as on some integration parameters. It is to be illustrated that the enhancement or reduction of mass of a black hole is independent of the mass or size of the black hole itself. Rather it depends only upon the radius of the event horizon of the universe. Finally, the generalized second law of thermodynamics has been studied on the event horizon to be assured that the law holds even if when the black hole mass is decreasing though it is engrossing some mass.