The influence of central black holes on gravitational lenses

Recent observations indicate that many if not all galaxies host massive central black holes. In this paper we explore the influence of black holes on the lensing properties. We model the lens as an isothermal ellipsoid with a finite core radius plus a central black hole. We show that the presence of the black hole substantially changes the critical curves and caustics. If the black hole mass is above a critical value, then it will completely suppress the central images for all source positions. Realistic central black holes are likely to have masses below this critical value. Even in such subcritical cases, the black hole can suppress the central image when the source is inside a zone of influence, which depends on the core radius and black hole mass. In the subcritical cases, an additional image may be created by the black hole in some regions, which for some radio lenses may be detectable with high-resolution and large dynamic range VLBI maps. The presence of central black holes should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.     

Imaging optically-thin hotspots near the black hole horizon of Sgr A* at radio and near-infrared wavelengths

Submilliarcsecond astrometry and imaging of the black hole Sgr A* at the Galactic Centre may become possible in the near future at infrared and submillimetre wavelengths. Motivated by the observations of short-term infrared and X-ray variability of Sgr A*, in a previous paper, we computed the expected images and light curves, including polarization, associated with a compact emission region orbiting the central black hole. We extend this work, using a more realistic hotspot model and including the effects of opacity in the underlying accretion flow. We find that at infrared wavelengths, the qualitative features identified by our earlier work are present, namely it is possible to extract the black hole mass and spin from spot images and light curves of the observed flux and polarization. At radio wavelengths, disc opacity produces significant departures from the infrared behaviour, but there are still generic signatures of the black hole properties. Detailed comparison of these results with future data can be used to test general relativity and to improve existing models for the accretion flow in the immediate vicinity of the black hole.     

The runaway instability of thick discs around black holes I. The constant angular momentum case

We present results from a numerical study of the runaway instability of thick discs around black holes. This instability is an important issue for most models of cosmic gamma-ray bursts, where the central engine responsible for the initial energy release is such a system consisting of a thick disc surrounding a black hole. We have carried out a comprehensive number of time-dependent simulations aimed at exploring the appearance of the instability. Our study has been performed using a fully relativistic hydrodynamics code. The general relativistic hydrodynamic equations are formulated as a hyperbolic flux-conservative system and solved using a suitable Godunov-type scheme. We build a series of constant angular momentum discs around a Schwarzschild black hole. Furthermore, the self-gravity of the disc is neglected and the evolution of the central black hole is assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. The black hole mass increase is thus determined by the mass accretion rate across the event horizon. In agreement with previous studies based on stationary models, we find that by allowing the mass of the black hole to grow the disc becomes unstable. Our hydrodynamical simulations show that for all disc-to-hole mass ratios considered (between 1 and 0.05), the runaway instability appears very fast on a dynamical time-scale of a few orbital periods, typically a few 10 ms and never exceeding 1 s for our particular choice of the mass of the black hole (2.5 M) and a large range of mass fluxes  ( m 10^-3 M s^-1)  . The implications of our results in the context of gamma-ray bursts are briefly discussed.     

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.     

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.     

自引力辐射体系的熵与引力坍缩

本文利用李立新和刘辽导出的黑洞视界附近的辐射态方程，计算了约束在一个球形盒子中的目引力辐射体系的墙（不含中心黑洞和含有中心黑洞两种情况）．与Sorkin等人的计算比较，本文的结果不会出现发散困难，而且体系的总摘（包括中心黑洞的墙）的上阳正好等于坍缩后形成的同质量的黑洞嫡．作者认为，自引力辐射体系坍绩的合理模式是先形成中心黑洞，然后中心黑洞逐渐长大直至整个体系全部坍缩为黑洞．在坍缩过程中，任一中间态的媳总是比末态的黑洞墙小，到坍缩过程结束总熵才等于对应的黑洞摘．这一结果为黑洞滴的起源提供了一个合理的解释．     

The estimations of four basic parameters for gamma-ray loud blazars

The method used in our previous papers is adopted to estimate four basic pa-rameters (the central black hole mass (M), the boosting factor (or Doppler factor) (δ), the (d)) for 59 γ-ray loud blazars (20 BL Lacertae objects and 39 fiat spectrum radio quasars).The central black hole masses estimated for this sample are in a range of from 107 M⊙to 109 M⊙. In the case of black hole mass, there is no clear difference between BL Lacertae objects and flat spectrum radio quasars, which is consistent with the previous results sug-gesting that the central black hole masses do not play an important role in the evolutionary sequence of blazars.     

Relation between radio core length and black hole mass for active galactic nuclei

We explore the relation between the linear length of radio core and the central black hole mass for a sample of radio-loud active galactic nuclei (AGNs). An empirical relation between the size of the broad line region (BLR) and optical luminosity is used to estimate the size of the BLR. The black hole mass is derived from H β linewidth and the radius of the BLR on the assumption that the clouds in BLRs are orbiting with Keplerian velocities. A significant intrinsic correlation is found between the linear length of the core and the black hole mass, which implies that the jet formation is closely related with the central black hole. We also find a strong correlation between the black hole mass and the core luminosity.     

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.     

Extreme gravitational lensing near rotating black holes

We describe a new approach to calculating photon trajectories and gravitational lensing effects in the strong gravitational field of the Kerr black hole. These techniques are applied to explore both the imaging and spectral properties of photons emitted from an accretion disc, which perform multiple orbits of the central mass before escaping to infinity. Viewed at large inclinations, these higher-order photons contribute ∼20 per cent of the total luminosity of the system for a Schwarzschild hole, while for an extreme Kerr black hole this fraction rises to ∼60 per cent. In more realistic models, these photons will be reabsorbed by the disc at large distances from the hole, but this returning radiation could provide a physical mechanism to resolve the discrepancy between the predicted and observed optical/ultraviolet colours in active galactic nuclei. Conversely, at low inclinations, higher-order images reintercept the disc plane close to the black hole, so need not be absorbed by the disc if this is within the plunging region. These photons form a bright ring carrying approximately 10 per cent of the total disc luminosity for a Schwarzschild black hole. The spatial separation between the inner edge of the disc and the ring is similar to the size of the event horizon. This is resolvable for supermassive black holes with proposed X-ray interferometery missions such as the Microarcsecond X-ray Imaging Mission (MAXIM), and so has the potential to provide an observational test of strong field gravity.     

Electromagnetic counterparts from counter-rotating relativistic kicked discs

We show the results of two dimensional general relativistic inviscid and isothermal hydrodynamical simulations comparing the behavior of co-rotating (with respect to the black hole rotation) and counter-rotating circumbinary quasi-Keplerian discs in the post merger phase of a supermassive binary black hole system. While confirming the spiral shock generation within the disc due to the combined effects of mass loss and recoil velocity of the black hole, we find that the maximum luminosity of counter-rotating discs is a factor ∼(2-12) higher than in the co-rotating case, depending on the spin of the black hole. On the other hand, the luminosity peak happens ∼10 days later with respect to the co-rotating case. Although the global dynamics of counter-rotating discs in the post merger phase of a merging event is very similar to that for co-rotating discs, an important difference has been found. In fact, increasing the spin of the central black hole produces more luminous co-rotating discs while less luminous counter-rotating ones.     

Effects of the Blandford–Znajek process on the evolution of the central black holes of accretion discs

The effects of the Blandford–Znajek (BZ) process on the evolution of the central black holes of accretion discs are investigated by an analytical method and numerical calculations in this paper. It is shown that the BZ process reduces the rates of change of some parameters of the black hole, such as mass, angular momentum, dimensionless angular momentum and temperature, and the evolution of the central black hole towards the extreme Kerr black hole is depressed effectively. However, the rate of change of entropy of the central black hole is augmented in the BZ process. In addition, the consistency of the BZ process with the three laws of black hole thermodynamics is discussed.     

Black hole mergers: can gas discs solve the 'final parsec' problem?

We compute the effect of an orbiting gas disc in promoting the coalescence of a central supermassive black hole binary. Unlike earlier studies, we consider a finite mass of gas with explicit time dependence: we do not assume that the gas necessarily adopts a steady state or a spatially constant accretion rate, i.e. that the merging black hole was somehow inserted into a pre-existing accretion disc. We consider the tidal torque of the binary on the disc, and the binary's gravitational radiation. We study the effects of star formation in the gas disc in a simple energy feedback framework.
The disc spectrum differs in detail from that found before. In particular, tidal torques from the secondary black hole heat the edges of the gap, creating bright rims around the secondary. These rims do not in practice have uniform brightness either in azimuth or time, but can on average account for as much as 50 per cent of the integrated light from the disc. This may lead to detectable high-photon-energy variability on the relatively long orbital time-scale of the secondary black hole, and thus offer a prospective signature of a coalescing black hole binary.
We also find that the disc can drive the binary to merger on a reasonable time-scale only if its mass is at least comparable with that of the secondary black hole, and if the initial binary separation is relatively small, i.e.   a ₀≲ 0.05  pc. Star formation complicates the merger further by removing mass from the disc. In the feedback model we consider, this sets an effective limit to the disc mass. As a result, binary merging is unlikely unless the black hole mass ratio is ≲0.001. Gas discs thus appear not to be an effective solution to the 'last parsec' problem for a significant class of mergers.     

A search for the third lensed image in JVAS B1030+074

Central gravitational image detection is very important for the study of the mass distribution of the inner parts (∼100 pc) of lens galaxies. However, the detection of such images is extremely rare and difficult. We present a 1.7-GHz High Sensitivity Array (HSA) observation of the double-image radio lens system B1030+074. The data are combined with archive Very Long Baseline Array and global very long baseline interferometry (VLBI) observations, and careful consideration is given to the effects of noise, clean ing and self-calibration. An upper limit is derived for the strength of the central image of 180 μJy (90 per cent confidence level), considerably greater than would have been expected on the basis of a simple analysis. This gives a lower limit of ∼10³ for the ratio of the brightest image to the central image. For cusped models of lens mass distributions, we have made use of this non-detection to constrain the relation between inner power-law slope β of the lensing galaxy mass profile, and its break radius r _b. For   r _b > 130 pc  the power-law slope is required to be close to isothermal  (β > 1.8)  . A flatter inner slope is allowed if a massive black hole is present at the centre of the lensing galaxy, but the effect of the black hole is small unless it is ∼10 times more massive than that implied by the relation between black hole mass and stellar velocity dispersion. By comparing four epochs of VLBI observations, we also detected possible superluminal motion in the jet in the brighter image A. The B jet remains unresolved, as expected from a simple lens model of the system.     

Source mergers and bubble growth during reionization

The recently introduced models of reionization bubbles based on extended Press–Schechter theory (by Furlanetto, Hernquist & Zaldarriaga) are generalized to include mergers of ionization sources. Sources with a recent major merger are taken to have enhanced photon production due to star formation, and accretion on to a central black hole if a black hole is present. This produces a scatter in the number of ionized photons corresponding to a halo of a given mass and a change in photon production over time for any given halo mass. By extending previous methods, photon production histories, bubble distributions and ionization histories are computed for several different parameter and recombination assumptions. The resulting distributions interpolate between previously calculated limiting cases.     

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.     

Evolution and instabilities of disks harboring super massive black holes

The bar formation is still an open problem in modern astrophysics. In this paper we present numerical simulations performed with the aim of analyzing the growth of the bar instability inside stellar-gaseous disks, where the star formation is triggered, and a central black hole is present. The aim of this paper is to point out the impact of such a central massive black hole on the growth of the bar. We use N-body-SPH simulations of the same isolated disk-to-halo mass systems harboring black holes with different initial masses and a different energy feedback on the surrounding gas. We compare the results of these simulations with the one of the same disk without a black hole in its center. We make the same comparison (disk with and without black hole) for a stellar disk in a fully cosmological scenario. A stellar bar, lasting 10 Gyrs, is present in all our simulations.     

Evaporation of Accretion Disks around Black Holes: The Disk-Corona Transition and the Connection to the Advection-dominated Accretion Flow

We apply the disk-corona evaporation model (Meyer & Meyer-Hofmeister) originally derived for dwarf novae to black hole systems. This model describes the transition of a thin cool outer disk to a hot coronal flow. The mass accretion rate determines the location of this transition. For a number of well-studied black hole binaries, we take the mass flow rates derived from a fit of the advection-dominated accretion flow (ADAF) model to the observed spectra (for a review, see Narayan, Mahadevan, & Quataert) and determine where the transition of accretion via a cool disk to a coronal flow/ADAF would be located for these rates. We compare this with the observed location of the inner disk edge, as estimated from the maximum velocity of the Halpha emission line. We find that the transition caused by evaporation agrees with this determination in stellar disks. We also show that the ADAF and the "thin outer disk + corona" are compatible in terms of the physics in the transition region.     

The Effect of Radiative Efficiency on the Growth of the Black Hole Mass

The effect of variation of radiative efficiency on the growth of the black hole mass is discussed. In the process of accretion, the black hole's angular momentum varies, resulting in a variation of the radiative efficiency, and the growth of the black hole mass is thereby affected. For the exponential growth model of back holes and taking into account the effect of a varying radiative efficiency, the equation for the growth of the black hole mass is solved numerically. Compared to the model that assumes a constant radiative efficiency, the result indicates that variation of radiative efficiency has a marked, retarding effect on the growth of the black hole mass. This model can explain quantitatively some recent observational results.     

Global Dynamics in Self-Consistent Models of Elliptical Galaxies

We compare two different N-body models simulating elliptical galaxies. Namely, the first model is a non-rotating triaxial N-body equilibrium model with smooth center, called SC model. The second model, called CM model, is derived from the SC by inserting a central mass in it, so that all possible differences between the two models are due to the effect of the central mass. The central mass is assumed to be mainly due to a massive central black hole of mass about 1% of the total mass of the galaxy. By using the fundamental frequency analysis, the two systems are thoroughly investigated as regards the types of orbits described either by test particles, or by the real particles of the systems at all the energy levels. A comparison between the orbits of test particles and the orbits of real particles at various energy levels is made on the rotation number plane. We find that extensive stable regions of phase space, detected by test particles remain empty, i.e. these regions are not occupied by real particles, while many real particles move in unstable regions of phase space describing chaotic orbits. We run self-consistently the two models for more than a Hubble time. During this run, in spite of the noise due to small variations of the potential, the SC model maintains (within a small uncertainly) the number of particles moving on orbits of each particular type. In contrast, the CM model is unstable, due to the large amount of mass in chaotic motion caused by the central mass. This system undergoes a secular evolution towards an equilibrium state. During this evolution it is gradually self-organized by converting chaotic orbits to ordered orbits mainly of the short axis tube type approaching an oblate spheroidal equilibrium. This is clearly demonstrated in terms of the fundamental frequencies of the orbits on the rotation number plane and the time evolution of the triaxiality index.