Temperature profile of accretion disk around a kerr black hole

We use a rigorous, general relativistic, viscous, fluiddynamical equation to calculate the temperature profile of the accretion disk around a Kerr black hole. Our result shows that there is indeed a maximum in the profile. If the radiation in the disk is black-body radiation, then the result is independent of the viscosity mechanism. Using a free-free radiation and the Lα viscosity law, our results are similar to our previous findings [1]. Our calculation also shows that within the radius of the temperature maximum, there exists a rapidly cooling ring-shaped region, possessing characteristics that are not found in the case with the usual temperature profile.     

Extracting Energy from Accretion into a Kerr Black Hole

The highest efficiency of converting rest mass into energy by accreting matter into a Kerr black hole is approximately 31% (Thorne 1974). We propose a new process in which periods of accretion from a thin disk, and the associated spin-up of the black hole, alternate with the periods of no accretion and magnetic transfer of energy from the black hole to the disk. These cycles can repeat indefinitely, at least in principle, with the black hole mass increasing by approximately 66% per cycle and up to approximately 43% of accreted rest mass radiated away by the disk.     

Large Proper-Motion Infrared

When some magnetic field lines connect a Kerr black hole with a disk rotating around it, energy and angular momentum are transferred between them. If the black hole rotates faster than the disk, ca&solm0;GMH>0.36 for a thin Keplerian disk, then energy and angular momentum are extracted from the black hole and transferred to the disk (MH is the mass and aMH is the angular momentum of the black hole). This way, the energy originating in the black hole may be radiated away by the disk. The total amount of energy that can be extracted from the black hole spun down from ca&solm0;GMH=0.998 to ca&solm0;GMH=0.36 by a thin Keplerian disk is approximately 0.15MHc2. This is larger than approximately 0.09MHc2, which can be extracted by the Blandford-Znajek mechanism.     

Emission Line Profiles and Images of Geometrically Thin and Optically Thick Accretion Disks

Under the assumption that the accretion disk around a Kerr (spinning) black hole is geometrically thin and optically thick, the trajectories of photons in Kerr metric are calculated by using the photon tracing method. And by numerical calculations, we have made a study on the relativistic iron line profiles and images of thin accretion disks. The result shows that viewing at large inclination angles, because of the contribution of the photons from the lower surface of the accretion disk, the line profile becomes double-peaked and the flux image is also significantly modified.     

几何薄光学厚吸积盘谱线轮廓及成像研究

假设位于黑洞赤道面上做圆形轨道运动的吸积盘是几何薄、光学厚的.利用光子追踪法计算在Kerr度规下的光子运动轨迹,通过数值计算研究薄吸积盘的相对论谱线轮廓及成像.在大角度观测时,吸积盘下表面的光子对谱线轮廓及成像的影响是显著的.     

Bridging the gap between stellar-mass black holes and ultraluminous X-ray sources

The X-ray spectral and timing properties of ultraluminous X-ray sources (ULXs) have many similarities with the very high state of stellar-mass black holes (power-law dominated, at accretion rates greater than the Eddington rate). On the other hand, their cool disk components, large characteristic inner-disk radii and low characteristic timescales have been interpreted as evidence of black hole masses ～1000 M _⊙ (intermediate-mass black holes). Here we re-examine the physical interpretation of the cool disk model, in the context of accretion states of stellar-mass black holes. In particular, XTE J1550–564 can be considered the missing link between ULXs and stellar-mass black holes, because it exhibits a high-accretion-rate, low-disk-temperature state (ultraluminous branch). On the ultraluminous branch, the accretion rate is positively correlated with the disk truncation radius and the bolometric disk luminosity, while it is anti-correlated with the peak temperature and the frequency of quasi-periodic-oscillations. Two prototypical ULXs (NGC?1313 X-1 and X-2) also seem to move along that branch. We use a phenomenological model to show how the different range of spectral and timing parameters found in the two classes of accreting black holes depends on both their masses and accretion rates. We suggest that ULXs are consistent with black hole masses ～50–100 M _⊙, moderately inefficiently accreting at ≈20 times Eddington.     

Comparison of two methods for determining the magnetic fields near black holes

We compare two methods for estimating the magnetic field near a black hole—based on a statistical formula that relates the magnetic field on the horizon of the black hole to its mass and on a direct magnetic field determination from optical polarimetric observations. An optically thick magnetized accretion disk is usually formed around the black hole in active galactic nuclei. The linear polarization of the radiation emerging from the disk is related to the local magnetic field and the polarization in Milne’s classical problem. The magnetic field in the region from where the radiation with the observed wavelength comes can be estimated by measuring this polarization. On the other hand, this field can be estimated from the above statistical formula if the field near the black hole is extrapolated into the accretion disk using a standard power law. Comparison of the magnetic field obtained from the observed polarization with the extrapolated field can serve to estimate the accuracy of the latter and the exponent in the adopted extrapolation law. As an example, we compare these two methods for the source NGC 4258.     

Profiles of spectral lines of an accretion ring around a Kerr black hole

Profiles of spectral lines emitted from an accretion ring around an object with strong gravitational field should be affected by Doppler shift, gravitational redshift, and deflection of light. Taking these effects into account, precise line profile of a Keplerian ring around a Kerr black hole for a distant observer is obtained by solving the kinetic equation of photons.     

Runaway instabilities in geometrically thin accretion disks around Kerr black holes

The stability of the innermost disk region orbiting a Kerr black hole is investigated for geometrically thin accretion disks. The infalling matter transports mass and angular momentum into the Kerr hole. This affects the inner disk boundary and leads to runaway instabilities in some cases.     

Generalized uncertainty principle and Bekenstein-Hawking entropy in tunneling rate of Kerr black hole

We study the effects of the generalized uncertainty principle in the tunneling formalism for Hawking radiation to evaluate the quantum-corrected Hawking temperature and entropy for a Kerr black hole. By assumption of a spatially flat universe accompanied with expansion of metric, the modified area and entropy of Kerr black hole are calculated and we could obtain an expression for entropy of black hole that is changing with respect to time and Bekenstein-Hawking temperature.     

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.     

General relativistic study of perfect fluid disk in linearised kerr geometry

In this chapter we present a detailed general relativistic formulation for the study of structure of perfect fluid disk rotating around Kerr black hole. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical Simulation of Small Perturbation on an Accretion Disk Due to the Collision of a Star with the Disk Near the Black Hole

In this paper, perturbations of an accretion disk by a star orbiting around a black hole are studied. We report on a numerical experiment, which has been carried out by using a parallel-machine code originally developed by Dönmez (2004). An initially steady state accretion disk near a non-rotating (Schwarzschild) black hole interacts with a “star”, modeled as an initially circular region of increased density. Part of the disk is affected by the interaction. In some cases, a gap develops and shock wave propagates through the disk. We follow the evolution for order of one dynamical period and we show how the non-axisymetric density perturbation further evolves and moves downwards where the material of the disk and the star become eventually accreted onto the central body. When the star perturbs the steady state accretion disk, the disk around the black hole is destroyed by the effect of perturbation. The perturbed accretion disk creates a shock wave during the evolution and it loses angular momentum when the gas hits on the shock waves. Colliding gas with the shock wave is the one of the basic mechanism of emitting the X-rays in the accretion disk. The series of supernovae occurring in the inner disk could entirely destroy the disk in that region which leaves a more massive black hole behind, at the center of galaxies.     

Variation of the gas and radiation content in the sub-Keplerian accretion disk around black holes and its impact to the solutions

We investigate the variation of the gas and the radiation pressure in accretion disks during the infall of matter to the black hole and its effect to the flow. While the flow far away from the black hole might be non-relativistic, in the vicinity of the black hole it is expected to be relativistic behaving more like radiation. Therefore, the ratio of gas pressure to total pressure (β) and the underlying polytropic index (γ) should not be constant throughout the flow. We obtain that accretion flows exhibit significant variation of β and then γ, which affects solutions described in the standard literature based on constant β. Certain solutions for a particular set of initial parameters with a constant β do not exist when the variation of β is incorporated appropriately. We model the viscous sub-Keplerian accretion disk with a nonzero component of advection and pressure gradient around black holes by preserving the conservations of mass, momentum, energy, supplemented by the evolution of β. By solving the set of five coupled differential equations, we obtain the thermo-hydrodynamical properties of the flow. We show that during infall, β of the flow could vary up to ∼300%, while γ up to ∼20%. This might have a significant impact to the disk solutions in explaining observed data, e.g. super-luminal jets from disks, luminosity, and then extracting fundamental properties from them. Hence any conclusion based on constant γ and β should be taken with caution and corrected.     

On the disk wind mass loss rates in QSOs

We derive here a relatively simple expression for the total wind mass loss rates in QSOs within the accretion disk wind scenario. We show that the simple expression derived here for QSO disk wind mass loss rate is in a very good agreement with the more “exact” values obtained through significantly more complex and detailed numerically intensive 2.5D time-dependent simulations. Additionally we show that for typical QSO parameters, the disk itself will be emitting mostly in the UV/optical spectrum, in turn implying that the X-ray emission from QSOs likely is produced through some physical mechanism acting at radii smaller than the inner disk radius (for a standard accretion disk, half of the initially gravitational potential energy of the accreting disk mass is emitted directly by the disk, while the other half “falls” closer towards the black hole than the inner disk radius). We also show that for typical QSO parameters, the disk itself is dominated by continuum radiation pressure (rather than thermal pressure), resulting in a “flat disk” (except for the innermost disk regions).     

Accretion disk spectra of super-luminal jet sources and ultra-luminous compact X-ray sources in nearby spiral galaxies

The Ultra-luminous Compact X-ray Sources (ULXs)in nearby spiral galaxies and the Galactic super-luminaljet sources sharethe common spectral characteristic that they haveextremely high disk temperatures which cannot be explainedin the framework of the standard accretion disk modelin the Schwarzschild metric. We have calculated an extreme Kerr disk model to examine if the Kerr disk model can instead explain the observed `too hot' accretion disk spectra.We found that the Kerr disk spectrum becomes significantly hardercompared to the Schwarzschild disk only when the disk is highlyinclined.For super-luminal jet sources, which are known to beinclined systems, the Kerr disk model may thuswork if we choose proper values for the black hole angular momentum. For the ULXs, however, the Kerr disk interpretation will be problematic,as is is highly unlikely that their accretion disks are preferentiallyinclined.     

Line Shapes Emitted from Spiral Structures around Symmetric Orbits of Supermassive Binary Black Holes

Variability of active galactic nuclei is not well understood. One possible explanation is existence of supermassive binary black holes (SMBBH) in their centres. It is expected that major mergers are common in the Universe. It is expected that each supermassive black hole of every galaxy eventually finish as a SMBBH system in the core of newly formed galaxy. Here we model the emission line profiles of active galactic nuclei (AGN) assuming that the flux and emission line shape variations are induced by supermassive binary black hole systems (SMBBH). We assume that the accreting gas inside the circumbinary (CB) disk is photo ionized by mini accretion disk emission around each SMBBH. We calculate variations of emission line flux, shifts and shapes for different parameters of SMBBH orbits. We consider cases with different masses and inclinations for circular orbits and measure the effect to the shape of emission line profiles and flux variability.     

恒星级黑洞的观测证认研究进展

具有不同质量的恒星在耗尽其热核能源后,最终可能会坍缩成为性质完全不同的致密天体,如白矮星、中子星或者黑洞。从20世纪30年代起,黑洞的观测及其证认一直是天体物理学的研究热点之一。首先简要地回顾了恒星级黑洞的形成及其候选天体的研究历史;然后介绍了如何从观测上证认恒星级黑洞:接着详细讨论了恒星级黑洞的质量和自转参数的测量方法;最后介绍恒星级黑洞观测及其证认的最新研究进展,并做出结论:目前已经有充分的证据宣告在部分吸积X射线双星中存在恒星级黑洞。