Stochastic Resonance of Accretion Disk and the Persistent Low-Frequency Quasi-Periodic Oscillations in Black Hole X-ray Binaries

In this paper, we use a Langevin type equation with a damping term and stochastic force to describe the stochastic oscillations on the vertical direction of the accretion disk around a black hole, and calculate the luminosity and power spectral density (PSD) for an oscillating disk. Then we discuss the stochastic resonance (SR) phenomenon in PSD curves for different parameter values of viscosity coefficient, accretion rate, mass of black hole and outer radius of the disk. The results show that our simulated PSD curves of luminosity for disk oscillation have the same profile as the observed PSD of black hole X-ray binaries (BHXBs) in the lowhard state, and the SR of accretion disk oscillation may be an alternative interpretation of the persistent low-frequency quasi-periodic oscillations (LFQPOs).     

吸积盘随机振荡光度功率谱密度中低频准周期振荡现象的研究

采用含有频率涨落噪声和指数形式关联随机力作用的广义朗之万(Langevin)方程模型描述黑洞吸积盘的垂向振荡,推导出吸积盘随机振荡光度功率谱密度的解析表达式,并讨论了系统参数对功率谱密度中低频准周期振荡(Low Frequency Quasi-Periodic Oscillations,LFQPOs)现象的影响。研究结果发现选取合适的系统参数时,功率谱密度曲线上出现了一个基频和一个二次谐频的共振双峰低频准周期振荡,基频峰对应的中心频率为吸积盘振荡的特征频率;随机力关联时间决定了基频峰的高度和宽度,频率噪声强度和粘滞阻尼只对二次谐频峰产生影响。结果说明吸积盘的随机振荡模型可以作为低频准周期振荡起源的一种解释。     

Modelling the IDV Emissions of the BL Lac Objects with a Langevin Type Stochastic Differential Equation

In this paper, we introduce a simplified model for explaining the observations of optical intra-day variability (IDV) of the BL Lac Objects. We assume that the source of the IDV are the stochastic oscillations of an accretion disk around a supermassive black hole. The stochastic fluctuations on the vertical direction of the accretion disk are described by using a Langevin type equation with a damping term and a random, white noise type force. Furthermore, preliminary numerical simulation results are presented, which are based on the numerical analysis of the Langevin stochastic differential equation.     

Deterministic Chaos in the X-ray Sources

Hardly any of the observed black hole accretion disks in X-ray binaries and active galaxies shows constant flux. When the local stochastic variations of the disk occur at specific regions where a resonant behaviour takes place, there appear the quasi-periodic oscillations (QPOs). If the global structure of the flow and its non-linear hydrodynamics affects the fluctuations, the variability is chaotic in the sense of deterministic chaos. Our aim is to solve a problem of the stochastic versus deterministic nature of the black hole binary variabilities. We use both observational and analytic methods. We use the recurrence analysis and we study the occurence of long diagonal lines in the recurrence plot of observed data series and compare it to the surrogate series. We analyze here the data of two X-ray binaries – XTE J1550-564 and GX 339-4 observed by Rossi X-ray Timing Explorer. In these sources, the non-linear variability is expected because of the global conditions (such as the mean accretion rate) leading to the possible instability of an accretion disk. The thermal-viscous instability and fluctuations around the fixed-point solution occurs at high accretion rate, when the radiation pressure gives dominant contribution to the stress tensor.     

On the change of the inner boundary of an optically thick accretion disk around white dwarfs using the dwarf nova SS Cyg as an example

We present the results of our studies of the aperiodic optical flux variability for SS Cyg, an accreting binary systemwith a white dwarf. The main set of observational data presented here was obtained with the ANDOR/iXon DU-888 photometer mounted on the RTT-150 telescope, which allowed a record (for CCD photometers) time resolution up to 8 ms to be achieved. The power spectra of the source’s flux variability have revealed that the aperiodic variability contains information about the inner boundary of the optically thick flow in the binary system. We show that the inner boundary of the optically thick accretion disk comes close to the white dwarf surface at the maximum of the source’s bolometric light curve, i.e., at the peak of the instantaneous accretion rate onto the white dwarf, while the optically thick accretion disk is truncated at distances 8.5 × 10⁹ cm ∼10R _WD in the low state. We suggest that the location of the inner boundary of the accretion disk in the binary can be traced by studying the parameters of the power spectra for accreting white dwarfs. In particular, this allows the mass of the accreting object to be estimated.     

Accretion disc variability in the hard state of black hole X-ray binaries

XMM–Newton X-ray spectra of the hard state black hole X-ray binaries (BHXRBs) SWIFT J1753.5−0127 and GX 339−4 show evidence for accretion disc blackbody emission, in addition to hard power laws. The soft and hard band power spectral densities (PSDs) of these sources demonstrate variability over a wide range of time-scales. However, on time-scales of tens of seconds, corresponding to the putative low-frequency Lorentzian in the PSD, there is additional power in the soft band. To interpret this behaviour, we introduce a new spectral analysis technique, the 'covariance spectrum', to disentangle the contribution of the X-ray spectral components to variations on different time-scales. We use this technique to show that the disc blackbody component varies on all time-scales, but varies more, relative to the power law, on longer time-scales. This behaviour explains the additional long-term variability seen in the soft band. Comparison of the blackbody and iron line normalizations seen in the covariance spectra in GX 339−4 implies that the short-term blackbody variations are driven by thermal reprocessing of the power-law continuum absorbed by the disc. However, since the amplitude of variable reflection is the same on long and short time-scales, we rule out reprocessing as the cause of the enhanced disc variability on long time-scales. Therefore, we conclude that the long time-scale blackbody variations are caused by instabilities in the disc itself, in contrast to the stable discs seen in BHXRB soft states. Our results provide the first observational evidence that the low-frequency Lorentzian feature present in the PSD is produced by the accretion disc.     

A simplified model of ADAF with the jet driven by the large-scale magnetic field

We propose a simplified model of outflow/jet driven by the Blandford–Payne (BP) process from advection-dominated accretion flows (ADAF) and derive the expressions of the BP power and disk luminosity based on the conservation laws of mass, angular momentum and energy. We fit the 2–10 keV luminosity and kinetic power of 15 active galactic nucleus (AGNs) of sub-Eddington luminosity. It is found that there exists an anti-correlation between the accretion rate and the advection parameter, which could be used to explain the correlation between Eddington-scaled kinetic power and bolometric luminosity of the 15 samples. In addition, the Ledlow–Owen relation for FR I/II dichotomy is re-expressed in a parameter space consisting of logarithm of dimensionless accretion rate versus that of the BH mass. It turns out that the FR I/II dichotomy is determined mainly by the dimensionless accretion rate, being insensitive to the BH mass. And the dividing accretion rate is less than the critical accretion rate for ADAFs, suggesting that FR I sources are all in the ADAF state.     

Thomson Thick X-Ray Absorption in a Broad Absorption Line Quasar, PG 0946+301

We present results of new ASCA observations of the low-luminosity active galactic nucleus (LLAGN) NGC 4579 obtained on 1998 December 18 and 28, and we report on the detection of variability of an iron K emission line. The X-ray luminosities in the 2-10 keV band for the two observations are nearly identical (LX approximately 2x1041 ergs s(-1)), but they are approximately 35% larger than that measured in 1995 July by Terashima et al. An Fe K emission line is detected at 6.39+/-0.09 keV (source rest frame), which is lower than the line energy 6.73+0.13-0.12 keV in the 1995 observation. If we fit the Fe lines with a blend of two Gaussians centered at 6.39 and 6.73 keV, the intensity of the 6.7 keV line decreases, while the intensity of the 6.4 keV line increases, within an interval of 3.5 yr. This variability rules out thermal plasmas in the host galaxy as the origin of the ionized Fe line in this LLAGN. The detection and variability of the 6.4 keV line indicates that cold matter subtends a large solid angle viewed from the nucleus and that it is located within approximately 1 pc from the nucleus. It could be identified with an optically thick standard accretion disk. If this is the case, a standard accretion disk is present at the Eddington ratio of Lbol/LEdd approximately 2x10-3. A broad disk-line profile is not clearly seen, and the structure of the innermost part of accretion disk remains unclear.     

The effect of an optically thin region on stability of an accretion disk around a supermassive black hole

We analyse conditions of the innermost portion of an accretion disk and establish a set of equations for this region. A stable innermost region may exist, which can probably explain the observed UV and X-ray spectra, avoiding the unstable emission. We then discuss the detailed radial structure of a disk around a black hole for typical AGN parameters and obtain different kinds of- relationships for different regions of a disk. On the basis of this, we discuss the stability. A new type of cycle is present, which we call a double S shaped cycle. In this cycle, the extent of accretion rate variability is much larger than that in dwarf nova cycles. This probably solves the problem of violent variability of AGN. In the meantime, the very high accretion rate at the hottest state in limit cycles in the unstable region may provide continuous injection of matter to the jet and power the relativistic motion of the jet.     

Towards a new standard model for black hole accretion

We briefly review recent developments in black hole accretion disk theory, emphasizing the vital role played by magnetohydrodynamic (MHD) stresses in transporting angular momentum. The apparent universality of accretion-related outflow phenomena is a strong indicator that large-scale MHD torques facilitate vertical transport of angular momentum. This leads to an enhanced overall rate of angular momentum transport and allows accretion of matter to proceed at an interesting rate. Furthermore, we argue that when vertical transport is important, the radial structure of the accretion disk is modified at small radii and this affects the disk emission spectrum. We present a simple model demonstrating how energetic, magnetically-driven outflows modify the emergent disk emission spectrum with respect to that predicted by standard accretion disk theory. A comparison of the predicted spectra against observations of quasar spectral energy distributions suggests that mass accretion rates inferred using the standard disk model may be severely underestimated.     

Investigating a fluctuating-accretion model for the spectral-timing properties of accreting black hole systems

The fluctuating-accretion model of Lyubarskii and its extension by Kotov, Churazov & Gilfanov seek to explain the spectral-timing properties of the X-ray variability of accreting black holes in terms of inward-propagating mass accretion fluctuations produced at a broad range of radii. The fluctuations modulate the X-ray emitting region as they move inwards and can produce temporal-frequency-dependent lags between energy bands, and energy-dependent power spectral densities (PSDs) as a result of the different emissivity profiles, which may be expected at different X-ray energies. Here, we use a simple numerical implementation to investigate in detail the X-ray spectral-timing properties of the model and their relation to several physically interesting parameters, namely the emissivity profile in different energy bands, the geometrical thickness and viscosity parameter of the accretion flow, the strength of damping on the fluctuations and the temporal coherence (measured by the 'quality factor', Q ) of the fluctuations introduced at each radius. We find that a geometrically thick flow with large viscosity parameter is favoured, and we confirm that the predicted lags are quite robust to changes in the emissivity profile and physical parameters of the accretion flow, which may help to explain the similarity of the lag spectra in the low/hard and high/soft states of Cyg X-1. We also demonstrate the model regime where the light curves in different energy bands are highly spectrally coherent. We compare model predictions directly to X-ray data from the narrow line Seyfert 1 galaxy NGC 4051 and the black hole X-ray binary (BHXRB) Cyg X-1 in its high/soft state, and we show that this general scheme can reproduce simultaneously the time lags and energy-dependence of the PSD.     

Peculiarities of the accretion flow in the system HL CMa

The properties of the aperiodic luminosity variability for the dwarf novaHLCMa are considered. The variability of the system HL CMa is shown to be suppressed at frequencies above 0.7 × 10^?2 Hz. Different variability suppression mechanisms related to the radiation reprocessing time, partial disk evaporation, and characteristic variability formation time are proposed. It has been found that the variability suppression frequency does not change when the system passes from the quiescent state to the outburst one, suggesting that the accretion flow geometry is invariable. It is concluded from the optical and Xray luminosities of the system that the boundary layer on the white dwarf surface is optically thick in both quiescent and outburst states. The latter implies that the optically thick part of the accretion flow (disk) reaches the white dwarf surface. The accretion rate in the system and the accretion flow geometry and temperature have been estimated from the variability power spectra and spectral characteristics in a wide energy range, from the optical to X-ray ones.     

Modeling of high-frequency variability in X-ray binaries with black holes

The properties of the aperiodic variability in X-ray binaries with black holes are considered. The power spectra of the luminosity variability for a flat accretion disk that is an emission source with a powerlaw energy spectrum have been modeled. At low frequencies the derived power spectrum has the form of a power law with a slope ? ≈ ?1 and a cutoff at a frequency corresponding to the characteristic frequency of fluctuations at the inner disk edge; at higher frequencies the power spectrum has a complex form. The high-frequency variability is suppressed due to the arrival time delays of photons emerged in different parts of the disk. The presence of azimuthal accretion rate fluctuations in the disk and the disk surface brightness nonuniformity in the observer’s imaginary plane caused by the relativistic effects give rise to an additional variability component at frequencies ～ 200 Hz.     

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.     

Constraints on black hole spins with a general relativistic accretion disk corona model

The peaks in the spectra of the accretion disks surrounding massive black holes in quasars are in the far-UV or soft X-ray band, which are usually not observed. However, in the disk corona model, soft photons from the disk are Comptonized to high energy in the hot corona, and the hard X-ray spectra(luminosity and spectral shape) contain information on the incident spectra from the disk. The values of black hole spin parameter a*are inferred from the spectral fitting, which are spread over a large range, ~-0.94 to 0.998. We find that the inclination angles and mass accretion rates are well determined by the spectral fitting, but the results are sensitive to the accuracy of black hole mass estimates. No tight constraints on the black hole spins are achieved, if the uncertainties in black hole mass measurements are a factor of four,which are typical for the single-epoch reverberation mapping method. Recently, the accuracy of black hole mass measurement has been significantly improved to 0.2- 0.4 dex with the velocity resolved reverberation mapping method. The black hole spin can be well constrained if the mass measurement accuracy is50%. In the accretion disk corona scenario, a fraction of power dissipated in the disk is transported into the corona, and therefore the accretion disk is thinner than a bare disk for the same mass accretion rate,because the radiation pressure in the disk is reduced. We find that the thin disk approximation, H/R0.1,is still valid if 0.3 m 0.5, provided half of the dissipated power is radiated in the corona above the disk.     

Timing evidence in determining the accretion state of the Seyfert galaxy NGC 3783

Previous observations with the Rossi X-ray Timing Explorer ( RXTE ) have suggested that the power spectral density (PSD) of NGC 3783 flattens to a slope near zero at low frequencies, in a similar manner to that of Galactic black hole X-ray binary systems (GBHs) in the 'hard' state. The low radio flux emitted by this object, however, is inconsistent with a hard state interpretation. The accretion rate of NGC 3783 (∼7 per cent of the Eddington rate) is similar to that of other active galactic nuclei (AGN) with 'soft'-state PSDs and higher than that at which the GBH Cyg X-1, with which AGN are often compared, changes between 'hard' and 'soft' states (∼2 per cent of the Eddington rate). If NGC 3783 really does have a 'hard'-state PSD, it would be quite unusual and would indicate that AGN and GBHs are not quite as similar as we currently believe. Here we present an improved X-ray PSD of NGC 3783, spanning from ∼10⁻⁸ to ∼10⁻³ Hz, based on considerably extended (5.5 yr) RXTE observations combined with two orbits of continuous observation by XMM–Newton . We show that this PSD is, in fact, well fitted by a 'soft' state model which has only one break, at high frequencies. Although a 'hard'-state model can also fit the data, the improvement in fit by adding a second break at low frequency is not significant. Thus NGC 3783 is not unusual. These results leave Arakelian 564 as the only AGN which shows a second break at low frequencies, although in that case the very high accretion rate implies a 'very high', rather than 'hard' state PSD. The break frequency found in NGC 3783 is consistent with the expectation based on comparisons with other AGN and GBHs, given its black hole mass and accretion rate.     

X-ray variability of SS 433: Evidence for supercritical accretion

We study the X-ray variability of SS 433 based on data from the ASCA observatory and the MAXI and RXTE/ASM monitoring missions. Based on the ASCA data, we have constructed the power spectrum of SS 433 in the frequency range from 10^?6 to 0.1 Hz, which confirms the presence of a flat portion in the spectrum at frequencies 3 × 10^?5?10^?3 Hz. The periodic variability (precession, nutation, eclipses) begins to dominate significantly over the stochastic variability at lower frequencies, which does not allow the stochastic variability to be studied reliably. The model in which the flat portion extends to 9.5 × 10^?6 Hz, while a power-law rise with an index of 2.6 occurs below provides the best agreement with the observations. The nutational oscillations of the jets with a period of about three days suggests that the time for the passage of material through the disk is less than this value. At frequencies below 4 × 10^?6 Hz, the shape of the power spectrum probably does not reflect the disk structure but is determined by external factors, for example, by a change in the amount of material supplied by the donor. The flat portion can arise from a rapid decrease in the viscous time in the supercritical or radiative disk zones. The flat spectrum is associated with the variability of the X-ray jets that are formed in the supercritical disk region.     

The Effect of Tidal Interaction with a Gas Disk on Formation of Terrestrial Planets

We have performed N-body simulation on final accretion stage of terrestrial planets, including the effect of damping of eccentricity and inclination caused by tidal interaction with a remnant gas disk. As a result of runway and oligarchic accretion, about 20 Mars-sized protoplanets would be formed in nearly circular orbits with orbital separation of several to ten Hill radius. The orbits of the protoplanets would be eventually destabilized by long-term mutual gravity and/or secular resonance of giant gaseous planets. The protoplanets would coalesce with each other to form terrestrial planets through the orbital crossing. Previous N-body simulations, however, showed that the final eccentricities of planets are around 0.1, which are about 10 times higher than the present eccentricities of Earth and Venus. The obtained high eccentricities are the remnant of orbital crossing. We included the effect of eccentricity damping caused by gravitational interaction with disk gas as a drag force (“gravitational drag”) and carried out N-body simulation of accretion of protoplanets. We start with 15 protoplanets with 0.2M⊕ and integrate the orbits for 10⁷ years, which is consistent with the observationally inferred disk lifetime (in some runs, we start with 30 protoplanets with 0.1M⊕). In most runs, the damping time scale, which is equivalent to the strength of the drag force, is kept constant throughout each run in order to clarify the effects of the damping. We found that the planets' final mass, spatial distribution, and eccentricities depend on the damping time scale. If the damping time scale for a 0.2M⊕ mass planet at 1 AU is longer than 10⁸ years, planets grow to Earth's size, but the final eccentricities are too high as in gas-free cases. If it is shorter than 10⁶ years, the eccentricities of the protoplanets cannot be pumped up, resulting in not enough orbital crossing to make Earth-sized planets. Small planets with low eccentricities are formed with small orbital separation. On the other hand, if it is between 10⁶ and 10⁸ years, which may correspond to a mostly depleted disk (0.01-0.1% of surface density of the minimum mass model), some protoplanets can grow to about the size of Earth and Venus, and the eccentricities of such surviving planets can be diminished within the disk lifetime. Furthermore, in innermost and outermost regions in the same system, we often find planets with smaller size and larger eccentricities too, which could be analogous to Mars and Mercury. This is partly because the gravitational drag is less effective for smaller mass planets, and partly due to the “edge effect,” which means the innermost and outermost planets tend to remain without collision. We also carried out several runs with time-dependent drag force according to depletion of a gas disk. In these runs, we used exponential decay model with e-folding time of 3×10⁶ years. The orbits of protoplanets are stablized by the eccentricity damping in the early time. When disk surface density decays to ?1% of the minimum mass disk model, the damping force is no longer strong enough to inhibit the increase of the eccentricity by distant perturbations among protoplanets so that the orbital crossing starts. In this disk decay model, a gas disk with 10⁻⁴-10⁻³ times the minimum mass model still remains after the orbital crossing and accretional events, which is enough to damp the eccentricities of the Earth-sized planets to the order of 0.01. Using these results, we discuss a possible scenario for the last stage of terrestrial planet formation.     

黑洞吸积的双模式特征

黑洞吸积必定是跨声速的。对于静态、绝热吸积流,比能量E、比角动量L和质量吸积率M都是空间的常量。跨声速解的非奇异条件,F(E,L,M)=0,使独立参数减为只有两个。对于一对给定的E和L的符合条件E_c>E>E_(Barr)的值(这里E_c是一临界值,E_(Barr)是引力和离心力的联合势垒),上述非奇异条件给出两个不同的吸积率值,对应着两个不同的吸积流声速点位置。然而,物理上合理的整体解却是唯一的,它总是使两个吸积率值中之较小者得到实现。 对于一个不转动的黑洞,吸积以两种模式之一进行。一是类球吸积或称Bondi吸积,角动量的影响和相对论效应均微不足道;另一是盘吸积,这两个因素起决定性作用。两种模式之间的转换是基于声速点位置的间断性跳跃,而这种跳跃是由吸积流参数(例如角动量)的连续变化所引发。Bondi吸积可称为高态而盘吸积为低态,因为前者总对应着较高的吸积率。 随时间变化的吸积流很可能在这两种模式之间来回振荡,呈现出周期性或准周期性或无规则行为。这可以用来解释天鹅座X-1和若干活动星系核的光变现象,从而为黑洞的存在提供有力的观测依据。