Rayleigh - Taylor Gravity Waves and Quasiperiodic Oscillation Phenomenon in X-ray Binaries

Accretion onto compact objects in X-ray binaries [black hole, neutron star (NS), white dwarf] is characterized by non-uniform flow density profiles. Such an effect of heterogeneity in presence of gravitational forces and pressure gradients exhibits Raylegh-Taylor gravity waves (RTGW). They should be seen as quasioperiodic wave oscillations (QPO). In this paper I show that the main QPO frequency, which is very close to the Keplerian frequency, is split into separate frequencies (hybrid and low branch) under the influence of the gravitational forces in the rotational frame of reference. The observed low and high QPO frequencies are an intrinsic signature of the RTGW. I elaborate the conditions for the density profile when the RTGW oscillations are stable. A comparison of the inferred QPO frequencies with QPO observations is presented. I find that hectohertz frequencies detected from NS binaries can be identified as the RTGW low branch frequencies. I also predict that an observer can see the double NS spin frequency during the NS long (super) burst events when the pressure gradients and buoyant forces are suppressed. The Coriolis force is the only force which acts in the rotational frame of reference and its presence causes perfect coherent pulsations with a frequency twice of the NS spin.Comment: 14 pages and 2 figures, ApJ in pres

Spectral Properties of Accretion Disks Around Galactic and Extragalactic Black Holes

We study the spectral properties of a very general class of accretion disks which can be decomposed into three distinct components apart from a shock at $r=r_s$: (1) An optically thick Keplerian disk on the equatorial plane ($r>r_s$), (2) A sub-Keplerian optically thin halo above and below this Keplerian disk $r>r_s$ and (3) A hot, optically slim, $\tau\sim 1$ postshock region $r<r_s\sim 5-10 r_g$ where $r_g$ is the Schwarzschild radius. The postshock region intercepts soft photons from the Keplerian component and reradiates them as hard X-rays and $\gamma$ rays after Comptonization. We solve two-temperature equations in the postshock region with Coulomb energy exchange between protons and electrons, and incorporating radiative processes such as bremsstrahlung and Comptonization. We also present the exact prescription to compute the reflection of the hard X-rays from the cool disk. We produce radiated spectra from both the disk components as functions of the accretion rates and compare them with the spectra of galactic and extragalactic black hole candidates. We find that the transition from hard state to soft state is smoothly initiated by a single parameter, namely, the mass accretion rate of the disk. In the soft state, when the postshock region is very optically thick and cooled down, bulk motion of the converging flow determines the spectral index to be about $1.5$ in agreement with observations.Comment: 45 pages of Latex file + 10 figures (Misprints in Description and Caption of Figure 2 are corrected

The Extended Power Law as Intrinsic Signature For a Black Hole

We analyze the exact general relativistic exact integro-differential equation of radiative transfer describing the interaction of low energy photons with a Maxwellian distribution of hot electrons in gravitational field of a Schwarzschild black hole. We prove that due to Comptonization an initial arbitrary spectrum of low energy photons unavoidably results in spectra characterized by an extended power-law feature. We examine the spectral index by using both analytical and numerical methods for a variety of physical parameters as such the plasma temperature and the mass accretion rate. The presence of the event horizon as well as the behaviour of the null geodesics in its vicinity largely determine the dependence of the spectral index on the flow parameters. We come to the conclusion that the bulk motion of a converging flow is more efficient in upscattering photons than thermal Comptonization provided that the electron temperature in the flow is of order of a few keV or less. In this case, the spectrum observed at infinity consists of a soft component produced by those input photons that escape after a few scatterings without any significant energy change and of hard component (described by a power law) produced by the photons that underwent significant upscattering. The luminosity of the power-law component is relatively small compared to that of the soft component. For accretion into black hole the spectral energy index of the power-law is always higher than one for plasma temperature of order of a few keV. This result suggests that the bulk motion Comptonization might be responsible for the power-law spectra seen in the black-hole X-ray sources.Comment: 31 pages, 3 figures; Astrophysical Journal accepte

X-ray Spectral Formation in a Converging Fluid Flow: Spherical Accretion into Black Holes

We study Compton upscattering of low-frequency photons in a converging flow of thermal plasma. The photons escape diffusively and electron scattering is the dominant source of opacity. We solve numerically and approximately analytically the equation of radiative transfer in the case of spherical, steady state accretion into black holes. Unlike previous work on this subject, we consider the inner boundary at a finite radius and this has a significant effect on the emergent spectrum. It is shown that the bulk motion of the converging flow is more efficient in upscattering photons than thermal Comptonization, provided that the electron temperature in the flow is of order a few keV or less. In this case, the spectrum observed at infinity consists of a soft component coming from those input photons which escaped after a few scatterings without any significant energy change and of a power law which extends to high energies and is made of those photons which underwent significant upscattering. The luminosity of the power law is relatively small compared to that of the soft component. The more reflective the inner boundary is, the flatter the power-law spectrum becomes. The spectral energy power-law index for black-hole accretion is always higher than 1 and it is approximately 1.5 for high accretion rates. This result tempts us to say that bulk motion Comptonization might be the mechanism behind the power-law spectra seen in black-hole X-ray sources.Comment: 37 pages, LaTex, AAS Macros, 8 ps figures, to appear in Ap

The hard X-ray tails in neutron star low mass X-ray binaries: BeppoSAX observations and possible theoretical explanation of the GX 17+2 case

We report results of a new spectral analysis of two BeppoSAX observations of the Z source GX 17+2. In one of the two observations the source exhibits a powerlaw-like hard (> 30 keV) X-ray tail which was described in a previous work by a hybrid Comptonization model. Recent high-energy observations with INTEGRAL of a sample of Low Mass X-Ray Binaries including both Z and atoll classes have shown that bulk (dynamical) Comptonization of soft photons can be a possible alternative mechanism for producing hard X-ray tails in such systems. We start from the INTEGRAL results and we exploit the broad-band capability of BeppoSAX to better investigate the physical processes at work. We use GX 17+2 as a representative case. Moreover, we suggest that weakening (or disappearance) of the hard X-ray tail can be explained by increasing radiation pressure originated at the surface of the neutron star (NS). As a result the high radiation pressure stops the bulk inflow and consequently this radiation feedback of the NS surface leads to quenching the bulk Comptonization.Comment: 6 pages, 3 figures, Accepted for publication in Ap

The converging inflow spectrum is an intrinsic signature for a black hole: Monte-Carlo simulations of Comptonization on free-falling electrons

An accreting black hole is, by definition, characterized by the drain. Namely, the matter falls into a black hole much the same way as water disappears down a drain - matter goes in and nothing comes out. As this can only happen in a black hole, it provides an unique way to see it. The accretion proceeds almost in free fall close to the black hole horizon. In this paper we calculate (by using Monte -Carlo simulations) the specific features of X-ray spectra formed as a result of upscattering of the soft (disk) photons in the converging inflow (CI) within about 3 Schwarzschild radii of the black hole. The full relativistic treatment has been implemented to reproduce these spectra. We show that spectra in the soft state of black hole systems can be described as the sum of a thermal (disk) component and the convolution of some fraction of this component with the CI upscattering spread function. The latter boosted photon component is seen as an extended power-law at energies much higher than the characteristic soft photons energy. We demonstrate the stability of the power spectral index (alpha= 1.8) over a wide range of the plasma temperature 0-10 keV and mass accretion rates (higher than 2 in Eddington units). We also demonstrate that the sharp high energy cutoff occurs at energies of 200-400 keV which are related to the average rest energy of electrons impinging upon the horizon. The spectrum is practically identical to the standard thermal Comptonization spectrum when the CI plasma temperature is getting of order of 50 keV (hard state of BHS). Also, the change of spectral shapes from the soft to the hard X-ray state is clearly to be related with the temperature of the bulk flow. These Monte-Carlo simulated CI spectra are then a inevitable stamp of the BHS.Comment: 30 pages TeX format, 6 PS figures, accepted for ApJ Main Journa

Broad redshifted line as a signature of outflow

We formulate and solve the diffusion problem of line photon propagation in a bulk outflow from a compact object (black hole or neutron star) using a generic assumption regarding the distribution of line photons within the outflow. Thomson scattering of the line photons within the expanding flow leads to a decrease of their energy which is of first order in v/c, where v is the outflow velocity and c is the speed of light. We demonstrate that the emergent line profile is closely related to the time distribution of photons diffusing through the flow (the light curve) and consists of a broad redshifted feature. We analyzed the line profiles for the general case of outflow density distribution. We emphasize that the redshifted lines are intrinsic properties of the powerful outflow that are supposed to be in many compact objects.Comment: 16 pages, 1 black-white figure and 2 color figures; accepted for publication in the Astrophysical Journa

Correlations between X-ray Spectral and Timing Characteristics in Cyg X-2

Correlations between the quasi-periodic oscillations (QPOs) and the spectral power-law index have been reported for a number of black hole candidate sources and for four neutron star (NS) sources, 4U 0614+09, 4U 1608-52, 4U 1728-34 and Sco X-1. An examination of QPO frequencies and index relationship in Cyg X-2 is reported herein. The RXTE spectrum of Cyg X-2 can be adequately represented by a simple two-component model of Compton up-scattering with a soft photon electron temperature of about 0.7 keV and an iron K-line. Inferred spectral power-law index shows correlation with the low QPO frequencies. We find that the Thomson optical depth of the Compton cloud (CC) tau, in framework of spherical geometry, is in the range of ~4-6, which is consistent with the neutron star's surface being obscured. The NS high frequency pulsations are presumably suppressed as a result of photon scattering off CC electrons because of such high values of tau. We also point out a number of similarities in terms timing (presence of low and high frequency QPOs) and spectral (high CC optical depth and low CC plasma temperature) appearances between Cyg X-2 and Sco X-1.Comment: 7 pages, 4 figures, accepted for publication in ApJ (October 1, 2007, v667n2 issue

Power-law Tails from Dynamical Comptonization in Converging Flows

The effects of bulk motion comptonization on the spectral formation in a converging flow onto a black hole are investigated. The problem is tackled by means of both a fully relativistic, angle-dependent transfer code and a semi-analytical, diffusion-approximation method. We find that a power-law high-energy tail is a ubiquitous feature in converging flows and that the two approaches produce consistent results at large enough accretion rates, when photon diffusion holds. Our semi-analytical approach is based on an expansion in eigenfunctions of the diffusion equation. Contrary to previous investigations based on the same method we find that, although the power-law tail at really large energies is always dominated by the flatter spectral mode, the slope of the hard X-ray portion of the spectrum is dictated by the second mode and it approaches Gamma=3 at large accretion rate, irrespective of the model parameters. The photon index in the tail is found to be largely independent on the spatial distribution of soft seed photons when the accretion rate is either quite low ( 10). On the other hand, the spatial distribution of source photons controls the photon index at intermediate accretion rates, when Gamma switches from the first to the second mode. Our analysis confirms that a hard tail with photon index Gamma <3 is produced by the up-scattering of primary photons onto infalling electrons if the central object is a black hole.Comment: to be published in the Astrophysical Journal, 16 pages and 9 figure