Spectral Index as a Function of Mass Accretion Rate in Black Hole Sources. Monte-Carlo Simulations and an Analytical Description

In this Paper, we present theoretical arguments that the observationally established index saturation effect vs mass accretion rate is a signature of the bulk (converging) flow onto the black hole. We demonstrate that the index saturation value depends on the plasma temperature of converging flow. We self-consistently calculate the Compton cloud (CC) plasma temperature as a function of mass accretion rate using the energy balance between energy dissipation and Compton cooling. We explain the observable phenomenon, index- mdot correlations using a Monte-Carlo simulation of radiative processes in the innermost part (CC) of a BH source and we account for the Comptonization processes in the presence of thermal and bulk motions, as basic types of plasma motion. We show that, when mdot increases, BH sources evolve to high and very soft states (HSS and VSS, respectively), in which the strong blackbody-like and steep power-law components are formed in the resulting X-ray spectrum. The simultaneous detections of these two components strongly depends on sensitivity of high energy instruments, given that the relative contribution of the hard power-law tail in the resulting VSS spectrum can be very low, which is why, to date {\it RXTE} observations of the VSS X-ray spectrum has been characterized by the presence of the strong BB-like component only. We also predict specific patterns for high-energy efold (cutoff) energy (E_{fold}) evolution with mdot for thermal and dynamical (bulk) Comptonization cases. For the former case, E_{fold} monotonically decreases with mdot, in the latter case, the E_{fold}-decrease is followed by its increase at high values of mdot. The observational evolution of E_{fold} vs mdot can be one more test for the presence of a converging flow effect in the formation of the resulting spectra in the close vicinity of BHs.Comment: 15 pages, 11 figures, accepted for the publication in the Astrophysical Journa

Discovery of photon index saturation in the black hole binary GRS 1915+105

We present a study of the correlations between spectral, timing properties and mass accretion rate observed in X-rays from the Galactic Black Hole (BH) binary GRS 1915+105 during the transition between hard and soft states. We analyze all transition episodes from this source observed with RXTE, coordinated with Ryle Radio Telescope (RT) observations. We show that broad-band energy spectra of GRS 1915+105 during all these spectral states can be adequately presented by two Bulk Motion Comptonization (BMC) components: a hard component (BMC1, photon index Gamma_1=1.7-3.0) with turnover at high energies and soft thermal component (BMC2, Gamma_2=2.7-4.2) with characteristic color temperature <1 keV, and the redskewed iron line (LAOR) component. We also present observable correlations between the index and the normalization of the disk "seed" component. The use of "seed" disk normalization, which is presumably proportional to mass accretion rate in the disk, is crucial to establish the index saturation effect during the transition to the soft state. We discovered the photon index saturation of the soft and hard spectral components at values of 4.2 and 3 respectively. We present a physical model which explains the index-seed photon normalization correlations. We argue that the index saturation effect of the hard component (BMC1) is due to the soft photon Comptonization in the converging inflow close to BH and that of soft component is due to matter accumulation in the transition layer when mass accretion rate increases. In addition to our spectral model components we also find a strong feature of "blackbody-like" bump which color temperature is about 4.5 keV in eight observations of the intermediate and soft states. We discuss a possible origin of this "blackbody-like" emission.Comment: 33 pages, 16 figures, accepted for publication in ApJ, on December 10, 2009, v. 70

Numerical solution of the radiative transfer equation: X-ray spectral formation from cylindrical accretion onto a magnetized neutron star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. To this aim, we have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system tau using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth tau produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. The algorithm has been implemented in the XSPEC package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (> 10^{12} G), which is expected to be typical of accreting systems such as X-ray pulsars and supergiant fast X-ray transients.Comment: 13 pages, 20 figures, accepted for publication in A&

Discovery of Red-Skewed K_alpha iron line in Cyg X-2 with Suzaku

We report on the Suzaku observation of neutron star low-mass X-ray binary Cygnus X-2 which reveals a presence of the iron K_alpha emission line. The line profile shows a significant red wing. This discovery increases the number of neutron star sources where red-skewed iron lines were observed and strongly suggests that this phenomenon is common not only in black holes but also in other types of accreting compact objects. We examine the line profile in terms of models which attribute its production to the relativistic effects due to reflection of X-ray radiation from a cold accretion disk and also as a result of the line formation in the extended wind/outflow configuration. Both models are able to adequately represent the observed line profile. We consider the results of line modeling in the context of subsecond variability. While we were unable to conclusively disqualify one of the models, we find that the wind paradigm has several advantages over the relativistic disk reflection model.Comment: accepted for publication in Ap

On the stability of the thermal Comptonization index in neutron star low-mass X-ray binaries in their different spectral states

Most of the spectra of neutron star low mass X-ray binaries (NS LMXBs), being them persistent or transient, are characterized by the presence of a strong thermal Comptonization bump, thought to originate in the transition layer (TL) between the accretion disk and the NS surface. The observable quantities which characterize this component dominating the emission below 30 keV, are the spectral index alpha and the rollover energy, both related to the electron temperature and optical depth of the plasma. Starting from observational results on a sample of NS LMXBs in different spectral states, we formulate the problem of X-ray spectral formation in the TL of these sources. We predict a stability of the thermal Comptonization spectral index in different spectral states if the energy release in the TL is much higher than the intercepted flux coming from the accretion disk. We use an equation for the energy balance and the radiative transfer diffusion equation for a slab geometry in the TL, to derive a formula for the thermal Comptonization index alpha. We show that in this approximation the TL electron temperature kTe and optical depth tau_0 can be written as a function of the energy flux from the disk intercepted by the corona (TL) and that in the corona itself Qdisk/Qcor, in turn leading to a relation alpha=f(Qdisk/Qcor), with alpha ~ 1 when Qdisk/Qcor <<1. We show that the observed spectral index alpha for the sample of sources here considered lies in a belt around 1 +/- 0.2 a part for the case of GX 354--0. Comparing our theoretical predictions with observations, we claim that this result, which is consistent with the condition Qdisk/Qcor <<1, can give us constraints on the accretion geometry of these systems, an issue that seems difficult to be solved using only the spectral analysis method.Comment: 7 pages, 3 figures, accepted for publication in A&

On the Non-relativistic Origin of Red-skewed Iron Lines in CV, Neutron Star and Black Hole Sources

We perform the analysis of the iron K_alpha lines detected in three sources representing of three types of accreting compact sources: cataclysmic variable (CV) GK Per, neutron star (NS) Serpens X-1 and black hole (BH) GX 339-4. We find, using data from Epic-PN Camera on-board XMM-Newton observatory,that the iron K_alpha emission line in GK Per has a noticeable red-skewed profile. We compare the GK Per asymmetric line with the red-skewed lines observed by XMM-Newton in Serpens X-1 and GX 339-4. The observation of the K_alpha emission with red-skewed features in CV GK Per cannot be related to the redshift effects of General Relativity (GR). Therefore, if the mechanism of the K_alpha-line formation is the same in CVs, NSs and BHs then it is evident that the GR effects would be ruled out as a cause of red skewness of K_alpha line. The line reprocessing in an outflowing wind has been recently suggested an alternative model for a broad red-shifted iron line formation. In the framework of the outflow scenario the red-skewed iron line is formed in the strong extended wind due to its illumination by the radiation emanating from the innermost part of the accreting material. In this Paper we demonstrate that the asymmetric shapes of the lines detected from these CV, NS and BH sources are well described with the wind (outflow) model. While this fact is hard to reconcile with the relativistic models, it is consistent with the outflowing gas washing out high frequency modulations of the radiation presumably originated in the innermost part of the source.Comment: 24 pages, 4 Tables, 9 figures, Accepted for publication in Ap

Effects of Resonance in Quasiperiodic Oscillators of Neutron Star Binaries

Using a large quantity of Rossi X-ray Timing Explorer data presented in the literature I offer a detailed investigation into the accuracy of quasiperiodic oscillations (QPO) frequency determination. The QPO phenomenon seen in X-ray binaries is possibly a result of the resonance of the intrinsic (eigen) oscillations and harmonic driving forces of the system. I show that the resonances, in the presence of the damping of oscillations, occur at the frequencies which are systematically and randomly shifted with respect to the eigenfrequencies of the system. The shift value strongly depends on the damping rate which is measured by the halfwidth of the QPO feature. Taking into account this effect I analyze the QPO data for four Z-sources: Sco X-1, GX 340+0, GX 5-1, GX 17+2 and two atoll sources: 4U 1728-34, 4U 0614+09. The transition layer model (TLM) predicts the existence of the invariant quantity: delta, an inclination angle of the magnetospheric axis with respect to the normal to the disk. I calculate delta and the error bars of delta using the resonance shift and I find that the inferred delta-values are consistent with constants for these four Z-sources, where horizontal branch oscillation and kilohertz frequencies have been detected and correctly identified. It is shown that the inferred delta are in the range between 5.5 and 6.5 degrees. I conclude that the TLM seems to be compatible with data.Comment: 9 pages and 2 figures. Accepted for publication in the Astrophysical Journal Letters 2002 August 2

Correlations of Power-law Spectral and QPO Features In Black Hole Candidate Sources

Recent studies have shown that strong correlations are observed between low frequency QPO`s and the spectral power law index for a number of black hole candidate sources (BHC's), when these sources exhibit quasi-steady hard x-ray emission states. The dominant long standing interpretation of QPO's is that they are produced in and are the signature of the thermal accretion disk. Paradoxically, strong QPO`s are present even in the cases where the thermal component is negligible. We present a model which identifies the origin of the QPO's and relates them directly to the properties of a compact coronal region which is bounded by the adjustment from Keplerian to sub-Keplerian inflow into the BH and which is primarily responsible for the observed power law spectrum. The model also predicts the relationship between high and low frequency QPO's and shows how BH's can be unique identified from observations of the soft states of NS's and BHC's.Comment: 2 pages, to be published in Proc. of International Conference on Stellar Mass, Intermediate Mass and Super Massive Black Holes, Oct. 28-31, 2003, Kyoto, Japa

Determination of Black Hole Masses in Galactic Black Hole Binaries using Scaling of Spectral and Variability Characteristics

We present a study of correlations between X-ray spectral and timing properties observed from a number of Galactic Black Hole (BH) binaries during hard-soft state spectral evolution. We analyze 17 transition episodes from 8 BH sources observed with RXTE. Our scaling technique for BH mass determination uses a correlation between spectral index and quasi-periodic oscillation (QPO) frequency. In addition, we use a correlation between index and the normalization of the disk "seed" component to cross-check the BH mass determination and estimate the distance to the source. While the index-QPO correlations for two given sources contain information on the ratio of the BH masses in those sources, the index-normalization correlations depend on the ratio of the BH masses and the distance square ratio. In fact, the index-normalization correlation also discloses the index-mass accretion rate saturation effect given that the normalization of disk "seed" photon supply is proportional to the disk mass accretion rate. We present arguments that this observationally established index saturation effect is a signature of the bulk motion (converging) flow onto black hole which was early predicted by the dynamical Comptonization theory. We use GRO J1655-40 as a primary reference source for which the BH mass, distance and inclination angle are evaluated by dynamical measurements with unprecedented precision among other Galactic BH sources. We apply our scaling technique to determine BH masses and distances forCygnus X-1, GX 339-4, 4U 1543-47, XTE J1550-564, XTE J1650-500, H 1743-322 and XTE J1859-226. Good agreement of our results for sources with known values of BH masses and distance provides an independent verification for our scaling technique.Comment: 25 pages, 9 figures, 5 tables. Accepted and scheduled for publication in The Astrophysical Journa