The Bursting Behavior of 4U 1728-34: Parameters of a Neutron Star and Geometry of a NS-disk system

We analyze a set of Type I X-ray bursts from the low mass X-ray binary 4U 1728 -34, observed with Rossi X-ray Timing Explorer (RXTE). and we implement an analytical model of X-ray spectral formation in the neutron star (NS) atmosphere during a burst. We infer the dependence of the neutron star mass and radius with respect to the assumed distance to the system using an analytical model of X-ray burst spectral formation. The model behavior clearly indicates that the burster atmosphere is helium-dominated. Our results strongly favor the soft equation of state (EOS) of NS for 4U 1728-34. We find that distance to the source should be within 4.5-5.0 kpc range. We obtain rather narrow constrains for the NS radius in 8.7-9.7 km range and interval 1.2-1.6 solar masses for NS mass for this particular distance range. We uncover a temporal behavior of red-shift corrected burst flux for the radial expansion episodes and we put forth a dynamical evolution scenario for the NS--accretion disk geometry during which an expanded envelope affects the accretion disk and increases the area of the neutron star exposed to the Earth observer. Our scenario enables us to explain the timing characteristics and peak flux variation observed during the burst expansion stage, which is now believed to be common phenomenon. In the framework of this scenario we provide a new method for the estimation of the inclination angle which leads to the value of 50 degrees for 4U 1728-34 .Comment: 8 pages, 3 figures and one table, accepted for publication in the Astrophysical Journal Letter

Comprehensive Analysis of RXTE Data from Cyg X-1: Spectral Index-Quasi-Periodic Oscillation Frequency-Luminosity Correlations

We present timing and spectral analysis of ~ 2.2 Ms of RXTE archival data from Cyg X-1. Using a generic Comptonization model we reveal that the spectrum of Cyg X-1 consists of three components: a thermal seed photon spectrum, a Comptonized part of the seed photon spectrum and the iron line. We find a strong correlation between the 0.1-20 Hz frequencies of quasiperiodic oscillations (QPOs) and the spectral index. Presence of two spectral phases (states) are clearly seen in the data when the spectral indices saturate at low and high values of QPO frequencies. This saturation effect was discovered earlier in a number of black hole candidate (BHC) sources and now we strongly confirm this phenomenon in Cyg X-1. In the soft state this index-QPO frequency correlation shows a saturation of the photon index Gamma ~ 2.1 at high values of the low frequency \nu_{L}. The saturation level of Gamma~ 2.1 is the lowest value found yet in BHCs. The bolometric luminosity does not show clear correlation with the index. We also show that Fe K_{\alpha} emission line strength (equivalent width, EW) correlates with the QPO frequency. The EW increases from 200 eV in the low/hard state to 1.5 keV in the high/soft state. The observational correlations revealed compel us to propose a scenario for the spectral transition and iron line formation which occur in BHC sources. We also present the spectral state (power-law index) evolution for eight years of Cyg X-1 observations by RXTE.Comment: 28 pages, 15 figures and two tables. Accepted for publication in the Ap

Three Type I X-ray bursts from Cyg X-2: Application of Analytical Models for Neutron Star Mass and Radius Determination

We study the spectral and temporal properties of three Type I X-ray bursts observed from Cyg X-2 with the Rossi X-ray Timing Explorer. Despite the short time durations (~ 5 sec) these bursts show radial expansion of order of several neutron star (NS) radii. We apply the analytical models of spectral formation during the expansion and contraction stages to derive physical conditions for the matter in the burning zone close to the surface of the NS as well as the NS mass-radius relation. Our results, combined with statistical errors, show that the central object is a compact star with mass ~1.4 solar masses and radius ~9 km. Our results favor the softer equation of state for neutron star matter.Comment: 9 pages, 2 figures. To be published in the Astrophysical Journal Letter

On the nature of the flux variability during an expansion stage of a type I X-ray burst: Constraints on Neutron Star Parameters for 4U 1820-30

Powerful Type I X-ray burst with strong radial expansion was observed from the low mass X-ray binary 4U 1820-30 with Rossi X-ray Timing Explorer on May 2, 1997. We investigate closely the flux profile during the burst expansion stage. Applying a semi-analytical model we are able to uncover the behavior of a photospheric radius and to simulate the evolution of neutron star (NS)-accretion disk system. The bottom flux L_{bot} is a few times the Eddington limit L_{Edd} for outer layers, because the electron cross-section is a few times less than the Thomson cross-section at such a high temperatures. The surplus of energy flux with respect to the Eddington, $L_{bot}-L_{Edd}$, goes into the potential energy of the expanded envelope. As cooling of the burning zone starts the surplus decreases and thus the envelope shrinks while the emergent photon flux stays the same $L=L_{Edd}$. At a certain moment the NS low-hemisphere, previously screened by the disk, becomes visible to the observer. Consequently, the flux detected by the observer increases. Indeed, we observe to the paradoxical situation when the burning zone cools, but the apparent flux increases because of the NS-accretion disk geometry. We demonstrate a strong observational evidence of NS-accretion disk occultation in the behavior of the observed bolometric flux. We estimate the anisotropy due to geometry and find that the system should have a high inclination angle. Finally, we apply an analytical model of X-ray spectral formation in the neutron star atmosphere during burst decay stage to infer the neutron star (NS) mass-radius relation.Comment: 15 pages, 3 figures, accepted to ApJ

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

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

How To Distinguish Neutron Star and Black Hole X-ray Binaries? Spectral index and Quasi-Periodic Oscillation Frequency Correlation

Recent studies have revealed strong correlations between 1-10 Hz frequencies of quasiperiodic oscillations (QPOs) and the spectral power law index of several Black Hole (BH) candidate sources when seen in the low/hard state, the steep power-law (soft) state, and in transition between these states. In the soft state these index-QPO frequency correlations show a saturation of the photon index Γ ∼ 2.7 at high values of the low frequency νL. This saturation effect was previously identified as a black hole signature. In this paper we argue that this saturation does not occur, at least for one neutron star (NS) source 4U 1728-34, for which the index Γ monotonically increases with νL to the values of 6 and higher. We base this conclusion on our analysis of ∼ 1.5 Msec of RXTE archival data for 4U 1728-34. We reveal the spectral evolution of the Comptonized blackbody spectra when the source transitions from the hard to soft states. The hard state spectrum is a typical thermal Comptonization spectrum of the soft photons which originate in the disk and the NS outer photospheric layers. The hard state photon index is Γ ∼ 2. The soft state spectrum consists of two blackbody components which are only slightly Comptonized. Thus we can claim (as expected from theory) that in NS sources thermal equilibrium is established for the soft state. To the contrary in BH sources, the equilibrium is never established due to the presence of the BH horizon. The emergent BH