No Arabic abstract
We investigate the limitations of thermonuclear X-ray bursts as a distance indicator for the weakly-magnetized accreting neutron star 4U 1728-34. We measured the unabsorbed peak flux of 81 bursts in public data from the Rossi X-Ray Timing Explorer (RXTE). The distribution of peak fluxes was bimodal: 66 bursts exhibited photospheric radius expansion and were distributed about a mean bolometric flux of 9.2e-8 erg/cm^2/s, while the remaining (non-radius expansion) bursts reached 4.5e-8 erg/cm^2/s, on average. The peak fluxes of the radius-expansion bursts were not constant, exhibiting a standard deviation of 9.4% and a total variation of 46%. These bursts showed significant correlations between their peak flux and the X-ray colors of the persistent emission immediately prior to the burst. We also found evidence for quasi-periodic variation of the peak fluxes of radius-expansion bursts, with a time scale of approximately 40 d. The persistent flux observed with RXTE/ASM over 5.8 yr exhibited quasi-periodic variability on a similar time scale. We suggest that these variations may have a common origin in reflection from a warped accretion disk. Once the systematic variation of the peak burst fluxes is subtracted, the residual scatter is only approximately 3%, roughly consistent with the measurement uncertainties. The narrowness of this distribution strongly suggests that i) the radiation from the neutron star atmosphere during radius-expansion episodes is nearly spherically symmetric, and ii) the radius-expansion bursts reach a common peak flux which may be interpreted as a standard candle intensity.Adopting the minimum peak flux for the radius-expansion bursts as the Eddington flux limit, we derive a distance for the source of 4.4-4.8 kpc.
We analyzed 123 thermonuclear (type-I) X-ray bursts observed by the Rossi X-ray Timing Explorer from the low-mass X-ray binary 4U 1636-536. All but two of the 40 radius-exansion bursts in this sample reached peak fluxes which were normally distributed about a mean of 6.4e-8 ergs/cm^2/s, with a standard deviation of 7.6%. The remaining two radius-expansion bursts reached peak fluxes a factor of 1.69+/-0.13 lower than this mean value; as a consequence, the overall variation in the peak flux of the radius-expansion bursts was a factor of ~2. This variation is comparable to the range of the Eddington limit between material with solar H-fraction (X=0.7) and pure He. Such a variation may arise if, for the bright radius-expansion bursts, most of the accreted H is eliminated either by steady hot CNO burning or expelled in a radiatively-driven wind. However, steady burning cannot exhaust the accreted H for solar composition material within the typical ~2 hr burst recurrence time, nor can it result in sufficient elemental stratification to allow selective ejection of the H only. An additional stratification mechanism appears to be required to separate the accreted elements and thus allow preferential ejection of the hydrogen. We found no evidence for a gap in the peak flux distribution between the radius-expansion and non-radius expansion bursts, previously observed in smaller samples. Assuming that the faint radius-expansion bursts reached the Eddington limit for H-rich material (X~0.7), and the brighter bursts the limit for pure He (X=0), we estimate the distance to 4U 1636-536 (for a canonical neutron star with M_NS=1.4M_sun, R_NS=10 km) to be 6.0+/-0.5 kpc, or for M_NS=2M_sun at most 7.1 kpc. (Abstract abridged)
Eddington-limited X-ray bursts from neutron stars can be used in conjunction with other spectroscopic observations to measure neutron star masses, radii, and distances. In order to quantify some of the uncertainties in the determination of the Eddington limit, we analysed a large sample of photospheric radius-expansion thermonuclear bursts observed with the Rossi X-ray Timing Explorer. We identified the instant at which the expanded photosphere touches down back onto the surface of the neutron star and compared the corresponding touchdown flux to the peak flux of each burst. We found that for the majority of sources, the ratio of these fluxes is smaller than 1.6, which is the maximum value expected from the changing gravitational redshift during the radius expansion episodes (for a 2M_sun neutron star). The only sources for which this ratio is larger than 1.6 are high inclination sources that include dippers and Cyg X-2. We discuss two possible geometric interpretations of this effect and show that the inferred masses and radii of neutron stars are not affected by this bias. On the other hand, systematic uncertainties as large as ~50% may be introduced to the distance determination.
It has recently been shown that the persistent emission of a neutron star low-mass X-ray binary (LMXB) evolves during a thermonuclear (type-I) X-ray burst. The reason of this evolution, however, is not securely known. This uncertainty can introduce significant systematics in the neutron star radius measurement using burst spectra, particularly if an unknown but significant fraction of the burst emission, which is reprocessed, contributes to the changes in the persistent emission during the burst. Here, by analyzing individual burst data of AstroSat/LAXPC from the neutron star LMXB 4U 1728--34 in the soft state, we show that the burst emission is not significantly reprocessed by a corona covering the neutron star. Rather, our analysis suggests that the burst emission enhances the accretion disk emission, possibly by increasing the accretion rate via disk. This enhanced disk emission, which is Comptonized by a corona covering the disk, can explain an increased persistent emission observed during the burst. This finding provides an understanding of persistent emission components, and their interaction with the thermonuclear burst emission. Furthermore, since burst photons are not significantly reprocessed, non-burst and burst emissions can be reliably separated, which is required to reduce systematic uncertainties in the stellar radius measurement.
With the excellent angular resolution of the Chandra X-ray Observatory, it is possible to geometrically determine the distance to variable Galactic sources, based on the phenomenon that scattered radiation appearing in the X-ray halo has to travel along a slightly longer path than the direct, unscattered radiation. By measuring the delayed variability, constraints on the source distance can be obtained if the halo brightness is large enough to dominate the point spread function (PSF) and to provide sufficient statistics. The distance to Cyg X-3, which has a quasi-sinusoidal light curve, has been obtained with this approach by Predehl et al. Here we examine the feasibility of using the delayed signature of type I X-ray bursts as distance indicators. We use simulations of delayed X-ray burst light curves in the halo to find that the optimal annular region and energy band for a distance measurement with a grating observation is roughly 10-50 and 1-5 keV respectively, assuming Chandras effective area and PSF, uniformly distributed dust, the input spectrum and optical depth to GX 13+1, and the Weingartner & Draine interstellar grain model. We find that the statistics are dominated by Poisson noise rather than systematic uncertainties, e.g., the PSF contribution to the halo. Using Chandra, a distance measurement to such a source at 4 (8) kpc could be made to about 23% (30%) accuracy with a single burst with 68% confidence. By stacking many bursts, a reasonable estimate of systematic errors limit the distance measurement to about 10% accuracy.
While kilohertz quasi-periodic oscillations (kHz QPOs) have been well studied for decades since their initial discovery, the cause of these signals remains unknown, as no model has been able to accurately predict all of their spectral and timing properties. Separately, X-ray reverberation lags have been detected in AGN and stellar-mass black hole binaries, and reverberation may be expected to occur in neutron star systems as well, producing lags of the same amplitude as the lags measured of the kHz QPOs. Furthermore, the detection of a relativistically reflected Fe K line in the time-averaged spectra of many neutron star systems provides an additional motivation for testing reverberation. While it has been shown that the lag-energy properties of the lower kHz QPOs are unlikely to be produced by X-ray reverberation, the upper kHz QPOs have not yet been explored. We therefore model the upper kHz QPO lag-energy spectra using relativistic ray-tracing functions and apply them to archival RXTE data on 4U 1728-34 where upper kHz QPOs have been detected. By modeling the time-averaged spectra in which upper kHz QPOs had been significantly detected, we determine the reflected flux fraction across all energies and produce a model for the lag-energy spectra from X-ray reverberation. We explore the dependence of the modeled lag properties on several different types of reflection models, but are unable to successfully reproduce the measured lags of 4U 1728-34. We conclude that reverberation alone does not explain the measured time lags detected in upper kHz QPOs.