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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.
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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)
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.
Observations of thermonuclear X-ray bursts from accreting neutron stars (NSs) in low-mass X-ray binary systems can be used to constrain NS masses and radii. Most previous work of this type has set these constraints using Planck function fits as a proxy: both the models and the data are fit with diluted blackbody functions to yield normalizations and temperatures which are then compared against each other. Here, for the first time, we fit atmosphere models of X-ray bursting NSs directly to the observed spectra. We present a hierarchical Bayesian fitting framework that uses state-of-the-art X-ray bursting NS atmosphere models with realistic opacities and relativistic exact Compton scattering kernels as a model for the surface emission. We test our approach against synthetic data, and find that for data that are well-described by our model we can obtain robust radius, mass, distance, and composition measurements. We then apply our technique to Rossi X-ray Timing Explorer observations of five hard-state X-ray bursts from 4U 1702-429. Our joint fit to all five bursts shows that the theoretical atmosphere models describe the data well but there are still some unmodeled features in the spectrum corresponding to a relative error of 1-5% of the energy flux. After marginalizing over this intrinsic scatter, we find that at 68% credibility the circumferential radius of the NS in 4U 1702-429 is R = 12.4+-0.4 km, the gravitational mass is M=1.9+-0.3 Msun, the distance is 5.1 < D/kpc < 6.2, and the hydrogen mass fraction is X < 0.09.
The radius of neutron stars can in principle be measured via the normalisation of a blackbody fitted to the X-ray spectrum during thermonuclear (type-I) X-ray bursts, although few previous studies have addressed the reliability of such measurements. Here we examine the apparent radius in a homogeneous sample of long, mixed H/He bursts from the low-mass X-ray binaries GS 1826-24 and KS 1731-26. The measured blackbody normalisation (proportional to the emitting area) in these bursts is constant over a period of up to 60s in the burst tail, even though the flux (blackbody temperature) decreased by a factor of 60-75% (30-40%). The typical rms variation in the mean normalisation from burst to burst was 3-5%, although a variation of 17% was found between bursts observed from GS 1826-24 in two epochs. A comparison of the time-resolved spectroscopic measurements during bursts from the two epochs shows that the normalisation evolves consistently through the burst rise and peak, but subsequently increases further in the earlier epoch bursts. The elevated normalisation values may arise from a change in the anisotropy of the burst emission, or alternatively variations in the spectral correction factor, f_c, of order 10%. Since burst samples observed from systems other than GS 1826-24 are more heterogeneous, we expect that systematic uncertainties of at least 10% are likely to apply generally to measurements of neutron-star radii, unless the effects described here can be corrected for.
X-ray spectral analysis of quiescent low-mass X-ray binaries (LMXBs) has been one of the most common tools to measure the radius of neutron stars (NSs) for over a decade. So far, this method has been mainly applied to NSs in globular clusters, primarily because of their well-constrained distances. Here, we study Chandra data of seven transient LMXBs in the Galactic plane in quiescence to investigate the potential of constraining the radius (and mass) of the NSs inhabiting these systems. We find that only two of these objects had X-ray spectra of sufficient quality to obtain reasonable constraints on the radius, with the most stringent being an upper limit of $Rlesssim$14.5 km for EXO 0748-676 (for assumed ranges for mass and distance). Using these seven sources, we also investigate systematic biases on the mass/radius determination; for Aql X-1 we find that omitting a power-law spectral component when it does not seem to be required by the data, results in peculiar trends in the obtained radius with changing mass and distance. For EXO 0748-676 we find that a slight variation in the lower limit of the energy range chosen for the fit leads to systematically different masses and radii. Finally, we simulated Athena spectra and found that some of the biases can be lifted when higher quality spectra are available and that, in general, the search for constraints on the equation of state of ultra-dense matter via NS radius and mass measurements may receive a considerable boost in the future.
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