Systematic Uncertainties in the Spectroscopic Measurements of Neutron-Star Masses and Radii from Thermonuclear X-ray Bursts. II. Eddington Limit

Time resolved X-ray spectroscopy of thermonuclear bursts observed from low mass X-ray binaries offer a unique tool to measure neutron star masses and radii. In this paper, we continue our systematic analysis of all the X-ray bursts observed with RXTE from X-ray binaries. We determine the events which show clear evidence for photospheric radius expansion and measure the Eddington limits for these accreting neutron stars using the bolometric fluxes attained at the touchdown moments of each X-ray burst. We employ a Bayesian technique to investigate the degree to which the Eddington limit for each source remains constant between bursts. We find that for sources with a large number of radius expansion bursts, systematic uncertainties are at a 5-10% level. Moreover, in six sources with only pairs of Eddington-limited bursts, the distribution of fluxes is consistent with a ~10% fractional dispersion. This indicates that the spectroscopic measurements of neutron star masses and radii using thermonuclear X-ray bursts can reach the level of accuracy required to distinguish between different neutron star equations of state, provided that uncertainties related to the overall flux calibration of X-ray detectors are of comparable magnitude.