Systematic Uncertainties in the Spectroscopic Measurements of Neutron-Star Masses and Radii from Thermonuclear X-ray Bursts. I. Apparent Radii

摘要

The masses and radii of low-magnetic field neutron stars can be measured bycombining different observable quantities obtained from their X-ray spectraduring thermonuclear X-ray bursts. One of these quantities is the apparentradius of each neutron star as inferred from the X-ray flux and spectraltemperature measured during the cooling tails of bursts, when the thermonuclearflash is believed to have engulfed the entire star. In this paper, we analyze13,095 X-ray spectra of 446 X-ray bursts observed from 12 sources in order toassess possible systematic effects in the measurements of the apparent radii ofneutron stars. We first show that the vast majority of the observed X-rayspectra are consistent with blackbody functions to within a few percent. Wefind that most X-ray bursts follow a very well determined correlation betweenX-ray flux and temperature, which is consistent with the whole neutron-starsurface emitting uniformly during the cooling tails. We develop a BayesianGaussian mixture algorithm to measure the apparent radii of the neutron starsin these sources, while detecting and excluding a small number of X-ray burststhat show irregular cooling behavior. This algorithm also provides us with aquantitative measure of the systematic uncertainties in the measurements. Wefind that those errors in the spectroscopic determination of neutron-star radiithat are introduced by systematic effects in the cooling tails of X-ray burstsare in the range $\simeq 3-8$%. Such small errors are adequate to distinguishbetween different equations of state provided that uncertainties in thedistance to each source and the absolute calibration of X-ray detectors do notdominate the error budget.