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

The Astrophysical Journal (Impact Factor: 6.73). 03/2011; DOI:10.1088/0004-637X/747/1/76
Source: arXiv

ABSTRACT The masses and radii of low-magnetic field neutron stars can be measured by
combining different observable quantities obtained from their X-ray spectra
during thermonuclear X-ray bursts. One of these quantities is the apparent
radius of each neutron star as inferred from the X-ray flux and spectral
temperature measured during the cooling tails of bursts, when the thermonuclear
flash is believed to have engulfed the entire star. In this paper, we analyze
13,095 X-ray spectra of 446 X-ray bursts observed from 12 sources in order to
assess possible systematic effects in the measurements of the apparent radii of
neutron stars. We first show that the vast majority of the observed X-ray
spectra are consistent with blackbody functions to within a few percent. We
find that most X-ray bursts follow a very well determined correlation between
X-ray flux and temperature, which is consistent with the whole neutron-star
surface emitting uniformly during the cooling tails. We develop a Bayesian
Gaussian mixture algorithm to measure the apparent radii of the neutron stars
in these sources, while detecting and excluding a small number of X-ray bursts
that show irregular cooling behavior. This algorithm also provides us with a
quantitative measure of the systematic uncertainties in the measurements. We
find that those errors in the spectroscopic determination of neutron-star radii
that are introduced by systematic effects in the cooling tails of X-ray bursts
are in the range $\simeq 3-8$%. Such small errors are adequate to distinguish
between different equations of state provided that uncertainties in the
distance to each source and the absolute calibration of X-ray detectors do not
dominate the error budget.

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