A Bayesian Approach to Matching Thermonuclear X-ray Burst Observations with Models

Abstract

We present a new method of matching observations of Type I (thermonuclear) X-ray bursts with models, comparing the predictions of a semi-analytic ignition model with X-ray observations of the accretion-powered millisecond pulsar SAX J1808.4--3658 in outburst. We used a Bayesian analysis approach to marginalise over the parameters of interest and determine parameters such as fuel composition, distance/anisotropy factors, neutron star mass and neutron star radius. Our study includes a treatment of the system inclination effects, inferring that the rotation axis of the system is inclined ${\left(69_{-2}^{+4}\right)}^{\circ }$ from the observers line of sight, assuming a flat disc model. This method can be applied to any accreting source that exhibits Type I X-ray bursts. We find a hydrogen mass fraction of $0.57_{-0.14}^{+0.13}$ and CNO metallicity of $0.013_{-0.004}^{+0.006}$ for the accreted fuel is required by the model to match the observed burst energies, for a distance to the source of $3.3_{-0.2}^{+0.3}\mathrm{kpc}$. We infer a neutron star mass of $1.5_{-0.3}^{+0.6}{\mathrm{M}}_{\odot }$ and radius of $11.8_{-0.9}^{+1.3}\mathrm{km}$ for a surface gravity of $1.9_{-0.4}^{+0.7}\times 10^{14}\mathrm{cm}{\mathrm{s}}^{-2}$ for SAX J1808.4--3658.

14 pages, 10 figures, revised version 1, accepted by MNRAS