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

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 $\left(69^{+4}_{-2}\right)^\circ$ 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 $0.57^{+0.13}_{-0.14}$ and CNO metallicity of $0.013^{+0.006}_{-0.004}$ for the accreted fuel is required by the model to match the observed burst energies, for a distance to the source of $3.3^{+0.3}_{-0.2}\,\mathrm{kpc}$. We infer a neutron star mass of $1.5^{+0.6}_{-0.3}\,\mathrm{M}_{\odot}$ and radius of $11.8^{+1.3}_{-0.9}\,\mathrm{km}$ for a surface gravity of $1.9^{+0.7}_{-0.4}\times10^{14}\,\mathrm{cm}\,\mathrm{s}^{-2}$ for SAX J1808.4--3658.