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.
Categories: astro-ph.HE
