2019MNRAS.490.2228G

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 marginalize 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 (69⁺⁴_–2^○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 kpc. We infer a neutron star mass of 1.5^+0.6_–0.3 M_☉ and radius of 11.8^+1.3_–0.9 km for a surface gravity of 1.9^+0.7_–0.4×10¹⁴ cm s^–2 for SAX J1808.4-3658.