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 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 Xray 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 × 10 14 cm s −2 for SAX J1808.4-3658.

Timing the Pulsations of the Accreting Millisecond Pulsar SAX J1808.4–3658 during Its 2019 Outburst

“…Thus, from theory, we expect that the scale of our count-rate dependent bias should be b=−1.09, which is offset by about 20% from the b=−0.87 that we actually measured using our flux-adjusted phase model (Table 1). This offset can be accounted for by changing the assumed neutron star mass ( M 2  ), radius (8 km), and distance (3.8 kpc) (Galloway & Cumming 2006;Hartman et al 2008;Goodwin et al 2019a), but only if m <1.2 10 G cm 26 3 (see Figure 6). The magnetic moment of SAXJ1808 has been constrained to -0.7 1.4 10 G cm 26 3 ( ) (Hartman et al 2008;.…”

Gaia EDR3 parallaxes of type I X-ray bursters and their implications on the models of type I X-ray bursts: A generic approach to the Gaia parallax zero point and its uncertainty

“…As is mentioned in Section 1, PRE models are not the only pathway to the distances of type I X-ray bursters. Bayesian inference based on a burst ignition model (Cumming & Bildsten 2000) was recently realised to estimate parameters including X and D (Goodwin et al 2019). We believe such inferences will be made for more type I X-ray bursters in the near future.…”

“…Hereafter, we refer to this spherically symmetric model as the simplistic PRE model, and the simplistic-PRE-model-based PRE distances as nominal PRE distances. Besides PRE models, a Bayesian framework has been recently developed to infer parameters, including the distance and the composition of nuclear fuel on the NS surface, for the type I X-ray burster SAX J1808.4-3658 (Goodwin et al 2019), by matching the burst observables (such as burst flux and recurrence time) of non-PRE type I X-ray bursts with the prediction from a burst ignition model (Cumming & Bildsten 2000).…”

Sensitivity Study of Nuclear Reactions Influencing Photospheric Radius Expansion X-Ray Bursts

“…An example is the accretion-powered millisecond pulsar SAX J1808.4−3658 [3,4] that powered up the brightest Type-I X-ray burst (XRB) recorded by NICER in recent history [5]. The first 1D multi-zone model of SAX J1808.4−3658 was recently constructed [6,7]. The pioneering model offers a first concurrent and direct comparison with the observed light curves, fluences, and recurrence times.…”

“…A close match of modeled and observed PRE burst permit us to probe the complicated burst mechanism of PRE bursters. Johnston et al [6] recently constructed the first PRE burst model quantitatively describing the accretion-powered millisecond pulsar SAX J1808.4−3658, whereas the other simplified model built by Goodwin et al [7] provides an intuitive grasp of the observables of SAX J1808.4−3658 burster. The host neutron star of this PRE burster spins up to millisecond periods by the accretion of stellar matter from a low-mass companion star in its X-ray binary system [3].…”