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Multi-epoch X-ray burst modelling: MCMC with large grids of 1D simulations

Type-I X-ray bursts are recurring thermonuclear explosions on the surface of accreting neutron stars. Matching observed bursts to computational models can help to constrain system properties, such as the neutron star mass and radius, crustal heating rates, and the accreted fuel composition, but systematic parameter studies to date have been limited. We apply Markov chain Monte Carlo methods to 1D burst models for the first time, and obtain system parameter estimations for the `Clocked Burster', GS 1826$-$238, by fitting multiple observed epochs simultaneously. We explore multiple parameters which are often held constant, including the neutron star mass, crustal heating rate, and hydrogen composition. To improve the computational efficiency, we precompute a grid of 3840 KEPLER models - the largest set of 1D burst simulations to date - and by interpolating over the model grid, we can rapidly sample burst predictions. We obtain estimates for a CNO metallicity of $Z_\mathrm{CNO} = 0.010^{+0.005}_{-0.004}$, a hydrogen fraction of $X_0 = 0.74^{+0.02}_{-0.03}$, a distance of $d \sqrt{ξ_\mathrm{b}} = 6.5^{+0.4}_{-0.6}\, \mathrm{kpc}$, and a system inclination of $i = {69^{+2}_{-3}}^{\circ}$.