Multiscale modelling of neutron star oceans

Abstract

Type I X-ray bursts are thermonuclear burning events which occur on the surface of accreting neutron stars. Burning begins in a localised spot in the star’s ocean layer before spreading across the entire surface. By gaining a better understanding of X-ray bursts, tighter limits can be determined for other neutron star properties such as the mass, radius, spin frequency and magnetic field. The ocean environment is very extreme, involving much higher pressure, temperature and magnetic field strength compared to the conditions typically found in terrestrial systems. We shall be looking at the effects of the strong gravitational field, modelling the ocean using general relativistic hydrodynamics.

The physics of X-ray bursts acts over a wide range of scales, which introduces a number of challenges when modelling them. In this work, we use the multiscale approach to couple together multiple physical models in order to best capture the physics across these various scales. On the smallest scales, the physics is dominated by turbulent burning. The speed of propagation of the burning front is much slower than the acoustic speed, making it difficult to model this with conventional numerical schemes. We therefore instead use the low Mach number approximation, which we have derived and implemented for the relativistic fluid equations based on the existing approach developed for the Newtonian case. On larger scales, the burning front can be thought of as a discontinuity. To model this, we investigate the reactive Riemann problem for relativistic deflagrations and detonations and develop a numerical solver. The large scale propagation of the burning front is believed to be dominated by the Coriolis force. To capture this behaviour, we have derived and implemented a model for the relativistic form of the shallow water equations. Finally, we construct a hybrid scheme to combine the best features of these approximations, extending existing adaptive mesh refinement techniques to include different physical models at different scales.

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Identifiers

ORCID for Ian Hawke: orcid.org/0000-0003-4805-0309

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