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| - Angular momentum transport during X-ray bursts in neutron stars: a numerical general relativistic hydrodynamical study
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| - Aims. The distribution of angular momentum of matter during X-ray bursts in neutron stars is studied by means of axi-symmetric general relativistic hydrodynamics. Methods. The set of fully general relativistic Navier-Stokes equations is solved implicitly using the implicit solver GR-I-RMHD in combination with a third order spatial and second order temporal advection scheme. The viscous operators are formulated using a Kerr-like metric in the fixed background of a slowly rotating neutron star whose radius coincides with the corresponding last stable orbit. The importance of these operators and their possible simplifications are discussed as well. To verify the consistency and accuracy of the solution procedure, the time-dependent evolution of non-rotating heat bubbles during their rise to the surface of a white dwarf are followed and compared with previous calculations. Results. In the rotating case and depending on the viscosity parameter, $\alpha_{\rm tur}$, it is found that the viscously-initiated fronts at the center of bursts propagate at much faster speed than the fluid motion. These fast fronts act to decouple angular momentum from matter: angular momentum is transported outwards while matter sinks inwards into the deep gravitational well of the neutron star, thereby enhancing the compression of matter necessary to initiate ignition, that subsequently spreads over the whole surface of the neutron star on the viscous time scale. Based on the numerical simulations, we find that a viscosity parameter $\alpha_{\rm tur} = \mathcal{O}(0.1)$ is most suitable for fitting observations of neutron stars during X-ray bursts. It is argued that the spin up observed in the cooling tails of X-ray bursts is a transient phase, which eventually should be followed by a spin down phase. This delay can be attributed to a significant lengthening of the viscous time scale due to rapid cooling of matter in the outer layers.
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