Numerical Approach to Compressible Shallow-water Dynamics of Neutron-star Spreading Layers

A weakly magnetized neutron star (NS) undergoing disk accretion should release about half of its power in a compact region known as the accretion boundary layer. Latitudinal spread of the accreted matter and efficient radiative cooling justify the approach to this flow as a two-dimensional spreading layer (SL) on the surface of the star. Numerical simulations of SLs are challenging because of the curved geometry and supersonic nature of the problem. We develop and test a new two-dimensional hydrodynamics code, SPLASH, which uses the multislope second-order Monotonic Upstream-centered Scheme for Conservation Law scheme in combination with an HLLC+ Riemann solver on an arbitrary irregular mesh on a spherical surface. The code is suitable and accurate for Mach numbers up to 5-10. Adding sinks and sources to the conserved variables, we simulate early stages of constant-rate accretion onto a spherical NS. During these stages of accretion, heating in the equatorial region triggers convective instability that causes rapid mixing in the latitudinal direction. One of the outcomes of the instability is the development of a “tennis ball” pattern rotating at a frequency considerably different from the rotation frequency of the matter. In the simulated variability curves, there are signatures of both the pattern rotation and the rotation of the SL, as well as their harmonics. The pattern and cyclonal vortices associated with it are probably a manifestation of an inertial oscillation mode excited within the layer (https://github.com/TURBOLOSE/SPLASH).