Source term method for binary neutron stars initial data

Abstract

The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value problem are: a) the boundary is not known a-priori, but constitutes part of the solution of the problem. b) Various terms become singular at the boundary. In this work, we use the source term method proposed by Towers [1] to embed the star inside a rectangular grid where the boundary condition is treated as a jump condition and is incorporated as additional source terms in the Poisson equation, which is then solved iteratively. The treatment of singular terms is resolved with an additional separation in the level set that shifts the boundary to the interior of the star. The solution is then extrapolated to the original boundary for the final result. We present two-dimensional tests to show the convergence of the source term method, and we further apply this solver to a realistic three-dimensional binary neutron star problem. By comparing our solution with the one coming from the initial data solver COCAL, we demonstrate agreement at the level of 1% . Our method can be used in other problems with discontinuous solutions like in magnetized neutron stars.