Exact Mass Conservation in Binary Neutron Star Merger Simulations

A long-standing problem in the simulation of neutron star spacetimes is the treatment of vacuum regions outside the stars. The use of an artificial low-density atmosphere is a common robust approach within Eulerian hydrodynamics that, however, introduces baryon-mass violation even with conservative numerical schemes. We propose a simple numerical algorithm that ensures exact mass conservation by means of an appropriate local rescaling of the atmosphere. The scheme is combined with a low-order flux correction and it can be further augmented by a pseudo-vacuum treatment that enforces strict vacuum in the outer regions far from the central objects. We demonstrate the effectiveness of these vacuum treatments with binary neutron star mergers simulations spanning multiple orbits and the postmerger phase, and including a microphysical equation of state. The rescaling algorithm guarantees mass and electron number conservation to round-off precision. The pseudo-vacuum treatment shows slightly larger but approximately constant violations and can improve the computation of fast tail ejecta as well as provide convergent gravitational waves of quality comparable to the standard atmosphere. Overall, results from different atmosphere treatments and a two-code comparison suggest that current computations of gravitational waves and (dynamical) ejecta in the presence of an artifical atmosphere are robust, provided that conservative adaptive mesh refinement with flux correction is employed.