Improving the convergence order of binary neutron star merger simulations in the Baumgarte-Shapiro-Shibata-Nakamura formulation

TL;DR

This paper enhances the accuracy of binary neutron star merger simulations by addressing convergence issues related to constraint damping schemes and equation of state parametrizations within the BSSN formulation, improving gravitational waveform modeling.

Contribution

It introduces a continuous constraint damping scheme and compares different equation of state parametrizations to improve simulation convergence and physical accuracy.

Findings

Continuous damping scheme preserves convergence longer.

Generalized equation of state reduces unphysical artifacts.

Differences in gravitational wave signals depend on EOS parametrization.

Abstract

High-accuracy numerical relativity simulations of binary neutron star mergers are a necessary ingredient for constructing gravitational waveform templates to analyze and interpret observations of compact object mergers. Numerical convergence in the post-merger phase of such simulations is challenging to achieve with many modern codes. In this paper, we study two ways of improving the convergence properties of binary neutron star merger simulations within the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations. We show that discontinuities in a particular constraint damping scheme in this formulation can destroy the post-merger convergence of the simulation. A continuous prescription, in contrast, ensures convergence until late times. We additionally study the impact of the equation of state parametrization on the pre- and post-merger convergence properties of the simulations. In particular, we compare results for a piecewise polytropic parametrization, which is commonly used in merger simulations but suffers unphysical discontinuities in the sound speed, with results using a "generalized" piecewise polytropic parametrization, which was designed to ensure both continuity and differentiability of the equation of state. We report on the differences in the gravitational waves and any spurious pre-merger heating, depending on which equation of state parametrization is used.