Beyond second-order convergence in simulations of binary neutron stars in full general-relativity

TL;DR

This paper introduces a new high-order numerical relativity code that surpasses second-order convergence, enabling more accurate simulations of binary neutron star inspirals and tidal effects with minimal phase errors.

Contribution

The authors develop and demonstrate a high-order, high-resolution shock-capturing scheme that achieves above third-order convergence in binary neutron star simulations, surpassing previous second-order limitations.

Findings

Achieved above third-order convergence in gravitational wave phase and amplitude.

Obtained accurate tidal effect estimates with minimal numerical viscosity.

Found excellent agreement with post-Newtonian models, with phase differences less than 0.2 radians.

Abstract

Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the Einstein-Euler system of equations. We report simulations of the inspiral of binary neutron stars in quasi-circular orbits computed with a new code employing high-order, high-resolution shock-capturing, finite-differencing schemes that, for the first time, go beyond the second-order barrier. In particular, without any tuning or alignment, we measure a convergence order above three both in the phase and in the amplitude of the gravitational waves. Because the new code is able to calculate waveforms with very small phase errors already at modest resolutions, we are able to obtain accurate estimates of tidal effects in the inspiral that are essentially free from the large numerical viscosity typical of lower-order methods, and even for the challenging large compactness and small-deformability binary considered here. We find a remarkable agreement between our Richardson-extrapolated waveform and the one from the tidally corrected post-Newtonian (PN) Taylor-T4 model, with a de-phasing smaller than 0.2 radians during the seven orbits of the inspiral and up to the contact point. Because our results can be used reliably to assess the validity of the PN or other approximations at frequencies significantly larger than those considered so far in the literature, they seem to exclude at these compactnesses significant tidal amplifications from next-to-next-to-leading--order terms in the PN expansion.