Exploring tidal effects of coalescing binary neutron stars in numerical relativity II: Longterm simulations

TL;DR

This paper presents long-term numerical relativity simulations of binary neutron star mergers, compares the results with effective-one-body waveforms, and assesses the accuracy of current models for different neutron star radii.

Contribution

It introduces improved long-term simulation techniques and provides a detailed comparison with EOB waveforms, highlighting their agreement and discrepancies based on neutron star compactness.

Findings

Waveforms for compact neutron stars agree within 1 radian phase error.

Less compact stars show significant phase disagreement (~3 radians).

New simulations converge faster than third order, enabling more accurate waveform extrapolation.

Abstract

We perform new longterm (15-16 orbits) simulations of coalescing binary neutron stars in numerical relativity using an updated Einstein's equation solver, employing low-eccentricity initial data, and modeling the neutron stars by a piecewise polytropic equation of state. A convergence study shows that our new results converge more rapidly than the third order and using the determined convergence order, we construct an extrapolated waveform for which the estimated total phase error should be less than 1 radian. We then compare the extrapolated waveforms with those calculated by the latest effective-one-body (EOB) formalism in which the so-called tidal deformability, higher post-Newtonian corrections, and gravitational self-force effects are taken into account. We show that for a binary of compact neutron stars with their radius 11.1 km, the waveform by the EOB formalism agrees quite well with the numerical waveform so that the total phase error is smaller than 1 radian for the total phase of $\sim 200$ radian up to the merger. By contrast, for a binary of less compact neutron stars with their radius 13.6 km, the EOB and numerical waveforms disagree with each other in the last few wave cycles, resulting in the total phase error of $\sim 3$ radian.