Accuracy of numerical relativity waveforms from binary neutron star mergers and their comparison with post-Newtonian waveforms

TL;DR

This paper presents high-accuracy numerical relativity simulations of binary neutron star mergers, analyzes their convergence and errors, compares them with post-Newtonian waveforms, and discusses implications for gravitational wave data analysis.

Contribution

It provides detailed error analysis of numerical waveforms and compares them with post-Newtonian models, highlighting the importance of tidal effects in late inspiral.

Findings

Second order convergence up to contact

Phase uncertainty minimized to 0.13 rad

T4 approximants underestimate tidal effects

Abstract

We present numerical relativity simulations of nine-orbit equal-mass binary neutron star covering the quasicircular late inspiral and merger. The extracted gravitational waveforms are analyzed for convergence and accuracy. Second order convergence is observed up to contact, i.e. about 3-4 cycles to merger; error estimates can be made up to this point. The uncertainties on the phase and the amplitude are dominated by truncation errors and can be minimized to 0.13 rad and less then 1%, respectively, by using several simulations and extrapolating in resolution. In the latter case finite-radius extraction uncertainties become a source of error of the same order and have to be taken into account. The waveforms are tested against accuracy standards for data analysis. The uncertainties on the waveforms are such that accuracy standards are generically not met for signal-to-noise ratios relevant for detection, except for some best cases using extrapolation from several runs. A detailed analysis of the errors is thus imperative for the use of numerical relativity waveforms from binary neutron stars in quantitative studies. The waveforms are compared with the post-Newtonian Taylor T4 approximants both for point-particle and including the analytically known tidal corrections. The T4 approximants accumulate significant phase differences of 2 rad at contact and 4 rad at merger, underestimating the influence of finite size effects. Tidal signatures in the waveforms are thus important at least during the last six orbits of the merger process.