Initial-data contribution to the error budget of gravitational waves from neutron-star binaries

TL;DR

This paper investigates how small differences in initial data for neutron-star binary simulations can significantly affect gravitational waveforms, emphasizing the importance of consistent initial conditions for accurate modeling.

Contribution

It provides a comparative analysis of initial data impact on gravitational waveforms using different initial-data codes and highlights the nonlinear effects of initial data errors.

Findings

Initial data differences of less than 0.02% can cause phase differences of about 0.5 radians.

The initial data errors have a highly nonlinear impact on waveform evolution.

Using consistent initial data is crucial for accurate comparative studies.

Abstract

As numerical calculations of inspiralling neutron-star binaries reach values of accuracy that are comparable with those of binary black holes, a fine budgeting of the various sources of error becomes increasingly important. Among such sources, the initial data is normally not accounted for, the rationale being that the error on the initial spacelike hypersurface is always far smaller than the one gained during the evolution. We here consider critically this assumption and perform a comparative analysis of the gravitational waveforms relative to essentially the same physical binary configuration when computed with two different initial-data codes, and then evolved with the same evolution code. More specifically, we consider the evolution of irrotational neutron-star binaries computed either with the pseudo-spectral code \lorene{}, or with the newly developed finite-difference code \cocal{}; both sets of initial data are subsequently evolved with the high-order evolution code \whiskythc{}. In this way we find that despite the initial data shows global (local) differences that are $\lesssim 0.02\%\ (1\%)$, the gravitational-wave phase at the merger time differs by $\sim 0.5$ radians after $\sim 3$ orbits, a surprisingly large value. Our results highlight the highly nonlinear impact that errors in the initial data can have on the subsequent evolution and the importance of using exactly the same initial data when comparative studies are done.