Accurate evolutions of inspiralling neutron-star binaries: assessment of the truncation error

TL;DR

This paper analyzes the convergence and truncation errors in numerical simulations of inspiraling neutron-star binaries, emphasizing the importance of error assessment for accurate gravitational-wave modeling.

Contribution

It provides a detailed convergence analysis and an error budget for simulations of neutron-star binaries, highlighting the impact of shocks and turbulence on numerical accuracy.

Findings

Convergence deteriorates during merger and turbulence development.

Low-resolution results can have large truncation errors.

An error budget quantifies simulation uncertainties.

Abstract

We have recently presented an investigation in full general relativity of the dynamics and gravitational-wave emission from binary neutron stars which inspiral and merge, producing a black hole surrounded by a torus (see arXiv:0804.0594). We here discuss in more detail the convergence properties of the results presented in arXiv:0804.0594 and, in particular, the deterioration of the convergence rate at the merger and during the survival of the merged object, when strong shocks are formed and turbulence develops. We also show that physically reasonable and numerically convergent results obtained at low-resolution suffer however from large truncation errors and hence are of little physical use. We summarize our findings in an "error budget", which includes the different sources of possible inaccuracies we have investigated and provides a first quantitative assessment of the precision in the modelling of compact fluid binaries.