Accuracy requirements for the calculation of gravitational waveforms from coalescing compact binaries in numerical relativity

TL;DR

This paper evaluates the accuracy needed in numerical relativity simulations of binary coalescences for gravitational wave detection, finding that higher order methods are essential for reliable waveform extraction.

Contribution

It provides a detailed analysis of accuracy requirements and compares them with current simulation capabilities, highlighting the need for advanced numerical methods.

Findings

Current simulations are less accurate than required by several orders of magnitude.

Higher order numerical methods are necessary for reliable gravitational waveform extraction.

Adaptive mesh refinement with second order methods is insufficient for the needed accuracy.

Abstract

I discuss the accuracy requirements on numerical relativity calculations of inspiraling compact object binaries whose extracted gravitational waveforms are to be used as templates for matched filtering signal extraction and physical parameter estimation in modern interferometric gravitational wave detectors. Using a post-Newtonian point particle model for the pre-merger phase of the binary inspiral, I calculate the maximum allowable errors for the mass and relative velocity and positions of the binary during numerical simulations of the binary inspiral. These maximum allowable errors are compared to the errors of state-of-the-art numerical simulations of multiple-orbit binary neutron star calculations in full general relativity, and are found to be smaller by several orders of magnitude. A post-Newtonian model for the error of these numerical simulations suggests that adaptive mesh refinement coupled with second order accurate finite difference codes will {\it not} be able to robustly obtain the accuracy required for reliable gravitational wave extraction on Terabyte-scale computers. I conclude that higher order methods (higher order finite difference methods and/or spectral methods) combined with adaptive mesh refinement and/or multipatch technology will be needed for robustly accurate gravitational wave extraction from numerical relativity calculations of binary coalescence scenarios.