Notes on the integration of numerical relativity waveforms

TL;DR

This paper discusses the challenges of converting Weyl curvature data into gravitational wave strain in numerical relativity, and proposes a frequency domain integration method to reduce non-linear drifts.

Contribution

It identifies fundamental issues in integrating finite, noisy data streams and introduces a simple frequency domain procedure to improve strain estimation accuracy.

Findings

Frequency domain integration reduces secular drifts in strain.

Integration issues are independent of simulation gauge or method.

Proposed method improves waveform post-processing accuracy.

Abstract

A primary goal of numerical relativity is to provide estimates of the wave strain, $h$, from strong gravitational wave sources, to be used in detector templates. The simulations, however, typically measure waves in terms of the Weyl curvature component, $\psi_4$. Assuming Bondi gauge, transforming to the strain $h$ reduces to integration of $\psi_4$ twice in time. Integrations performed in either the time or frequency domain, however, lead to secular non-linear drifts in the resulting strain $h$. These non-linear drifts are not explained by the two unknown integration constants which can at most result in linear drifts. We identify a number of fundamental difficulties which can arise from integrating finite length, discretely sampled and noisy data streams. These issues are an artifact of post-processing data. They are independent of the characteristics of the original simulation, such as gauge or numerical method used. We suggest, however, a simple procedure for integrating numerical waveforms in the frequency domain, which is effective at strongly reducing spurious secular non-linear drifts in the resulting strain.