Model Waveform Accuracy Requirements for the Allen $\chi^2$ Discriminator

TL;DR

This paper establishes new waveform accuracy standards for the Allen χ² discriminator in gravitational wave data analysis, ensuring reliable detection and significance evaluation beyond previous SNR-based criteria.

Contribution

It derives specific accuracy standards for waveform models to properly utilize the Allen χ² discriminator, distinct from prior detection-focused requirements.

Findings

Provides formulae for evaluating model errors' impact on χ²

Defines accuracy standards for waveform reliability in GW analysis

Enhances the robustness of χ² as a detection and significance tool

Abstract

This paper derives accuracy standards for model gravitational waveforms required to ensure proper use of the Allen $\chi^2$ discriminator in gravitational wave (GW) data analysis. These standards are different from previously established requirements for detection and waveform parameter measurement based on signal-to-noise optimization. We present convenient formulae for evaluating and interpreting the contribution of model errors to measured values of this $\chi^2$ statistic. The new accuracy standards derived here are needed to ensure the reliability of measured values of the Allen $\chi^2$ statistic, both in their traditional role as vetoes and in their current role as elements in evaluating the significance of candidate detections.