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

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.