Use and interpretation of signal-model indistinguishability measures for gravitational-wave astronomy

The difference (“mismatch”) between two gravitational-wave signals is often used to estimate the signal-to-noise ratio (SNR) at which they will be distinguishable in a measurement or, alternatively, when the errors in a signal model will lead to biased measurements. It is well known that the standard approach to calculate this “indistinguishability SNR” is too conservative: a model may fail the criterion at a given SNR, but not necessarily incur a biased measurement of any individual parameters. This problem can be solved by taking into account errors orthogonal to the model space (which, therefore, do not induce a bias), and calculating indistinguishability SNRs for individual parameters, rather than the full <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>N</a:mi></a:mrow></a:math>-dimensional parameter space. We illustrate this approach with the simple example of aligned-spin binary black hole signals, and calculate accurate estimates of the SNR at which each parameter measurement will be biased. In general, biases occur at much higher SNRs than predicted from the standard mismatch calculation. Which parameters are most easily biased depends sensitively on the details of a given waveform model, and the location in parameter space, and in some cases the bias SNR is as high as the conservative estimate. We also illustrate how the parameter bias SNR can be used to robustly specify waveform accuracy requirements for future detectors.