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

Creators: Thompson, Jonathan E.^{1, 2}; Hoy, Charlie³; Fauchon-Jones, Edward⁴; Hannam, Mark⁴

1. University of Southampton
2. California Institute of Technology
3. University of Portsmouth
4. Cardiff University

Abstract

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 N-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.

Copyright and License

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Acknowledgement

The authors would like to thank Alvin Chua, Stephen Fairhurst, and Frank Ohme for enlightening discussions on waveform systematics and bias estimation. We thank Jannik Mielke for comments during the LIGO-Virgo-KAGRA internal review. J. T. acknowledges support from the NASA LISA Preparatory Science Grant 20-LPS20-0005. C. H. thanks the UKRI Future Leaders Fellowship for support through the Grant MR/T01881X/1. E. F.-J and M. H. were supported in part by Science and Technology Facilities Council (STFC) Grant ST/V00154X/1. This research used the supercomputing facilities at Cardiff University operated by Advanced Research Computing at Cardiff (ARCCA) on behalf of the Cardiff Supercomputing Facility and the HPC Wales and Supercomputing Wales (SCW) projects. We acknowledge the support of the latter, which is part-funded by the European Regional Development Fund (ERDF) via the Welsh Government. In part, the computational resources at Cardiff University were also supported by STFC Grant ST/I006285/1. We are also grateful for the Sciama High Performance Compute (HPC) cluster, which is supported by the Institute of Cosmology and Gravitation (ICG), SEPNet, and the University of Portsmouth. The authors are grateful for computational resources provided by the LIGO Laboratory and supported by National Science Foundation grants PHY-0757058 and PHY-0823459. The authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work.

Data Availability

The data that support the findings of this article are not publicly available. The data are available from the authors upon reasonable request.

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