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Tests of general relativity with gravitational-wave observations from merging compact binaries continue to confirm Einstein’s theory of gravity with increasing precision. However, these tests have so far been applied only to signals that were first confidently detected by matched-filter searches assuming general relativity templates. This raises the question of selection biases: What is the largest deviation from general relativity that current searches can detect, and are current constraints on such deviations necessarily narrow because they are based on signals that were detected by templated searches in the first place? In this paper, we estimate the impact of selection effects for tests of the inspiral phase evolution of compact binary signals with a simplified version of the gstlal search pipeline. We find that selection biases affect the search for very large values of the deviation parameters, much larger than the constraints implied by the detected signals. Therefore, combined population constraints from confidently detected events are mostly unaffected by selection biases, with the largest effect being a broadening at the ∼10% level for the −1 PN term. These findings suggest that current population constraints on the inspiral phase are robust without factoring in selection biases. Our study does not rule out a disjoint, undetectable binary population with large deviations from general relativity or stronger selection effects in other tests or search procedures.
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A Fisher matrix for gravitational-wave population inference
ABSTRACT We derive a Fisher matrix for the parameters characterizing a population of gravitational-wave events. This provides a guide to the precision with which population parameters can be estimated with multiple observations, which becomes increasingly accurate as the number of events and the signal-to-noise ratio of the sampled events increase. The formalism takes into account individual event measurement uncertainties and selection effects, and can be applied to arbitrary population models. We illustrate the framework with two examples: an analytical calculation of the Fisher matrix for the mean and variance of a Gaussian model describing a population affected by selection effects, and an estimation of the precision with which the slope of a power-law distribution of supermassive black hole masses can be measured using extreme-mass-ratio inspiral observations. We compare the Fisher predictions to results from Monte Carlo analyses, finding very good agreement.
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- Award ID(s):
- 2207502
- PAR ID:
- 10406209
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 519
- Issue:
- 2
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 2736 to 2753
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1093/mnras/stac3560
