Eccentricity-induced systematic error on parametrized tests of general
relativity: hierarchical Bayesian inference applied to a binary black hole
population
One approach to testing general relativity (GR) introduces free parameters in
the post-Newtonian (PN) expansion of the gravitational-wave (GW) phase. If
systematic errors on these testing GR (TGR) parameters exceed the statistical
errors, this may signal a false violation of GR. Here, we consider systematic
errors produced by unmodeled binary eccentricity. Since the eccentricity of GW
events in ground-based detectors is expected to be small or negligible, the use
of quasicircular waveform models for testing GR may be safe when analyzing a
small number of events. However, as the catalog size of GW detections
increases, more stringent bounds on GR deviations can be placed by combining
information from multiple events. In that case, even small systematic biases
may become significant. We apply the approach of hierarchical Bayesian
inference to model the posterior probability distributions of the TGR
parameters inferred from a population of eccentric binary black holes (BBHs).
We assume each TGR parameter value varies across the BBH population according
to a Gaussian distribution. We compute the posterior distributions for these
Gaussian hyperparameters. This is done for LIGO and Cosmic Explorer (CE). We
find that systematic biases from unmodeled eccentricity can signal false GR
violations for both detectors when considering constraints set by a catalog of
events. We also compute the projected bounds on the 10 TGR parameters when
eccentricity is included as a parameter in the waveform model. We find that the
first four dimensionless TGR deformation parameters can be bounded at 90%
confidence to Ξ΄Ο^βiββ²10β2 for LIGO and β²10β3 for CE [where i=(0,1,2,3)]. In comparison to the circular orbit
case, the combined bounds on the TGR parameters worsen by a modest factor of
β²2 when eccentricity is included in the waveform.Comment: 23 pages, 9 figures, 1 tabl