Systematic bias on parameterized tests of general relativity due to neglect of orbital eccentricity

TL;DR

Neglecting residual orbital eccentricity in gravitational-wave tests of general relativity can introduce significant systematic biases, especially for future detectors, highlighting the need to include eccentricity effects in waveform models.

Contribution

This study quantifies the systematic biases caused by ignoring orbital eccentricity in parametrized tests of GR with gravitational waves.

Findings

Biases become comparable to statistical errors at moderate eccentricities.

Lower eccentricity thresholds cause biases in third-generation detectors.

Inclusion of eccentricity effects is crucial for accurate gravitational-wave analysis.

Abstract

Gravitational-wave observations provide a unique opportunity to test general relativity (GR) in the strong-field and highly dynamical regime of the theory. Parametrized tests of GR are one well-known approach for quantifying violations of GR. This approach constrains deviations in the coefficients of the post-Newtonian phasing formula, which describes the gravitational-wave phase evolution of a compact binary as it inspirals. Current bounds from this test using LIGO/Virgo observations assume that binaries are circularized by the time they enter the detector frequency band. Here, we investigate the impact of residual binary eccentricity on the parametrized tests. We study the systematic biases in the parameter bounds when a phasing based on the circular orbit assumption is employed for a system that has some small residual eccentricity. We find that a systematic bias (for example, on the leading Newtonian deformation parameter) becomes comparable to the statistical errors for even moderate eccentricities of $\sim 0.04$ at $10$ Hz in LIGO/Virgo band for binary black holes, and $\sim 0.008$ for binary neutron stars. This happens at even lower values of orbital eccentricity in the frequency band of third-generation (3G) detectors like Cosmic Explorer ($\sim 0.005$ at $10$ Hz for binary black holes and $\sim 0.002$ for binary neutron stars). These results demonstrate that incorporating physical effects like eccentricity in waveform models is important for accurately extracting science results from future detectors.