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

Abstract

Gravitational-wave observations provide a unique opportunity to test General Relativity (GR) in the strong-field and highly-dynamical regime of the theory. Parameterized tests of GR are one well-known approach for quantifying violations of GR. This approach constrains deviations in the coefficients of the post-Newtonian (PN) 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 parameterized 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 ∼ 0.04 at 10 Hz in LIGO/Virgo band. This happens at an even lower value of orbital eccentricity (∼ 0.005 at 10 Hz) in the frequency band of third-generation (3G) detectors like Cosmic Explorer. These results demonstrate that incorporating physical effects like eccentricity in waveform models is important for accurately extracting science results from future detectors.

Systematic bias on the inspiral-merger-ringdown consistency test due to neglect of orbital eccentricity

“…The parameterized test then attempts to constrain the size of those perturbations (with zero perturbation corresponding to GR). In [54] we found that the systematic bias on parameterized deviation coefficients become significant at e 0 ∼ 0.04 at 10 Hz in the LIGO band and at e 0 ∼ 0.005 at 10 Hz in the CE band.…”

“…(2.13) is the leading-order [i.e., O(e 2 0 )] eccentric correction to the inspiral stationary phase approximation (SPA) phasing [60] discussed earlier. See [49,54] for more details and applications of systematic errors arising from eccentric corrections. Note that the eccentric corrections ∆Ψ that induce systematic parameter errors in Eq.…”

“…In Ref. [54] we studied the effect of neglecting the orbital eccentricity on parameterized tests of GR. That test considers only the inspiral phase of the binary evolution in the regime where a post-Newtonian (PN) expansion of the GW phase is valid.…”

New Avenue for Accurate Analytical Waveforms and Fluxes for Eccentric Compact Binaries

“…The accurate computation of the gravitational waves (GW) from eccentric compact binary mergers has recently prompted a vibrant activity by the analytical and numerical relativity community [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. A main goal of this programme is to provide GW templates for binaries on generic orbits to be used in the next scientific observational runs of the LIGO-Virgo-Kagra (LVK) collaboration [19][20][21] and in the future LISA observations [26][27][28].…”