Eccentricity evolution consistency test to distinguish eccentric gravitational-wave signals from eccentricity mimickers

TL;DR

This work tackles the challenge of distinguishing truly eccentric gravitational-wave signals from eccentricity mimickers that arise from other physical or beyond-GR effects. It introduces the eccentricity Evolution Consistency Test (EECT), which tests GR-consistent eccentric evolution by comparing eccentricities recovered at a low reference frequency to those inferred at higher frequencies after evolving under GR, thereby avoiding exhaustive model comparisons. In a proof-of-concept with zero noise and an O4-like detector network, EECT rejects mimickers with ≥68% confidence while preserving genuine eccentric signals, across multiple mimicker scenarios including microlensing, LOSA, massive graviton, and dipole radiation. The approach leverages a 3PN GR eccentricity evolution and Bayesian parameter estimation to provide a robust, scalable discriminator for eccentricity in current and future GW observations. Its practical relevance grows with improved bandwidth and sensitivity, and future work will extend EECT to higher harmonics, spin effects, and more complex detector networks.

Abstract

Eccentric compact binary coalescences (CBCs) are expected to be observed in current and future gravitational-wave (GW) detector networks. However, it has been recently pointed out that a number of other physical and beyond-GR effects, could imitate, or be mimicked by, eccentric CBCs. In this work, we propose a conceptually simple but powerful method to directly confirm or reject the eccentric hypothesis, without needing to compare the hypothesis with the plethora of other possible hypotheses. The key idea is that while spurious non-zero values of eccentricity, at some reference frequency, could be acquired when a non-eccentric CBC with additional physical/beyond-GR effects is recovered with an eccentric CBC waveform model, the {\itshape evolution} of eccentricity with frequency will in general not be mimicked. We accordingly formulate an eccentricity evolution consistency test (EECT). The method compares the eccentricity recovered at some low frequency value (e.g, $10$ Hz), evolved to higher frequencies assuming GR, with eccentricities recovered at those same higher frequencies. Discrepancy between the two eccentricities at any reference frequency would violate EECT and indicate the presence of a mimicker. As a proof of concept, assuming a few eccentric CBC systems, quasi-circular CBCs with additional physics mimicking eccentricity, and an O4-like three-detector-network configuration, we demonstrate that our proposed method is indeed able to reject mimickers at $\geq 68\%$ confidence, while ensuring that truly eccentric CBCs satisfy EECT.

Figures (6)

• Figure 1: Top: Violins representing eccentricity deviation $\delta_{e}$ are plotted as a function of GW frequency for null-test wherein we inject eccentric GW signal using TaylorF2Ecc waveform model in zero-noise and recover the binary parameters of the GW signal using the same waveform model. Bottom: Individual GR-predicted (left-half) and observed (right-half) eccentricity (i.e, $e_{\rm GR}$ and $e_{\rm obs}$) half-violins are plotted as a function of GW frequency. Left, middle and right panels in each row correspond to binaries with parameters ($m_1=5\,M_{\odot},\,m_2= 2.5\, {M_{\odot}}$, $d_{\rm L}= 100$ Mpc, $e_{10}=0.20$), ($m_1=18\,M_{\odot},\,m_2= 15\, {M_{\odot}}$, $d_{\rm L}= 400$ Mpc, $e_{10}=0.16$) and ($m_1=36\,M_{\odot},\,m_2= 29\, {M_{\odot}}$, $d_{\rm L}= 1000$ Mpc, $e_{10}=0.27$), respectively.
• Figure 2: Violins representing eccentricity deviation $\delta_{e}$ are plotted as a function of GW frequency for the case of a non-spinning quasi-circular microlensed CBC injected in zero-noise. The microlensing injection parameters, i.e., redshifted lens-mass $M_{\rm lz}$ and dimensionless impact parameter $y$ are chosen to be $300\, {M_{\odot}}$ and $0.1$, respectively. Here top and bottom rows correspond to binary of total mass $33\, {M_{\odot}}$ (with mass ratio $q= 0.83$) and GW150914-like system of total mass $65\, {M_{\odot}}$ (with mass ratio $q= 0.805$), respectively. The left and right columns correspond to luminosity distances of $400\, {\rm Mpc}$ and $1\, {\rm Gpc}$, respectively. In all cases, EECT is found to be violated at $\geq 68\%$ beyond a reference frequency.
• Figure 3: Same as Figure \ref{['fig: Mcl_diff_post']} except that here individual GR-predicted ($e_{\rm GR}$, left-half) and observed ($e_{\rm obs}$, right-half) eccentricity half-violins are plotted as a function of GW frequency. The increasing divergence between the Theory and Observed posteriors with increasing frequency is a tell-tale sign that EECT is being violated in the presence of a mimicker.
• Figure 4: Violins representing eccentricity deviation $\delta_{e}$ are plotted against GW frequency for the case of non-spinning quasi-circular zero-noise injection corrected for LOSA effect. CBC system has component masses ($5,\,2.5\, M_{\odot}$) with center of mass having LOSA parameter $a/c = - 2.25 \times 10^{-4}\, \rm s^{-1}$. Left, middle and right panels correspond to the systems situated at luminosity distances of $40\, \rm Mpc$, $80\, \rm Mpc$ and $200\, \rm Mpc$, respectively. In all cases, violation of EECT is clearly observed for $f \geq 25$ Hz, at $\geq 68\%$ confidence.
• Figure 5: Violins representing eccentricity deviation $\delta_{e}$ are plotted against GW frequency for the case of non-spinning quasi-circular zero-noise injection corrected for massive graviton effect. CBC has component masses ($60,\,55\, M_{\odot}$) with massive graviton parameter $A_0 = - 10^{-45}\, \rm eV^{2}$. The CBC is located at a luminosity distance of $1.8\, \rm Gpc$. At reference frequency $40$Hz, $\delta_e$ is found to be inconsistent with zero at $\geq 68\%$ confidence.