Misinterpreting Spin Precession as Orbital Eccentricity in Gravitational-Wave Signals

TL;DR

This paper investigates whether eccentricity and spin-precession in gravitational-wave signals can be degenerate, particularly for short, massive BBHs. It uses a two-stage approach— a mismatch-based survey with SEOBNRv5EHM and SEOBNRv5PHM, followed by Bayesian parameter estimation with RIFT—to locate and test possible degeneracies. The study finds that the degeneracy is highly localized, with only one of eight precessing injections showing a significant, albeit mild, eccentricity bias ($e_{10}=0.16^{+0.05}_{-0.06}$; $\mathcal{B}_{E/C}=2.64$). The results underscore the need for fully self-consistent waveform models that incorporate both eccentricity and precession, especially for short signals where misidentifications can mislead formation-channel inferences.

Abstract

The increasing scope and breadth of gravitational wave detectors is providing the opportunity to explore new parameters in gravitational-wave astronomy. Eccentricity and spin-precession are two key observables to infer the origin of a gravitational wave (GW) source. The interpretation of GW source parameters can be plagued by degeneracy, such as the well-known degeneracy between mass and spin. As the field has explored new parameters, questions have been raised about possible degeneracies between eccentricity and spin-precession. Although some state-of-the-art models now include these effects individually, models that incorporate spin-precession and eccentricity are only in their infancy. Until models faithfully cover the complete parameter space of compact binary coalescence, our ability to correctly measure the source parameters and infer the formation of the binary is compromised. Here, we present a study of the distinguishability of these two key parameters. Our work finds that there is indeed a degeneracy between eccentricity and spin-precession; however, it is a highly localized effect. We find that the misidentified eccentricity estimates get worse as the signal gets shorter. Additionally, this misidentification is highly sensitive to the inclination angle of the source system. We provide quantifiable estimates of the potency of this degeneracy in addition to identifying some of the regions of parameter space where this degeneracy exists.

Figures (12)

• Figure 1: Overlay of an eccentric aligned-spin waveform (orange) and a quasi-circular precessing waveform (blue), illustrating qualitatively similar waveform features.
• Figure 2: Example signals from precessing systems with $q=1$ and total masses $200\,M_\odot$, $250\,M_\odot$ and $300\,M_\odot$. These same signals are used as injections for studying eccentric inferences across total mass in Sec. \ref{['sec:PE']}. Left: The signals in frequency domain, as compared to the amplitude spectral density used in this study. Center: The signals in time domain, with the shaded portions outside the sensitive band of the detectors. Right: The effective in-band cycles for a detector sensitivity beginning at $20$ Hz, highlighting the reduction in cycles with increasing total mass and the growing dominance of the merger–ringdown regime.
• Figure 3: Configuration of the mismatch suites. The left grid shows mismatches between precessing and non-spinning eccentric systems, while the right grid shows mismatches between precessing and aligned-spin eccentric systems with $\chi_{1,z}=\chi_{2,z}=0.5$. The total mass $M_{\mathrm{tot}}$ is given in units of $M_{\odot}$, and the mass ratio is defined as $q=m_{1}/m_{2}$, where $m_{1}\geq m_{2}$. The check symbol indicates the regions of parameter space where an eccentric system i.e. $e_\mathrm{10} > 0.05$ was found to be the best match to a precessing system
• Figure 4: This figure presents some results from the mismatch study. The plots show mismatch as a function of eccentricity for the various values of in-plane spins of the precessing system. We show 2 of the 9 ($M_{\text{tot}},\:q$) combinations here: $M_{\text{tot}}=200M_{\odot},\:q=2$ (top panel) and $M_{\text{tot}}=250M_{\odot},\:q=1$ (bottom panel). The two columns correspond to the different suite of mismatches, precessing systems versus A) non-spinning eccentric systems (left) and B) aligned-spin eccentric systems (right).
• Figure 5: This plot shows the recovered marginalized posterior KDEs for $e_\mathrm{10}$ for each of our precessing injections.