Biased parameter inference of eccentric, spin-precessing binary black holes

TL;DR

This work quantifies how orbital eccentricity and spin precession jointly bias gravitational-wave parameter estimation for binary black holes. By injecting eccentric and/or precessing signals with NR hybrids and SpEC NR simulations and performing Bayesian inference against both eccentric and quasi-circular waveform models, the study reveals that parameters such as the chirp mass $\mathcal{M}$ and the spin-precession parameter $χ_p$ become increasingly biased as eccentricity grows. Bayes factors $\mathcal{B}_{E/C}$ robustly favor eccentric, spin-aligned models when eccentricity is present, underscoring a degeneracy between eccentricity and spin precession and the need for inspiral-merger-ringdown waveforms that fully incorporate both effects. The results highlight the importance of developing ready-to-use eccentric, spin-precessing waveform families to achieve unbiased parameter estimation and reliable astrophysical inferences about BBH formation channels and population properties.

Abstract

While the majority of gravitational wave (GW) events observed by the LIGO and Virgo detectors are consistent with mergers of binary black holes (BBHs) on quasi-circular orbits, some events are also consistent with non-zero orbital eccentricity, indicating that the binaries could have formed via dynamical interactions. Moreover, there may be GW events which show support for spin-precession, eccentricity, or both. In this work, we study the interplay of spins and eccentricity on the parameter estimation of GW signals from BBH mergers. We inject eccentric signals with no spins, aligned spins, and precessing spins using hybrids, TEOBResumS-DALI, and new Numerical Relativity (NR) simulations, respectively, and study the biases in the posteriors of source parameters when these signals are recovered with a quasi-circular precessing-spin waveform model, as opposed to an aligned-spin eccentric waveform model. We find significant biases in the source parameters, such as chirp mass and spin-precession ($χ_p$), when signals from highly-eccentric BBHs are recovered with a quasi-circular waveform model. Moreover, we find that for signals with both eccentricity and spin-precession effects, Bayes factor calculations confirm that an eccentric, aligned-spin model is preferred over a quasi-circular precessing-spin model. Our study highlights the complex nature of GW signals from eccentric, precessing-spin binaries and the need for readily usable inspiral-merger-ringdown eccentric, spin-precessing waveform models for unbiased parameter estimation.

Figures (6)

• Figure 1: The recovery of various parameters of non-spinning hybrid injections (see Sec. \ref{['subsec:NR_hyb']}). The colours red, blue, and green indicate mass ratios 1, 2, and 3, respectively. The horizontal dashed lines in the top two plots denote injected values for the respective parameters. The small black lines inside the violins mark the median values of the posteriors, and the small white lines denote the 90% credible intervals. Top: Recovery of chirp mass ($\mathcal{M}_c$) parameter with IMRPhenomXPPratten:2020ceb waveform in precessing-spin configuration. Middle: Recovery of precessing spin parameter ($\chi_p$) when the injections are recovered with IMRPhenomXP in precessing-spin configuration. Bottom: Recovery of eccentricity ($e_{20}$) parameter at a reference frequency of 20 Hz when the injected signals are recovered with TaylorF2Ecc in non-spinning eccentric configuration. The bottom and top labels on the horizontal axis list the injected values of eccentricity ($e_{20}$) and mean anomaly ($l_{20}$).
• Figure 2: Recovery of the chirp mass ($\mathcal{M}_c$) parameter when injections are aligned-spin eccentric signals, generated using the TEOBResumS-DALI waveform model. The colours red, blue, and green indicate mass ratios $1.25, 2$, and $3$, respectively. The horizontal dashed lines denote injected values for the respective mass ratio cases. The small black lines inside the violins mark the median values of the posteriors, and the small white lines denote the 90% credible intervals. The injected signals are recovered with the IMRPhenomXP waveform model in the precessing-spin configuration.
• Figure 3: Recovery of spin-precession parameter ($\chi_p$) when injections are aligned-spin eccentric signals generated using the TEOBResumS-DALI waveform model. The colours red, blue, and green indicate mass ratios 1.25, 2, and 3, respectively. The horizontal dashed line denotes the injected value. The small black lines inside the violins mark the median values of the posteriors, and the small white lines denote the 90% credible intervals. The injections are recovered with IMRPhenomXP in the precessing-spin configuration.
• Figure 4: Aligned spin injections with TEOBResumS-DALI. Bayes factors for the eccentric aligned-spin recovery with TaylorF2Ecc over the quasi-circular precessing-spin recovery with IMRPhenomXP. The IMRPhenomXP analysis is truncated at 110 Hz to facilitate a fair comparison in the calculation of the Bayes factors against TaylorF2Ecc.
• Figure 5: Figures show the recovery of the spin-precession parameter ($\chi_p$) and eccentricity ($e_{20}$) when the injections are using the NR simulations described in Sec. \ref{['subsec:NR_sims']} and Table \ref{['table:ICTS_sims']}. The small black lines inside the violins mark the median values of the posteriors, and the small white lines denote the 90% credible intervals. Left: Recovery of the spin-precession parameter ($\chi_p$) when the injections are recovered with IMRPhenomXP in quasi-circular precessing-spin configuration. The posteriors are arranged in ascending order of injected eccentricities ($e_{20}$) at a reference frequency of $20$ Hz calculated using the gw_eccentricity package. The injected values of $\chi_p$ are shown as red stars on the plot. Right: Recovery of the eccentricity parameter ($e_{20}$) at a reference frequency of $20$Hz when the injection signals are analysed with IMRESIGMA in aligned-spin eccentric configuration. The posteriors are arranged in ascending order of injected $\chi_p$ values. The red stars denote the injected value of the eccentricities ($e_{20}$). As the definition of eccentricity is different in IMRESIGMA waveform as opposed to the value calculated using the gw_eccentricity package for the injections, the posteriors for eccentricity have been converted to the values obtained from the gw_eccentricity package for IMRESIGMA waveform for a fair comparison with the injected values.