Bayesian inference of binary black holes with inspiral-merger-ringdown waveforms using two eccentric parameters

TL;DR

This study introduces a Bayesian inference method for eccentric binary black hole waveforms using two eccentric parameters, improving parameter estimation accuracy and assessing eccentricity in real GW signals.

Contribution

It is the first to incorporate two eccentric parameters in Bayesian inference for inspiral-merger-ringdown waveforms, enhancing sampling efficiency and bias assessment.

Findings

New parametrization improves sampling efficiency.

Neglecting relativistic anomaly causes biases in parameter estimation.

No significant eccentricity detected in analyzed GW signals.

Abstract

Orbital eccentricity is a crucial physical effect to unveil the origin of compact-object binaries detected by ground- and spaced-based gravitational-wave (GW) observatories. Here, we perform for the first time a Bayesian inference study of inspiral-merger-ringdown eccentric waveforms for binary black holes with non-precessing spins using two (instead of one) eccentric parameters: eccentricity and relativistic anomaly. We employ for our study the multipolar effective-one-body (EOB) waveform model SEOBNRv4EHM, and use initial conditions such that the eccentric parameters are specified at an orbit-averaged frequency. We show that this new parametrization of the initial conditions leads to a more efficient sampling of the parameter space. We also assess the impact of the relativistic-anomaly parameter by performing mock-signal injections, and we show that neglecting such a parameter can lead to significant biases in several binary parameters. We validate our model with mock-signal injections based on numerical-relativity waveforms, and we demonstrate the ability of the model to accurately recover the injected parameters. Finally, using standard stochastic samplers employed by the LIGO-Virgo-KAGRA Collaboration, we analyze a set of real GW signals observed by the LIGO-Virgo detectors during the first and third runs. We do not find clear evidence of eccentricity in the signals analyzed, more specifically we measure $e^{\text{GW150914}}_{\text{gw, 10Hz}}= 0.08^{+0.09}_{-0.06}$, $e^{\text{GW151226}}_{\text{gw, 20Hz}}= {0.04}^{+0.05}_{-0.04} $, and $e^{\text{GW190521}}_{\text{gw, 5.5Hz}}= 0.15^{+0.12}_{-0.12}$.