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

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 nonprecessing 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 eGW150914 gw; 10 Hz 1/4 0.08+0.09 -0.06 , eGW151226 gw; 20 Hz 1/4 0.04+0.05 -0.04 , and eGW190521 gw;5.5 Hz 1/4 0.15+0.12 -0.12 .