Eccentricity matters: Impact of eccentricity on inferred binary black hole populations

Gravitational waves (GWs) emanating from binary black holes (BBHs) encode vital information about their sources, enabling us to infer critical properties of the BBH population across the Universe, including mass, spin, and eccentricity distribution. While the masses and spins of binary components are already recognized for their insights into formation, eccentricity stands out as a distinct and quantifiable indicator of formation and evolution. However, despite its significance, eccentricity is notably absent from most parameter estimation analyses associated with GW signals. To evaluate the precision with which the eccentricity distribution can be deduced, we generated two synthetic populations of eccentric binary black holes (EBBHs) characterized by nonspinning, nonprecessing dynamics, and mass ranges between $10$ and $50{M}_{\ensuremath{\bigodot}}$. This was achieved using an eccentric power law model, encompassing 100 events with eccentricity distributions set at ${\ensuremath{\sigma}}_{\ensuremath{\epsilon}}=0.05$ and ${\ensuremath{\sigma}}_{\ensuremath{\epsilon}}=0.15$. This synthetic EBBH ensemble contrasts against a circular binary black holes collection to discern how parameter inferences would vary without eccentricity. Employing Markov chain Monte Carlo techniques, we constrained model parameters, including the event rate ($\mathcal{R}$), minimum mass (${m}_{\mathrm{min}}$), maximum mass (${m}_{\mathrm{max}}$), and ${\ensuremath{\sigma}}_{\ensuremath{\epsilon}}$ which is uncertainty in eccentricity. Our analysis demonstrates that eccentric population inference can identify the signatures of even modest eccentricity distribution. In addition, our study shows that an analysis neglecting eccentricity may draw biased conclusions of population inference for the larger values of eccentricity distribution.