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

Gravitational waves (GW), emanating from binary black holes (BBH), encode vital information about their source. GW signals enable us to deduce key 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. Yet, despite its significance, eccentricity is notably absent from most parameter estimation (PE) 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 (EBBH) characterized by non-spinning, non-precessing dynamics and mass ranges between $10 M_\odot$ and $50 M_\odot$. This was achieved using an eccentric power law model, encompassing $100$ events with eccentricity distributions set at $\sigma_\epsilon = 0.05$ and $\sigma_\epsilon = 0.15$. This synthetic EBBH ensemble was contrasted against a circular binary black holes (CBBH) collection to discern how parameter inferences would vary without eccentricity. Employing Markov Chain Monte Carlo (MCMC) techniques, we constrained vital model parameters, including the event rate ($\mathcal{R}$), mass distribution, minimum mass ($m_{min}$), maximum mass ($m_{max}$), and the eccentricity distribution ($\sigma_\epsilon$). Our analysis demonstrates that eccentric population inference can identify the signatures of even modest eccentricities, given sufficiently many events. Conversely, our study shows that an analysis neglecting eccentricity may draw biased conclusions about population parameters for populations with the optimistic values of eccentricity distribution used in our research.