Characterizing the effect of eccentricity on the dynamics of binary black hole mergers in numerical relativity

Many articles have partially studied the configuration of eccentric orbital binary black hole (BBH) mergers. However, there is a scarcity of systematic and comprehensive research on the effect of eccentricity on BBH dynamics. Thanks to the rich and numerous numerical relativistic simulations of eccentric orbital BBH mergers from Rochester Institute of Technology catalog, this paper aims to investigate the impact of initial eccentricity e0 on various dynamic quantities such as merger time Tmerger, peak luminosity Lpeak of gravitational waves, recoil velocity Vf, mass Mf, and spin alpha f of merger remnants. We cover configurations of no spin, spin alignment, and spin precession, as well as a broad parameter space of mass ratio ranging from 1/32 to 1 and initial eccentricity from 0 to 1. For nonspinning BBH with an initial coordinate separation of 11.3M (M is the total mass of BBH), we make the first discovery of a ubiquitous oscillation in the relationship between dynamic quantities Lpeak, Vf, Mf, alpha f, and initial eccentricity e0. Additionally, at 24.6M, we observe the same oscillation phenomenon in the case of mass ratio q 1/4 1 but do not see it in other mass ratios, suggesting that this oscillation will be evident in numerical simulations with sufficiently dense initial eccentricity. By associating the integer numbers of the orbital cycle of Norbits with the peaks and valleys observed in the curves depicting the relationship between the dynamic quantities and the initial eccentricity, we reveal the significant oscillatory behavior attributed to orbital transitions. This discovery sheds light on the presence of additional orbital transitions in eccentric BBH mergers, extending beyond the widely recognized transition from inspiral to plunge. We perform an analysis to understand the different behaviors exhibited by the dynamic quantities and attribute them to variations in the calculation formulas. Furthermore, we demonstrate that finely adjusting the initial eccentricity can lead to the remnant black hole becoming a Schwarzschild black hole in the case of spin alignment. In a comprehensive analysis that surpasses previous studies by encompassing cases of no spin, spin alignment, and spin precession, we reveal consistent variations in the correlation between dynamic quantities and initial eccentricity, regardless of the presence of spin. This discovery underscores the universality of the impact of eccentricity on BBH dynamics and carries profound implications for astrophysical research.