The influence of the mean anomaly on the dynamical quantities of binary black hole mergers in eccentric orbits

In studies of binary black hole (BBH) mergers in eccentric orbits, the mean anomaly, traditionally regarded as less significant than eccentricity, has been thought to encode only the orbital phase, leading to the assumption that it exerts minimal influence on the dynamics of eccentric mergers. In a previous investigation, we identified consistent oscillations in dynamical quantities peak luminosity $L_{\text{peak}}$, remnant mass $M_{\text{rem}}$, spin $α_{\text{rem}}$, and recoil velocity $V_{\text{rem}}$ in relation to the initial eccentricity $e_0$. These oscillations are associated with integer orbital cycles within a phenomenological framework. In this paper, we aim to explore the underlying physical nature of these oscillations through gravitational waveforms. Our examination of remnant mass and spin reveals that while the initial ADM mass $M_{\mathrm{ADM}}$ and orbital angular momentum $L_0$ exhibit gradual variations with $e_0$, the radiated energy $E_{\text{rad}}$ and angular momentum $L_{\text{rad}}$ display oscillatory patterns akin to those observed in $M_{\text{rem}}$ and $α_{\text{rem}}$. By decomposing the waveforms into three distinct phases inspiral, late inspiral to merger, and ringdown, we demonstrate that these oscillations persist across all phases, suggesting a common origin. Through a comparative analysis of $E_{\text{rad}}$ and $L_{\text{rad}}$ derived from numerical relativity (NR), post-Newtonian (PN) waveforms, and orbital-averaged PN fluxes during the inspiral phase, we identify the initial mean anomaly $l_0$ as the source of the observed oscillations. ...