A complete waveform comparison of post-Newtonian and numerical relativity in eccentric orbits

Abstract: This study presents a thorough comparative analysis between post-Newtonian (PN) and numerically relativistic (NR) waveforms in eccentric orbits, covering nonspinning and spin-aligned configurations. The comparison examines frequency, amplitude, and phase characteristics of various harmonic modes, such as 22, 21, 33, 32, 44, 43, and 55 modes. The study utilizes eccentric PN waveforms based on 3PN quasi-Keplerian parameterization with 3PN radiative reaction, surpassing Newtonian quadrupole moment with higher-order moments. NR waveforms from RIT and SXS catalogs span mass ratios from 1/4 to 1, eccentricities up to 0.45, and durations exceeding $17000M$ across nonspinning and spin-aligned configurations. Focusing on the 22 mode, frequency comparisons between quadrupole and higher-order moments of $\Psi_4^{22}$ and $h^{22}$ were conducted. Amplitude comparisons revealed superior accuracy in quadrupole moments of $\Psi_4^{22}$. Analysis of total 180 sets of eccentric waveforms showed increasing fitting residuals with rising eccentricity, correlating with smaller mass ratios. Comparisons of initial eccentricity from PN fitting, 3PN quasi-Keplerian parameterization, and RIT/SXS catalogs revealed alignment discrepancies. Frequency, phase, and amplitude comparisons of 22 modes showed consistent inspiral behavior between PN and NR, with divergences near merger for nonspinning PN and pre-200M for spin-aligned PN.