Persistence of post-Newtonian structure in binary black hole mergers

Abstract: We analyze the spherical harmonic mode amplitudes of quasi-circular, nonprecessing binary black hole mergers using 283 numerical relativity (NR) simulations from the SXS, RIT, and MAYA catalogs. We construct fits using the leading-order post-Newtonian (PN) dependence on intrinsic parameters, replacing the PN velocity with fit coefficients. We compare these to polynomial fits in symmetric mass ratio and spin. We analyze $(\ell, m)$ modes with $\ell \leq 4$ from late inspiral ($t = -500M$ relative to the $(2,2)$ peak) to post-merger ($t = 40M$). For nonspinning systems, the $(2,2)$, $(2,1)$, and $(3,3)$ modes retain the leading-order PN dependence on mass ratio throughout the merger. Higher-order modes deviate from the PN dependence only near and after the merger, where polynomial fits of degree $N \leq 3$ can capture the amplitude behavior up to $40M$. For aligned-spin systems at fixed mass ratio, the $(2,1)$ mode retains its PN spin dependence, while the $(3,2)$ and $(4,3)$ modes exhibit a quadratic spin dependence near merger. The PN-inspired fits lose accuracy with increasing mass ratio, particularly near merger. Results broadly agree across catalogs, though discrepancies appear in the $(3,1)$, $(4,2)$, and $(4,1)$ modes, likely from resolution differences. Our results clarify the extent to which PN structure persists in mode amplitudes and show that simple polynomial models can capture strong-field behavior near merger, enabling efficient and interpretable waveform modeling in this regime.