# Persistence of post-Newtonian amplitude structure in binary black hole mergers

## TL;DR

This study examines the persistence of post-Newtonian amplitude structures in binary black hole mergers, using numerical relativity data to develop polynomial fits that model mode amplitudes from inspiral to postmerger.

## Contribution

It introduces polynomial fitting methods that extend post-Newtonian amplitude models through merger, improving waveform modeling accuracy in strong gravitational fields.

## Key findings

- PN dependence persists in certain modes throughout merger.
- Polynomial fits of degree ≤ 3 effectively model amplitude behavior near merger.
- Discrepancies across catalogs highlight resolution effects.

## Abstract

We analyze the spherical harmonic mode amplitudes of quasicircular, nonprecessing binary black hole mergers using 275 numerical relativity 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 postmerger ($t = 40M$). 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. Although the fits cannot be fully interpreted within the PN formalism near merger, low-degree polynomial corrections to the PN amplitude Ans\"atze can capture strong-field behavior, enabling closed-form and efficient modeling of waveform amplitudes in this regime.