Universal phenomenological relations between spherical harmonic modes in nonprecessing eccentric binary black hole merger waveforms

Using publicly available numerical relativity (NR) simulations for nonspinning eccentric binary black hole (BBH) mergers, [Tousif Islam, Straightforward mode hierarchy in eccentric binary black hole mergers and associated waveform model, arXiv:2403.15506.] demonstrated that the eccentricity-induced modulations in the amplitudes and frequencies of different spherical harmonic modes are mutually consistent and can be modeled using a single time series modulation. We extend the validity of the results to all nonprecessing binaries by using 83 NR simulations from the SXS, RIT, and MAYA catalogs for aligned-spin eccentric BBH mergers with mass ratios ranging from $1\ensuremath{\mathbin:}1$ to $1\ensuremath{\mathbin:}4$. Based on these phenomenological relations, we provide a framework named gwnrxhme to compute multimodal eccentric nonprecessing waveforms using two inputs: quadrupolar eccentric waveforms, and the corresponding multimodal quasicircular nonprecessing waveforms. Furthermore, we compute an overall degree of departure in SXS, RIT, and MAYA NR data from these relations and find that SXS NR simulations generally adhere to these relations more strictly than RIT and MAYA data. We also show that these relations can offer a cost-effective way to filter out noisy higher-order spherical harmonic modes extracted from NR data. Our framework is publicly available through the gwmodels package.