Including higher order modes in quadrupolar eccentric numerical relativity surrogate using universal eccentric modulation functions

gwNRHME is a framework that converts multi-modal (i.e., containing several spherical harmonic modes) quasi-circular waveforms into their eccentric counterparts, provided the quadrupolar eccentric mode is known, by exploiting universal eccentric modulation functions. Leveraging this framework, we combine the quasi-circular NR surrogate model \texttt{NRHybSur3dq8} with the quadrupolar, non-spinning, eccentric surrogateNRSurE_q4NoSpin_22 to construct a multi-modal, non-spinning, eccentric model, denoted as gwNRHME NRSur q4, which includes nine modes: (2,{1,2}, (3,{1,2,3}), (4,{2,3,4}), and (5,5). When compared against 157 eccentric SXS NR waveforms, gwNRHME NRSur q4 achieves median frequency-domain mismatches (computed using the Advanced LIGO design sensitivity) of 10^-5. To demonstrate the modularity of the framework, we further combine NRSurE_q4NoSpin_22 with effective-one-body (EOB) models SEOBNRv5HM and TEOBResumS in their non-spinning limits, yielding NR-faithful eccentric waveforms with median mismatches of 10^-4 and 10^-3, respectively. When extrapolated to include (aligned-)spins, gwNRHME NRSur q4 recovers NR data with median mismatches of 10^-3. Finally, we provide both a surrogate model, gwEccEvolve_q4NoSpin_Sur, and an analytical model, gwEccEvNSv2, for the eccentricity evolution up to 2M before merger, based on eccentricity definitions derived from the universal modulation 

functions. The gwNRHME framework is publicly available through the gwModels package, and the resulting waveform models will be released via the gwsurrogate package.