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

Abstract: \texttt{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 surrogate \texttt{NRSurE_q4NoSpin_22} to construct a multi-modal, non-spinning, eccentric model, denoted as \model{}, which includes nine modes: $(2,{1,2})$, $(3,{1,2,3})$, $(4,{2,3,4})$, and $(5,5)$. When compared against 156 eccentric SXS NR waveforms, \model{} achieves median frequency-domain mismatches (computed using the Advanced LIGO design sensitivity) of $\sim 9\times 10<sup>{-5}$, with a standard deviation of $\sim 2 \times 10<sup>{-4}$. To demonstrate the modularity of the framework, we further combine \texttt{NRSurE_q4NoSpin_22} with effective-one-body (EOB) models \texttt{SEOBNRv5HM} and \texttt{TEOBResumS-Dali} in their non-spinning limits, yielding eccentric waveforms with median mismatches of $\sim 2\times10<sup>{-4}$ and $\sim 10<sup>{-3}$, respectively, with standard deviation of $\sim 2 \times 10<sup>{-3}$ and $\sim 2 \times 10<sup>{-2}$ respectively. Finally, we provide both a surrogate model, \texttt{gwEccEvolve_q4NoSpin_Sur}, and an analytical model, \texttt{gwEccEvNSv2}, for the eccentricity evolution up to $2M$ before merger, based on eccentricity definitions derived from the universal modulation functions. The \texttt{gwNRHME} framework is publicly available through the \texttt{gwModels} package, and the resulting waveform models will be released via the \texttt{gwsurrogate} package.