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

    Tousif Islam1,*, Adhrit Ravichandran2, Peter James Nee3, Scott E. Field2, Vijay Varma2, Harald P. Pfeiffer3, Andrea Ceja4, Noora Ghadiri4,5, Lawrence E. Kidder6 et al.

    Prayush Kumar7, Marlo Morales4, Abhishek Ravishankar2, Antoni Ramos-Buades8, Katie Rink9, Hannes R. Rüter10, Mark A. Scheel11, Md Arif Shaikh12, and Daniel Tellez4

    • *Contact author: tousifislam@ucsb.edu

    Phys. Rev. D 114, 044078 – Published 24 August, 2026

    DOI: https://doi.org/10.1103/fq4r-rt3z

    Abstract

    gwNRHME is a framework that converts multimodal (i.e., containing several spherical harmonic modes) quasicircular waveforms into their eccentric counterparts, provided the quadrupolar eccentric mode is known, by exploiting universal eccentric modulation functions. Leveraging this framework, we combine the quasicircular numerical relativity (NR) surrogate model NRHybSur3dq8 with the quadrupolar, nonspinning, eccentric surrogate NRSurE_q4NoSpin_22 to construct a multimodal, nonspinning, 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 156 eccentric Simulating eXtreme Spacetimes NR waveforms, gwNRHME_NRSur_q4 achieves median frequency-domain mismatches (computed using the Advanced LIGO design sensitivity) of ∼9×10−5, with a standard deviation of ∼2×10−4. To demonstrate the modularity of the framework, we further combine NRSurE_q4NoSpin_22 with effective-one-body models SEOBNRv5HM and TEOBResumS-Dali in their nonspinning limits, yielding eccentric waveforms with median mismatches of ∼2×10−4 and ∼10−3, respectively, with standard deviation of ∼2×10−3 and ∼2×10−2, respectively. 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.

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