Chase Orbits, not Time: A Scalable Paradigm for Long-Duration Eccentric Gravitational-Wave Surrogates

Abstract

Orbital eccentricity is a key tracer of the astrophysical origins of compact binaries. Yet it remains absent from routine LIGO-Virgo-KAGRA analyses, in part because of the prohibitive computational cost of generating eccentric template waveforms. The complicated morphology of these waveforms due to the eccentric orbital timescale variations makes it difficult to construct their accurate and efficient surrogate models, especially for waveforms long enough to comprehensively cover the sensitivity bands of current ground-based gravitational-wave detectors. We present a novel and scalable surrogate building technique which makes surrogate modeling of long-duration eccentric binary black hole waveforms both feasible and highly efficient. The technique aims to simplify the harmonic content of intermediate eccentric waveform data-pieces by modeling them in terms of an angular orbital element called the mean anomaly, instead of time. We show that this parameterization yields much more compressed surrogates than the standard time-based parameterizations. We also significantly simplify variations in waveform data-pieces across the parameter space by expressing them in terms of the instantaneous orbital eccentricity and mean anomaly to ease their parametric fitting. Building on these developments, we construct InspiralESIGMASur: a $2.77 \times 10^6M$ (850-1250 orbits) long non-spinning surrogate for the inspiral-only eccentric waveform model InspiralESIGMA [K. Paul et al., Phys. Rev. D 111, 084074 (2025)]. The methods presented in this work make it feasible to build long-duration eccentric surrogates for current as well as future third-generation gravitational-wave detectors.