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

Surrogate modeling of eccentric binary black hole waveforms has remained challenging. The complicated morphology of these waveforms due to the eccentric orbital timescale variations makes it difficult to construct accurate and efficient surrogate models, especially for waveforms long enough to cover the sensitivity band of the 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 the intermediate eccentric surrogate data pieces by modeling them in terms of an angular orbital element called the mean anomaly, instead of time. We show that this novel parameterization yields an order of magnitude fewer surrogate basis functions than using the contemporary parameterization in terms of time. We show that variations in surrogate data-pieces across parameter space become much more regular when expressed in terms of the instantaneous waveform eccentricity and mean anomaly, greatly easing their parameter-space fitting. The methods presented in this work make it feasible to build long-duration eccentric surrogates for the current as well as future third-generation gravitational wave detectors.