Straightforward mode hierarchy in eccentric binary black hole mergers and associated waveform model

TL;DR

This paper introduces a simplified waveform model for eccentric binary black hole mergers that leverages a universal eccentric modulation, significantly reducing modeling complexity and achieving high accuracy compared to numerical simulations.

Contribution

The authors present a universal eccentric modulation model that converts quasi-circular waveforms into eccentric ones, simplifying the modeling of eccentric BBH mergers.

Findings

Model mismatches are mostly around 10^{-3}

The model is comparable to numerical errors in simulations

The approach reduces complexity by using a single modulation time-series

Abstract

Utilizing publicly available non-spinning eccentric binary black hole (BBH) merger simulations (\href{https://data.black-holes.org/waveforms/catalog.html}{https://data.black-holes.org/waveforms/catalog.html}) from the SXS collaboration~\cite{Hinder:2017sxy}, we present convincing evidence that the waveform phenomenology in eccentric BBH mergers is significantly simpler than previously thought. We find that the eccentric modulations in the amplitudes, phases, and frequencies in different spherical harmonic modes are all related and can be modeled using a single time series modulation. Using this universal eccentric modulation, we provide a model named \texttt{gwNRHME} to seamlessly convert a multi-modal (i.e with several spherical harmonic modes) quasi-circular waveform into multi-modal eccentric waveform if the quadrupolar eccentric waveform is known. This reduces the modelling complexity of eccentric BBH mergers drastically as we now have to model only a single eccentric modulation time-series instead of modelling the effect of eccentricity in all modes. When compared with the NR simulations, our model mismatches are mostly $\sim 10^{-3}$ and are comparable to the numerical errors in the NR simulations. Our method is modular and can be readily added to any quadrupolar non-spinning eccentric waveform model. We make our model publicly available through the \texttt{gwModels} (\href{https://github.com/tousifislam/gwModels}{https://github.com/tousifislam/gwModels}) waveform package.