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

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.