Fusing numerical relativity and deep learning to detect higher-order multipole waveforms from eccentric binary black hole mergers.

Motivated by recent electromagnetic observations which suggest the existence of compact binary populations in the Galactic Cluster M22 [Nature 490, 71 (2012)] and in the Galactic center [Nature 556, 70 (2018)], and considering that eccentricity provides one of the cleanest signatures to identify these compact binary populations, in this article we study the importance of including higher-order waveform multipoles to enable gravitational wave observations of eccentric binary black hole mergers. Using a catalog of Einstein Toolkit numerical relativity simulations that describe eccentric, non-spinning black holes mergers with mass-ratios $1\leq q \leq 10$, and eccentricities $e_0\lesssim0.2$ ten cycles before merger, we determine the mass-ratio, eccentricity and binary inclination angle combinations that maximize the contribution of the higher-order waveform multipoles $(\ell, \, |m|)= \{(2,\,2),\, (2,\,1),\, (3,\,3),\, (3,\,2), \, (3,\,1),\, (4,\,4),\,(4,\,3),$ $(4,\,2),\,(4,\,1)\}$ for gravitational wave detection. We then explore the implications of these results in the context of stellar mass black holes that are detectable by LIGO detectors at design sensitivity, and show that compared to models that only include the $(\ell, \, |m|)=(2,\,2)$ mode, the inclusion of higher-order waveform multipoles can increase the signal-to-noise ratio of eccentric binary black hole mergers by up to $\sim45\%$ for mass-ratio binaries $q\leq10$. Furthermore, building upon our pioneering deep learning work [George & Huerta Phys. Rev. D 97, 044039 (2018); George & Huerta Physics Letters B 778, 64 (2018)], we show for the first time that machine learning can accurately reconstruct higher-order waveform multipole signals from eccentric binary black hole mergers embedded in real LIGO data.