A higher-multipole gravitational waveform model for an eccentric binary black holes based on the effective-one-body-numerical-relativity formalism

We have previously constructed a waveform model, SEOBNRE, for spinning binary black hole moving along eccentric orbit based on effective-one-body (EOB) formalism. In the current paper, we update SEOBNRE waveform model in the following three respects. Firstly, we update the EOB dynamics from SEOBNRv1 to SEOBNRv4. Secondly we properly treat the Schott term which has been ignored in previous SEOBNRE. Thirdly, we construct a new factorized waveform including (l,|m|)=(2,2),(2,1),(3,3),(4,4) modes based on effective-one-body (EOB) formalism, which is valid for spinning binary black holes (BBH) in general equatorial orbit. Following our previous SEOBNRE waveform model, we call our new waveform model SEOBNREHM. The (l,|m|)=(2,2) mode waveform of SEOBNREHM can fit the original SEOBNRv4 waveform very well in the case of a quasi-circular orbit. We have validated SEOBNREHM waveform model through comparing the waveform against the Simulating eXtreme Spacetimes (SXS) catalog. The comparison is done for BBH with total mass in (20,200)M_sun using Advanced LIGO designed sensitivity. For the quasi-circular cases we have compared our (2,2) mode waveforms to the 281 numerical relativity (NR) simulations of BBH along quasi-circular orbits. All of the matching factors are bigger than 98\%. For the elliptical cases, 24 numerical relativity simulations of BBH along an elliptic orbit are used. For each elliptical BBH system, we compare our modeled gravitational polarizations against the NR results for different combinations of the inclination angle, the initial orbit phase and the source localization in the sky. We use the minimal matching factor respect to the inclination angle, the initial orbit phase and the source localization to quantify the performance of the higher modes waveform. We found that after introducing the higher modes, the minimum of the minimal matching factor among the 24 tested elliptical BBHs increases from 90\% to 98\%. Our SEOBNREHM waveform model can match all tested 305 SXS waveforms better than 98\% including highly spinning ($\chi=0.99$) BBH, highly eccentric ($e\approx0.6$ at reference frequency $Mf_0=0.002$) BBH and large mass ratio ($q=10$) BBH.