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

Abstract

We have previously constructed a waveform model, , for spinning binary black hole (BBH) moving along eccentric orbit based on effective-one-body (EOB) formalism. In the current paper, we update waveform model in the following three respects. Firstly, we update the EOB dynamics from to . Secondly we properly treat the Schott term which has been ignored in previous . Thirdly, we construct a new factorized waveform including (l, |m|) = (2, 2), (2, 1), (3, 3), (4, 4) modes based on EOB formalism, which is valid for spinning BBHs in general equatorial orbit. Following our previous waveform model, we call our new waveform model . The (l, |m|) = (2, 2) mode waveform of can fit the original waveform very well in the case of a quasi-circular orbit. We have validated 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 ⊙ 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 NR 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 waveform model can match all tested 305 SXS waveforms better than 98% including highly spinning (χ = 0.99) BBH, highly eccentric (e ≈ 0.6 at reference frequency Mf 0 = 0.002) BBH and large mass ratio (q = 10) BBH.