Black-hole perturbation theory with post-Newtonian theory: Towards hybrid waveforms for neutron-star binaries

We consider the motion of nonspinning compact objects orbiting around a Kerr black hole with tidal couplings. The tide-induced quadrupole moment modifies both the orbital energy and outgoing fluxes, so that over the inspiral timescale there is an accumulative shift in the orbital and gravitational wave phase. Previous studies on compact object tidal effects have been carried out in the post-Newtonian (PN) and effective-one-body (EOB) formalisms. In this work, within the black-hole perturbation framework, we propose to characterize the tidal influence in the expansion of mass ratios, while higher-order PN corrections are naturally included. For the equatorial and circular orbit, we derive the leading-order frequency dependent tidal phase shift which agrees with the post-Newtonian result at low frequencies but deviates at high frequencies. We also find that such phase shift has weak dependence (??? 10%) on the spin of the primary black hole. Combining this black-hole perturbation waveform with the post-Newtonian waveform, we have developed a theoretical framework towards a frequency-domain hybrid waveform. The comparison with a limited number of numerical relativity waveform shows an almost comparable phase error to the EOB waveform in characterizing the tidal effects, although more systematic tests within the parameter space are needed to faithfully address the accuracy of this waveform model. Further improvement is expected as the next-to-leading order in mass ratio and the higher-PN tidal corrections are included. This hybrid approach is also applicable for generating binary black-hole waveforms.