Black-Hole Perturbation Plus Post-Newtonian Theory: Hybrid Waveform for Neutron Star Binaries

TL;DR

This paper develops a hybrid gravitational waveform model for neutron star binaries by combining black hole perturbation theory with post-Newtonian corrections, capturing tidal effects with high accuracy across frequencies.

Contribution

It introduces a novel hybrid waveform method that integrates black hole perturbation theory with post-Newtonian corrections to model tidal effects in neutron star binaries.

Findings

The frequency-dependent tidal phase shift agrees with PN results at low frequencies.

The hybrid waveform achieves accuracy comparable to EOB waveforms.

The approach is applicable for binary black hole waveform generation.

Abstract

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 ($\le 10\%$) on the spin of the primary black hole. Combining this black hole perturbation waveform with the Post-Newtonian waveform, we propose a frequency-domain, hybrid waveform that shows comparable accuracy as the EOB waveform in characterizing the tidal effects, as calibrated by numerical relativity simulations. Further improvement is expected as the next-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.