Post-1-Newtonian tidal effects in the gravitational waveform from binary inspirals

TL;DR

This work delivers a 1PN-accurate treatment of tidal effects in the gravitational waveform from inspiralling binary neutron stars by deriving the conservative dynamics and GW emission for a system with adiabatically induced quadrupoles in circular orbits, linear in the quadrupole moments and described by the tidal deformability $\lambda$. The authors provide explicit expressions for the radius–frequency relation $r(\omega)$, the binding energy $E(\omega)$, the energy flux $\dot E(\omega)$, and the waveform phase $\psi(\omega)$, including cross-terms $\hat{\lambda} = \lambda \omega^{10/3}/M^{5/3}$ and PN corrections through order $x = (M\omega)^{2/3}/c^2$. Notably, the 1PN tidal corrections increase the tidal signal by about 17–20% at GW frequencies around $400$ Hz for representative neutron-star binaries, enhancing the prospects for EOS constraints using analytic templates and guiding integration with EOB models. The results enable more accurate GW templates, facilitate comparisons with numerical simulations, and support future extensions to higher multipoles and generic orbital configurations.

Abstract

The gravitational wave signal from an inspiralling binary neutron star system will contain detailed information about tidal coupling in the system, and thus, about the internal physics of the neutron stars. To extract this information will require highly accurate models for the gravitational waveform. We present here a calculation of the gravitational wave signal from a binary with quadrupolar tidal interactions which includes all post-1-Newtonian-order effects in both the conservative dynamics and wave generation. We consider stars with adiabatically induced quadrupoles moving in circular orbits, and work to linear in the stars' quadrupole moments. We find that post-1-Newtonian corrections increase the tidal signal by approximately 20% at gravitational wave frequencies of 400 Hz.