Gravitomagnetic tidal effects in gravitational waves from neutron star binaries

TL;DR

This paper investigates the influence of gravitomagnetic tidal effects on gravitational waves from neutron star binaries, introducing a new effective action approach to compute their impact on wave phase and mode amplitudes.

Contribution

It presents the first calculation of gravitomagnetic tidal effects on gravitational wave mode amplitudes using an effective action method, simplifying previous complex derivations.

Findings

Gravitomagnetic tides affect gravitational wave modes at leading order.

These effects are suppressed in phase but significant in certain mode amplitudes.

The work introduces a new approach to include arbitrary current-quadrupoles in tidal calculations.

Abstract

Gravitational waves emitted by coalescing binary systems containing neutron stars (or other compact objects) carry signatures of the stars' internal equation of state, notably, through the influence of tidal deformations during the binary's inspiral stage. While the leading-order tidal effects for post-Newtonian binaries of compact bodies in general relativity are due to the bodies' mass-quadrupole moments induced by gravitoelectric tidal fields, we consider here the leading effects due to current-quadrupole moments induced by gravitomagnetic tidal fields. We employ an effective action approach to determine the near-zone gravitational field and the conservative orbital dynamics, initially allowing for arbitrary (not just tidally induced) current-quadrupoles; our approach significantly reduces the complexity of the calculation compared to previous derivations of the conservative dynamics for arbitrary multipoles. We finally compute the leading contributions from gravitomagnetic tides to the phase and (for the first time) the mode amplitudes of the gravitational waves from a quasi-circular binary inspiral, given in terms of the bodies' quadrupolar gravitomagnetic tidal Love numbers (tidal linear response coefficients in an adiabatic approximation). In the phase, gravitomagnetic tides are suppressed by one post-Newtonian order relative to gravitoelectric ones, but this is not always the case for the mode amplitudes. In the $(\ell,|m|)=(2,1)$ and $(3,2)$ modes for example, they appear at the same leading orders.