Post-Newtonian spin-tidal couplings for compact binaries

TL;DR

This paper calculates how spin and tidal effects influence gravitational waves from compact binaries at leading post-Newtonian order, including new rotational tidal Love numbers, to improve waveform models and parameter estimation.

Contribution

It introduces the leading-order spin-tidal couplings, including rotational tidal Love numbers, into gravitational wave phase calculations at high PN orders.

Findings

Spin-tidal couplings affect GW phase at 1.5PN order relative to quadrupolar tidal effects.

All leading-order spin-tidal terms enter at 1.5PN order for certain configurations.

The GW phase includes all tidal terms up to 6.5PN order, linear in spin.

Abstract

We compute the spin-tidal couplings that affect the dynamics of two orbiting bodies at the leading order in the post-Newtonian (PN) framework and to linear order in the spin. These corrections belong to two classes: (i) terms arising from the coupling between the ordinary tidal terms and the point-particle terms, which depend on the standard tidal Love numbers of order $l$ and affect the gravitational-wave (GW) phase at $(2l+5/2)$PN order and (ii) terms depending on the rotational tidal Love numbers, recently introduced in previous work, that affect the GW phase at $(2l+1/2+\delta_{2l})$PN order. For circular orbits and spins orthogonal to the orbital plane, all leading-order spin-tidal terms enter the GW phase at $1.5$PN order relative to the standard, quadrupolar, tidal deformability term (and, thus, before the standard octupolar tidal deformability terms). We present the GW phase that includes all tidal terms up to $6.5$PN order and to linear order in the spin. We comment on a conceptual issue related to the inclusion of the rotational tidal Love numbers in a Lagrangian formulation and on the relevance of spin-tidal couplings for parameter estimation in coalescing neutron-star binaries and for tests of gravity.