Post-Newtonian spin-tidal couplings for compact binaries

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+δ2l)PN order. For circular orbits and spins orthogonal to the orbital plane, all leading-order spin-tidal terms enter the GW phase at 1.5PN 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 6.5PN 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