Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description

TL;DR

This work develops an effective-action framework for relativistic tidal interactions in compact binaries and embeds them into the EOB formalism to extend tidal descriptions beyond leading order. By computing the 2PN corrections to the tidal energy and mapping them to a deformed EOB radial potential $A(u)$, it provides explicit expressions for the dominant electric quadrupole and subleading tidal terms, yielding a distance-dependent amplification factor with coefficients $ ext{α}_1^{2e}=rac{5}{2}X_1$ and $ ext{α}_2^{2e}=rac{85}{14}$ in the equal-mass case. The authors also derive test-mass limits, discuss light-ring (pole) behavior, and propose a Padé-type resummation to capture higher-order effects, along with a strategy to validate the results against resolution-extrapolated numerical simulations. These results enhance the analytical modeling of late-inspiral dynamics and strengthen the ability to extract neutron-star equation-of-state information from gravitational-wave data. The approach thereby improves the accuracy and reliability of tidal parameter inferences in neutron-star binaries relevant for advanced GW detectors.

Abstract

The gravitational-wave signal from inspiralling neutron-star--neutron-star (or black-hole--neutron-star) binaries will be influenced by tidal coupling in the system. An important science goal in the gravitational-wave detection of these systems is to obtain information about the equation of state of neutron star matter via the measurement of the tidal polarizability parameters of neutron stars. To extract this piece of information will require to have accurate analytical descriptions of both the motion and the radiation of tidally interacting binaries. We improve the analytical description of the late inspiral dynamics by computing the next-to-next-to-leading order relativistic correction to the tidal interaction energy. Our calculation is based on an effective-action approach to tidal interactions, and on its transcription within the effective-one-body formalism. We find that second-order relativistic effects (quadratic in the relativistic gravitational potential $u=G(m_1 +m_2)/(c^2 r)$) significantly increase the effective tidal polarizability of neutron stars by a distance-dependent amplification factor of the form $1 + α_1 \, u + α_2 \, u^2 +...$ where, say for an equal-mass binary, $α_1=5/4=1.25$ (as previously known) and $α_2=85/14\simeq6.07143$ (as determined here for the first time). We argue that higher-order relativistic effects will lead to further amplification, and we suggest a Padé-type way of resumming them. We recommend to test our results by comparing resolution-extrapolated numerical simulations of inspiralling-binary neutron stars to their effective one body description.