First-post-Newtonian quadrupole tidal interactions in binary systems

TL;DR

This paper derives first-post-Newtonian order equations for tidal interactions in binary systems, including spin and quadrupole effects, with implications for gravitational wave modeling of neutron star mergers.

Contribution

It provides a comprehensive derivation of 1PN orbital equations with spin and quadrupole coupling, highlighting the importance of momentum conservation and adiabatic quadrupole modeling.

Findings

Derived 1PN equations of motion including spin and quadrupole effects.

Demonstrated the necessity of including spin-orbit coupling for momentum conservation.

Presented simplified equations for adiabatic quadrupole dynamics in binary systems.

Abstract

We consider tidal coupling in a binary stellar system to first-post-Newtonian order. We derive the orbital equations of motion for bodies with spins and mass quadrupole moments and show that they conserve the total linear momentum of the binary. We note that spin-orbit coupling must be included in a 1PN treatment of tidal interactions in order to maintain consistency (except in the special case of adiabatically induced quadrupoles); inclusion of 1PN quadrupolar tidal effects while omitting spin effects would lead to a failure of momentum conservation for generic evolution of the quadrupoles. We use momentum conservation to specialize our analysis to the system's center-of-mass-energy frame; we find the binary's relative equation of motion in this frame and also present a generalized Lagrangian from which it can be derived. We then specialize to the case in which the quadrupole moment is adiabatically induced by the tidal field (in which case it is consistent to ignore spin effects). We show how the adiabatic dynamics for the quadrupole can be incorporated into our action principle and present the simplified orbital equations of motion and conserved energy for the adiabatic case. These results are relevant to gravitational wave signals from inspiralling binary neutron stars.