Gravitoelectric dynamical tides at second post-Newtonian order

TL;DR

This paper derives a second post-Newtonian order gravitoelectric tidal Hamiltonian for compact binaries using effective field theory, aiding the development of precise gravitational wave models.

Contribution

It introduces a novel second-order post-Newtonian gravitoelectric tidal Hamiltonian derived via diagrammatic effective field theory, including validation and gauge-invariant observables.

Findings

Derived the dynamical tidal Hamiltonian to second post-Newtonian order.

Validated the Hamiltonian by verifying the Poincaré algebra.

Calculated gauge-invariant observables like binding energy and scattering angle.

Abstract

We present a gravitoelectric quadrupolar dynamical tidal-interaction Hamiltonian for a compact binary system, that is valid to second order in the post-Newtonian expansion. Our derivation uses the diagrammatic effective field theory approach, and involves Feynman integrals up to two loops, evaluated with the dimensional regularization scheme. We also derive the effective Hamiltonian for adiabatic tides, obtained by taking the appropriate limit of the dynamical effective Hamiltonian, and we check its validity by verifying the complete Poincar\'e algebra. In the adiabatic limit, we also calculate two gauge-invariant observables, namely, the binding energy for a circular orbit and the scattering angle in a hyperbolic scattering. Our results are important for developing accurate gravitational waveform models for neutron-star binaries for present and future gravitational-wave observatories.