Adiabatic tides in compact binaries on quasi-elliptic orbits: Radiation at the second-and-a-half relative post-Newtonian order

TL;DR

This paper calculates gravitational wave fluxes and waveforms for eccentric compact binaries with tidal effects at 2.5PN order, revealing eccentricity-induced dephasing potentially detectable in gravitational wave observations.

Contribution

It introduces a detailed 2.5PN order computation of tidal effects on eccentric binaries, including amplitude modes and secular evolution, advancing gravitational wave modeling.

Findings

Eccentric corrections cause measurable dephasing in gravitational wave signals.

Derived secular evolution equations for orbital elements in eccentric binaries.

Provided detailed amplitude modes including tail and post-adiabatic corrections.

Abstract

We compute the gravitational fluxes and waveform for eccentric compact binaries including matter effects through adiabatic tidal interactions within the post-Newtonian approximation. The computations are performed at the relative 2.5PN order. Using the dynamics derived in the companion paper, we first derive the radiated energy and angular momentum, from which we deduce the equations describing the secular evolution of the orbital elements. We numerically solve for the secular dynamics for various systems. We find that the eccentric corrections to tidal terms induce a dephasing that could potentially be detectable in some regions of the parameter space of gravitational wave sources. Finally, we compute the amplitude of the strain, decomposed in spin-weighted spherical harmonics. Besides the memory contributions that are left for future works, we provide the amplitude modes containing the instantaneous, tail and post-adiabatic corrections expanded to the twelfth order in eccentricity. All relevant results are provided in an ancillary file.