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

TL;DR

The paper extends the PN framework to eccentric compact binaries with adiabatic tides, deriving radiated fluxes and the full waveform up to relative $2.5$PN and expanding the waveform amplitudes to $e_t^{12}$. Building on the dynamics established in Paper I, it unifies instantaneous and tail fluxes, computes their orbit-averages (with eccentricity resummation), and obtains the secular evolution of orbital elements along with PA corrections to the dominant waveform mode. A phase-redefinition is introduced to absorb tail logs, yielding phase-consistent waveform modes that are validated against circular limits. The findings indicate that eccentric tidal corrections can produce measurable dephasing in certain parameter ranges, motivating further work on dynamical tides and memory effects for future GW detector eras.

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.