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

TL;DR

This paper develops a detailed post-Newtonian model for eccentric neutron star-black hole binaries, incorporating tidal effects at the second-and-a-half order, to improve gravitational wave templates for eccentric mergers.

Contribution

It derives a quasi-Keplerian parametrization including tidal effects at high post-Newtonian order, with explicit eccentricity expansions up to fourteenth order, enhancing waveform modeling accuracy.

Findings

Derived the quasi-Keplerian parametrization with tidal effects.

Provided explicit eccentricity expansions up to 14th order.

Analyzed the convergence of eccentricity-expanded results.

Abstract

GW200105 is the first gravitational wave detection to show signs of eccentricity, it also is a neutron star - blackhole binary. This raises the need for waveforms that incorporate tidal effects on quasi-elliptic orbits. We tackle the problem of finite size effects within the post-Newtonian framework, including the mass-type quadrupole and octupole, as well as the current-type quadrupole deformations in the adiabatic approximation. The computations are performed at the second-and-a-half relative post-Newtonian order. We first derive the quasi-Keplerian parametrization of the conservative motion; we then express the radial separation and phase with their time derivatives in terms of the orbital frequency, the time eccentricity and the eccentric anomaly. To obtain these as functions of time, we invert the generalized Kepler equation while also discussing the convergence of eccentricity expanded results. We provide those results to the fourteenth order in eccentricity. Finally, we exploit the already known radiation reaction term of the acceleration in order to derive the secular and oscillatory evolutions of the orbital elements. The companion paper contains the derivation of the radiated fluxes and the amplitude modes of the strain. All relevant results are provided in an ancillary file.