Second post-Newtonian gravitational wave polarizations for compact binaries in elliptical orbits

TL;DR

This paper derives the second post-Newtonian level expressions for gravitational wave polarizations from non-spinning compact binaries in elliptical orbits, including eccentricity and periastron precession effects.

Contribution

It provides the first 2PN accurate formulas for gravitational wave polarizations for eccentric binaries using a generalized quasi-Keplerian parametrization.

Findings

Derived 2PN accurate gravitational wave polarizations for elliptical orbits

Incorporated effects of eccentricity and periastron precession

Provided formulas modulo tail terms

Abstract

The second post-Newtonian (2PN) contribution to the `plus' and `cross' gravitational wave polarizations associated with gravitational radiation from non-spinning, compact binaries moving in elliptic orbits is computed. The computation starts from our earlier results on 2PN generation, crucially employs the 2PN accurate generalized quasi-Keplerian parametrization of elliptic orbits by Damour, Sch\"afer and Wex and provides 2PN accurate expressions modulo the tail terms for gravitational wave polarizations incorporating effects of eccentricity and periastron precession.