Phasing of gravitational waves from inspiralling eccentric binaries

TL;DR

This paper develops an analytical method to accurately model gravitational wave signals from inspiralling eccentric binaries by incorporating multiple time scales without the adiabatic approximation, enhancing template precision for detectors.

Contribution

It introduces a novel 'method of variation of constants' to combine three different time scales in eccentric inspiral modeling at 2.5PN accuracy, improving gravitational wave templates.

Findings

Derived high-accuracy gravitational wave templates for eccentric binaries.

Implemented a 2.5PN post-Newtonian correction to orbital phasing.

Provided explicit short-period contributions to gravitational wave polarizations.

Abstract

We provide a method for analytically constructing high-accuracy templates for the gravitational wave signals emitted by compact binaries moving in inspiralling eccentric orbits. By contrast to the simpler problem of modeling the gravitational wave signals emitted by inspiralling {\it circular} orbits, which contain only two different time scales, namely those associated with the orbital motion and the radiation reaction, the case of {\it inspiralling eccentric} orbits involves {\it three different time scales}: orbital period, periastron precession and radiation-reaction time scales. By using an improved `method of variation of constants', we show how to combine these three time scales, without making the usual approximation of treating the radiative time scale as an adiabatic process. We explicitly implement our method at the 2.5PN post-Newtonian accuracy. Our final results can be viewed as computing new `post-adiabatic' short period contributions to the orbital phasing, or equivalently, new short-period contributions to the gravitational wave polarizations, $h_{+,\times}$, that should be explicitly added to the `post-Newtonian' expansion for $h_{+,\times}$, if one treats radiative effects on the orbital phasing of the latter in the usual adiabatic approximation. Our results should be of importance both for the LIGO/VIRGO/GEO network of ground based interferometric gravitational wave detectors (especially if Kozai oscillations turn out to be significant in globular cluster triplets), and for the future space-based interferometer LISA.