Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order

TL;DR

This paper derives explicit 3PN order gravitational-wave phase corrections for low-eccentricity inspiralling binaries, improving waveform models crucial for accurate gravitational-wave detection and parameter estimation.

Contribution

It specializes the quasi-Keplerian formalism to low eccentricities, providing simple, explicit expressions for phase corrections at 3PN order, enhancing existing waveform models.

Findings

Eccentricity corrections significantly affect the number of gravitational wave cycles.

Explicit 3PN order phase corrections are derived for low-eccentricity binaries.

Incorporating eccentricity improves the accuracy of gravitational-wave templates.

Abstract

[abridged] Although gravitational radiation causes inspiralling compact binaries to circularize, a variety of astrophysical scenarios suggest that binaries might have small but nonnegligible orbital eccentricities when they enter the low-frequency bands of ground and space-based gravitational-wave detectors. If not accounted for, even a small orbital eccentricity can cause a potentially significant systematic error in the mass parameters of an inspiralling binary. Gravitational-wave search templates typically rely on the quasi-circular approximation, which provides relatively simple expressions for the gravitational-wave phase to 3.5 post-Newtonian (PN) order. The quasi-Keplerian formalism provides an elegant but complex description of the post-Newtonian corrections to the orbits and waveforms of inspiralling binaries with any eccentricity. Here we specialize the quasi-Keplerian formalism to binaries with low eccentricity. In this limit the non-periodic contribution to the gravitational-wave phasing can be expressed explicitly as simple functions of frequency or time, with little additional complexity beyond the well-known formulas for circular binaries. These eccentric phase corrections are computed to 3PN order and to leading order in the eccentricity for the standard PN approximants. For a variety of systems these eccentricity corrections cause significant corrections to the number of gravitational wave cycles that sweep through a detector's frequency band. This is evaluated using several measures, including a modification of the useful cycles. We also evaluate the role of periodic terms that enter the phasing and discuss how they can be incorporated into some of the PN approximants. While the eccentric extension of the PN approximants is our main objective, this work collects a variety of results that may be of interest to others modeling eccentric relativistic binaries.