Frequency and time domain inspiral templates for comparable mass compact binaries in eccentric orbits

TL;DR

This paper develops two new post-Newtonian inspiral templates for eccentric compact binaries, improving waveform accuracy by incorporating eccentricity evolution in frequency and time domains for gravitational wave detection.

Contribution

It introduces an extended post-circular Fourier-domain model and an efficient time-domain TaylorT4 model that include eccentricity effects up to 6th order and 2PN order, respectively.

Findings

Fourier-domain waveform includes eccentricity effects up to sixth order.

Time-domain TaylorT4 approximant accurately models eccentricity up to 0.9.

Preliminary data analysis shows improved match estimates with new templates.

Abstract

Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the post-circular scheme of Yunes {\it et al.} [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian amplitude and 2PN order Fourier phase while incorporating eccentricity effects up to sixth order at each PN order. The importance of incorporating eccentricity evolution contributions to the Fourier phase in a PN consistent manner is also demonstrated. Second, we present an accurate and efficient prescription to incorporate orbital eccentricity into the quasi-circular time-domain {\texttt{TaylorT4}} approximant at 2PN order. New features include the use of rational functions in orbital eccentricity to implement the 1.5PN order tail contributions to the far-zone fluxes. This leads to closed form PN-accurate differential equations for evolving eccentric orbits and the resulting time-domain approximant is accurate and efficient to handle initial orbital eccentricities $\leq 0.9$. Preliminary GW data analysis implications are probed using match estimates.