Combining Post-Circular and Pad\'e approximations to compute Fourier domain templates for eccentric inspirals

TL;DR

This paper develops an analytic method combining Post-Circular and Padé approximations to create frequency domain templates for eccentric inspirals, extending modeling accuracy to initial eccentricities up to 0.6.

Contribution

It introduces a novel approach that combines Post-Circular and Padé approximations to improve the accuracy of eccentric inspiral templates up to 1PN order for initial eccentricities as high as 0.6.

Findings

The combined approximation faithfully models eccentric inspirals with initial eccentricity up to 0.6.

The method extends the applicability of analytic templates beyond the previous limit of 0.2 eccentricity.

Discussion of challenges in extending to higher PN orders.

Abstract

Observations of transient gravitational wave (GW) events with non-negligible orbital eccentricity can be highly rewarding from astrophysical considerations. Ready-to-use fully analytic frequency domain inspiral GW templates are crucial ingredients to construct eccentric inspiral-merger-ringdown waveform families, required for the detection of such GW events. It turns out that a fully analytic, post-Newtonian (PN) accurate frequency domain inspiral template family, which uses certain post-circular approximation, may only be suitable to model events with initial eccentricities $e_0 \leq 0.2$.We here explore the possibility of combining Post-Circular and Pad\'e approximations to obtain fully analytic frequency domain eccentric inspiral templates. The resulting 1PN-accurate approximant is capable of faithfully capturing eccentric inspirals having $e_0 \leq 0.6$ while employing our 1PN extension of a frequency domain template family that does not use post-circular approximation, detailed in Moore, B., et al.\ 2018, Classical and Quantum Gravity, 35, 235006. We also discuss subtleties that arise while combining post-circular and Pad\'e approximations to obtain higher PN order templates for eccentric inspirals.