Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform

TL;DR

This paper derives a 4PN order quasi-Keplerian solution for eccentric, non-spinning compact binaries, and develops an improved IMR waveform for gravitational wave modeling, incorporating tail effects and extending validity to higher eccentricities.

Contribution

It provides the first explicit 4PN quasi-Keplerian solution including tail effects and applies it to generate more accurate gravitational waveforms for eccentric binary mergers.

Findings

Derived explicit 4PN parametric solution for eccentric binaries.

Developed an updated IMR waveform incorporating 4PN tail effects.

Extended waveform validity to eccentricities up to 0.85.

Abstract

We derive fourth post-Newtonian (4PN) contributions to the Keplerian-type parametric solution associated with the conservative dynamics of eccentric, non-spinning compact binaries. The solution has been computed while ignoring certain zero-average, oscillatory terms arising due to 4PN tail effects. We provide explicit expressions for the parametric solution and various orbital elements in terms of the conserved energy, angular momentum and symmetric mass ratio. Canonical perturbation theory (along with the technique of Pade approximant) is used to incorporate the 4PN nonlocal-in-time tail effects within the action-angles framework. We then employ the resulting solution to obtain an updated inspiral-merger-ringdown (IMR) waveform that models the coalescence of non-spinning, moderately eccentric black hole binaries, influenced by arXiv:1709.02007. Our updated waveform is expected to be valid over similar parameter range as the above reference. We also present a related waveform which makes use of only the post-Newtonian equations and thus is valid only for the inspiral stage. This waveform is expected to work for a much larger range of eccentricity ($e_t \lesssim 0.85$) than our full IMR waveform (which assumes circularization of the binaries close to merger). We finally pursue preliminary data analysis studies to probe the importance of including the 4PN contributions to the binary dynamics while constructing gravitational waveform templates for eccentric mergers.