Generalized quasi-Keplerian solution for eccentric, nonspinning compact binaries at 4PN order and the associated inspiral-merger-ringdown waveform

We derive fourth post-Newtonian (4PN) contributions to the Keplerian type parametric solution associated with the conservative dynamics of eccentric, nonspinning 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 nonspinning, moderately eccentric black hole binaries, influenced by Hinder et al. [Phys. Rev. D 98, 044015 (2018)]. Our updated waveform is expected to be valid over a 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) less than or similar to 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.

Automated summary

This paper investigates the fourth post-Newtonian (4PN) contributions to the parametric solution of eccentric, nonspinning compact binaries. The authors derive explicit expressions for the solution and various orbital elements, and incorporate the 4PN nonlocal-in-time tail effects using canonical perturbation theory. The resulting updated waveform is expected to be valid for modeling the merger of nonspinning, moderately eccentric black hole binaries.