Eccentric first post-Newtonian waveforms for compact binaries in frequency domain with Hansen coefficients

TL;DR

This paper derives analytic first post-Newtonian eccentric gravitational waveforms in the frequency domain using Hansen coefficients, accounting for high eccentricity effects relevant to supermassive black hole binaries.

Contribution

It introduces a generalized Hansen expansion at the first post-Newtonian order for eccentric waveforms, providing a systematic, tabulated form suitable for gravitational wave analysis.

Findings

Waveforms expressed in a systematic, tabular form.

Elimination of secular terms via phase shift.

Applicable to high-eccentricity black hole binaries.

Abstract

The inspiral and merger of supermassive black hole binary systems with high orbital eccentricity are among the promising sources of the advanced gravitational wave observatories. In this paper we derive analytic ready-to-use first post-Newtonian eccentric waveform in Fourier domain with the use of Hansen coefficients. Introducing generic perturbations of celestial mechanics we have generalized the Hansen expansion to the first post-Newtonian order which are then used to express the waveforms. Taking into account the high eccentricity of the orbit leads to the appearance of secular terms in the waveform which are eliminated with the introduction of a phase shift. The waveforms have a systematic structure and as our main result these are expressed in a tabular form.