A note on the conversion of orbital angles for extreme mass ratio inspirals

TL;DR

This paper presents a practical numerical scheme for converting between different orbital angle parametrizations used in modeling extreme mass ratio inspirals, facilitating better integration of various gravitational wave source modeling techniques.

Contribution

It introduces an efficient numerical method for converting between orbital angles, including the challenging inverse conversion, and provides implementations in multiple programming languages.

Findings

The scheme accurately converts between orbital angles for eccentric, inclined Kerr orbits.

Numerical root-finding effectively handles inverse conversions where analytical solutions are unavailable.

Implementations are publicly available in Mathematica, C, and Python.

Abstract

We outline a practical scheme for converting between three commonly used sets of phases to describe the trajectories of extreme mass ratio inspirals; quasi-Keplerian angles, Mino time action-angles, and Boyer-Lindquist time action-angles (as utilised by the FastEMRIWaveform package). Conversion between Boyer-Lindquist time action angles and quasi-Keplerian angles is essential for the construction of a source frame for adiabatic inspirals that can be related to the source frames used by other gravitational wave source modelling techniques. While converting from quasi-Keplerian angles to Boyer-Lindquist time action angles via Mino time action-angles can be done analytically, the same does not hold for the converse, and so we make use of an efficient numerical root-finding method. We demonstrate the efficacy of our scheme by comparing two calculations for an eccentric and inclined geodesic orbit in Kerr spacetime using two different sets of orbital angles. We have made our implementations available in Mathematica, C, and Python.