Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications

TL;DR

This paper develops a second post-Newtonian order quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories, enabling detailed analysis of orbital evolution, energy flux, and gravitational waveforms.

Contribution

It introduces a 2PN order generalized parametrization for eccentric binaries in scalar-tensor theories, extending previous models and providing new tools for waveform analysis.

Findings

Derived orbit-averaged energy and angular momentum flux at 1PN order.

Found the semi-major axis-eccentricity relation independent of scalar-tensor parameters.

Extended waveform decomposition to eccentric orbits at Newtonian order.

Abstract

The generalized post-Keplerian parametrization for compact binaries on eccentric bound orbits is established at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories. This result is used to compute the orbit-averaged flux of energy and angular momentum at Newtonian order, which means relative 1PN order beyond the leading-order dipolar radiation of scalar-tensor theories. The secular evolution of the orbital elements is then computed at 1PN order. At leading order, the closed form "Peters and Mathews" relation between the semi-major axis $a$ and the eccentricity $e$ is found to be independent of any scalar-tensor parameter, and is given by $a \propto e^{4/3}/(1-e^2)$. Finally, the waveform is obtained at Newtonian order in the form of a spherical harmonic mode decomposition, extending to eccentric orbits the results obtained in arXiv:2201.10924.