Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications
David Trestini
Abstract
The generalized quasi-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 semimajor axis $a$ and the eccentricity $e$ is found to be independent of any scalar-tensor parameter, and is given by $a\ensuremath{\propto}{e}^{4/3}/(1\ensuremath{-}{e}^{2})$. 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 L. Bernard et al. [Gravitational waves in scalar-tensor theory to one-and-a-half post-Newtonian order, J. Cosmol. Astropart. Phys. 08 (2022) 008.].