Gravitational waves from quasielliptic compact binaries in scalar-tensor theory to one-and-a-half post-Newtonian order

TL;DR

This paper derives 1.5PN order energy and angular momentum fluxes for nonspinning compact binaries in scalar-tensor theories, advancing the understanding of gravitational wave emission in alternative gravity models.

Contribution

It introduces new methods for calculating fluxes and orbital evolution at 1.5PN accuracy in scalar-tensor theories, including Fourier decomposition and hereditary term treatment.

Findings

Derived energy and angular momentum fluxes at 1.5PN order.

Analyzed secular evolution of orbital elements with improved accuracy.

Revisited and corrected memory integral treatment in general relativity.

Abstract

The orbit-averaged fluxes of energy and angular momentum generated by a compact binary system of nonspinning particles are obtained in a popular class of massless scalar-tensor theories with first-and-a-half post-Newtonian (1.5PN) accuracy, i.e., 2.5PN accuracy beyond the leading -1PN dipolar radiation. The secular evolution of the orbital elements (frequency and eccentricity) are then also obtained with 1.5PN accuracy. Three technical advances were necessary to obtain these results: (i) the decomposition of the scalar dipole moment as a Fourier series at 1PN order, along with the other moments at Newtonian order, (ii) the derivation of the formula for the passage to the center-of-mass frame at 2.5PN, including a novel hereditary term arising from the contribution of the radiation, and (iii) the complete treatment of the memory-like term appearing in the angular momentum flux. Moreover, as a byproduct of this work, I revisit in the Appendix the treatment in general relativity of the memory integral appearing at 2.5PN order in the angular momentum flux [arXiv:0908.3854], and find that the spurious divergence in the initial eccentricity $e_1$ found there is cured by a careful split between AC and DC terms.