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

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.

61 pages, 3 figures, 1 ancillary file. v2: updated title of ancillary file and corrected typos. v3: minor corrections and reference updates (matches published version)