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arXiv · 1501.01529

Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order

Alejandro Bohé·Guillaume Faye·Sylvain Marsat·Edward K Porter
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Abstract

We investigate the dynamics of spinning binaries of compact objects at the next-to-leading order in the quadratic-in-spin effects, which corresponds to the third post-Newtonian order (3PN). Using a Dixon-type multipolar formalism for spinning point particles endowed with spin-induced quadrupoles and computing iteratively in harmonic coordinates the relevant pieces of the PN metric within the near zone, we derive the post-Newtonian equations of motion as well as the equations of spin precession. We find full equivalence with available results. We then focus on the far-zone field produced by those systems and obtain the previously unknown 3PN spin contributions to the gravitational-wave energy flux by means of the multipolar post-Minkowskian (MPM) wave generation formalism. Our results are presented in the center-of-mass frame for generic orbits, before being further specialized to the case of spin-aligned, circular orbits. We derive the orbital phase of the binary based on the energy balance equation and briefly discuss the relevance of the new terms.

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Alejandro Bohé, Guillaume Faye, Sylvain Marsat, Edward K Porter. 2015-01-07. Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order. https://doi.org/10.1088/0264-9381%2F32%2F19%2F195010

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