Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin–orbit and leading order in spin(1)–spin(2) and spin-squared couplings

Abstract

A quasi-Keplerian parameterization for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin–spin and next-to-leading order spin–orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin–orbit and 1PN spin–spin contributions, whereby the spins are assumed to be of 0PN order.