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 parameterisation 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, where the spins are counted of 0PN order.