Spinning compact binary inspiral II: Conservative angular dynamics

TL;DR

This paper derives detailed 2PN conservative dynamics equations for spinning compact binaries, including spin effects and orbital evolution, revealing specific spin configurations are preserved during inspiral.

Contribution

It provides a comprehensive set of evolution equations for orbital and spin variables in generic orbits, incorporating leading order spin effects at 2PN order, which was not previously established.

Findings

Spin angles remain constant for equal mass black holes.

Special spin configurations are preserved at 2PN level.

Largest recoil configuration is maintained during inspiral.

Abstract

We establish the evolution equations of the set of independent variables characterizing the 2PN rigorous conservative dynamics of a spinning compact binary, with the inclusion of the leading order spin-orbit, spin-spin and mass quadrupole - mass monopole effects, for generic (noncircular, nonspherical) orbits. More specifically, we give a closed system of first order ordinary differential equations for the orbital elements of the osculating ellipse and for the angles characterizing the spin orientations with respect to the osculating orbit. We also prove that (i) the relative angle of the spins stays constant for equal mass black holes, irrespective of their orientation, and (ii) the special configuration of equal mass black holes with equal, but antialigned spins, both laying in the plane of motion (leading to the largest recoil found in numerical simulations) is preserved at 2PN level of accuracy, with leading order spin-orbit, spin-spin and mass quadrupolar contributions included.