Secular precessing compact binary dynamics, spin and orbital angular momentum flip-flops

TL;DR

This paper develops a second-order post-Newtonian secular evolution model for precessing compact binaries, including spin effects, and investigates phenomena like spin flip-flops and orbital angular momentum flips.

Contribution

It introduces an autonomous secular evolution framework that accurately describes precessing binary dynamics over multiple timescales, extending understanding of spin and orbital behavior.

Findings

Secular dynamics effectively model precessional timescales.

Spin flip-flops are limited to specific parameter regimes.

Orbital angular momentum can flip from pole to pole in certain conditions.

Abstract

We derive the conservative secular evolution of precessing compact binaries to second post-Newtonian order accuracy, with leading-order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. The emerging closed system of first-order differential equations evolves the pairs of polar and azimuthal angles of the spin and orbital angular momentum vectors together with the periastron angle. In contrast with the instantaneous dynamics, the secular dynamics is autonomous. This secular dynamics reliably characterizes the system over timescales starting from a few times the radial period to several precessional periods, but less than the radiation reaction timescale. We numerically compare the instantaneous and secular evolutions and estimate the number of periods for which dissipation has no significant effect, e.g. the conservative timescale. We apply the analytic equations to study the spin flip-flop effect, recently found by numerical relativity methods. Our investigations show that the effect does not generalize beyond its original parameter settings, although we reveal distinct configurations exhibiting one half flip-flops. In addition, we find a flip-flopping evolution of the orbital angular momentum vector, which ventures from one pole to another through several precessional periods. This is a new effect, occurring for mass ratios much less than one.