Cassini states for black hole binaries

TL;DR

This paper develops a Hamiltonian-based model to analyze the spin dynamics of black hole binaries, revealing how Cassini states evolve during inspiral and influence the final spin distribution.

Contribution

It introduces a Hamiltonian formalism for black hole binary spin dynamics, clarifies the nature of Cassini states, and predicts their evolution during inspiral.

Findings

Cassini states are shifted during inspiral due to radiation reaction.

The model predicts the final spin distribution of black hole binaries.

Spin dynamics are integrable in the absence of dissipation.

Abstract

Cassini states correspond to the equilibria of the spin axis of a body when its orbit is perturbed. They were initially described for planetary satellites, but the spin axes of black hole binaries also present this kind of equilibria. In previous works, Cassini states were reported as spin-orbit resonances, but actually the spin of black hole binaries is in circulation and there is no resonant motion. Here we provide a general description of the spin dynamics of black hole binary systems based on a Hamiltonian formalism. In absence of dissipation the problem is integrable and it is easy to identify all possible trajectories for the spin for a given value of the total angular momentum. As the system collapses due to radiation reaction, the Cassini states are shifted to different positions, which modifies the dynamics around them. This is why the final spin distribution may differ from the initial one. Our method provides a simple way of predicting the distribution of the spin of black hole binaries at the end of the inspiral phase.