Unstable binary black-hole spins: post-Newtonian theory and numerical relativity

TL;DR

This paper investigates the instability of certain spin configurations in binary black holes, combining post-Newtonian theory and numerical relativity to understand how misaligned spins lead to precession and affect gravitational-wave signals.

Contribution

It introduces two methods to analyze the onset of spin instability and demonstrates this precessional instability in strong-field numerical relativity simulations.

Findings

Aligned configurations are stable; 'up-down' is unstable.

Instability causes spins to tilt by ~90 degrees.

Precessional effects significantly impact gravitational-wave signals.

Abstract

Spin precession occurs in binary black holes whose spins are misaligned with the orbital angular momentum. Otherwise, the spin configuration is constant and the subsequent binary dynamics and gravitational-wave emission are much simpler. We summarize a series of works which has shown that, while three of the aligned configurations are stable equilibria, the `up-down' configuration, in which the heavier (lighter) black hole is (anti) aligned with the orbital angular momentum, is unstable when perturbed; at a critical point in the inspiral the black hole spins begin to tilt wildly as precession takes over. We present two equivalent approaches to derive the instability onset based on multitimescale post-Newtonian techniques, and point out that the instability has a predictable endpoint. Finally, we demonstrate the presence of this precessional instability in the strong-field regime of numerical relativity with simulations of aligned-spin binaries lasting $\sim100$ orbits before merger. The spins of up-down systems can tilt by $\sim90^\circ$, leaving a notable imprint in the emitted gravitational-wave signals and providing a possible mechanism to form precessing systems in astrophysical environments from which sources are preferentially born with (anti) aligned spins.