Up-down instability of binary black holes in numerical relativity

TL;DR

This paper presents the first numerical relativity simulations of the up-down instability in binary black holes, demonstrating how small perturbations can lead to large spin misalignments and distinctive gravitational wave signatures.

Contribution

It provides the first full numerical relativity simulations capturing the up-down instability, extending over 100 orbits and showing the growth of spin misalignments.

Findings

Instability causes spin misalignments to grow dramatically.

Strong imprint on gravitational wave subdominant modes.

Post-Newtonian models can reproduce the instability dynamics.

Abstract

Binary black holes with spins that are aligned with the orbital angular momentum do not precess. However, post-Newtonian calculations predict that "up-down" binaries, in which the spin of the heavier (lighter) black hole is aligned (antialigned) with the orbital angular momentum, are unstable when the spins are slightly perturbed from perfect alignment. This instability provides a possible mechanism for the formation of precessing binaries in environments where sources are preferentially formed with (anti) aligned spins. In this paper, we present the first full numerical relativity simulations capturing this instability. These simulations span $\sim 100$ orbits and $\sim 3$-$5$ precession cycles before merger, making them some of the longest numerical relativity simulations to date. Initialized with a small perturbation of $1^{\circ}$-$10^{\circ}$, the instability causes a dramatic growth of the spin misalignments, which can reach $\sim 90^{\circ}$ near merger. We show that this leaves a strong imprint on the subdominant modes of the gravitational wave signal, which can potentially be used to distinguish up-down binaries from other sources. Finally, we show that post-Newtonian and effective-one-body approximants are able to reproduce the unstable dynamics of up-down binaries extracted from numerical relativity.