# Up-down instability of binary black holes in numerical relativity

**Authors:** Vijay Varma, Matthew Mould, Davide Gerosa, Mark A. Scheel, Lawrence E. Kidder, Harald P. Pfeiffer  
**arXiv:** [2012.07147](https://arxiv.org/abs/2012.07147)  
**Date:** 2020-12-13  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2012.07147v1/

## Key points

- The paper explores the behavior of binary black holes with spins that are aligned or anti-aligned with the orbital angular momentum.
- Aligned binaries do not precess, but up-down binaries (where the spin of one black hole is aligned and the other is anti-aligned) are predicted to be unstable when their spins are slightly perturbed from perfect alignment.
- This instability could provide a mechanism for the formation of precessing binaries in environments where sources are preferentially formed with (anti) aligned spins.
- Several simulations were conducted using full numerical relativity to confirm this instability's existence, with a small perturbation of 1°-10° causing a dramatic growth of spin misalignments which could reach approximately 90° near merger.
- The study shows that this leaves a strong imprint on the subdominant modes of the gravitational wave signal, potentially distinguishing up-down binaries from other sources.
- Post-Newtonian and effective-one-body approximants were used to reproduce unstable dynamics extracted from numerical relativity successfully.
- The authors suggest that these findings have implications for future gravitational wave detections and can help us better understand how binary black holes form and evolve in different astrophysical environments.

## Summary

The paper "Up-down instability of binary black holes in numerical relativity" explores the behavior of binary black holes with spins that are aligned or anti-aligned with the orbital angular momentum. While aligned binaries do not precess, post-Newtonian calculations predict that up-down binaries, in which the spin of the heavier (lighter) black hole is aligned (anti-aligned) with the orbital angular momentum, are unstable when their spins are slightly perturbed from perfect alignment. This instability provides a potential mechanism for the formation of precessing binaries in environments where sources are preferentially formed with (anti) aligned spins. To confirm this instability's existence, several simulations spanning approximately 100 orbits before merger were conducted using full numerical relativity. The simulations were initialized with a small perturbation of 1°-10° and it was observed that the instability caused a dramatic growth of spin misalignments which could reach approximately 90° near merger. The study shows that this leaves a strong imprint on the subdominant modes of the gravitational wave signal, potentially distinguishing up-down binaries from other sources. Post-Newtonian and effective-one-body approximants were used to reproduce unstable dynamics extracted from numerical relativity successfully. The authors suggest that these findings have implications for future gravitational wave detections and can help us better understand how binary black holes form and evolve in different astrophysical environments.