Parameter estimation of binary black holes in the endpoint of the up-down instability

Black-hole binary spin precession admits equilibrium solutions corresponding to systems with (anti) aligned spins. Among these, binaries in the up-down configuration, where the spin of the heavier (lighter) black hole is co(counter)aligned with the orbital angular momentum, might be unstable to small perturbations of the spin directions. The occurrence of the up-down instability leads to gravitational wave sources that formed with aligned spins but are detected with precessing spins. We present a Bayesian procedure based on the Savage-Dickey density ratio to test the up-down origin of gravitational-wave events. This is applied to both simulated signals, which indicate that achieving strong evidence is within the reach of current experiments, and the LIGO/Virgo events released to date, which indicate that current data are not informative enough.

Automated summary

The mathematical problem of black-hole binary spin precession is related to systems with black hole spins parallel or antiparallel to the orbital angular momentum. In these systems, the up-down configuration, where the spin of the heavier (lighter) black hole is aligned (counter-aligned) with the orbital angular momentum, might be unstable to small perturbations of the spin directions. The up-down instability gives rise to gravitational wave sources with precessing spins, even if they formed with aligned spins. We propose a Bayesian procedure based on the Savage-Dickey density ratio to test the up-down origin of gravitational-wave events. This procedure is applied to simulated signals and current data from LIGO/Virgo events, indicating that strong evidence is achievable with current experiments, but the current data are not informative enough.