Measurement of spin-orbit misalignment in binary black holes via the total spin

Abstract

The degree of spin-orbit alignment in merging binary black holes is a powerful probe of their formation history. However, assessing spin-orbit misalignment in individual events remains challenging, as most parameters commonly used to characterize precession tend to be poorly constrained. In this work, we introduce the angle between the total spin and orbital angular momentum, $\theta_{LS}$, as an alternative measure of spin-orbit misalignment. Using synthetic observations, we show that $\theta_{LS}$ retains more information to discriminate between the aligned- and isotropic-spins hypotheses than commonly used alternatives, including $\chi_{\rm p}$. We then study this parameter on binary black hole mergers observed in the GWTC-5.0 catalog, and identify multiple events that are inconsistent with having aligned spins. In several of the examples, this is not apparent from the posteriors of the effective spin parameters ($\chi_{\rm p}$ or $\chi_\mathrm{eff}$) nor the individual spin-orbit tilts ($\theta_1$ or $\theta_2$) alone, and thus had not been previously identified. We highlight GW241127_061008 as a compelling case for a second-generation merger, with a large, tilted primary spin, unequal masses, and a large primary mass near the pair-instability-supernova mass gap. Finally, we perform population inference using $\cos\theta_{LS}$ and confirm that the binary black hole population is inconsistent with either a purely isotropic or a purely aligned-spin distribution, and requires substantial spin-orbit misalignment.