Hierarchical analysis of gravitational-wave measurements of binary black hole spin–orbit misalignments

Binary black holes (BBHs) may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the BH spins and the orbital angular momentum. Gravitational waves (GW) from these systems directly encode information about the spin–orbit misalignment angles, allowing them to be (weakly) constrained. Identifying subpopulations of spinning BBHs will inform us about compact binary formation and evolution. We simulate a mixed population of BBHs with spin–orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock GW observations of these populations. Assuming a population with dimensionless spin magnitudes of χ = 0.7, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With 100 observations, it will be possible to infer the relative fraction of coalescing BBHs with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of ∼40 per cent. Meanwhile, only ∼5 observations are sufficient to distinguish between extreme models – all BBHs either having exactly aligned spins or isotropic spin directions.