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

Black hole binaries may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. During the formation and evolution of isolated binaries, several processes can alter the orientation of the black hole spin vectors with respect to the binary's orbital angular momentum. A subset of binary black holes merge through the emission of gravitational radiation and are observable with advanced ground-based gravitational-wave detectors. Gravitational waves from these systems directly encode information about the spin--orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution, potentially shedding light on the ratio of dynamically formed binary black holes to those formed through isolated binary evolution. We simulate a mixed population of binary black holes with spin--orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. We show that with tens of observations it will be 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 binary black holes with isotropic spin directions (corresponding to dynamical formation) with a fractional uncertainty of $\sim 40\%$. Meanwhile, only $\sim 5$ observations are sufficient to distinguish between extreme models---all binary black holes either having exactly aligned spins or isotropic spin directions---if all black holes are rapidly spinning ($\chi \sim 0.7$).

Comments: 11 pages, 8 figures. Submittied to MNRAS

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