A Possible Mass Ratio and Spin-Orbit Misalignment Correlation for Mergers of Binary Black Holes in Nuclear Star Clusters

Despite a decade's worth of gravitational wave observation, the origin of the binary black hole (BBH) mergers detected by the LIGO-VIRGO-Kagra (LVK) collaboration remains an open question. Towards assessing the feasibility and prevalence of the many proposed BBH formation channels, the spin properties of the merging black holes (BHs) hold significant promise, particularly their orientations. The combined trends of a moderate preferential alignment of BH spins with their orbit normals and an apparent correlation of BBH effective spin parameters $\chi_{\rm eff}$ with their mass ratios seem to favor hydrodynamical BBH formation mechanisms over purely dynamical ones, as they introduce a preferred orientation to the system. However, such processes are filled with physical and modeling uncertainties. In this paper, we highlight a dynamical route to easily characterizable spin evolution that results in analytically-predictable spin distributions. We show that, when a stellar binary forms a BBH through two phases of stable mass transfer, and the BBH is subsequently driven to merger by the gravitational perturbation of a distant massive object (such as a supermassive black hole), the resulting spin-orbit misalignment angles are anti-correlated with the binary mass ratio. While the mechanism as proposed only operates in a somewhat narrow region of parameter space, it also predicts significantly tighter correlations than are seen in the LVK systems. We discuss avenues for future work that may significantly expand the parameter space of our mechanism while still remaining broadly consistent with observations.