Getting More Out of Black Hole Superradiance: a Statistically Rigorous Approach to Ultralight Boson Constraints from Black Hole Spin Measurements

Black hole (BH) superradiance can provide strong constraints on the properties of ultralight bosons (ULBs). While most of the previous work has focused on the theoretical predictions, here we investigate the most suitable statistical framework to constrain ULB masses and self-interactions using BH spin measurements. We argue that a Bayesian approach based on a simple timescales analysis provides a clear statistical interpretation, deals with limitations regarding the reproducibility of existing BH analyses, incorporates the full information from BH data, and allows us to include additional nuisance parameters or to perform hierarchical modelling with BH populations in the future. We demonstrate the feasibility of our approach using mass and spin posterior samples for the X-ray binary BH M33 X-7 and, for the first time in this context, the supermassive BH IRAS 09149-6206. We explain the differences to existing ULB constraints in the literature and illustrate the effects of various assumptions about the superradiance process (equilibrium regime vs cloud collapse, higher occupation levels). As a result, our procedure yields the most statistically rigorous ULB constraints available in the literature, with important implications for the QCD axion and axion-like particles. We encourage all groups analysing BH data to publish likelihood functions or posterior samples as supplementary material to facilitate this type of analysis, and for theory developments to compress their findings to effective timescale modifications.