Environmental Dependence of Ultralight Boson Constraints from Black Hole Superradiance

Black-hole superradiance provides a powerful probe of ultralight bosons through their effect on observed spin distributions. This work develops a hierarchical Bayesian framework employing an MCMC sampler to study how astrophysical environments modify the constraints on μ (the ultralight-boson mass parameter) derived from black-hole spin measurements. A phenomenological model with parameters a₀​ (environmental suppression scale) and q (coupling strength) describes the disc-induced suppression of boson field's growth rate. By sweeping a grid of (a₀, q) values, the analysis quantifies how environmental coupling shifts the inferred boson-mass posterior and exclusion probability for systems such as the supermassive black hole IRAS 09149-6206 and X-ray binary M33 X-7. The resulting sensitivity maps of μ versus a₀ for multiple q values extend the statistically rigorous superradiance framework to include environment-dependent effects and enabling joint inference over (μ, a₀, q), assessing the robustness of superradiance limits under astrophysical uncertainties.