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

TL;DR

This work develops a Bayesian, timescale-based framework to constrain ultralight bosons via BH superradiance, using BH mass–spin posteriors and Regge-trajectory logic to translate observations into exclusions on boson mass μ and self-interaction scale f^{-1}. By computing SR rates with nonrelativistic and relativistic (continued fraction) methods and incorporating self-interactions (equilibrium vs. bosenova), the authors produce statistically rigorous ULB limits from two representative BHs, M33 X-7 and IRAS 09149-6206, and compare against previous approaches. The method, which marginalizes over BH parameters (M,a_*) with MC integration, naturally handles correlations and non-Gaussian posteriors, enabling combination across multiple BHs and future hierarchical modelling. They demonstrate that higher SR levels and precise BH masses extend the constrained μ range, emphasize the value of sharing full posteriors for reproducible ULB analyses, and discuss limitations and directions for including GW data and population-level effects. Overall, the paper delivers a transparent, versatile framework that strengthens constraints on QCD axions and axion-like particles from BH spin measurements and sets the stage for integrated global analyses.

Abstract

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.

Figures (6)

• Figure 1: The $\left|211\right\rangle$ superradiance rate (times the gravitational radius, $M$), computed using different methods. For benchmark values of $M = 10\,\mathrm{M}_\odot\xspace$ and $a_*\xspace = 0.99$, we compare the continued fraction method (CFM; orange line), adopted in this work, to the SuperRad code (dotted, black line), and our implementation of the next-to-leading-order corrections (NLO; dashed, blue line). For completeness, we also show the non-relativistic approximation (NRA; dashed-dotted, red line).
• Figure 2: The sampled BH mass and spin distribution (black points) of M33 X-7 and Regge trajectories of the non-interacting (grey lines and shaded region) and self-interacting $\left|211\right\rangle$ level (dotted, grey line; equilibrium regime, $f\xspace^{-1}\xspace = 2e-15\GeV^{-1}$), $\mu\xspace = 0.27e-12\eV$, and $\tau_\text{BH}\xspace = 3e6\yr$. The full distribution, whose mean is marked with a white star, is compared to its $2\sigma$ error bars for an uncorrelated (dashed, orange line) and full (blue line) Gaussian, and a '$2\sigma$ box' (dotted, red line).
• Figure 3: The sampled BH mass and spin distribution (black points) of IRAS 09149-6206 and Regge trajectories of the non-interacting (grey lines and shaded region) and self-interacting $\left|211\right\rangle$ level (dotted, grey line; equilibrium regime, $f\xspace^{-1}\xspace = 3e-16\GeV^{-1}$), $\mu\xspace = 3e-19\eV$, and $\tau_\text{BH}\xspace = 4.5e8\yr$. The full distribution, whose median is marked with a white star, is compared to its $2\sigma$ error bars for an uncorrelated (dashed, orange line) and full (blue line) Gaussian, and a '$2\sigma$ box' (dotted, black lines).
• Figure 4: Normalised posterior probability density distributions for $(\mu\xspace,f\xspace^{-1}\xspace)$ for IRAS 09149-6206 (left) and M33 X-7 (right). We show the 95% credible regions at highest posterior density for both the equilibrium (solid line) and bosenova (dashed lines) scenarios and, in the right panel, the QCD axion model line (dashed-dotted line) predicted by \ref{['eq:qcd_axion_mass']}). Note that we highlight (grey shading) the $\mu$ region where more than 5% of BH mass samples imply $\alpha > 0.2$ (dotted line) and, meaning that the computation of the superradiance rate involves large theoretical uncertainties and may not be valid.
• Figure 5: Comparison of exclusion methods at fixed mass $\mu$ for non-interacting ULBs for IRAS 09149-6206 (left) and M33 X-7 (right). We compare our approach for the full posterior distribution with $n = 2$ (solid blue lines) and $n \leq 6$ (dotted blue lines) compared to uncorrelated Gaussians ('Uncorr.'; dashed-dotted, purple line) and the 'box method' ('Box'; dashed, red line).