Direct mass measurements of superradiance clouds near black holes

Ultralight scalars emerge naturally in several motivated particle physics scenarios and are viable candidates for dark matter. While laboratory detection of such bosons is challenging, their existence in nature can be imprinted on measurable properties of black holes (BHs). The phenomenon of superradiance can convert the BH spin kinetic energy into a bound cloud of scalars. In this work, we propose a new technique for directly measuring the mass of a dark cloud around a spinning BH. We compare the measurement of the BH spin obtained with two independent electromagnetic techniques: continuum fitting and iron Kα spectroscopy. Since the former technique depends on a dynamical observation of the BH mass while the latter does not, a mismatch between the two measurements can be used to infer the presence of additional extended mass around the BH. We find that a precision of ∼1% on the two spin measurements is required to exclude the null hypothesis of no dark mass around the BH at a 2σ confidence level for dark masses about a few percent of the BH mass, as motivated in some superradiance scenarios.