Superradiant evolution of the shadow and photon ring of Sgr A$^\star$

Abstract: Ultralight bosons can affect the dynamics of spinning black holes (BHs) via superradiant instability, which can lead to a time evolution of the supermassive BH shadow. We study prospects for witnessing the superradiance-induced BH shadow evolution, considering ultralight vector and tensor fields. We introduce two observables sensitive to the shadow time-evolution: the shadow drift, and the variation in the azimuthal angle lapse associated to the photon ring autocorrelation. The two observables are shown to be highly complementary, depending on the observer's inclination angle. Focusing on the supermassive object Sgr A$^\star$ we show that both observables can vary appreciably over human timescales of a few years in the presence of superradiant instability, leading to signatures which are well within the reach of the Event Horizon Telescope for realistic observation times (but benefiting significantly from extended observation periods), and paving the way towards probing ultralight bosons in the $\sim 10^{-17}\,{\rm eV}$ mass range.