Superradiance evolution of black hole shadows revisited

Black hole (BH) shadows can be used to probe new physics in the form of ultra-light particles via the phenomenon of superradiant instability. By directly affecting the BH mass and spin, superradiance can lead to a time evolution of the BH shadow, which nonetheless has been argued to be unobservable through Very Long Baseline Interferometry (VLBI) over realistic observation timescales. We revisit the superradiance-induced BH shadow evolution including the competing effects of gas accretion and gravitational wave (GW) emission and, as a first step towards modelling realistic new physics scenarios which predict the existence of multiple ultra-light species, we study the system in the presence of two ultra-light bosons, whose combined effect could help reducing the shadow evolution timescale. We find that accretion and GW emission play a negligible role in our results (justifying previous simplified analyses), and that contrary to our intuition the inclusion of an additional ultra-light boson does not shorten the BH shadow evolution timescale and hence improve detection prospects. However, we point out an important subtlety concerning the observationally meaningful definition of the superradiance-induced BH shadow evolution timescale, which reduces the latter by about an order of magnitude, opening up the possibility of observing the superradiance-induced BH shadow evolution with upcoming VLBI arrays, provided angular resolutions just below the $\mu{\rm as}$ level can be reached. As a concrete example, we show that the angular size of the shadow of SgrA$^*$ can change by up to $0.6\,\mu{\rm as}$ over a period as short as $16$ years, which further strengthens the scientific case for targeting the shadow of SgrA$^*$ with next-generation VLBI arrays.