Constraining Self-interacting Scalar Field Dark Matter From the Black Hole Shadow of the Event Horizon Telescope

An exciting possibility to constrain dark matter (DM) scenarios is to search for their gravitational imprints on Black Hole (BH) observations. In this paper, we investigate the impact of self-interacting scalar field DM on the shadow radius of a Schwarzschild BH. We implement a self-consistent formulation, paying attention to the enhancement of the DM density due to the BH gravitational influence and the accretion flow onto the BH. First, we calculate the first-order correction to the shadow radius caused by a general DM environment. Then, we apply this perturbative method to the case of self-interacting scalar field DM and derive analytical expressions for the critical impact parameter. We find that self-consistency requirements, involving the lifetime and the mass of the central DM soliton, or the mass and the size of the extended virialized DM halo, ensure that the impact of the DM environment on the shadow radius is below the observational upper bound. This emphasizes the importance of taking into account the self-consistency constraints of the underlying DM scenario, which can strongly limit the range of possible DM density profiles and their impact on the shadow radius.