  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.
