Accretion of Self-interacting Scalar Field Dark Matter Onto a Reissner-Nordström Black Hole

Self-interacting scalar field dark matter can be seen as an extension of the free case known as Fuzzy dark matter. The interactive case is capable of reproducing the positive features of the free case at both astrophysical and cosmological scales. On the other hand, current imaging black holes (BHs) observations provided by the Event Horizon Telescope (EHT) collaboration cannot rule out the possibility that BHs can carry some amount of charge. Motivated by these aspects, and by the possibility of detecting dark matter through its gravitational imprints on BH observations, in this paper, we extend previous studies of accretion of self-interacting scalar field dark matter to the charged BH case. Our analysis is based on the assumption on spherically symmetric flow and employs a test fluid approximation. All analytical expressions are derived from the ground up in Schwarzschild coordinates. Concretely, we implement analytical and numerical approaches to investigate the impact of the charge on the energy flux. From this analysis, we notice that the mass accretion rate efficiency is reduced up to $\sim 20\%$ for the maximum allowed charge. Additionally, considering the mass accretion rate of M87$^{\star}$ inferred from Polarization data of the EHT, we infer the conservative bound $ \lambda_4 > (1.49-10.2)( m / 1 \rm {eV} )^4$ based on the simple criterion that ensures the mass accretion rate caused by DM remains subdominant compared to the baryonic component.