Shadow and quasi-normal modes of Schwarzschild–Hernquist black hole

In this paper we study the shadow and quasi-normal modes (QNMs) of a black hole (BH) surrounded by a dark matter halo with Hernquist-type density distribution, which was reported in Cardoso et al. (Phys. Rev. D 105(6):L061501, 2022). In astrophysical scenarios, we find that the shadow radius enlarges as the compactness of halo increases. Therefore, we obtain an upper bound for the compactness C≤ 0.092 C ≤ 0.092 with the Event Horizon Telescope (EHT) observations. We calculate axial gravitational QNMs of the galactic BH up to C~ O(1) C ∼ O ( 1 ) , and fit the redshift relative to Schwarzschild QNMs up to second order in the compactness (for C≤ 0.3) C ≤ 0.3 ) . These highly redshifted QNMs, resulting from large compactness, are key to modeling the dark matter halo.