Shadow and Quasi-Normal Modes of Schwarzschild-Hernquist Black Hole

Abstract: 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 Ref. \cite{Cardoso:2021wlq}. 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 ${\cal C}\le0.092$ with the Event Horizon Telescope (EHT) observations. We calculate axial gravitational QNMs of the galactic BH up to ${\cal C}\sim{\cal O}(1)$, and fit the redshift relative to Schwarzschild QNMs up to second order in the compactness (for ${\cal C}\le0.3)$. These highly redshifted QNMs, resulting from large compactness, are key to modeling the dark matter halo.