Considering a black hole immersed in a dark halo described by an exponential density profile, and following Ref. [1], we derive the general analytical solution to the Einstein’s equations for the case where the mass of the galaxy is much smaller than the length-scale of the halo. Then, we study the null geodesics and calculate the black hole shadow radius and compare it with the shadow of the black hole surrounded by various matter distribution profiles in the galactic halo, such as the Hernquist, Navarro-Frenk-White, Burkert, Taylor -Silk profiles. Using the M87* and Sgr A* shadow data obtained by the Event Horizon Telescope, we constrain the compactness parameter of the exponential dark matter halo. Finally, we investigate the electromagnetic properties of the accretion disk around such a black hole and compare its luminosity with those of other profiles. Our results show that the shadow radius is larger than that predicted by general relativity and larger than the shadow of a black hole surrounded by other density profiles. Furthermore, accretion disks in the presence of an exponential density profile are hotter and more luminous than those in halos described by other profiles.
