Shadows and Observational Images of a Schwarzschild-like Black Hole Surrounded by a Dehnen-type Dark Matter Halo

This study investigates the optical appearance of a Schwarzschild-like black hole (BH) surrounded by a Dehnen-type dark matter (DM) halo, with a focus on how the DM halo's density ρₛ and radius rₛ influence the BH's shadow and photon ring. First, the radius rₕ of the BH's event horizon and the equation of motion for photons were derived, and observational data from the Event Horizon Telescope (EHT) for M87* were used to constrain the parameters ρₛ and rₛ of the DM halo. Afterward, by varying the values of ρₛ and rₛ, key parameters such as the effective potential Veff of photons, the critical impact parameter bₚₕ, the radius risco of the innermost stable circular orbit,and the the radius rₚₕ of the photon sphere were calculated for each case. It was found that as ρₛ and rₛ increase, the above mentioned parameters all show an increasing trend. Subsequently, we examined the optical appearance of the BH under two models: one with an optically and geometrically thin accretion disk and the other with a static spherical accretion model. The findings indicate that as ρₛ and rₛ increase, the peak of the received intensity shifts toward a higher impact parameter b, resulting in a distinct optical appearance.