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 ₒ and radius rₒ 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 ₒ and rₒ of the DM halo. Afterward, by varying the values of ₒ and rₒ, key parameters such as the effective potential V₄₅₅ of photons, the critical impact parameter b₇, the radius r₈ₒ₂₎ of the innermost stable circular orbit, and the the radius r₇ of the photon sphere were calculated for each case. It was found that as ₒ and rₒ 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 ₒ and rₒ increase, the peak of the received intensity shifts toward a higher impact parameter b, resulting in a distinct optical appearance.
Luo et al. (Mon,) studied this question.