Shadows and observational images of a Schwarzschild-like black hole surrounded by a Dehnen-type dark matter halo

This paper investigates the optical appearance of a Schwarzschild-like black hole (BH) surrounded by a Dehnen-(1, 4, 5/2) 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 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 investigated the optical appearance of the BH illuminated by two types of accretion models: optically and geometrically thin disk models and spherical accretion models. 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.