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

Abstract 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 ρ s and radius r s influence the BH's shadow and photon ring. First, the radius r h 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 ρ s and r s of the DM halo. Afterward, by varying the values of ρ s and r s , key parameters such as the effective potential V eff of photons, the critical impact parameter b ph , the radius r isco of the innermost stable circular orbit, and the radius r ph of the photon sphere were calculated for each case. It was found that as ρ s and r s 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 ρ s and r s increase, the peak of the received intensity shifts toward a higher impact parameter b , resulting in a distinct optical appearance.