The shadows and photon rings of two minimal deformations of Schwarzschild black holes*

Abstract This paper primarily investigates the optical properties of two minimal deformations of the Schwarzschild black hole—the Kazakov-Solodukhin and Ghosh-Kumar black holes—under different accretion models. The event horizon, photon sphere, and critical impact parameter of the former increase relative to the Schwarzschild case, whereas those of the latter decrease. Data from the Event Horizon Telescope Collaboration are used to constrain the parameter ranges of the two black holes. Under spherical accretion, the quantum correction of the Kazakov-Solodukhin black hole enlarges the black hole shadow and reduces the integrated intensity, while the shadow of the magnetically charged Ghosh-Kumar black hole shrinks and the integrated intensity increases. The black hole’s shadow radius is independent of the choice of spherical accretion model. For an optically and geometrically thin accretion disk, the integrated intensity is dominated by direct emission, with photon-ring and lensed-ring contributions being negligible. In addition, the photon and lensed rings of the Kazakov-Solodukhin black hole are narrower, whereas those of the Ghosh-Kumar black hole are broader. Whereas the Kazakov-Solodukhin black hole is brighter, the Ghosh-Kumar black hole is dimmer. Additionally, bringing the disk closer to the black hole yields a smaller shadow radius. This paper proposes a method to distinguish different black holes within a specific thin-disk model.