Observational features of deformed Schwarzschild black holes illuminated by an anisotropic accretion disk

The projection effect of an anisotropic accretion disk causes its electromagnetic radiation to depend on the emission angle. Although this dependency has the potential to influence the observational characteristics of black holes, it has not received sufficient attention. In this paper, we employ a relativistic ray-tracing algorithm to numerically simulate 86 GHz and 230 GHz images of deformed Schwarzschild black holes illuminated by an equatorial anisotropic accretion disk, aiming to reveal the observational signatures of the target black hole and the impact of the projection effect on the images. The study demonstrates that while the introduction of the projection effect does not alter the profiles of the black hole's inner shadow and critical curve, it significantly suppresses the specific intensity of light rays, particularly in direct emission, thereby reducing image brightness. The extent of this reduction depends on both the observation inclination and frequency. This phenomenon aids in the extraction of geometric information from higher-order subrings in the image. Furthermore, we find that increasing the deformation parameter enhances the brightness of the deformed Schwarzschild black hole image, accompanied by a reduction in the size of the critical curve and inner shadow. This relationship establishes a connection between the intrinsic properties of deformed Schwarzschild black holes and their observational characteristics, providing a reliable tool for testing the no-hair theorem and gravitational theories. Specifically, we propose a novel method for constraining parameters based on the silhouette of the inner shadow, which holds promise for extension to any spherically symmetric black hole in other gravitational theories.