Plasma Influence on the Shadow and its Observables of a Black Hole Immersed in Dark Matter

Plasma, as a medium around the black hole for light propagation, is known to visibly alter the shape of its shadow and the observables, which could impact the interpretation of the Event Horizon Telescope results. In this study, we examine how dark matter and non-magnetized, pressureless plasma influence the shadow of a rotating black hole. We find that astrophysically reasonable amounts of dark matter have no significant impact on the photon trajectories for the black hole model we consider. We also analyze the null-geodesics in the presence of both homogeneous and inhomogeneous plasma profiles and show how their influence on photon orbits affects the resulting black hole shadow. Our findings indicate that increasing the black hole's spin generally enlarges both the shadow radius and deformation. Additionally, the viewing angle lengthens the shadow radius while reducing deformation as the observer moves farther from the equatorial plane. We also observe that increasing plasma density increases both the shadow radius and deformation for homogeneous plasma, while it decreases them for inhomogeneous plasma. Overall, the plasma density has noticeable effects on the shadow observables, which reveal the possibilities of potential parameter tuning and interpretation of the EHT telescopes' results in future experiments.