Gravitational lensing and shadow around a non-minimally coupled Horndeski black hole in plasma medium

We investigate the light deflection and the shadow characteristics of a non-minimally coupled Horndeski black hole surrounded by a magnetized, cold, pressureless plasma medium, while considering both homogeneous and non-homogeneous plasma distributions. We consider an analytical expression for the deflection angle of light and analyze how it is influenced by the plasma properties and the Horndeski coupling constant. The circular light orbits, which define the photon sphere, are also analyzed for both types of plasma media, highlighting their impact on the shadow boundary. The shadow properties of the black hole are examined in detail, and constraints on the model parameters are derived by comparing the theoretical shadow radius with observational measurements of Sgr A* and M87* obtained by the Event Horizon Telescope Collaboration. We also study the black hole shadow images along with the corresponding intensity profiles produced by a radially infalling accretion flow in the plasma environment. The results are particularly interesting, as they reveal how the modified black hole geometry affects both the plasma distribution and the black hole parameters in a realistic astrophysical context.