Influence of plasma on the observational appearance of rotating black holes in Horndeski gravity

Abstract: Exploring the influence of plasma on the light rays trajectories in the vicinity of black holes is significat since that astrophysical black holes are generally surrounded by a plasma medium. In this work, we analyze the null geodesics in the space-time of rotating hairy Horndeski black holes immersed in a plasma medium using the Hamilton-Jacobi method. By considering both uniform and non-uniform plasma distributions, we perform a comparative study of their effects on the black hole shadow. The impact of the hair parameter and the inclination angle on the black hole shadow is also investigated. Finally, the shadow results are compared with observational data of the Event Horizon Telescope for M87* to constrain the plasma parameter.