Chameleon Screening and Fifth Force in Globular Clusters I: King Model

Those globular clusters that are located in the halo of galaxy experience a weak gravitational force due to their great distance from the center of their host galaxy, so they are characterized by extremely low gravitational potential. This unique characteristics make them important subjects of research in various fields. The study of clusters, analyzing the dynamics and gravitational interactions within them, offers a unique opportunity to explore the implications of modified gravity theories, such as fifth force interactions or unscreened regions. In our paper, we explore the presence and extent of an unscreened region in the outer layers of an isothermal sphere, as represented by the King model and influenced by a chameleon field. Also we consider the acceleration resulting from the chameleon field and then proceed to calculate the line-of-sight velocity dispersion under the influence of the chameleon and compare it with Newtonian predictions. Our findings reveal that the dynamical impact of the fifth force can be observed throughout the entire of the globular cluster.