Structural Implications of the Chameleon Mechanism on White Dwarfs

Abstract: We study the impact of the chameleon mechanism on the structure of white dwarfs. Using a shooting method of our design, we solve the corresponding scalar-tensor equilibrium equations for a Chandrasekhar equation of state, exploring various energy scales and couplings of the chameleon field to matter. For the considered parameter ranges, we find the chameleon field to be in a thick-shell configuration, identifying for the first time in the literature a similarity relation of the theory for the radially normalised scalar field gradient. Our analysis reveals that the chameleon mechanism alters the internal pressure of white dwarfs, leading to a reduction in the stellar radii and masses and shifting the mass-radius curves below those predicted by Newtonian gravity. This lowers also the specific heat of white dwarfs, accelerating their cooling process. Finally, we derive parametric expressions from our results to expedite future analyses of white dwarfs in scalar-tensor theories.