Screening Mechanisms on White Dwarfs: Symmetron & Dilaton

This work provides the first comparison of the symmetron and dilaton fields in white dwarfs. We show how these screening mechanisms behave inside {such stars} and their impact on stellar properties. Employing a custom-developed shooting method, we solve the scalar-tensor equilibrium equations in the Newtonian approximation. We consider a Chandrasekhar equation of state and examine a range of potential mass scales and coupling strengths for both fields. Both fields enhance the pressure drop in low-density white dwarfs, leading to smaller stellar masses, radii, and luminosities. Unlike chameleon models, their effects are suppressed in more massive stars, with symmetron fields fully decoupling and dilaton fields weakening but not vanishing. Consequently, no mass-radius curve for screened white dwarfs exceeds the Newtonian prediction in any of these three mechanisms. The mass-radius deviations are generally more pronounced at lower densities, depending on model parameters. Due to their common runaway potential, we confirm that dilaton and chameleon fields display similar field and gradient profiles. In contrast, due to their environment-dependent coupling, the dilaton and symmetron mechanisms exhibit stronger density-dependent screening effects. These findings highlight both phenomenological differences and theoretical similarities among these mechanisms, motivating asteroseismology studies to constrain the symmetron and dilaton parameter spaces.