Modified electron dispersion relations in degenerate white dwarfs

Abstract

We investigate how modified electron dispersion relations affect the structure of cold white dwarfs (WDs). The deformation is introduced only in the degenerate electron equation of state, through the energy of a single particle and the group velocity, while the stellar mass density remains dominated by ions through the relation $ρ\simeq μ_e m_u n_e$ imposed by charge neutrality. The resulting equations of state are coupled to the standard TOV equations, with no modification of the gravitational field equations. For a baseline composed of carbon and oxygen with $μ_e=2$, the undeformed limit recovers a maximum mass in the Chandrasekhar scale, validating the normalization of the calculation before the modified cases are considered. The first model of modified dispersion produces only a modest stiffening over the parameter range studied, whereas the logarithmic model depends strongly on the sign of the deformation parameter: negative values increase the pressure and the maximum mass, while positive values soften the sequence. These results show that WDs can isolate the impact of modified electron kinematics on compact star structure, but the logarithmic branch in particular requires further restrictions from its physical domain, stability conditions, and observational constraints on mass and radius.