White dwarfs as a probe of dark energy

Abstract

We investigate the radial density distribution of the dynamical dark energy inside the white dwarfs (WDs) and its possible impact on their intrinsic structure. The minimally-coupled dark energy with barotropic equation of state which has three free parameters (density, equation of state and effective sound speed) is used. We analyse how such dark energy affects the mass-radius relation for the WDs because of its contribution to the joint gravitational potential of the system. For this we use Chandrasekhar model of the WDs, where model parameters are the parameter of the chemical composition and the relativistic parameter. To evaluate the dark energy distribution inside a WD we solve the conservation equation in the spherical static metric. Obtained distribution is used to find the parameters of dark energy for which the deviation from the Chandrasekhar model mass-radius relation become non-negligible. We conclude also, that the absence of observational evidence for existence of WDs with untypical intrinsic structure (mass-radius relation) gives us lower limit for the value of effective sound speed of dark energy $c_s^2 \gtrsim 10^{-4}$ (in units of speed of light).