Self-gravitating barotropic equilibrium configurations of rotating bodies with SPH

We present a novel relaxation method to build three-dimensional rotating structures of barotropic bodies using the SPH technique. The method is able to relax gaseous structures in rigid as well as differential rotation. The relaxation procedure strongly relies on the excellent conservation of angular momentum that characterizes the SPH technique. The method has been successfully applied to a variety of zero-temperature white dwarfs and polytropic self-gravitating structures. Our SPH results have been validated by comparing the main features (energies, central densities and the polar to equatorial radius ratio) to those obtained with independent, albeit grid-based methods, as for example, the self-consistent field method, showing that both methods agree within few percents.