A versatile numerical method for obtaining structures of rapidly rotating baroclinic stars: self-consistent and systematic solutions with shellular-type rotation

This paper develops a novel numerical method for obtaining structures of rapidly rotating stars based on a self-consistent field scheme. The solution is obtained iteratively. Both rapidly rotating barotropic and baroclinic equilibrium states are calculated self-consistently using this method. Two types of rotating baroclinic stars are investigated by changing the isentropic surfaces inside the star. Solution sequences of these are calculated systematically and critical rotation models beyond which no rotating equilibrium state exists are also obtained. All of these rotating baroclinic stars satisfy necessarily the Bjerknes-Rosseland rules. Self-consistent solutions of baro-clinic stars with shellular-type rotation are successfully obtained where the isentropic surfaces are oblate and the surface temperature is hotter at the poles than at the equator if it is assumed that the star is an ideal gas star. These are the first self-consistent and systematic solutions of rapidly rotating baroclinic stars with shellular-type rotations. Since they satisfy the stability criterion due to their rapid rotation, these rotating baroclinic stars would be dynamically stable. This novel numerical method and the solutions of the rapidly rotating baroclinic stars will be useful for investigating stellar evolution with rapid rotations.

A Novel Formulation by Lagrangian Variational Principle for Rotational Equilibria: Toward Multi-Dimensional Stellar Evolutions

We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic equations of state, for which angular momentum distributions are not necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional, which is evaluated on a triangulated mesh. This letter is a proof of principle and detailed comparisons with existing results will be reported in the sequel, but some test calculations are presented, in which we have achieved an error of $O(10^{-4})$ in the Virial relation. We have in mind the application of this method to two-dimensional calculations of the evolutions of rotating stars, for which the Lagrangian formulation is best suited.