Rotational equilibria by Lagrangian variational principle: toward multi-dimensional stellar evolutions

TL;DR

This paper introduces a new Lagrangian variational formulation for modeling self-gravitating, axisymmetric rotating stars, capable of handling complex equations of state and aiming to improve multi-dimensional stellar evolution simulations.

Contribution

The authors develop a novel Lagrangian variational approach with a triangulated mesh for axisymmetric stellar configurations, including barotropic and baroclinic cases, suitable for multi-dimensional evolution modeling.

Findings

Validated against existing self-consistent field schemes.

Successfully modeled shellular-type rotation configurations.

Provides a foundation for future two-dimensional stellar evolution simulations.

Abstract

We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.