Using the Method of Orthogonal Collocation for Certain Three-Dimensional Problems of Stellar Structure

Abstract

The method is developed for two specific problems: (if computation of the structure of the primary component (assumed to consist of a polytropic gas) in a synchronous close binary sysiem and (ii) search for non-axisymmetric configurations of diffeentially rotating polytropes. In both cases the structure equations reduce to a mildly non-linear elliptic partial differential equation in three dimensions with boundary conditions at the center, on a sphere containing the star and involving a 'free' boundary. The present method has several advantages over the 'standard' methods (namely, improvements of Chandrasekhar's perturbation analysis). The most important of these are consistency and easier application to real stars. However, the method becomes computationally inefficient when used for computing of configurations with strong angular dependence. In such cases (related) Galerkin methods offer significant advantages.