NEWTON ITERATION METHOD FOR OBTAINING EQUILIBRIA OF RAPIDLY ROTATING STARS

A new computational method for the construction of rapidly rotating stellar models is described; it combines the high (quadratic) convergence of the Newton-Raphson procedure with the use of a fine mesh, typical of self-consistent field schemes. For the presentation of the gravitational potential a finite difference approximation to the Poisson equation is used, and the iterations of the potential are used to find the distribution of matter consistent with its gravity. It is necessary to solve a huge system of linear equations on every iteration step, but the matrix of the system is sparse, so that powerful sparse matrix solvers can be applied here. The high convergence rate of the iteration procedure and a robust sparse system solver warrant the high accuracy of calculations. The method is powerful enough for the description of models with a large density contrast and high T/\W\, where T and W are total kinetic and gravitational energy respectively. The efficiency of the method is tested in calculations of the stationary states for polytropes for T/\W\ up to 0.425.