Structure of rapidly rotating axisymmetric stars. I, A numerical method for stellar structure and meridional circulation

We present a numerical method to calculate the mechanical and thermal structure of stationary axisymmetric inviscid rotating stars in which the velocity of the meridional flow is very slow. We further assume that the centrifugal force can be derived from a rotational potential. With these assumptions surfaces of constant temperature, pressure, and density coincide, i.e. the structure and the flow can be treated separately. Thus we first compute the structure of the rotating configuration and then calculate the flow pattern for the given configuration. In order to demonstrate how our method works, we have computed several sequences of stationary configurations for three different rotation laws.