The Structure of Rotating Stars: the J2 Method and Results for Uniform Rotation

The J² method for solving the structure of uniformly and non-uniformly rotating stars is briefly described and compared with other methods. The method is restricted to rotation laws of the form $$\Omega = \Omega(\omega)$$, but involves no approximation regimes and is capable of creating a self-consistent density and potential field. The structure equations are written in essentially the same form as they would take in the absence of rotation. The explicit effects of rotation are included through correction factors which depend only on the total potential. Results are given for uniform rotation using a Roche approximation in order to calculate the correction factors. Corrections arising from a better approximation to the potential are shown to be small. The results show good agreement with other authors but some discrepancies are pointed out.