High Altitude Observatory, National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO 80307

A new formulation of the self-consistent-field (SCF) method for computing models of rapidly, differentially rotating stars is described. The angular velocity is assumed to depend only on the distance from the axis of rotation. In the modified SCF iterative scheme, normalized distributions of two thermodynamic variables - pressure and temperature - are used as trial functions, while the central values of the pressure and temperature are adjusted by a Newton-Raphson iteration. A two-dimensional density distribution, which is needed to compute the gravitational potential, is readily obtained from the pressure and temperature through the equation of state in conjunction with a third trial function specifying the two-dimensional shape of the constant-density surfaces. Rotating models of chemically homogeneous main-sequence stars have been computed as necessary in order to illustrate the algorithm and to make comparisons with existing models. Unlike previous implementations of the SCF method, the method described here is not limited to the upper main-sequence: it converges for all main-sequence masses, including those well below 9M. Moreover, the method converges for all values of the parameter  t = T ⁄ |W|  (the ratio of rotational kinetic energy to gravitational potential energy) that are at least as high as those obtained by Clement's relaxation technique. The method is also capable of producing models with deep concavities about the poles as well as models with extreme oblateness (far greater than that possible in uniformly rotating stars). For cases with moderate degrees of differential rotation (say for ₀ ⁄ _e < 10, where ₀ and _e denote the angular velocity at the center and at the equator, respectively), the method has been found to be remarkably robust. For higher degrees of differential rotation, models are restricted to a portion of parameter space away from two regions of nonconvergence, inside which some of the models evidently develop toroidal level surfaces.

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