Interior structure of rotationally and tidally distorted stars

A simple but powerful method for determining the interior equilibrium structure of a non-spherical star is derived for uniformly rotating and tidally distorted stars. The vector differential equations governing the interior structure are reduced to a form identical with the standard equations of a spherical star, except for the presence of two dimensionless form factors representing the effects of distortion. One factor accounts for the buoyancy of centrifugal force and is evaluated exactly. The other factor expresses the effect of the non-spherical stellar shape, and it is shown that the factor can be determined very accurately, even if the stellar shape is known only approximately. With these factors determined, the problem of constructing the distorted model is identical to that for the spherical model, and computational schemes developed for spherical stars are applicable to distorted stars as well. The method is applied to several rotationally and tidally distorted, zero age main sequence models of ten, five, and one solar mass, and the results are compared to the results of several other methods. It is shown that the present method computes models as accurately as those of Sackmann (1970) and Naylor and Anand (1972b) who used the more complicated double approximation method. An inaccuracy is identified in a similar form factor method formulated by Kippenhahn and Thomas (1970). The versatility of the present method makes it readily applicable to determining the evolution of distorted stars, and guidelines are presented for its use in evolution computations. Also, a means is proposed for extending the method to differentially rotating stellar models which at present may be constructed only by the complex self consistent field method of Jackson (1970b).