A form-factor method for determining the structure of distorted stars

Abstract

The equilibrium equations of a uniformly rotating and tidally distorted star are reduced to the same form as for a spherical star except for the inclusion of two form factors. One factor, expressing the buoyancy effects of centrifugal force, is determined directly from the integrated structure variables. The other factor, expressing the deviation from spherical shape, is shown to be relatively insensitive to errors in the assumed shape, so that accurate solutions are obtained in spite of the use of an a priori shape. The method is employed by adding computations for the factors to an existing spherical model program. Upper Main Sequence models determined by this method compare closely with results from the double approximation method even for critical rotation and tidal distortion.