Roche-coordinates and metric coefficients for differentially rotating polytropic stars

Kopal introduced a new system of coordinates,to study the problems of close binary stars,called Roche-coordinates. Besides studying the other problems of close binary stars,Kopal also considered the possibility of using this system of coordinates to study the problem of stability and oscillations of rotating stars in close binary systems. This paper insists that the mathematical modeling may be applicable for the problems about the stars. Kopal obtained explicit expressions of three curvilinear coordinates for the system of Roche-coordinates associated with the Roche-model of a star,distorted by solid body rotational forces. One coordinate can be defined in by the equipotential surface,which is known in close algebraic form. Second becomes identical with the meridional planes of rotationally distorted model,while the third follows from the requirements of the orthogonality to the others. The expressions of these coordinates in terms of polar or cartesian system,but in the form of infinite series are converge rapidly for any distortion below that which is entail equatorial break-up. Following Kopal’s approach,we obtained the explicit expressions for Roche-coordinates associated with the polytropic models of stars distorted by differential rotation. These coordinates and harmonics can be used to define the structure and local/vibrational stability of the polytropic Roche-models. © School of Engineering,Taylor’s University.