EQUILIBRIUM STRUCTURE OF STARS OBEYING A GENERALIZED DIFFERENTIAL ROTATION LAW

In the present paper we have considered the problem of determining the equilibrium structure of differentially rotating stars in which the a ngular velocity of rotation varies both along the axis of rotation and in directions perpendicular to it. For this purpose, a generalized la w of differential rotation of the type omega2 = b0+b1s2+b2s4+b3z2+b4z4 +b5z2s2 (here omega is a nondimensional measure of the angular velocit y of a fluid element distant s from the axis of rotation and z from th e plane through the centre of the star perpendicular to the axis of ro tation, and b's are suitably chosen parameters) has been used. Whereas Kippenhahn and Thomas averaging approach has been used to incorporate the rotational effects in the stellar structure equations, Kopal's re sults on Roche equipotentials have been used to obtain the explicit fo rm of the stellar structure equations, which incorporate the rotationa l effects up to second order of smallness in the distortion parameters . The method has been used to compute the equilibrium structure of cer tain differentially rotating polytropes. Certain differentially rotati ng models of the Sun have also been computed by using this approach.