Equilibrium structure of differentially rotating polytropic models of the stars

In this paper we propose a method for computing the equilibrium structure of differentially rotating polytropic models of the stars. A general law of differential rotation of the type ²=b₀+b₁s²+b₂s⁴, which can account for a reasonably large variety of possible differential rotations in the stars has been used. The distortional effects have been incorporated in the structure equations up to second order of smallness in distortion parametersb₀,b₁, andb₂ using Kippenhahn and Thomas' averaging approach in conjunction with Kopal's results on Roche equipotentials in manner similar to the one earlier used by Mohan and Saxena for computing the equilibrium structure of polytropes having solid body rotation. Numerical results have been obtained for various types of differentially rotating polytropic models of stars of polytropic indices 1.5, 3, and 4. Certain differentially rotating models of the Sun which are possible with such a type of law of differential rotation, have also been computed.