EQUILIBRIUM STRUCTURES OF DIFFERENTIALLY ROTATING PRIMARY COMPONENTS OF BINARY STARS C. MOHAN Dept. of Mathematics, University of Roorkee, Roorkee, India A.K. LAL School of Basic and Applied Sciences, T.I.E.T., Patiala, India V.P. SINGH Department of Mathematics, I.P.T., Saharanpur, India (Received 25 February, 1997; accepted 4 December, 1997) Abstract. In this paper a method is proposed for computing the equilibrium structures and various other observable physical parameters of the primary components of stars in binary systems assuming that the primary is more massive than the secondary and is rotating differentially about its axis. Kippenhahn and Thomas averaging approach (1970) is used in a manner earlier used by Mohan, Saxena and Agarwal (1990) to incorporate the rotational and tidal effects in the equations of stellar structure. Explicit expressions for the distortional terms appearing in the stellar structure equations have been obtained by assuming a general law of differential rotation of the type 2 0 1 2 2 4 , where is the angular velocity of rotation of a fluid element in the star at a distance from the axis of rotation, and 0 1 2 are suitably chosen numerical constants. The expressions incorporate the effects of differential rotation and tidal distortions upto second order terms. The use of the proposed method has been illustrated by applying it to obtain the structures and observable parameters of certain differentially rotating primary components of the binary stars assuming the primary components to have polytropic structures. 1. Introduction Many of the observed stars are binary stars in which one of the stars (called the primary) is much more massive and larger as compared to its companion star (called the secondary). Most of the stars in binary systems are known to be rotating about their axes as well as revolving around their common centre of mass. Rotation in some of these stars is expected to be differential rotation. Equilibrium structures, shapes and other observed physical parameters of such stars obviously get influenced by the rotational forces as well as the tidal effects of the companion stars. In 1933 Chandrasekhar developed the theory of distorted polytropes to study such problems. Since then several investigators have addressed themselves to this problem. Whereas Chandrasekhar and Lebovitz (1962), Monaghan and Roxburgh (1965), Roberts (1965a,b), James (1964), Kopal (1983), Geroyannis and Valvi (1986) etc., considered the effects of solid body rotation on the equilibrium struc- tures of the polytropic models of the stars, Mohan et al. (1990) incorporated the effects of tidal forces as well by assuming these to be primary components of binary stars. Astrophysics and Space Science 254: 97–109, 1997. c 1997 Kluwer Academic Publishers. Printed in Belgium.