| Abstract: | In literature, there is no exact analytical solution available for determining the radius of Roche equipotential surfaces
of distorted close binary systems in synchronous rotation. However, Kopal (Roche Model and Its Application to Close Binary
Systems, Advances in Astronomy and Astrophysics, Academic Press, New York 1972) and Morris (Publ. Astron. Soc. Pac. 106:154, 1994) have provided the approximate analytical solutions in the form of infinite mathematical series. These series expressions
have been commonly used by various authors to determine the radius of the Roche equipotential surfaces, and hence the equilibrium
structures of rotating stars and stars in the binary systems. However, numerical results obtained from these approximating
series expressions are not very accurate. In the present paper, we have expanded these series expressions to higher orders
so as to improve their accuracy. The objective of this paper is to check, whether, there is any effect on the accuracy of
these series expressions when the terms of higher orders are considered. Our results show that in most of the cases these
expanded series give better results than the earlier series. We have further used these expanded series to find numerically
the volume radius of the Roche equipotential surfaces. The obtained results are in good agreement with the results available
in literature. We have also presented simple and accurate approximating formulas to calculate the radius of the primary component
in a close binary system. These formulas give very accurate results in a specified range of mass ratio. |
