Almost analytic solutions to equilibrium sequences of irrotational binary polytropic stars for n=1

Abstract

A solution to an equilibrium of irrotational binary polytropic stars in Newtonian gravity is expanded in a power of \epsilon=a_0/R, where R and a_0 are the separation of the binary system and the radius of each star for R=\infty. For the polytropic index n=1, the solutions are given almost analytically up to order \epsilon^6. We have found that in general an equilibrium solution should have the velocity component along the orbital axis and that the central density should decrease when R decreases. Our almost analytic solutions can be used to check the validity of numerical solutions.