Analytical approximations for some functions in the roche model

Abstract

Abstract Analytical approximations and tables are presented for the following functions in the Roche model: the ‘barotropic’ radius of the secondary companion r c, the characterising angles of the Roche lobe seen from the center of the other star and from the inner Lagrangian point, the coordinates of the points at the border line separating the illuminated part of the Roche lobe and the dark one. By using Eggleton's (1983) form for the effective radius, r = Aq 2/3(Bq 2/3 + log(1 + q 1/3), we derived the values A = 0.4990, 0.4394 and B = 0.5053, 0.5333 for the function sin θ in the y- and z- directions, respectively (where θ is the angular radius of the Roche lobe seen from the other star). For the mass ratio q = M 2/M 1 ≤ 4, the maximal relative errors do not exceed 0.2 and 0.5 per cent, respectively. A more precise approximation for the ‘inclination–eclipse duration’ relation is derived.