The minimum mass ratio of W UMa-type binary systems

Abstract

When the total angular momentum of a binary system J tot = J orb + J spin is at a certain critical (minimum) value, a tidal instability occurs which eventually forces the stars to merge into a single, rapidly rotating object. The instability occurs when J orb = 3J spin , which in the case of contact binaries corresponds to a minimum mass ratio q mm ≈ 0.071-0.078. The minimum mass ratio is obtained under the assumption that stellar radii are fixed and independent. This is not the case with contact binaries where, according to the Roche model, we have R 2 = R 2 (R 1, a, q). By finding a new criterion for contact binaries, which arises from dJ tot = 0, and assuming k 2 1 ≠ k 2 2 for the component's dimensionless gyration radii, a theoretical lower limit q min = 0.094-0.109 for overcontact degree f = 0-1 is obtained.