2007MNRAS.377.1635A

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_min~ 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 R₂= R₂(R₁, a, q). By finding a new criterion for contact binaries, which arises from dJ_tot= 0, and assuming k²₁≠ k²₂ 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.