The minimum mass ratio of W UMa-type contact binaries—a new calculation

A model is developed to establish the relationship between the critical gyration radius k of the primary component and the mass ratio ( q ) by considering the different dimensionless gyration radii of main-sequence stars with varying masses. The next step involves obtaining the low mass ratio limit ( qₘᵢₙ = 0.038 ~ 0.041 q min = 0.038 ∼ 0.041 for overcontact degree $$f = 0$$ f = 0 ~ 1) of W UMa-type contact binaries. Furthermore, the radial density distributions are estimated within the range of 0.3 M ~ 4.0 M 0.3 M ⊙ ∼ 4.0 M ⊙ , based on the mass-radius relationship of main-sequence stars. Subsequently, the physical meaning of the minimum k value is proposed, which leads to an explanation for the cause of the minimum mass ratio. Finally, a stability criterion is proposed, which is based on both the mass ratio ( q ) and the total mass of the two components ( Mₜₒₜ M tot ).