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 for overcontact degree f = 0 - 1) of W UMa-type contact binaries. Furthermore, the radial density distributions are estimated within the range of 0.3 Msun - 4.0 Msun, 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 mass of the primary component (M1).