Threshold mass–radius exponent, ﹩{\zeta }_{\mathrm{ad}}﹩, for the onset of dynamical timescale mass transfer as derived from this paper (dots) and composite polytropes (solid line), as a function of the core mass function (﹩{m}_{{\rm{c}}}\equiv (M-{M}_{\mathrm{ce}})/M﹩) of MS stars. The masses of the stellar models are labeled, and they are correlated to the ﹩{\zeta }_{\mathrm{ad}}﹩ derived from our ZAMS models. Composite polytropes give a good approximation for low-mass stars and show consistent results with our calculation.