Threshold mass–radius exponent, ﹩{\zeta }_{\mathrm{ad}}﹩, for the onset of dynamical timescale mass transfer as derived from this paper (dots) and condensed polytropes (solid line), as a function of the core mass function (﹩{m}_{{\rm{c}}}﹩) of GB stars. Black dots show results from RGB stars, and red dots show those derived from AGB stars. Four groups of the initial mass, which are (0.50, 0.56, 0.63, and 0.71), (0.80, 0.89, and 1.00), (1.14, 1.30, and 1.44), and (1.60, 1.80, 2.00, and 2.04), are shown by dots of four different sizes from small to large, respectively. Condensed polytropes do not contribute to the nonideal gas effect and inefficient convection, and we see an extended pattern of ﹩{q}_{\mathrm{ad}}﹩ from our calculation.