Critical mass–radius exponent ﹩{\zeta }_{\mathrm{ad}}﹩ and mass ratio ﹩{q}_{\mathrm{ad}}﹩ as functions of stellar radius for the ﹩3.2\,{M}_{\odot }﹩ models. The arrows point out the abrupt transition from delayed dynamical instability to prompt dynamical instability at ﹩\mathrm{log}(R/{R}_{\odot })=1.15﹩ (﹩R=14{R}_{\odot }﹩), as the star approaches the BGB. The solid curve corresponds to models with standard mixing-length envelopes (﹩{\zeta }_{\mathrm{ad}}﹩ and ﹩{q}_{\mathrm{ad}}﹩), and the dashed curve corresponds to models with artificially isentropic convective envelopes (﹩{\widetilde{\zeta }}_{\mathrm{ad}}﹩ and ﹩{\widetilde{q}}_{\mathrm{ad}}﹩).