Comparison of the constant density and two-zone analytical models, as described in Sects. 3.3 and 3.4, with the full calculations as described in Sect. 4.1 in terms of the predicted relative Applegate threshold energy. We consider the same general system configuration as in Fig. 1 and described in Sect. 3.4, but fixed the secondary mass to M_sec = 0.3 M_⊙, which enabled us to plot the calculated energies as functions of the Applegate parameter A (see Eq. (37)). The analytical two-zone model closely follows the full calculations with typical deviations of less than 10%, while the simple constant density model overestimates the energy threshold by several magnitudes except for the critical region close to unity.