Minimum mass-loss rate (left axis) and minimum mass-flux (right axis) for the sonic point of a radiation-driven outflow to lie in the temperature range of the He II-opacity bump (thick orange line) as a function of L/M. The helium-minimum mass-loss rate is derived based on the opacity tables (see Appendices B and C) adopting a sonic-point radius of 62 R_⊙ (Groh et al. 2011), Y = 0.6 (Groh et al. 2009), and a turbulent velocity broadening of 20 km s⁻¹ (Groh et al. 2011). The luminosity and mass adopted for AG Car are 1.5 ⋅ 10⁶ L_⊙  and 55 M_⊙  (Groh et al. 2011; Vamvatira-Nakou et al. 2015). The blue points indicate the minimum and maximum mass-loss rates of AG Carinae from Groh et al. (2011, stars), Leitherer et al. (1994 circles), and Stahl et al. (2001, pentagons), as well as the numerical predictions specific to AG Carinae by Vink & de Koter (2002, green asterisks). The black lines indicate the mass-loss rate predictions on the hot (25 kK, lower line) and cool (20 kK, upper line) side of the bistability temperature (Vink et al. 2001), derived adopting a mass-luminosity relation (Gräfener et al. 2011). The gray area indicates the L/M range where we predict massive main-sequence stars might undergo an S Dor phase (cf. Appendix D).