The Missing Luminous Blue Variables and the Bistability Jump

We discuss an interesting feature of the distribution of luminous blue variables (LBVs) on the H-R diagram, and we propose a connection with the bistability jump seen in the winds of early-type supergiants. There appears to be a deficiency of quiescent LBVs on the S Doradus instability strip at luminosities between log(L/L_☉) ≃ 5.6 and 5.8. The upper boundary, interestingly, is also where the temperature-dependent S Doradus instability strip intersects the bistability jump at about T_eff ≃ 21,000 K. Because of increased opacity, winds of early-type supergiants are slower and denser on the cool side of the bistability jump, and we postulate that this may trigger optically thick winds that inhibit quiescent LBVs from residing there. We conduct numerical simulations of radiation-driven winds for a range of temperatures, masses, and velocity laws at log(L/L_☉) = 5.7 to see what effect the bistability jump should have. We find that for relatively low stellar masses, the order-of-magnitude increase in the wind density at the bistability jump leads to the formation of a modest to strong pseudophotosphere that might alter a star's apparent position on the H-R diagram. The effect is strongest for LBVs approaching 10 M_☉, where the pseudophotospheres are sufficiently extended to make an early B-type star appear as a yellow hypergiant. Thus, the proposed mechanism will be most relevant for LBVs that are post-red supergiants [curiously, the upper boundary at log(L/L_☉) ≃ 5.8 coincides with the upper luminosity limit for red supergiants]. Further work is obviously needed, especially with regard to a possible evolutionary connection between the "missing" LBVs and the most luminous red supergiants and yellow hypergiants. Specifically, yellow hypergiants such as IRC +10420 and ρ Cas occupy the same luminosity range as the missing LBVs and show apparent temperature variations at constant luminosity. If these yellow hypergiants do eventually become Wolf-Rayet stars, we speculate that they may skip the normal LBV phase, at least as far as their apparent positions on the H-R diagram are concerned.