On the nature of the bi-stability jump in the winds of early-type supergiants

We study the origin of the bi-stability jump in the terminal velocity of the winds of supergiants near spectral type B1. Observations show that here the ratio v1/vesc drops steeply from about 2.6 at types earlier than B1 to a value of v1/vesc=1.3 at types later than B2. To this purpose, we have calculated wind models and mass-loss rates for early-type supergiants in a Te grid covering the range between Te = 12 500 and 40 000 K. These models show the existence of a jump in mass loss around Te = 25 000 K for normal supergiants, with _ M increasing by about a factor five from Te ' 27 500 to 22 500 K for constant luminosity. The wind efficiency number = _ Mv1=(L=c) also increases drastically by a factor o f2-3 near that tempera- ture. We argue that the jump in mass loss is accompanied by a decrease of the ratio v1/vesc, which is the observed bi-stability jump in terminal velocity. Using self-consistent models for two values of Te , we have derived v1/vesc = 2.4 for Te = 30 000 K and v1/vesc = 1.2 for Te = 17 500 K. This is within 10 percent of the observed values around the jump. Up to now, a theoretical explanation of the observed bi- stability jump was not yet provided by radiation driven wind theory. To understand the origin of the bi-stability jump, we have investigated the line acceleration for models around the jump in detail. These models demonstrate that _ M increases around the bi-stability jump due to an increase in the line acceleration of Fe iii below the sonic point. This shows that the mass-loss rate of B-type supergiants is very sensitive to the abundance and the ionization balance of iron. Furthermore, we show that the elements C, N and O are important line drivers in the supersonic part of the wind. The subsonic part of the wind is dominated by the line acceleration due to Fe. Therefore, CNO-processing is expected not to have a large impact on _ M but it might have impact on the terminal velocities. Finally, we discuss the possible role of the bi-stability jump on the mass loss during typical variations of Luminous Blue Variable stars.