3. Rotation and mass loss
We have shown in the previous Section that the concept of the limit is a consequence of omitting the effect of gravity darkening. As soon as the latter is taken into account the classical condition for critical rotation remains unaffected. Thus, any rotation dependent mass loss rate based on the limit (Langer 1997, 1998) is inconclusive. In particular, the mass loss rate does not diverge at the limit, which therefore has no meaning for stellar evolution. Accordingly, if the mass loss rate depends on rotation, it should rather be determined by the difference of the actual and the classical critical rotation rate (Friend & Abbott 1986). If at all, a divergence is expected to occur at most at the classical critical rotation rate.
The dependence on rotation of line-driven mass flux was studied by Friend & Abbott (1986). They ignored gravity darkening and the analysis was restricted to considering the equatorial plane. As a result, the mass flux was found to increase with decreasing effective gravity. Taking gravity darkening into account, however, the opposite dependence on effective gravity is obtained which was pointed out by Owocki et al. (1996) and Owocki & Gayley (1997) on the basis of the scaling laws for the mass flux in the standard CAK theory (Castor et al. 1975).
On the same level of approximation as Owocki et al. (1996) we find for the dependence on rotation of the mass flux by using Eqs. (4) and (8):
being the usual CAK exponent. We note that in this estimate the role of centrifugal support is even overestimated. Eq. (14) is identical to the result of Owocki et al. (1996) apart from the factor containing f which is not of interest in their analysis. For the mass loss rate and the asymptotic wind speed we obtain by integration:
f decreases from unity () to at most 0.6 for critical rotation. Thus, according to our estimate the mass loss rate is slightly increased () and the asymptotic wind speed is somewhat decreased by rotation. We emphasize that the mass loss rate (15) never diverges. Rather it exhibits a very weak dependence on the rotation rate.
© European Southern Observatory (ESO) 1998
Online publication: September 30, 1998