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Stellar evolution with rotation
VI. The Eddington and -limits, the rotational mass loss for OB and LBV stars
A. Maeder and
Received 12 May 2000 / Accepted 20 June 2000
Several properties of massive stars with large effects of rotation and radiation are studied. For stars with shellular rotation, i.e. stars with a constant angular velocity on horizontal surfaces (cf. Zahn 1992), we show that the equation of stellar surface has no significant departures with respect to the Roche model; high radiation pressure does not modify this property. Also, we note that contrarily to some current expressions, the correct Eddington factors in a rotating star explicitely depend on rotation. As a consequence, the maximum possible stellar luminosity is reduced by rotation.
We show that there are 2 roots for the equation giving the rotational velocities at break-up: 1) The usual solution, which is shown to apply when the Eddington ratio of the star is smaller than formally 0.639. 2) Above this value of , there is a second root, inferior to the first one, for the break-up velocity. This second solution tends to zero, when tends towards 1. This second root results from the interplay of radiation and rotation, and in particular from the reduction by rotation of the effective mass in the local Eddington factor. The analysis made here should hopefully clarify a recent debate between Langer (1997 , 1998) and Glatzel (1998).
The expression for the global mass loss-rates is a function of both and , and this may give raise to extreme mass loss-rates (-limit). In particular, for O-type stars, LBV stars, supergiants and Wolf-Rayet stars, even slow rotation may dramatically enhance the mass loss rates. Numerical examples in the range of 9 to 120 at various are given.
Mass loss from rotating stars is anisotropic. Polar ejection is favoured by the higher at the polar caps (-effect), while the ejection of an equatorial ring is favoured by the opacity effect (-effect), if the opacity grows fastly for decreasing .
Key words: stars: rotation stars: evolution stars: mass-loss
Send offprint requests to: A. Maeder (Andre.Maeder@obs.unige.ch)
Online publication: September 5, 2000