A. Maeder et G. Meynet, Stellar evolution with rotation VI. The Eddington and Omega-limits, the rotational mass loss for OB and LBV stars, ASTRON ASTR, 361(1), 2000, pp. 159-166
Several properties of massive stars with large effects of rotation and radi
ation are studied. For stars with shellular rotation, i.e. stars with a con
stant angular velocity Omega on horizontal surfaces (cf. Zahn 1992), we sho
w that the equation of stellar surface has no significant departures with r
espect to the Roche model; high radiation pressure does not modify this pro
perty. Also, we note that contrarily to some current expressions, the corre
ct Eddington factors Gamma in a rotating star explicitely depend on rotatio
n. 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 veloc
ities at break-up: 1) The usual solution, which is shown to apply when the
Eddington ratio Gamma of the star is smaller than formally 0.639. 2) Above
this value of Gamma, there is a second root, inferior to the first one, for
the break-up velocity. This second solution tends to zero, when Gamma tend
s towards 1. This second root results from the interplay of radiation and r
otation, 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 Omega a
nd Gamma, and this may give raise to extreme mass loss-rates (Omega Gamma-l
imit). In particular, for O-type stars, LBV stars, supergiants and Wolf-Ray
et stars, even slow rotation may dramatically enhance the mass loss rates.
Numerical examples in the range of 9 to 120 M. at various T-eff are given.
Mass loss from rotating stars is anisotropic. Polar ejection is favoured by
the higher T-eff at the polar caps (g(eff)-effect), while the ejection of
an equatorial ring is favoured by the opacity effect (kappa-effect), if the
opacity grows fastly for decreasing T-eff.