Rotation and Anisotropic Losses of Mass and Angular Momentum

Abstract

The expressions of the radiative flux at the surface of a non-uniformly rotating star are revised and this leads to a small extra-term in the von Zeipel theorem. The Eddington factor needs also to be carefully defined in a rotating star, as well as the critical break-up velocity. This leads us to reconsider the so-called Ω–limit. The most massive stars reach the Ω and Г limits almost simultaneously.

We also examine the latitudinal dependence of the mass loss rates Ṁ(υ) in rotating stars and find two main effects: 1) the “g_eff” effect which enhances the polar ejection; 2) the “opacity effect” (or “к–effect”), which favours equatorial ejection. In O–stars, the g_eff effect is expected to largely dominate. In B– and later type stars the opacity effect should favour equatorial ejection and the formation of equatorial rings. Possible relations with η Carinae and the inner and outer rings of SN 1987 A are mentioned. Opacity peaks produce some extrema in Ṁ(υ) and this may also lead to the formation non-equatorial symmetrical rings.

Anisotropic stellar winds remove selectively the angular momentum. For example, winds passing through polar caps in O–stars remove very little angular momentum, an excess of angular momentum is retained and rapidly redistributed by horizontal turbulence. These excesses may lead some Wolf–Rayet stars, those resulting directly from O–stars, to be fast spinning objects, while we predict that the WR–stars which have passed through the red supergiant phase will have lower rotation velocities on the average. We also show how anisotropic ejection can be treated in numerical models by properly modifying the outer boundary conditions for the transport of angular momentum.