5. Summary and conclusions
In this paper, we discussed the effect of mass outflow through the inner or outer boundary of a rigidly rotating envelope on its rotation frequency. It causes a change of the specific angular momentum in the envelope and alters its rotation rate besides what results from contraction or expansion (cf. Fig. 7). For constant upper and lower boundaries of the envelope, which we found a good approximation for convective envelopes (cf. Fig. 5), a spin-down occurs for mass outflow through the upper boundary - which corresponds, e.g., to the case of stellar wind mass loss from a convective envelope (cf. also Langer 1998) -, while a spin-up results from mass outflow through the lower boundary (cf. Fig. 1).
The latter situation is found in evolutionary models of a rotating star at the transition from the Hayashi-line to the blue supergiant stage. The star increased its rotational velocity one order of magnitude above the velocity which would result in the case of local angular momentum conservation. It would have increased its rotational velocity even further if it would not have arrived at critical rotation (cf. Sect. 3.2, Fig. 7), with the consequence of strong mass and angular momentum loss. At this point, the specific angular momentum loss reached about (cf. Fig. 6).
The geometry of circumstellar matter around stars which undergo a red blue transition may be strongly affected by the spin-up. We propose that this was the case for the progenitor of SN 1987A, the only star of which we know that it performed a red blue transition in the recent past. The blue supergiant in its neighborhood studied by Brandner et al. (1997), around which they found a ring nebula as well, is another candidate. Also, B[e] stars may be related with the post-red supergiant spin-up (cf. Sect. 4.1). Furthermore, the spin-up mechanism studied in this paper may be relevant for bipolar outflows from central stars of proto-planetary nebulae (Sect. 4.4), from stars in the transition phase from the red supergiant stage to the Wolf-Rayet stage (Sect. 4.2), and from pre-main sequence stars (Sect. 4.3).
© European Southern Observatory (ESO) 1998
Online publication: May 12, 1998