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Stellar evolution with rotation
I. The computational method and the inhibiting effect of the µ-gradient
Georges Meynet and
Received 30 January 1996 / Accepted 21 May 1996
We study the effects of rotation on the structure and evolution of massive stars. The method of Kippenhahn & Thomas (1970) to incorporate the hydrostatic effects of rotation in one dimensional stellar evolutionary codes is strictly valid only in case the angular velocity distribution has a cylindrical symmetry. We demonstrate how this method can be applied (cf. Appendix) in the case where the angular velocity is constant on isobars ("shellular rotation law", cf. Zahn 1992). We also investigate the structural effects of rotation on the stellar atmosphere. The effects of rotational mixing are considered with the theory of Zahn (1992) for the circulation and turbulence in rotating stars. We suppose that the angular momentum in a given shell remains constant with time (asymptotic regime). The subsequent developments brought to the Richardson criterion by Maeder (1995a) and Maeder and Meynet (1996) to account for thermal effects on the shear instability are also applied.
Evolutionary tracks are calculated for initial masses of 9, 20, 40 and 60 with account of the above hydrostatic and mixing effects. The main results are the following ones:
1) The hydrostatic effects alone are quite modest: when the initial angular velocity () increases from 0 to 90% of the surface critical velocity (), the lifetimes of massive star models (40 to 60 ) are increased by 1 to 2%. The evolutionary tracks are shifted towards lower luminosities, making them appear as the ones resulting from slightly lower initial mass stars, typically 0.5 to 2.5 smaller.
2) Surprisingly we find that the µ-gradients, when non zero, are always strong enough to inhibit mixing. Indeed, the effects of µ-gradients are quite difficult to overcome and this tends to make the rotationally induced mixing inoperant when the Richardson criterion is applied.
3) We suggest that different mixing criteria and/or diffusion coefficients must be searched for and applied if one wants to reproduce the observations by Herrero et al. (1992). Indeed these authors show that above a certain rotational velocity, quite efficient mixing processes are active and able to modify the surface abundances in helium during a fraction of the main sequence lifetime.
Key words: instabilities turbulence methods: numerical stars: early-type evolution rotation
Send offprint requests to: G. Meynet
Online publication: June 30, 1998