A. Maeder et Jp. Zahn, STELLAR EVOLUTION WITH ROTATION - III - MERIDIONAL CIRCULATION WITH MU-GRADIENTS AND NON-STATIONARITY, Astronomy and astrophysics (Berlin), 334(3), 1998, pp. 1000-1006
Models of stellar evolution with rotation are very much needed in orde
r to interpret recent stellar properties, in particular for massive st
ars. For that we proceed to a detailed investigation of some critical
physical processes in rotating stars: 1. The equation expressing the t
ransport of angular momentum by circulation and diffusion is revised t
o also account for expansion and contraction in non-stationary models.
2. We examine the current expressions for the velocity U(tau) of the
meridional circulation, also taking into account mu-gradients and hori
zontal turbulence. We show that there are no ''mu-currents'' but just
meridional currents which can be sizeably influenced by the gradients
of mean molecular weight mu. A proper account of the mu-gradients may
reduce U(tau) by one or two orders of magnitude with respect to curren
t expressions. 3. While the usual expressions for the meridional circu
lation would predict an infinite velocity at the edge of a radiative a
nd semiconvective zone and an inverted circulation in a semiconvective
zone, the present developments give a continuity of the solutions for
the circulation. 4. The approximation of a stationary circulation, wh
ich is no longer valid after the main-sequence phase, is also removed
and the case of a general equation of state is considered. We notice t
hat in the stationary regime the horizontal fluctuations of mu represe
nt some fixed fraction of the vertical mu-gradient. To first order, th
is fraction is not dependent on rotation, because the building of hori
zontal fluctuations by the circulation is compensated by the smoothing
due to horizontal turbulence.