*Astron. Astrophys. 334, 1000-1006 (1998)*
## Stellar evolution with rotation
### III. Meridional circulation with *µ*-gradients and
non-stationarity
**
André Maeder **^{ 1} and
Jean-Paul Zahn ^{ 2}
^{1} Observatoire de Genève, CH-1290 Sauverny,
Switzerland
^{2} Observatoire de Paris, Section de Meudon, F-92195 Meudon,
France
*Received 4 October 1997 / Accepted 18 March 1998*
**Abstract**
Models of stellar evolution with rotation are very much needed in
order to interpret recent stellar properties, in particular for
massive stars. For that we proceed to a detailed investigation of some
critical physical processes in rotating stars:
1. The equation expressing the transport of angular momentum
by circulation and diffusion is revised to also account for expansion
and contraction in non-stationary models.
2. We examine the current expressions for the velocity
of the meridional circulation, also taking into
account *µ*-gradients and horizontal turbulence. We show
that there are no "*µ*-currents" but just meridional
currents which can be sizeably influenced by the gradients of mean
molecular weight *µ*. A proper account of the
*µ*-gradients may reduce by one or
two orders of magnitude with respect to current expressions.
3. While the usual expressions for the meridional circulation
would predict an infinite velocity at the edge of a radiative and
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 The approximation of a stationary circulation, which is no
longer valid after the main-sequence phase, is also removed and the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 that in
the stationary regime the horizontal fluctuations of *µ*
represent some fixed fraction of the vertical *µ*-gradient.
To first order, this fraction is not dependent on rotation, because
the building of horizontal fluctuations by the circulation is
compensated by the smoothing due to horizontal turbulence.
**Key words:** stars:
rotation
stars:
early-type
stars: interior
SIMBAD Objects
### Contents
© European Southern Observatory (ESO) 1998
Online publication: June 2, 1998
helpdesk.link@springer.de |