On the possible existence of a self-regulating hydrodynamical process in slowly rotating stars - I. Setting the stage

It has been known for a long time (Mestel 1953) that the meridional circula tion velocity in stars, in the presence of mu-gradients, is the sum of two terms, one due to the classical thermal imbalance (Omega-currents) and the other one due to the induced horizontal mu-gradients (mu-induced currents, or mu-currents in short). In the most general cases, mu-currents are opposi te to Omega-currents. Simple expressions for these currents are derived und er some simplifying physical assumptions presented in the text, and their p hysical interpretations are discussed. Computations of the Omega and mu-cur rents in a 0.8 M. halo stellar model including classical element settling s how that the mu-currents are larger (in absolute values) than the Omega-cur rents in all the star: some new physics has thus to be invoked in this case . We show here how such processes could possibly lead to a quasi-equilibrium stage in which both the circulation and the helium settling could be cancel led out. As lithium disuses in the same way as helium, we expect a very sma ll lithium concentration gradient below the convective zone in "plateau sta rs" (main-sequence Pop II stars), much smaller than the one expected for pu rl element settling. This could possibly account for the very small dispers ion observed for the lithium abundances at the surface of these stars. This should also have important consequences in other contexts which will be di scussed in forthcoming papers. The present computations show that element settling in slowly rotating star s leads to surface abundances which depend on the competition between mu-cu rrents and Omega-currents, in a way which had not been taken into account i n previous computations. This may change our general understanding of the d iffusion processes of chemical species in rotating stars.