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 circulation velocity in stars, in the presence of μ-gradients, is the sum of two terms, one due to the classical thermal imbalance (Ω-currents) and the other one due to the induced horizontal μ-gradients (μ-induced currents, or μ-currents in short). In the most general cases, μ-currents are opposite to Ω-currents. Simple expressions for these currents are derived under some simplifying physical assumptions presented in the text, and their physical interpretations are discussed. Computations of the Ω and μ-currents in a 0.8 M halo stellar model including classical element settling show that the μ-currents are larger (in absolute values) than the Ω-currents 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 cancelled out. As lithium diffuses in the same way as helium, we expect a very small lithium concentration gradient below the convective zone in “plateau stars” (main-sequence Pop II stars), much smaller than the one expected for pure element settling. This could possibly account for the very small dispersion observed for the lithium abundances at the surface of these stars. This should also have important consequences in other contexts which will be discussed in forthcoming papers. The present computations show that element settling in slowly rotating stars leads to surface abundances which depend on the competition between μ-currents and Ω-currents, in a way which had not been taken into account in previous computations. This may change our general understanding of the diffusion processes of chemical species in rotating stars.