MAGNETOHYDRODYNAMICS AND DEEP MIXING IN EVOLVED STARS. I. TWO- AND THREE-DIMENSIONAL ANALYTICAL MODELS FOR THE ASYMPTOTIC GIANT BRANCH

Abstract

The advection of thermonuclear ashes by magnetized domains emerging from near\nthe H-shell was suggested to explain AGB star abundances. Here we verify this\nidea quantitatively through exact MHD models. Starting with a simple 2D\ngeometry and in an inertia frame, we study plasma equilibria avoiding the\ncomplications of numerical simulations. We show that, below the convective\nenvelope of an AGB star, variable magnetic fields induce a natural expansion,\npermitted by the almost ideal MHD conditions, in which the radial velocity\ngrows as the second power of the radius. We then study the convective envelope,\nwhere the complexity of macro-turbulence allows only for a schematic analytical\ntreatment. Here the radial velocity depends on the square root of the radius.\nWe then verify the robustness of our results with 3D calculations for the\nvelocity, showing that, for both the studied regions, the solution previously\nfound can be seen as a planar section of a more complex behavior, in which\nanyway the average radial velocity retains the same dependency on radius found\nin 2D. As a final check, we compare our results to approximate descriptions of\nbuoyant magnetic structures. For realistic boundary conditions the envelope\ncrossing times are sufficient to disperse in the huge convective zone any\nmaterial transported, suggesting magnetic advection as a promising mechanism\nfor deep mixing. The mixing velocities are smaller than for convection, but\nlarger than for diffusion and adequate to extra-mixing in red giants.\n