Magnetohydrodynamics and Deep Mixing in Evolved Stars. I. Two- And Three-Dimensional Analytical Models for the Asymptotic Giant Branch

Stellar MHD and Nuclear Physics Coupled Together Solve the Puzzle of Oxide Grain Composition

“…Since the three above conditions are verified (see Figure 1A), the assumption that magnetic field remains constant in time, allows us to use the simplest version of the analytical solutions by [1]. In this framework the radial component of the velocity, by which magnetize structures expand, is:…”

“…Nucci & Busso [1] demonstrated that the full MHD equations can be solved analytically in an exact way when applied to radiative layers of low mass stars. This is so because a set of three peculiar situations (which, together, represent a sufficient condition for the exact solution to hold) occur in the radiative region below the convective envelope:…”

“…where magnetized structures occupy a fraction f 1 of 1−2% of the whole area at the base of convective envelope ( [1] and [17]) and f 2 is the filling factor of each flux tube is of about 1/100 of its section.…”

“…Recently, [1] have shown that the magneto hydrodynamic (here after MHD) equations allow for exact analytical solutions in the radiative zones below the convective envelope of AGB stars. We apply this model of mixing driven by the buoyancy of magnetized materials to a 1.2M ⊙ star to verify whenever such a mechanism might reproduce at the same time the oxygen and aluminum isotopic ratios shown by group 1 and 2 grains.…”

“…However, a large part of oxide grains shows values of the 26 Al/ 27 Al isotopic ratio too high to be accounted for by the mixing models mentioned above. Recently, [1] demonstrated that the stellar magnetic field might promote the transport of material across the stellar radiative layers. We apply this magnetic mixing model to a 1.2M ⊙ AGB star of solar metallicity.…”