Ionization of the constituent gases in the solar plasma has long been held to influence convection in the Sun's interior. This is particularly true for the solar supergranulation. Its discoverers linked the 30 Mm horizontal extent of this structure to the ionization zone of helium occurring at a comparable depth (Simon and Leighton 1964). Yet comparatively little analysis or simulation has been performed to explain the size-selection effect in detail. This is partly because supergranulation is ``deep'' convection: its low Mach number makes compressible hydrodynamic simulations difficult. Simulations of shallow convection including ionization have been achieved (Rast and Toomre 1993), but the results tended to be dominated by high-Mach-number downflows, more characteristic of the smaller-scale solar granulation. To get around time step restrictions imposed by sound waves, the anelastic approximation (Gough 1969) is appropriate. However, investigators who have made use of it have preferred to focus on questions of global convection (Glatzmaier 1985), rather than on the supergranulation phenomenon. The author has proposed a method for incorporating ionization zones into the anelastic approximation (Lantz 1992). An isentropic condition is enforced on the lowest-order equations. This ``adiabatic'' stratification can be generalized to take into account an ionization state that varies according to Saha-type equations. Thermodynamic properties such as the specific heat become depth-dependent. With a reasonable subgrid model for heat diffusion, the anelastic equations can be rewritten in such a way that the perturbed entropy appears alone as the thermodynamic variable to first order. This formulation makes it is clear that the anelastic approximation is a generalization of the well-known Boussinesq approximation. Linear stability analysis proceeds analogously to classical, Rayleigh-Benard calculations. Spatial structures of convectively unstable modes will be presented and compared with predecessors' results. This is a first step toward fully-resolved anelastic simulations of convection across an ionization zone.
AAS/Solar Physics Division Meeting #28
- Pub Date:
- May 1997