EMERGENCE OF MAGNETIC-FLUX FROM THE CONVECTION ZONE INTO THE SOLAR ATMOSPHERE .1. LINEAR AND NONLINEAR ADIABATIC EVOLUTION OF THE CONVECTIVE-PARKER INSTABILITY

We study the linear and nonlinear properties of the evolution of emerging magnetic flux from the solar convection zone into the photosphere, chromosphere, and corona. An isolated flux sheet (approximately 400 km thick) initially embedded in a simple model convection zone (approximately 1000-2000 km thick) below a model solar atmosphere is susceptible to both convective instability and the Parker instability (the undular mode of the magnetic buoyancy instability). In the first portion of the paper, we perform a linear stability analysis of the partially magnetized convection zone. We find that the growth rate of this combined convective-Parker instability differs significantly from that of the Parker instability in the absence of convection. When beta(= p(g)/p(m)) > 10 in the initial flux sheet, the growth rate increases with horizontal wavenumber, and there is no maximum growth rate. A local maximum, however, can occur when the flux is initially located near the top of the convection zone. When beta < 10, the convective-Parker instability behaves like the Parker instability for long-wavelength modes, and like the convective instability for short-wavelength modes. In the second portion of the paper, we use a two-dimensional magnetohydrodynamic (MHD) code to study the nonlinear evolution of the system. When the initial flux sheet has beta < 10, the long-wavelength mode (i.e., Parker mode) dominates the nonlinear evolution of the system, independent of the initial perturbation wavelength, even if there is no local maximum growth rate in the linear dispersion relation. The subsequent further expansion of magnetic flux into the atmosphere is characterized by approximate self-similar expansion, and resembles the results of our previous work, where the flux sheet was initially in a convectively stable layer. The magnetic flux configuration and system dynamics resemble the observed behavior of solar emerging flux regions.