Resistive ballooning modes in line-tied coronal fields. I - Arcades

The stability of coronal arcades to localized resistive interchange modes in the ballooning ordering, including photospheric line tying, is investigated. It is found that the anchoring of magnetic footpoints in the photosphere is not sufficient to stabilize ballooning modes once resistivity is taken into account. All configurations with a pressure profile decreasing from the arcade axis at some point are unstable, a purely growing mode being excited. The dependence of the growth rate, gamma, on the parameter R/m of about k squared(eta), where eta is the resistivity and k the wavenumber in a direction perpendicular to the equilibrium field, can be described by a power law with varying index: for small values of k squared and an ideally stable field one finds gamma of about R/m. As k squared is increased, or marginal stability is approached, one finds gamma of about R/m exp 1/3. The implications of these localized instabilities to the temporal evolution and overall energy balance of arcade structures in the solar corona is discussed.