A magneto-hydrodynamic study of pre-flare loops

Abstract

The magnetohydrodynamic equilibrium and stability of a configuration which may apply to solar pre-flare loops is analyzed based on the following scenario: (1) the loops exist much prior to the flare and in equilibrium with their surroundings; (2) a few hours before the flare the configuration gradually acquires energy in the form of currents; (3) during the period of energy build-up, the loops are magnetohydrodynamically stable; and (4) the flare occurs only after there is adequate energy in the currents. Assuming a cylindrical geometry, equations are then presented and solved for the pressure and magnetic field equilibrium distribution within the loop using a typical energy value associated with a subflare and assuming the case of an approximately force-free field. An equation for the MHD stability of the system is then solved as an eigenvalue problem for the frequency of the normal modes. It is shown that the force-free configuration is unstable for all cases considered, with the wavenumber region for instability increasing inversely with pitch. It is concluded that stable configurations for loops possessing adequate energy for a flare are possible only if positive pressure gradients of sufficient magnitude exist.