Magnetohydrodynamic waves in a potential coronal arcade

An important result obtained from solar observations made in coronal emission lines has been to establish the existence of periodic oscillations or waves in the corona. These are detected, although not always simultaneously, in line intensity, line-width or Doppler velocity with oscillation periods of several minutes. For this reason, we have studied the magnetohydrodynamic modes of oscillation of a coronal potential arcade under different boundary conditions, solving the wave equations for different density profiles. Our results show that only the Alfvén and the fast mode exist in such a structure and that the slow mode is absent, because of the assumed low-β limit. The Alfvén mode produces a continuous spectrum of frequencies with periods which can vary from zero to infinity, depending on the assumed density profile. Due to the polarization direction of the plasma motions, these waves could in principle be detected in front-view observations of coronal arcades at the limb. Concerning the fast mode, we have obtained several diagnostic diagrams using different density profiles and boundary conditions. These diagrams would be useful for comparing the predicted and observed periods. However, the observational identification of fast modes could be harder since we would need lateral observations of the coronal arcades.