Simulation of f- and p-mode interactions with a stratified magnetic field concentration

The interaction of f- and p-modes with a slab of vertical magnetic field of sunspot strength is simulated numerically in two spatial dimensions. Both f-modes and p-modes are partially converted to slow magnetoatmospheric gravity (MAG) waves within the magnetic slab because of the strong gravitational stratification of the plasma along the magnetic lines of force. The slow MAG waves propagate away from the conversion layer guided by the magnetic field lines, and the energy they extract from the incident f- and p-modes results in a reduced amplitude for these modes as they exit from the back side of the slab. In addition, the incident p-modes are partially mixed into f-modes of comparable frequency, and therefore larger spherical harmonic degree, when they exit the magnetic flux concentration. These findings have important implications for the interpretation of observations of p-mode absorption by sunspots, both in terms of the successes and failures of this simple numerical simulation viewed in the sunspot seismology context.