THE CONVERSION OF P-MODES TO SLOW MODES AND THE ABSORPTION OF ACOUSTIC-WAVES BY SUNSPOTS

The possibility that the conversion of p-modes to flux tube-guided slow modes (s-modes) is responsible for the reported absorption of the solar acoustic oscillations in sunspots and neighboring plage is discussed in the context of a simple model atmosphere-a plane-parallel stratified adiabatic polytrope threaded by a uniform vertical magnetic field. The normal modes of oscillation of this atmosphere have complex eigenfrequencies. We argue that the acoustic absorption suffered by an incident p-mode scales like the imaginary part of these complex eigenfrequencies of the internal sunspot atmosphere. We find that (1) for the f-mode, the absorption coefficient increases monotonically from small to large horizontal wavenumbers, and (2) along the nth p-mode ridge, this same general trend is modulated by the presence of n localized absorption minima. These characteristic signatures of acoustic absorption by p-mode/s-mode conversion distinguish this mechanism from other competing proceses and afford the diagnostic possibility of determining the sunspot magnetic field strength from the location in wavenumber of the predicted absorption minima.