Numerical modeling of the absorption and scattering of acoustic radiation by sunspots

We present numerical calculations of the scattering of acoustic-gravity wav es by a model sunspot consisting of an inhomogeneous, vertically magnetized region embedded in a polytropically stratified layer. The calculations sho w the transformation of incoming f-mode and p-mode power into downward-prop agating, slow magnetoacoustic waves resulting in substantial absorption of incident f-modes and first-order p-modes and indicating that the slow-mode transformation model is a viable explanation for the observed absorption. I n addition to absorption, we find large scattering phase shifts for the f-m odes. Phase shifts are small for all p-modes. Coupling between modes of dif ferent radial order is generally small. The remaining differences between o ur results and the observations may constitute evidence that, if the mode t ransformation picture is correct, real sunspots must deviate significantly from the simple unidirectional field geometry we use here. In particular, w e suggest that a sunspot consisting of a bundle of fibrils, in each of whic h the magnetic flux density increases rapidly with depth, would reproduce m ore closely the measured strong absorption and scattering of p-modes.