The role of mode-mixing in the absorption of p-modes

Observations show that a p-mode may lose up to 70% of its energy flux when it interacts with a sunspot. Part of the absorbed energy is assumed to be converted into other types of waves, while part of it is re-emitted into modes with different radial orders n. In the present paper, we investigate absorption of p-modes with the azimuthal order m = 0 due to their interaction with magnetic flux tubes and attempt to determine the role of mode mixing in this phenomenon. We consider the linearized magnetohydrodynamic equations in two-dimensional, cylindrical geometry, with all the model parameters depending only on radius r and depth z. It is assumed that the wave field may be decomposed into incoming and outgoing components that separately satisfy the governing equations. These components are calculated numerically using a second-order Runge-Kutta finite difference scheme. The calculations reveal substantial scattering from higher-to-lower radial orders n, predominantly into the f-mode (n = 0). Only weak scattering occurs from lower-to-higher radial orders. At the same time, the amount of energy transferred from the p-modes to the f-mode can account for 25%-30% of the energy lost by an incoming p-mode.