Waves in magnetic flux concentrations: The critical role of mode mixing and interference

Time-dependent numerical simulations of nonlinear wave propagation in a two-dimensional (slab) magnetic field geometry show wave mixing and interference to be important aspects of oscillatory phenomena in starspots and sunspots. Discrete sources located within the umbra generate both fast and slow MHD waves. The latter are compressive acoustic waves which are guided along the magnetic field lines and steepen into N-waves with increasing height in the spot atmosphere. The former are less compressive, and accelerate rapidly upward through the overlying low-β portion of the umbral photosphere and chromosphere (β = 8πp/B²). As the fast wave fronts impinge upon the β ≈ 1 penumbral "magnetic canopy" from above, they interfere with the outward-propagating field-guided slow waves, and they also mode convert to (non-magnetic) acoustic-gravity waves as they penetrate into the weak magnetic field region which lies between the penumbral canopy and the base of the surrounding photosphere. In a three-dimensional situation, one expects additional generation, mixing and interference with the remaining torsional Alfvén waves.