Wave generation in a sunspot

In this paper we analyze the generation of waves in a sunspot by extending Stein's hydrodynamic approach to the turbulent medium permeated by a strong uniform magnetic field oriented parallel to the gravity. For wave sources appropriate to the sunspot, we consider magnetic perturbations and entropy changes as well as turbulent convection. To describe the anisotropy imposed by the sunspot, we use a one-dimensional correlation function relating the turbulent eddies separated along the symmetry axis of the spot. This treatment yields several interesting possibilities for wave generation in a sunspot. First, it is demonstrated that the entropy change and magnetic perturbation can lead to a relative enhancement of acoustic wave emission. Second, the energy flux of Alfvén waves may be comparable to that of acoustic waves in sunspots. Third, the anisotropy of the sunspot dynamics can lead to wave energy spectrum in a form which may explain the origin of umbral atmospheric oscillations.