Numerical simulations of conversion to Alfvén waves in sunspots

Abstract

We study the conversion of fast magnetoacoustic waves to Alfvén waves by means of 2.5D numerical simulations in a sunspot-like magnetic configuration. A fast, essentially acoustic, wave of a given frequency and wave number is generated below the surface and propagates upward through the Alfvén/acoustic equipartition layer where it splits into upgoing slow (acoustic) and fast (magnetic) waves. The fast wave quickly reflects off the steep Alfvén speed gradient, but around and above this reflection height it partially converts to Alfvén waves, depending on the local relative inclinations of the background magnetic field and the wavevector. To measure the efficiency of this conversion to Alfvén waves we calculate acoustic and magnetic energy fluxes. The particular amplitude and phase relations between the magnetic field and velocity oscillations help us to demonstrate that the waves produced are indeed Alfvén waves. We find that the conversion to Alfvén waves is particularly important for strongly inclined fields like those existing in sunspot penumbrae. Equally important is the magnetic field orientation with respect to the vertical plane of wave propagation, which we refer to as "field azimuth." For a field azimuth less than 90° the generated Alfvén waves continue upward, but above 90° downgoing Alfvén waves are preferentially produced. This yields negative Alfvén energy flux for azimuths between 90° and 180°. Alfvén energy fluxes may be comparable to or exceed acoustic fluxes, depending upon geometry, though computational exigencies limit their magnitude in our simulations. © 2012. The American Astronomical Society. All rights reserved.