Evolution of a Magnetic Flux Tube in a Sunspot Penumbra

The motion of an individual magnetic flux tube inside the penumbra of a sunspot is studied numerically. Here, we present preliminary results. The thin flux tube approximation together with a simplified radiative heat exchange with the surroundings is used to study the evolution of a flux tube embedded into a background given by a global magneto-static sunspot model. The investigation is undertaken in order to verify the conjecture that convection in sunspot penumbrae occurs by an interchange of magnetic flux tubes. The code being developed can be used to study dynamic aspects of filamentary structure in the penumbra: the temporal and spatial fluctuations of the temperature and the magnetic field, the motion of bright penumbral grains, or the Evershed effect. Here we present the evolution of a wave formed by the tube whose fragment emerges in the penumbral photosphere and migrates towards the umbra. The properties of this wave show qualitative features of the observed bright penumbral grains with corresponding upward velocity and its correlation with brightness and the inclination of the magnetic field, and also of the Evershed effect.