Temporal Evolution of Sunspot Areas and Estimation of Related Plasma Flows

The increased amount of information provided by ongoing missions such as the Solar Dynamics Observatory (SDO) represents a great challenge for the understanding of basic questions such as the internal structure of sunspots and how they evolve with time. Here, we contribute with the exploitation of new data, to provide a better understanding of the separate growth and decay of sunspots, umbra and penumbra. Using fuzzy sets to compute separately the areas of sunspot umbra and penumbra, the growth and decay rates for active regions NOAA 11117, NOAA 11428, NOAA 11429, and NOAA 11430 are computed, from the analysis of intensitygrams obtained by the Helioseismic and Magnetic Imager onboard SDO. A simplified numerical model is proposed for the decay phase, whereby an empirical irrotational and uniformly convergent horizontal velocity field interacting with an axially symmetric and height invariant magnetic field, reproduces the large-scale features of the much more complex convection observed inside sunspots.