Information entropy in solar atmospheric fields - I. Intensity photospheric structures

The existence of a quasi-regular pattern in solar photospheric convective fields is an open question. In the present work, this problem is quantitatively approached by means of the normalised information entropy measure H'(r) as introduced by Van Siclen (\cite{VanSic97}), which reports on the information content at different scales. Images were acquired at the THEMIS telescope of the European Northern Observatory by the IPM observing mode, and at the Richard B. Dunn Solar Telescope of the National Solar Observatory. The evaluation of H'(r) in the case of photospheric intensity binarized images shows the presence of maxima which are evidence of different prominent scales in the photospheric pattern. The relative positions of these maxima defines an ordering scale ~ 1.6 Mm in both instantaneous and average images. This is read as the evidence of a spatio-temporal organization in the evolution of convective pattern. The emergence of an ordering scale is discussed in the framework of pattern formation in random systems and in connection with the findings of previous works. By averaging images with time, an increase of the information content characterized by a coherence time of ~ 1 h is observed in the range of scales from 5.0 Mm to 10.0 Mm.