Information entropy in solar atmospheric fields

Abstract

Abstract. 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 (1997), 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.

A versatile entropic measure of grey level inhomogeneity

“…For evolving in time the photosphere granulation patterns the stability in time of the first peak position and temporary domination of the third one has been obtained by our GLI measure. The similar observations were reported by Consolini, Berrilli et al (2003, 2005. However, they used normalized information entropy for carefully binarized granulation images of different data set.…”

“…This indicates for a temporary grouping of granules at length scale that may belong to mesogranulation phenomenon. This behaviour has similarities with that reported by Consolini, Berrilli et al (2003, 2005 for binarized granulation images of a different data set.…”

“…Interestingly, the nearly constant with time the position of the first peak but around scale of 1 Mm has been reported in Ref. [13], where analysed photospheric intensity images of THEMIS telescope of the European Northern Observatory (Tenerife) recorded in 1999 and Dunn Solar Telescope (DST) of the National Solar Observatory (Sacramento Peak) recorded in 1996. However, instead of grey level patterns the authors used carefully prepared binary images and employed the normalized information entropy [5].…”

A generalization of the inhomogeneity measure for point distributions to the case of finite size objects

“…Thus its value should agree with the inter-distance between minimums at large scales. Recently, in this way the first quantitative evidence for the presence of a quasi-regular pattern in the photospheric intensity fields has been obtained [30].…”

“…Nevertheless, such a periodicity can be also extracted in a simple way that was described in Ref. [30]. Namely, one can decompose h ∆ (B) and S ∆ (B) into a superposition of a few contribution functions to obtain by the fitting procedure the sequential peak positions k fit except the position of the first asymmetric peak.…”