On the geometrical properties of the chromospheric network

A sequence of Ca-K images obtained in a period of minimum solar activity, from July to November 1996, at the Rome Observatory with the PSPT (Precision Solar Photometric Telescope) prototype instrument have been used to analyze the geometrical properties of cells identified by the chromospheric network. In particular, we used 256 x 256 sub-arrays of the calibrated full-disk PSPT images. These sub-arrays, centered on the solar disk, are reduced to two-levels (binary) images by means of a suitable threshold after an FFT high-pass filtering. A medial axis transform, better known as skeleton, combined with a cellular automaton, is applied to the two-level images, in order to derive the cell boundaries. The regions corresponding to the cells are then filled by a growing algorithm. In this way we can derive a set of output parameters describing the cells geometry. The size distribution of the identified cells shows a continuous increase toward the smaller scales, rather than a small dispersion around a characteristic scale. Nevertheless the analysis of the inter-cell distances and of the area distribution pointed out a characteristic scale (square root of the area) of approximate to 24 Mm. To describe the cells irregularity and to probe the nature of solar turbulence, we apply a Mandelbrot fractal analysis to such irregularly shaped features. Examining the cell perimeter-area relationship we found the existence of a 'critical' area at which a change in the geometrical properties occurs. This area corresponds to the scale of approximate to 24 Mm. The estimated fractal dimension for cells with area greater than the 'critical' one is 1.35. This value, close to that predicted for isobars in the Kolmogorov 3-D turbulent theory, does not exclude a turbulent origin for such cells. The analysis seems to point to a common origin for solar granulation and supergranulation.