SOLAR GRANULATION AND STATISTICAL CRYSTALLOGRAPHY - A MODELING APPROACH USING SIZE-SHAPE RELATIONS

The irregular polygonal pattern of solar granulation is analyzed for s ize-shape relations using statistical crystallography. In contrast to previous work which has assumed perfectly hexagonal patterns for granu lation, more realistic accounting of cell (granule) shapes reveals a b roader basis for quantitative analysis. Several features emerge as not eworthy: (1) a linear correlation between number of cell-sides and nei ghboring shapes (called Aboav-Weaire's law); (2) a linear correlation between both average cell area and perimeter and the number of cell-si des (called Lewis's law and a perimeter law, respectively) and (3) a l inear correlation between cell area and squared perimeter (called conv olution index). This statistical picture of granulation is consistent with a finding of no correlation in cell shapes beyond nearest neighbo rs. A comparative calculation between existing model predictions taken from luminosity data and the present analysis shows substantial agree ments for cell-size distributions. A model for understanding grain lif etimes is proposed which links convective times to cell shape using cr ystallographic results.