MULTIFRACTAL MODELS OF SMALL-SCALE SOLAR MAGNETIC-FIELDS

We generate, both analytically and numerically, artificial, two-dimensional images composed of a known self-similar, and thus multifractal, measure with added Gaussian white noise. These are used to interpret observed, line-of-sight, solar magnetic field distributions as noisy multifractals. The range of self-similar scaling of observed distributions is extended beyond that of previous work. Our interpretation of the data is then used to confront theoretical models for the generation of small-scale solar magnetic fields. We investigate the multifractal structure of the field generated by two-dimensional, random cell dynamos and find that self-similarity is relatively enhanced for more intermittent distributions and strong correlations between cells. An optimum value of the intercellular diffusion coefficient maximizes the degree of intermittency. The simulated field from a linear, kinematic, fast dynamo with two-dimensional, chaotic, ''ABC'' flow displays scaling properties resembling those of observed solar fields. We suggest that the chaotic element of this model is the crucial ingredient for the long-range correlations that lead to multifractal scaling.