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Numerical simulations of magneto-convection and analysis of solar magnetogramdata provide empirical probability density functions (PDFs) for theline-of-sight component of the magnetic field. In this paper, we theoreticallyexplore effects of several types of PDFs on polarized Zeeman line formation. Wealso propose composite PDFs to account for randomness in both field strengthand orientation. Such PDFs can possibly mimic random fields at the solarsurface.

Probability Density Functions to Represent Magnetic Fields at the Solar Surface