Distribution of magnetic flux density at the solar surface - Formulation and results from simulations

A formal description of the distribution of magnetic flux density in a quiet Sun region supplemented by an example and an application is presented. We define a flux-based probability density, which is useful to reveal the presence of any strong-field component in the region. The corresponding flux-based probability distribution gives the fraction of the total absolute magnetic flux with a given field-strength limit. Application to the simulations of convective field intensification of Grossmann-Doerth et al. (1998) shows, that, depending on the strength of the initial homogeneous vertical field, 1-50% of the total magnetic flux within the computational domain of 3 arcsec width is concentrated into flux fibrils with a flux density exceeding 0.1 T. It is shown that a low efficiency of the flux-concentration process is compatible with new observations that suggest a large fraction of the surface magnetic field to have a flux density below 0.1 T.