Modeling the distribution of magnetic fluxes in field concentrations in a solar active region

Much of the magnetic field in solar and stellar photospheres is arranged into clusters of ‘flux tubes’, i.e., clustered into compact areas in which the intrinsic field strength is approximately a kilogauss. The flux concentrations are constantly evolving as they merge with or annihilate against other concentrations, or fragment into smaller concentrations. These processes result in the formation of concentrations containing widely different fluxes. Schrijver et al. (1997, Paper I) developed a statistical model for this distribution of fluxes, and tested it on data for the quiet Sun. In this paper we apply that model to a magnetic plage with an average absolute flux density that is 25 times higher than that of the quiet network studied in Paper I. The model result matches the observed distribution for the plage region quite accurately. The model parameter that determines the functional form of the distribution is the ratio of the fragmentation and collision parameters. We conclude that this ratio is the same in the magnetic plage and in quiet network. We discuss the implications of this for (near-)surface convection, and the applicability of the model to stars other than the Sun and as input to the study of coronal heating.