Nature of the magnetic carpet - I. Distribution of magnetic fluxes

The distribution of magnetic fluxes found in the solar magnetic carpet, the photospheric magnetic field of the quiet-Sun, is investigated. A total of 27 500 concentrations are studied with fluxes ranging between a few times 10(17) and a few times 10(20) Mx. A histogram of the fluxes shows that there are more small fluxes and more large fluxes than anticipated by an exponential distribution. However, there are significantly fewer large and small fluxes than a power-law distribution fitted to the middle of the range. Thus, the fluxes are not distributed in the form of either an exponential or a power-law distribution, as previously suggested. Instead, the Weibull distribution, which involves both a power law and an exponential, is found to provide both a statistically good fit to the data and a physically reasonable prediction for the total absolute flux density. The best-fitting Weibull distribution has a Kolmogorov-Smirnov D statistic of approximately 0.07 - well below the 5 per cent significance level and the Weibull distribution predicts the observed total absolute flux densities to within better than 92 per cent. Physically, the observed distribution of fluxes can be explained as being made up of the following three elements: (i) emergence of new flux over all scales gives rise to an initial exponential distribution (observed); (ii) fragmentation and partial cancellation produce smaller and smaller fluxes thus creating excess small fluxes; (iii) excess large fluxes are created by coalescence and an additional (possibly significant) injection of flux from remnants of active regions. Finally, the equations of 'magneto-chemistry' are used to derive suitable forms for the rate of emergence, cancellation, coalescence and fragmentation consistent with a Weibull distribution of fluxes.