Broken power-law distributions of photospheric magnetic concentrations and implications for solar dynamo

Photospheric magnetic concentrations (MCs) are a direct manifestation of the solar dynamos that govern the solar magnetic field evolution and solar cycles. By studying the magnetic flux, spatial size, and magnetic energy of 2,941,532 MCs during 2011–2022, we find that the appearance rate of MCs fits well to a broken power-law distribution. The power index of small-scale MCs is almost invariant during the solar cycle; however, that of the large-scale MCs is logarithmically related to the sunspot number. These results suggest that small-scale MCs are more susceptible to local dynamical processes, which may weaken their solar cycle dependence and produce more stochastic statistical behavior. In contrast, the statistical properties of large-scale MCs retain a stronger solar cycle modulation, implying that they preserve more of the large-scale magnetic field evolution associated with the solar cycle. The findings provide observational constraints on models of solar magnetic field generation and evolution and offer new insights into the scale-dependent properties of photospheric MCs over the solar cycle.