Probability Distribution Functions of Sunspot Magnetic Flux

Abstract

We investigated the probability distributions of sunspot area and magnetic flux by using data from the Royal Greenwich Observatory and USAF/NOAA. We constructed a sample of 2995 regions with maximum-development areas ≥500 MSH (millionths of solar hemisphere), covering 146.7 yr (1874–2020). The data were fitted by a power-law distribution and four two-parameter distributions (tapered-power-law, gamma, lognormal, and Weibull distributions). The power-law model was unfavorable compared to the four models in terms of AIC, and was not acceptable according to the classical Kolmogorov–Smirnov test. The lognormal and Weibull distributions were excluded because their behavior extended to smaller regions (S ≪ 500 MSH) do not connect to previously published results. Therefore, our choices were tapered-power-law and gamma distributions. The power-law portion of the tapered-power-law and gamma distributions was found to have a power exponent of 1.35–1.9. Due to the exponential falloff of these distributions, the expected frequencies of large sunspots are low. The largest sunspot group observed had an area of 6132 MSH, and the frequency of sunspots larger than 104 MSH was estimated to be every 3–8 × 104 yr. We also estimated the distributions of the Sun-as-a-star total sunspot areas. The largest total area covered by sunspots on record was 1.67% of the visible disk, and can be up to 2.7% by artificially increasing the lifetimes of large sunspots in an area evolution model. These values are still smaller than those found on active Sun-like stars.