Probability Distribution Functions of Sunspot Magnetic Flux by Takashi Sakurai et al. on Sunday 27 November
We have investigated the probability distributions of sunspot area and
magnetic flux by using the data from Royal Greenwich Observatory and USAF/NOAA.
We have constructed a sample of 2995 regions with maximum-development areas
$\ge$ 500 MSH (millionths of solar hemisphere), covering 146.7 years
(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 by the classical Kolmogorov-Smirnov
test. The lognormal and Weibull distributions were excluded because their
behavior extended to smaller regions ($S \ll 500$ MSH) do not connect to the
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 fall-off 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 $10^4$ MSH was estimated to be every
3 -- 8 $\times 10^4$ years. We also have estimated the distributions of the
Sun-as-a-star total sunspot areas. The largest total area covered by sunspots
in the 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.
arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.13957v1
