Three-dimensional magnetohydrodynamic simulation of the solar magnetic flux emergence: Parametric study on the horizontal divergent flow

Solar active regions are formed through the emergence of magnetic flux from the deeper convection zone. Recent satellite observations have shown that a horizontal divergent flow (HDF) stretches out over the solar surface just before the magnetic flux appearance. The aims of this study are to investigate the driver of the HDF and to see the dependency of the HDF on the parameters of the magnetic flux in the convection zone. We conduct three-dimensional magnetohydrodynamic (3D MHD) numerical simulations of the magnetic flux emergence and vary the parameters in the initial conditions. An analytical approach is also taken to explain the dependency. The horizontal gas pressure gradient is found to be the main driver of the HDF. The maximum HDF speed shows positive correlations with the field strength and twist intensity. The HDF duration has a weak relation with the twist, while it shows negative dependency on the field strength only in the case of the stronger field regime. Parametric dependencies analyzed in this study may allow us to probe the structure of the subsurface magnetic flux by observing properties of the HDF.Comment: 7 pages, 5 figures, 1 table, accepted for publication in Astronomy & Astrophysic

Probability Distribution Functions of Sunspot Magnetic Flux

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