In this study, we analysed different types (C, M, and X classes) of X-ray solar flares occurring in sunspot groups. The data cover 1996–2014 time interval, and a total of 4262 active regions (ARs) were included in the data set. We defined the solar-flare-production potential as the ratio of the total number of flares observed in a sunspot group to the total number of the same-class sunspot groups. Our main findings are as follows: (1) large and complex sunspot groups (D+E+F) have the flare-production potential about eight times higher than the small and simple (A+B+C+H) ARs; (2) 79 per cent of all flares were produced by the large and complex sunspot groups, while only 21 per cent of flares were produced by the small groups; (3) the largest and the most complex F-class (very large and very complex) sunspot groups exhibit the highest flare-production potential (2.16 flare per sunspot group), while the smallest and the least complex A class sunspot groups show the lowest (0.05 flare per group) flare-production potential; (4) temporal variation of sunspot counts, sunspot group areas, and the total number of flares (including C flares) showed similar time profiles during both cycles with multiple peaks; (5) the mean area of ARs very well describes the flare-production potential of each group with the regression coefficient of R² = 0.99. Most of these sunspot groups (>70 per cent) are, according to the Zurich Classification, complex ARs.

Polar brightening of the Sun at radio frequencies has been studied for almost 50 years and yet a disagreement persists between solar atmospheric models and observations. Some observations reported brightening values much smaller than the expected values obtained from the models, with discrepancies being particularly large at millimeter wavelengths. New clues to calibrate the atmospheric models can be obtained with the advent of the Atacama Large Millimeter/submillimeter Array (ALMA) radio interferometer. In this work, we analyzed the lower limit of the polar brightening observed at 100 and 230 GHz by ALMA, during its Science Verification period, 2015 December 16–20. We find that the average polar intensity is higher than the disk intensity at 100 and 230 GHz, with larger brightness intensities at the south pole in eight of the nine maps analyzed. The observational results were compared with calculations of the millimetric limb brightening emission for two semi-empirical atmospheric models, FAL-C and SSC. Both models presented larger limb intensities than the average observed values. The intensities obtained with the SSC model were closer to the observations, with polar brightenings of 10.5% and 17.8% at 100 and 230 GHz, respectively. This discrepancy may be due to the presence of chromospheric features (like spicules) at regions close to the limb.

The questions asking whether the Sun shrinks with the solar activity and what causes this have been a subject of debate. Helioseismology provides a means to measure with high precision the radial displacement of subsurface layers, the so-called “seismic radius,” through the analysis of oscillation frequencies of surface gravity (f) modes. Here, we present results of a new analysis of 21 years of helioseismology data from two space missions, the Solar and Heliospheric Observatory and the Solar Dynamics Observatory, which allow us to resolve previous uncertainties and compare variations of the seismic radius in two solar cycles. After removing the f-mode frequency changes associated with the surface activity, we find that the mean seismic radius is reduced by 1–2 km during the solar maxima and that most significant variations of the solar radius occur beneath the visible surface of the Sun at a depth of about 5 ± 2 Mm, where the radius is reduced by 5–8 km. These variations can be interpreted as changes in the solar subsurface structure caused by the predominately vertical ∼10 kG magnetic field.