From the above it is clear that the choice of a function to fit a size distribution is not straightforward and the form used will affect the 100-year and 1000-year estimates obtained. For this reason we adopt a conservative empirical approach that favors the modified exponential function of Gopalswamy (2018) for several of the phenomena considered below; with its three free parameters, this function generally fits distributions well over their full parameter range, as in Fig. 6. Because power-law functions are commonly used for flare X-ray and radio distributions (e.g., Aschwanden 2014), we consider them as well, comparing exponential and power-law 100-year and 1000-year event estimates when both functions are available.
FULL Flare 2008 [32-64Bit]
A cartoon depicting estimated areas of sunspot groups (exclusive of any surrounding facular areas) needed to power flares with different energy budgets. These estimates were originally developed by, and depicted in, Aulanier et al. (2013) for the parts of the sunspot groups involved in the flaring, which is assumed to be up to a third of the overall group size. In this modified version, Schmieder (2018) tripled the areas of the groups for the bipole involved in flaring (with red outlines) to show the sizes of spot groups required to reach up to a maximum value of a large stellar flare of around 1036 erg. In the Sun and stars, the flux in two thirds of the region may not be fully contained in spots, of course, but could also be distributed over extended facular regions. In a modification of the figure from Schmieder (2018), we overlaid, in the solar image on the left, the largest observed sunspot group since 1874 (shown in Ca II K1v; full disk image in Fig. 14) for comparison with the group in the upper right quadrant which has an estimated peak flare energy of 1033 erg. The two symbols in the right-hand image that resemble tires are sunspot drawings of uncertain scale by John of Worcester from 1128 AD December 8 ( )
The lower limit of the spot area of superflare stars (Aspot) can be inferred from the ΔFrot (defined as the full amplitude of the rotational brightness variation normalized by the average brightness) as follows: 2ff7e9595c