From solar nanoflares to stellar giant flares: Scaling laws and non-implications for coronal heating

In this study we explore physical scaling laws applied to solar nanoflares, microflares, and large flares, as well as to stellar giant flares. Solar flare phenomena exhibit a fractal volume scaling, V(L)  L^1.9, with L being the flare loop length scale, which explains the observed correlation between the total emission measure EM_p and flare peak temperature T_p in both solar and stellar flares. However, the detected stellar flares have higher emission measures EM_p than solar flares at the same flare peak temperature T_p, which can be explained by a higher electron density that is caused by shorter heating scale height ratios s_H/L ≈ 0.04–0.1. Using these scaling laws we calculate the total radiated flare energies E_X and thermal flare energies E_T and find that the total counts C are a good proxy for both parameters. Comparing the energies of solar and stellar flares we find that even the smallest observed stellar flares exceed the largest solar flares, and thus their observed frequency distributions are hypothetically affected by an upper cutoff caused by the maximum active region size limit. The powerlaw slopes fitted near the upper cutoff can then not reliably be extrapolated to the microflare regime to evaluate their contribution to coronal heating.