Scaling Laws of Solar and Stellar Flares

Abstract

In this study we compile for the first time comprehensive data sets of solar and stellar flare parameters, including flare peak temperatures Tp, flare peak volume emission measures EMp, and flare durations τf from both solar and stellar data, as well as flare length scales L from solar data. Key results are that both the solar and stellar data are consistent with a common scaling law of EMp ∝ T4.7p, but the stellar flares exhibit ≈250 times higher emission measures (at the same flare peak temperature). For solar flares we observe also systematic trends for the flare length scale L(Tp) ∝ T0.9p and the flare duration τF(Tp) ∝ T0.9p as a function of the flare peak temperature. Using the theoretical RTV scaling law and the fractal volume scaling observed for solar flares, i.e., V(L) ∝ L2.4, we predict a scaling law of EMp ∝ T4.3p, which is consistent with observations, and a scaling law for electron densities in flare loops, np ∝ T2p/L ∝ T1.1p. The RTV-predicted electron densities were also found to be consistent with densities inferred from total emission measures, np = (EMp/qVV)1/2, using volume filling factors of qV = 0.03–0.08 constrained by fractal dimensions measured in solar flares. Solar and stellar flares are expected to have similar electron densities for equal flare peak temperatures Tp, but the higher emission measures of detected stellar flares most likely represent a selection bias of larger flare volumes and higher volume filling factors, due to low detector sensitivity at higher temperatures. Our results affect also the determination of radiative and conductive cooling times, thermal energies, and frequency distributions of solar and stellar flare energies.