Scaling laws of solar and stellar flares

TL;DR

This study compiles comprehensive solar and stellar flare data, revealing a common scaling law for emission measures and providing insights into flare properties, densities, and cooling times with implications for understanding flare energetics.

Contribution

It introduces the first combined analysis of solar and stellar flare parameters, establishing a unified scaling law and validating theoretical models with observational data.

Findings

Solar and stellar flares follow EM_p ~ T_p^4.7 scaling law.

Stellar flares have ~250 times higher emission measures at the same T_p.

Predicted electron densities scale as n_p ~ T_p^1.1, consistent with observations.

Abstract

In this study we compile for the first time comprehensive data sets of solar and stellar flare parameters, including flare peak temperatures T_p, flare peak volume emission measures EM_p, and flare durations t_f 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 EM_p ~ T_p^4.7, 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(T_p) ~ T_p^0.9 and the flare duration t_F(T_p) ~ T_p^0.9 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) ~ L^2.4, we predict a scaling law of EM_p ~ T_p^4.3, which is consistent with observations, and a scaling law for electron densities in flare loops, n_p ~ T_p^2/L ~ T_p^1.1. The RTV-predicted electron densities were also found to be consistent with densities inferred from total emission measures, n_p=(EM_p/q_V*V)^1/2, using volume filling factors of q_V=0.03-0.08 constrained by fractal dimensions measured in solar flares. Our results affect also the determination of radiative and conductive cooling times, thermal energies, and frequency distributions of solar and stellar flare energies.