Global energetics of solar flares. XII. Energy scaling laws 

Markus J. Aschwanden Submitted: 20210611 12:31
In this study we test 18 versions of 5 fundamental energy scaling laws that operate in large solar flares. We express scaling laws in terms of the magnetic potential field energy Ep, the mean potential field strength Bp, the free energy Efree, the dissipated magnetic flare energy Ediss, the magnetic length scale L, the thermal length scale Lth, the mean helically twisted flux tube radius R, the sunspot radius r, the emission measureweighted flare temperature Te, the electron density ne, and the total emission measure EM, measured from a data set of 173 GOES M and Xclass flare events. The 5 categories of physical scaling laws include (i) a scaling law of the potentialfield energy, (ii) a scaling law for helical twisting, (iii) a scaling law for Petschektype magnetic reconnection, (iv) the Rosner TuckerVaiana scaling law, and (v) the ShibataYokoyama scaling law. We test the selfconsistency of these theoretical scaling laws with observed parameters by requiring two criteria: a crosscorrleation coefficient of CCC>0.5 between the theoretically predicted scaling laws and observed values, and a linear regression fit with a slope of α ≈ 1 within one standard deviation σ. These two criteria enable us (i) to corroborate some existing (or modified) scaling laws, (ii) to reject other scaling laws that are not consistent with the observations, (iii) to probe the dimensionality of flare geometries, and (iv) to predict various energy parameters based on tested scaling laws.
Authors: Aschwanden, M.J.
Projects: GOES Xrays

Publication Status: Aschwanden,M.J. 2020, ApJ 903:23
Last Modified: 20210612 00:57


