In this study we test 30 variants of 5 physical scaling laws that describe different aspects of solar flares .
We express scaling laws in terms of the magnetic potential field energy E _ { p } , the mean potential field strength B _ { p } , the free energy E _ { free } , the dissipated magnetic flare energy E _ { diss } , the mean loop length scale L , the mean helically twisted flux tube radius R , the sunspot radius r , the emission measure-weighted flare temperature T _ { w } , the electron density n _ { e } , and the total emission measure EM , measured from a data set of \lower 1.72 pt \hbox { $ \buildrel < \over { \scriptstyle \sim } $ } 400 GOES M- and X-class flare events .
The 5 categories of physical scaling laws include ( i ) a scaling law of the potential-field energy , ( ii ) a scaling law for helical twisting , ( iii ) a scaling law for Petschek-type magnetic reconnection , ( iv ) the Rosner-Tucker-Vaiana scaling law , and ( v ) the Shibata-Yokoyama scaling law .
We test the self-consistency of these theoretical scaling laws with observed parameters by requiring two conditions : a cross-corrleation coefficient of CCC > 0.5 between the observed and theoretically predicted scaling laws , and a linear regression fit with a slope of \alpha \approx 1 .
With these two criteria we find that 10 out of the 30 tested scaling law variants are consistent with the observed data , which strongly corroborates the existence and validity of the tested flare scaling laws .