We explore the spatio-temporal evolution of solar flares by fitting a radial expansion model r ( t ) that consists of an exponentially growing acceleration phase , followed by a deceleration phase that is parameterized by the generalized diffusion function r ( t ) \propto \kappa ( t - t _ { 1 } ) ^ { \beta / 2 } , which includes the logistic growth limit ( \beta = 0 ) , sub-diffusion ( \beta = 0 - 1 ) , classical diffusion ( \beta = 1 ) , super-diffusion ( \beta = 1 - 2 ) , and the linear expansion limit ( \beta = 2 ) .
We analyze all M and X-class flares observed with GOES and AIA/SDO during the first two years of the SDO mission , amounting to 155 events .
We find that most flares operate in the sub-diffusive regime ( \beta = 0.53 \pm 0.27 ) , which we interpret in terms of anisotropic chain reactions of intermittent magnetic reconnection episodes in a low plasma- \beta corona .
We find a mean propagation speed of v = 15 \pm 12 km s ^ { -1 } , with maximum speeds of v _ { max } = 80 \pm 85 km s ^ { -1 } per flare , which is substantially slower than the sonic speeds expected for thermal diffusion of flare plasmas .
The diffusive characteristics established here ( for the first time for solar flares ) is consistent with the fractal-diffusive self-organized criticality ( FD-SOC ) model , which predicted diffusive transport merely based on cellular automaton simulations .