Photospheric Current Spikes and Their Possible Association with Flares - Results from an HMI Data Driven Model
A data driven, near photospheric magnetohydrodynamic model predicts spikes in the horizontal current density, and associated resistive heating rate per unit volume Q. The spikes appear as increases by orders of magnitude above background values in neutral line regions (NLRs) of active regions (ARs). The largest spikes typically occur a few hours to a few days prior to M or X flares. The spikes correspond to large vertical derivatives of the horizontal magnetic field. The model takes as input the photospheric magnetic field observed by the Helioseismic & Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) satellite. This 2.5 D field is used to determine an analytic expression for a 3 D magnetic field, from which the current density, vector potential, and electric field are computed in every AR pixel for 14 ARs. The field is not assumed to be force-free. The spurious 6, 12, and 24 hour Doppler periods due to SDO orbital motion are filtered out of the time series of the HMI magnetic field for each pixel using a band pass filter. The subset of spikes analyzed at the pixel level are found to occur on HMI and granulation scales of 1 arcsec and 12 minutes. Spikes are found in ARs with and without M or X flares, and outside as well as inside NLRs, but the largest spikes are localized in the NLRs of ARs with M or X flares. The energy to drive the heating associated with the largest current spikes comes from bulk flow kinetic energy, not the electromagnetic field, and the current density is highly non-force free. The results suggest that, in combination with the model, HMI is revealing strong, convection driven, non-force free heating events on granulation scales, and that it is plausible these events are correlated with subsequent M or X flares. More and longer time series need to be analyzed to determine if such a correlation exists. Above an AR dependent threshold value of Q, the number of events N(Q) with heating rates greater than or equal to Q obeys a scale invariant power law distribution for each AR given by N(Q) varies Q(sup -s), where 0.40 less than or equal to S less than or equal to 0.53, with a mean and standard deviation across the 14 ARs of 0.47 and 0.045, showing there is little variation of S from one AR to another. These properties of N(Q) are in close agreement with those of the distribution N(E) for the total energy E of solar flares, determined from observations to be N(E) = constant x E(sup -alpha). From observations of nanoflares in the 0.7 to 4 MK range, and from observations of flares in hard X-rays, it is found that 0.51 less than or equal to alpha less than or equal to 0.57, and 0.4 less than or equal to alpha less than or equal to 0.6, respectively (Crosby et al. 1993, Sol. Phys., 143, 275; Aschwanden & Parnell 2002, ApJ, 572, 1048). Observations also show that, as is found here for the exponent S, there is little variation of alpha with AR (Wheatland 2000, ApJ, 532, 1209), indicating N(E) and N(Q) are largely independent of individual properties of ARs such as area, total magnetic flux, and distribution of current density (i.e. non-potentiality). Therefore the power law scaling of the photospheric heating rate Q computed here on granulation scales is essentially identical to that found for coronal observations of flare energies on scales 1-2 orders of magnitude larger. This suggests the physical mechanisms that cause Q and coronal flares are closely related. It seems likely that Q is the signature of a magnetic reconnection process in an energy range and volume orders of magnitude smaller than those of flares. In this context, at least the larger spikes in Q might be signatures of UV photospheric or lower chromospheric bombs in which plasma is heated to temperatures approximately 10(exp -5) K (Peter et al. 2014, Science 346, 1255726; Judge 2015, ApJ, 808, 116). In addition, lattice based avalanche simulations of flare energy release predict 0.4 less than or equal to alpha less than or equal to 0.5, while analytic, fractal-diffusive self-organized criticality models predict 0.4 less than or equal to alpha less than or equal to 0.67, in excellent agreement with observations, and the results presented here (Aschwanden & Parnell 2002, ApJ, 572, 1048; Aschwanden 2012, A&A, 539, A2; Aschwanden 2013, in "Self Organized Criticality Systems"; Aschwanden et al. 2016, SSR, 198, 47).