HMI Data Driven Magnetohydrodynamic Model Predicted Active Region Photospheric Heating Rates: Their Scale Invariant, Flare Like Power Law Distributions, and Their Possible Association With Flares

A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model computes time series of the complete current density and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14... [ view full abstract ]

A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model computes time series of the complete current density and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14 active regions (ARs). The model is driven by time series of the magnetic field B measured by the Helioseismic & Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. Errors in B due to these periods can be significant. The number of occurrences N(q) of values of Q ≥ q for each AR time series is found to be close to a scale invariant power law distribution, N(Q) = constant x Q^-s, above an AR dependent threshold value of Q, where 0.3952 ≤ s ≤ 0.5298, with mean and standard deviation of 0.4678 and 0.0454, indicating little variation between ARs. For coronal flares, N(E), where E is total energy released, has the same form as N(q) but with 0.4 ≤ s ≤ 0.88, where almost all values of s are in the range 0.4 ≤ s ≤ 0.60, and with little variation of s with AR. This strong similarity between N(Q) and N(E) suggests the same process powers coronal flares and the photospheric Q. Model results also suggest it is plausible that the times of spikes in Q, several orders of magnitude above background values, are correlated with the subsequent occurrence of M or X flares.