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Effects of Cowling Resistivity in the Weakly-Ionized Chromosphere

The physics of the solar chromosphere is complex from both theoretical and modeling perspectives. The plasma temperature from the photosphere to corona increases from ~5,000 K to ~1 million K over a distance of only ~10,000 km from the chromosphere and the transition region. Certain regions of the solar atmosphere have sufficiently low temperature and ionization rates to be considered as weakly-ionized. In particular, this is true at the lower chromosphere. As a result, the Cowling resistivity is orders of magnitude greater than the Coulomb resistivity. Ohm's law therefore includes anisotropic dissipation. To evaluate the Cowling resistivity, we need to know the external magnetic field strength and to estimate the neutral fraction as a function of the bulk plasma density and temperature. In this study, we determine the magnetic field topology using the non-force-free field (NFFF) extrapolation technique based on SDO/HMI SHARP vector magnetogram data, and the stratified density and temperature profiles from the Maltby-M umbral core model for sunspots. We investigate the variation and effects of Cowling resistivity on heating and magnetic reconnection in the chromosphere as the flare-producing active region (AR) 11166 evolves. In particular, we analyze a C2.0 flare emerging from AR11166 and find a normalized reconnection rate of 0.051.