Nonlinear Processes in Geophysics Joule heating and anomalous resistivity in the solar corona

Abstract. Recent radioastronomical observations of Faraday rotation in the solar corona can be interpreted as evidence for coronal currents, with values as large as 2.5×109 Amperes (Spangler, 2007). These estimates of currents are used to de-velop a model for Joule heating in the corona. It is assumed that the currents are concentrated in thin current sheets, as suggested by theories of two dimensional magnetohydrody-namic turbulence. The Spitzer result for the resistivity is adopted as a lower limit to the true resistivity. The calcu-lated volumetric heating rate is compared with an indepen-dent theoretical estimate by Cranmer et al. (2007). This latter estimate accounts for the dynamic and thermodynamic prop-erties of the corona at a heliocentric distance of several solar radii. Our calculated Joule heating rate is less than the Cran-mer et al estimate by at least a factor of 3×105. The cur-rents inferred from the observations of Spangler (2007) are not relevant to coronal heating unless the true resistivity is enormously increased relative to the Spitzer value. However, the same model for turbulent current sheets used to calculate the heating rate also gives an electron drift speed which can be comparable to the electron thermal speed, and larger than the ion acoustic speed. It is therefore possible that the coro-nal current sheets are unstable to current-driven instabilities which produce high levels of waves, enhance the resistivity and thus the heating rate.