Abstract
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 develop 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 magnetohydrodynamic turbulence. The Spitzer result for the resistivity is adopted as a lower limit to the true resistivity. The calculated volumetric heating rate is compared with an independent theoretical estimate by Cranmer et al. (2007). This latter estimate accounts for the dynamic and thermodynamic properties of the corona at a heliocentric distance of several solar radii. Our calculated Joule heating rate is less than the Cranmer et al estimate by at least a factor of 3×105. The currents 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 coronal current sheets are unstable to current-driven instabilities which produce high levels of waves, enhance the resistivity and thus the heating rate.
Highlights
In a recent paper, Spangler (2007) reported radioastronomical observations which were consistent with the presence of coronal currents in the range of hundreds of MegaAmperes to a few GigaAmperes
Faraday rotation observations of a radio source occulted by the corona, and the coronal plasma probed was at heliocentric distances of 5.2 to 6.7 R
I consider the second of the possibilities listed at the end of Sect. 3.4.4, i.e. that the resistivity could be sufficiently enhanced in these coronal current sheets to make Joule heating a thermodynamically important process
Summary
In a recent paper, Spangler (2007) reported radioastronomical observations which were consistent with the presence of coronal currents in the range of hundreds of MegaAmperes to a few GigaAmperes The measured net current could be, and probably is, a residual due to numerous current filaments with alternate positive and negative current density within the Amperian loop This topic is of interest because Joule heating has been identified as the primary mechanism for heating the closedfield part of the corona (Gudiksen and Nordlund, 2005; Peter et al, 2006). This model is used to obtain an estimate of the volumetric heating rate due to Joule heating.
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