1. Joule Heating and Anomalous Resistivity in the Solar Corona Steven R. Spangler University of Iowa

2. Invocation to the Muse “Coronal Heating is one of the major problems in astrophysics”

3. Coronal heating theories: AC and DC Evaluation of DC (Joule heating) theories requires measurements of coronal currents

4. Radioastronomical measurement consistent with coronal currents within a coronal Amperian Loop Spangler, Astrophysical Journal 670, 841, 2007 Strongest case is for I=2.5 GA

5. The implication for Joule heating of the corona: dependence on distribution of currents 2D MHD turbulence (e.g. Spangler ApJ 522, 879, 1999)

6. Development of strong current sheets is a generic feature of 2D MHD turbulence

7. The “Mr. Donut” theory of coronal heating Use this model to calculate The volumetric heating rate

8. Two models for thin current sheets Random distribution of positive and negative current sheets Statistical preference for one sign of current

9. Expression for heating rate from model 1 Observational properties Properties of Current sheets resistivity

10. Main unknown is the resistivity: can calculate heating rate with Spitzer resistivity Ohm-m “suitable for observers” form For coronal conditions Ohm-m (35 times Resistivity of silver) Calculated heating rates

11. The significance of Joule heating rate: comparison with inferred heating rates Cranmer and Van Ballegooijen, ApJS 156, 265, 2005

12. Conclusion: Joule heating rate with Spitzer conductivity is too low by ~ 6 orders of magnitude Conclusion #1: currents detected by radio astronomy are irrelevant for coronal heating (strengthened by more common upper limits) Conclusion #2: currents are relevant, and resistivity is enhanced by many orders of magnitude

13. Postscript: current sheet model allows expression for electron drift speed Calculation is consistent with (or not inconsistent with) It is plausible that the electron drift speeds are sufficiently high To excite instabilities which would enhance resistivity Thanks