Joule Heating and Anomalous Resistivity in the Solar Corona

Steven R. Spangler

University of Iowa

Invocation to the Muse

“Coronal Heating is one of the major problems in astrophysics”

Coronal heating theories: AC and DC

Evaluation of DC (Joule heating) theories requires measurements of coronal currents

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

The implication for Joule heating of the corona: dependence on distribution of currents

2D MHD turbulence(e.g. SpanglerApJ 522, 879, 1999)

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

The “Mr. Donut” theory of coronal heating

Use this model to calculateThe volumetric heating rate

Two models for thin current sheets

• Random distribution of positive and negative current sheets

• Statistical preference for one sign of current

Expression for heating rate from model 1

Observationalproperties

Properties ofCurrent sheets

resistivity

Main unknown is the resistivity: can calculate heating rate with Spitzer resistivity

Ohm-m “suitable for observers”form

For coronal conditions Ohm-m (35 timesResistivity of silver)

Calculated heating rates

The significance of Joule heating rate: comparison with inferred heating rates

Cranmer and Van Ballegooijen,ApJS 156, 265, 2005

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

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 highTo excite instabilities which would enhance resistivity

Thanks