Post on 20-Jan-2016
description
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