Joule Heating and Anomalous Resistivity in the Solar Corona

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Joule Heating and Anomalous Resistivity in the
Solar Corona

• Steven R. Spangler
• University of Iowa

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Invocation to the Muse

• Coronal Heating is one of the major problems in
  astrophysics

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Coronal heating theories AC and DC

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

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Radioastronomical measurement consistent with
coronal currents within a coronal Amperian Loop

• Spangler, Astrophysical Journal 670, 841, 2007
• Strongest case is for I2.5 GA

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The implication for Joule heating of the corona
dependence on distribution of currents
2D MHD turbulence (e.g. Spangler ApJ 522, 879,
1999)
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Development of strong current sheets is a generic
feature of 2D MHD turbulence
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The Mr. Donut theory of coronal heating
Use this model to calculate The volumetric
heating rate
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Two models for thin current sheets

• Random distribution of positive and negative
  current sheets
• Statistical preference for one sign of current

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Expression for heating rate from model 1
resistivity
Properties of Current sheets
Observational properties
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Main unknown is the resistivity can calculate
heating rate with Spitzer resistivity
suitable for observers form
Ohm-m
For coronal conditions
Ohm-m (35 times Resistivity of silver)
Calculated heating rates
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The significance of Joule heating rate
comparison with inferred heating rates
Cranmer and Van Ballegooijen, ApJS 156, 265, 2005
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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

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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