Flare Thermal Energy

1
Flare Thermal Energy

• Brian R. Dennis
• NASA GSFC
• RHESSI SOHO - TRACE Workshop
• 8 11 December, 2004

2
Flare Thermal Energy

• Objective
• Determine thermal energy vs. time during flare.
• Estimate total thermal energy of flare.
• Simple Method
• Thermal energy at time of soft X-ray peak
• Assume a single temperature
• Advanced Methods
• Allow multi-temperature plasma
• Allow for conductive cooling
• Allow for radiative cooling
• Add thermal energy input during decay phase

3
Thermal Flare Energy

• Simple Method
• Assume a single temperature plasma.
• Ignore cooling during impulsive phase and heating
  afterwards.
• Use GOES fluxes at time of peak soft X-ray
  emission to obtain temperature (T in degrees K)
  and emission measure (EM).
• Use RHESSI 6 12 keV image at same time to
  obtain a volume V A3/2
• Assume 100 filling factor.
• Thermal energy, Uth 3nkT 4.14x10-16 (EM
  V)1/2 T ergs

4
21 April 2002
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GOES Temperature Emission Measure
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RHESSI Light Curve
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RHESSI Image (6 12 keV)
Area inside50 contour8576 arcsec2 Area
inside70 contour 3056 arcsec2
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RHESSI Images
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Peak Thermal Energy

• GOES Soft X-ray Peak - 21 April 2002
• Time 0145 UT
• Temperature (T) 16 MK
• Emission Measure (EM) 2 1050 cm-3
• RHESSI Area (A) 9 103 arcsec2
• (inside 50 contour, 6-12 keV at 0130 UT)
• Volume (V A3/2) 3 1029 cm3
• Density (EM/V)1/2 3 1010 cm-3
• Thermal Energy (Uth) 5 1031 ergs
• (Eth 4.14 x 10-16 (EM V)1/2 T ergs)

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RHESSI Spectra - 21 April 2002
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Advanced Method

• Allow multithermal plasma
• Assume DEM Q T-a cm-3 keV-1
• Fit RHESSI spectra to multithermal power-law
  function.
• Calculate thermal energy for Tmin TGOES
• Quote thermal energy at peak of RHESSI flux.

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RHESSI Spectral FitsMultithermal Power-law
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Peak Thermal Energy

• RHESSI Soft X-ray Peak - 21 April 2002
• Time 0130 UT
• ? (DEM Q T-?) 6.0
• Tmin TGOES 1.4 keV (16 MK)
• EM (Tmin to Tmax) 2 1049 cm-3
• RHESSI Area (A) 9 103 arcsec2
• (inside 50 contour, 6-12 keV at 0130 UT)
• Volume, V A3/2 3 1029 cm3
• Density, n (EM/V)1/2 0.9 1010 cm-3
• Thermal Energy (Uth) 23 1030 ergs
• (Uth 3 k/n ?DEM T dT ergs)
• (for density independent of T)

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23 July 2002
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GOES Temperature Emission Measure
16
RHESSI Light Curve
17
RHESSI Image (6 12 keV)
Area inside50 contour244 arcsec2 Area
inside70 contour 115 arcsec2
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RHESSI Images 23 July, 2002
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PIXON Images23 July 2002
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Peak Thermal Energy

• GOES Soft X-ray Peak - 23 July 2002
• Time 0035 UT
• Temperature (T) 22 MK
• Emission Measure (EM) 3.5 1050 cm-3
• RHESSI Area (A) 2.4 102 arcsec2
• (inside 50 contour, 6-12 keV at 0035 UT)
• Volume (V A3/2) 1.4 1027 cm3
• Density (EM/V)1/2 5 1011 cm-3
• Thermal Energy (Uth) 7 1030 ergs
• (Eth 4.14 x 10-16 (EM V)1/2 T ergs)

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Thermal Flare Energy

• More Advanced Method (Veronig et al.)
• Assume a single temperature plasma.
• Include conductive (Lcond) and radiative (Lrad)
  cooling losses.
• Include estimated gravitational (Ugravity) and
  kinetic (Ukinetic) plasma energies.
• Include heating after impulsive phase.
• Use GOES spectra throughout flare to obtain
  temperature T and emission measure EM as
  functions of time.
• Estimate volume V (assumed constant) from RHESSI
  footpoint area x loop length.
• Assume 100 filling factor.
• SXR plasma energy, USXR Uthermal Ugravity
  Ukinetic
• (3 10) nkTV (4 13) x 10-16 (EM V)1/2 T
  ergs
• Heating rate, P dU/dt Lcond Lrad erg s-1
• Total heating ?P dt erg

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Veronig - 21 April 2002
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Veronig - 23 July 2002
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Thermal Energies
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Conclusions

• Thermal energy estimates subject to
  order-of-magnitude uncertainties.
• SXR-emitting plasma has 10 times more energy at
  the peak of the 21 April flare than at the peak
  of the 23 July flare.
• Including conductive cooling losses can increase
  the total energy requirement by a large factor.
• Including the decay phase energy input increases
  the total flare energy by factor of 2.