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Flare Thermal Energy

Flare Thermal Energy. Brian Dennis NASA GSFC Solar Physics Laboratory. 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

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Flare Thermal Energy

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  1. Flare Thermal Energy Brian Dennis NASA GSFC Solar Physics Laboratory Solar Cycle 24, Napa, 8-12 December 2008

  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 multithermal plasma • Allow for cooling during impulsive phase • Add thermal energy required for 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 volumeV = A3/2 • Assume 100% filling factor. • Thermal energy, Uth = 3nkT = 4.14x10-16 (EM V)1/2 T ergs

  4. 21 April 2002

  5. GOES Temperature & Emission Measure

  6. RHESSI Light Curve

  7. RHESSI Image (6 – 12 keV) Area inside50% contour=8576 arcsec2 Area inside70% contour =3056 arcsec2

  8. Peak Thermal Energy • GOES Soft X-ray Peak - 21 April 2002 Time: 01:45 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 01:30 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)

  9. Advanced Method • Allow multithermal plasma • Assume DEM = A T- 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.

  10. Peak Thermal Energy • RHESSI Soft X-ray Peak - 21 April 2002 Time: 01:30 UT a (DEM Q T-a) 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 01:30 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 (Eth = 3 k/n DEM T dT ergs) (for density independent of T)

  11. 23 July 2002

  12. GOES Temperature & Emission Measure

  13. RHESSI Light Curve

  14. RHESSI Image (6 – 12 keV) Area inside50% contour=244 arcsec2 Area inside70% contour =115 arcsec2

  15. RHESSI Images

  16. Peak Thermal Energy • GOES Soft X-ray Peak - 23 July 2002 Time: 00:35 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 00:35 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)

  17. 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

  18. Veronig - 21 April 2002

  19. Veronig - 23 July 2002

  20. Thermal Energies

  21. 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.

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