Flare Thermal Energy

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.