1. Flare Thermal Energy Brian Dennis NASA GSFC Solar Physics Laboratory 12/6/20081Solar 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 volume V = A 3/2 – Assume 100% filling factor. – Thermal energy, U th = 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 inside 50% contour = 8576 arcsec 2 Area inside 70% contour = 3056 arcsec 2

8. Peak Thermal Energy GOES Soft X-ray Peak - 21 April 2002 Time: 01:45 UT Temperature (T): 16 MK Emission Measure (EM): 2 10 50 cm -3 RHESSI Area (A):9 10 3 arcsec 2 (inside 50% contour, 6-12 keV at 01:30 UT) Volume (V = A 3/2 ):3 10 29 cm 3 Density (EM/V) 1/2 3 10 10 cm -3 Thermal Energy (U th ):5 10 31 ergs (E th = 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 T min = T GOES 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 T min = T GOES : 1.4 keV (16 MK) EM (T min to T max ): 2 10 49 cm -3 RHESSI Area (A):9 10 3 arcsec 2 (inside 50% contour, 6-12 keV at 01:30 UT) Volume, V = A 3/2 :3 10 29 cm 3 Density, n = (EM/V) 1/2 0.9 10 10 cm -3 Thermal Energy (U th ):23 10 30 ergs (E th = 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 inside 50% contour = 244 arcsec 2 Area inside 70% contour = 115 arcsec 2

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 10 50 cm -3 RHESSI Area (A):2.4 10 2 arcsec 2 (inside 50% contour, 6-12 keV at 00:35 UT) Volume (V = A 3/2 ):1.4 10 27 cm 3 Density (EM/V) 1/2 5 10 11 cm -3 Thermal Energy (U th ):7 10 30 ergs (E th = 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 (L cond ) and radiative (L rad ) cooling losses. Include estimated gravitational (U gravity ) and kinetic (U kinetic ) 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, U SXR = U thermal + U gravity + U kinetic = (3 – 10) nkTV = (4 – 13) x 10 -16 (EM V) 1/2 T ergs Heating rate, P = dU/dt + L cond + L rad erg s -1 Total heating =  P dt erg

18. Veronig - 21 April 2002

19. Veronig - 23 July 2002

20. Thermal Energies Units 21 April 2002 x1.5 23 July 2002 X4.8 Author Spacecraft Dennis GOES Dennis RHESSI Veronig GOES Dennis GOES Veronig GOES Holman GOES Holman RHESSI Time – UT hh:mm01:4501:30<04:0000:35<02:0000:36 00:27 T MK1616-100O1722O292334 EM 10 50 cm -3 20.2O1.73.53.430.5 Loop Length (l)10 8 cm14035 Area (A)10 18 cm 2 50 111 Volume (V)10 26 cm 3 3000 1401440 O180/40 Density (EM/V) 1/2 10 10 cm -3 30.91150292710 Thermal Energy10 30 ergs50237116.6 Total Heating10 30 ergs90200 Nonthermal E10 30 ergs26  10

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.