# Presentation: 333436

## Flare Thermal Energy

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

## 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

## 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

## 21 April 2002

## GOES Temperature & Emission Measure

## RHESSI Light Curve

## RHESSI Image (6 – 12 keV)

- Area inside50% contour=8576 arcsec2
- Area inside70% contour
- =3056 arcsec2

## RHESSI Images

## 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 10****31**** ergs**
- (Eth = 4.14 x 10-16 (EM V)1/2 T ergs)

## RHESSI Spectra - 21 April 2002 

## 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.

## RHESSI Spectral FitsMultithermal + Power-law

## Peak Thermal Energy

- RHESSI Soft X-ray Peak - 21 April 2002
- Time: 	01:30 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 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 10****30**** ergs**
- (Uth = 3 k/n DEM T dT ergs)
- (for density independent of T)

## 23 July 2002

## GOES Temperature & Emission Measure

## RHESSI Light Curve

## RHESSI Image (6 – 12 keV)

- Area inside50% contour=244 arcsec2
- Area inside70% contour
- =115 arcsec2

## RHESSI Images – 23 July, 2002

## PIXON Images23 July 2002

## 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 10****30**** ergs**
- (Eth = 4.14 x 10-16 (EM V)1/2 T ergs)

## 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

## Veronig - 21 April 2002

## Veronig - 23 July 2002

## Thermal Energies

|  | Units | 21 April 2002x1.5 |  |  | 23 July 2002X4.8 |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| AuthorSpacecraft |  | DennisGOES | DennisRHESS | VeronigGOES | DennisGOES | VeronigGOES | HolmanGOES | Holman RHESSI |
| Time – UT | hh:mm | 01:45 | 01:30 | <04:00 | 00:35 | <02:00 | 00:36 | </>00:27 |
| T | MK | 16 | 16-100 | O17 | 22 | O29 | 23 | 34 |
| EM | 1050 cm-3 | 2 | 0.2 | O1.7 | 3.5 | 3.4 | 3 | 0.5 |
| Loop Length (l) | 108 cm |  |  | 140 |  | 35 |  |  |
| Area (A) | 1018 cm2 | 50 | 50 | 1 | 1 | 1 |  |  |
| Volume (V) | 1026 cm3 | 3000 | 3000 | 140 | 14 | 40 | 40 | O180/40 |
| Density (EM/V)1/2 | 1010 cm-3 | 3 | 0.9 | 11 | 50 | 29 | 27 | 10 |
| Thermal Energy | 1030 ergs | 50 | 23 |  | 7 |  | 11 | 6.6 |
| Total Heating | 1030 ergs |  |  | 90 |  | 200 |  |  |
| Nonthermal E | 1030 ergs |  |  |  |  |  |  | 2610 |

## 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.