Flare Thermal Energy

Brian DennisNASA GSFC

Solar Physics Laboratory

12/6/2008 1Solar Cycle 24, Napa, 8-12 December 2008

Flare Thermal EnergyObjective

– 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

Thermal Flare EnergySimple 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

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

Peak Thermal Energy• GOES Soft X-ray Peak - 21 April 2002

Time: 01:45 UTTemperature (T): 16 MKEmission 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)

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.

Peak Thermal Energy• RHESSI Soft X-ray Peak - 21 April 2002

Time: 01:30 UT

a (DEM Q T-a) 6.0Tmin = 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)

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

Peak Thermal Energy• GOES Soft X-ray Peak - 23 July 2002

Time: 00:35 UTTemperature (T): 22 MKEmission 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)

Thermal Flare EnergyMore 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

Veronig - 21 April 2002

Veronig - 23 July 2002

Thermal EnergiesUnits

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: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 2610

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.