flare thermal energy brian dennis nasa gsfc solar physics laboratory 12/6/20081solar cycle 24, napa,...
TRANSCRIPT
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
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)
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
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.