GLOBAL ENERGETICS OF FLARES Gordon Emslie (for a large group of people)

Initial Study (Emslie et al. 2004) ModeSymbolLog (Energy) April 21, 2002July 23, 2002 MagneticUBUB Flare ThermalU th ElectronsUeUe IonsUi CME KineticUKUK PotentialUU SEPsUPUP

Methodologies Magnetic Energy U B =

Methodologies Thermal Plasma U th = 3 n e V kT = 3 k T [EM. V] 1/2 erg Emission measure (EM) and temperature (T) obtained from both RHESSI and GOES soft X-ray observations. Source volumes (V) were obtained from RHESSI 12 – 25 keV images using V = f V apparent = f A 3/2 where f is the filling factor (assumed to be 1) and A is the area inside the contour at 50% of the peak value.

Figure 1. RHESSI image at the impulsive peak of the 2 Nov flare. Contours: blue: 12 – 25 keV (50%), magenta: 50 – 100 keV (30 & 70%)

Methodologies CME U K = ½ Mv 2 U  = -GM  M/R M determined from scattered brightness V determined from rate of change of position R

Methodologies Electrons U E = A   E 0 F 0 (E 0 ) dE 0 dt F 0 (E 0 ) determined from collisional thick target interpretation of HXR spectrum Depends on lower energy “cutoff” E C

The Electron “Problem” Efficiency of bremsstrahlung production ~ (ergs of X-rays per erg of electrons)  Electron flux ~ 10 5  hard X-ray flux Electron energy can be – ergs in large events Total number of accelerated electrons up to (cf. number of electrons in loop ~10 38 ). –replenishment and current closure necessary

Electrical Current Issue Rate of e - acceleration in large flares  s -1 Associated Current  e - s -1  A Width of Channel ~ 10 7 m –Ampère law  B =  o I/2  r ~ 10 4 T = 10 8 G –Faraday law  V = L dI/dt ~ (  o ) I/  ~ V These are impossibly large: –e.g.,  (B 2 /8  ) dV ~ ergs Dynamic pressure ~ (nv)(mv) –~ 10 dyne cm -2 (cf. 2nkT ~ 10 dyne cm -2 )

Resolution? – Multiple Channels Current density j ~ 10 4 A m -2 Maximum radius of current channel from (Ampère)  B ~ B/r =  o j  r = B/  o j ~ 10 m (Faraday) V=  o L(  r 2 j)/   r ~ 1 m (!)  Number of channels ~ (10 14 ) Operating simultaneously!?

Methodologies Ions U i = A   E 0 F 0 (E 0 ) dE 0 dt AF 0 (E 0 )  dt determined from fit to gamma-ray observations Also depends on lower energy “cutoff” E C (~ 1 MeV?) Electrical current issues not as large Impulse-momentum issues much more important - dynamic pressure ~ (nv)(mv) –100 dyne cm -2 (cf. 2nkT ~ 10 dyne cm -2 )

Electron vs. Ion Acceleration gives equality of ion acceleration and escape times E D ~ n(cm -3 )/T(K) V cm -1 ~ V cm -1  maximum electron energy ~ 1 MeV??

Methodologies SEPs U P determined from direct observations of SEP fluences at 1 AU Assumptions: –solid-angle extent –number of particles crossings

Results (Emslie et al. 2004) ModeSymbolLog (Energy) April 21, 2002July 23, 2002 MagneticUBUB Flare ThermalU th ElectronsUeUe IonsUi CME KineticUKUK PotentialUU SEPsUPUP

Results (Emslie et al. 2004) ModeSymbolLog (Energy) April 21, 2002July 23, 2002 MagneticUBUB 32.3 ± 0.3 Flare ThermalU th 31.3 (+0.4,-1)31.1 (+0.4,-1) ElectronsUeUe 31.3 (+?, -0.5)31.5 (+?, -0.5) IonsUi< ± 0.5 CME KineticUKUK 32.3 ± ± 0.3 PotentialUU 30.7 ± ± 0.3 SEPsUPUP 31.5 ± 0.6< 30

July 23, 2002 Summary

Refinement (Emslie, Dennis, Holman, Hudson 2005) Include Optical/EUV Continuum Recognize Primary Intermediate Final modes of energy

Refinement (Emslie, Dennis, Holman, Hudson 2005) Include Optical/EUV Continuum Recognize Primary Magnetic Field Intermediate Final modes of energy

Refinement (Emslie, Dennis, Holman, Hudson 2005) Include Optical/EUV Continuum Recognize Primary Magnetic Field Intermediate Electrons, Ions Final modes of energy

Refinement (Emslie, Dennis, Holman, Hudson 2005) Include Optical/EUV Continuum Recognize Primary Magnetic Field Intermediate Electrons, Ions Final Kinetic Energy, Radiation modes of energy

Revised Numbers ModeSymbolLog (Energy) April 21, 2002July 23, 2002 MagneticUBUB 32.3 ± 0.3 Flare Intermediate ThermalU th 31.3 (+0.4,-1)31.1 (+0.4,-1) ElectronsUeUe 31.3 (+?, -0.5)31.5 (+?, -0.5) IonsUi< ± 0.5 Final SXR RadiationURUR Total RadiationURUR > 31.7> 31.6 CME KineticUKUK 32.3 ± ± 0.3 PotentialUU 30.7 ± ± 0.3 SEPsUPUP 31.5 ± 0.6< 30

Revised Numbers ModeSymbolLog (Energy) April 21, 2002July 23, 2002 MagneticUBUB 32.3 ± 0.3 Flare Intermediate ThermalU th (+0.4,-1)31.1 (+0.4,-1) ElectronsUeUe (+?, -0.5)31.5 (+?, -0.5) IonsUi< ± 0.5 Final SXR RadiationURUR Total RadiationURUR > 31.7> 31.6 CME KineticUKUK 32.3 ± ± 0.3 PotentialUU 30.7 ± ± 0.3 SEPsUPUP 31.5 ± 0.6< 30

Revised Numbers ModeSymbolLog (Energy) April 21, 2002July 23, 2002 MagneticUBUB ± ± 0.3 Flare Intermediate ThermalU th 31.3 (+0.4,-1)31.1 (+0.4,-1) ElectronsUeUe 31.3 (+?, -0.5)31.5 (+?, -0.5) IonsUi< ± 0.5 Final SXR RadiationURUR Total RadiationURUR > 31.7 > 31.6 CME KineticUKUK ± ± 0.3 PotentialUU 30.7 ± ± 0.3 SEPsUPUP 31.5 ± 0.6< 30

Revised Numbers ModeSymbolLog (Energy) April 21, 2002July 23, 2002 MagneticUBUB 32.3 ± 0.3 Flare Intermediate ThermalU th 31.3 (+0.4,-1)31.1 (+0.4,-1) ElectronsUeUe 31.3 (+?, -0.5)31.5 (+?, -0.5) IonsUi< ± 0.5 Final SXR RadiationURUR Total RadiationURUR > 31.7> 31.6 CME KineticUKUK ± ± 0.3 PotentialUU 30.7 ± ± 0.3 SEPsUPUP ± 0.6< 30

Conclusion CME energy still dominant by factor of ~4BUT Within uncertainties, rough equipartition amongst –Flare intermediate –Flare final –CME SEP shock acceleration <~ 10% efficient

Extension to Oct/Nov 2003 Flares (RHESSI/SOHO/TRACE group) Thermal and CME energetics by B. Dennis et al., N. Gopalswamy Electron/ion energetics to follow

Figure 5.

Figure 6. Flare Energies vs. U peak

Conclusions Flare and CME energies are correlated for the Oct/Nov 2003 period. Total Flare and CME energies are comparable to within a factor of 10. Peak energy in SXR-emitting plasma is only ~1% of total flare energy in some cases. Energy radiated by SXR-emitting plasma is only ~10% of total flare energy in some cases. Energy in nonthermal electrons and ions can be a large fraction of the total flare energy. Dominant flare energy in impulsive phase may be electrons and/or ions leading to early peak in total solar irradiance increase seen with SORCE/TIM.