Predicting Coronal Predicting Coronal Emissions with Emissions with
Multiple Heating RatesMultiple Heating RatesLoraine LundquistLoraine Lundquist
George FisherGeorge Fisher
Tom MetcalfTom Metcalf
K.D. LekaK.D. Leka
Jim McTiernanJim McTiernan
AGU 2005AGU 2005
OutlineOutline Goal: predict emissions for different coronal heating Goal: predict emissions for different coronal heating
theories. theories.
MethodMethod Results from 3 active regionsResults from 3 active regions Possible sources of discrepancyPossible sources of discrepancy
Does any theory predict emission correctly?Does any theory predict emission correctly?
Non-constant alpha FFF model of
McTiernan, using method of
Wheatland et al. 2000
Photospheric magnetogra
m
Fieldline ExtrapolationFieldline Extrapolation
Gravity Cross-sectional area
variations (varies with B to conserve flux)
Radiative losses from Chianti atomic database
Allow arbitrary heat distribution along loop (currently uniform)
Steady-state flows, driven by heating asymmetries
Physics Included
EH
Energy BalanceEnergy Balance
Stochastic buildup
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B 2L−2V 2τCritica l ang le
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B 2L−1V 2 tan θCritica l twis t
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B2L−2VRφReconne ction ∝vA
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BL−2ρ1/ 2V 2RReconne ction ∝vA⊥
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B3 / 2L−3 / 2ρ1/ 4V 3 / 2R1/ 2
Current La yers ( 1)
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B2L−2V 2τ logRφ (2)
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B 2L−2V 2τ S 0.1
(3)
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B 2L−2V 2τCurrent Sh eets
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B2L−1R−1Vph2 τ
Taylor re laxation
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B2L−2Vph2 τ
Turbule nce with: Clos ure
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B5 / 3L−4 / 3ρ1/ 6V 4 / 3R1/ 3
Clos ure + s pect rum
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Bs+1L−1−sρ (1−s) / 2V 2−sRs
Consta nt dis s ipat ion coefficients
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B3 / 2L−3 / 2ρ1/ 4V 3 / 2R1/ 2
Resonan ce
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B1+mL−3−mρ−(1+m ) / 2
Resonant abso rption (1)
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B1+mL−1−mρ−(1+m ) / 2
(2)
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B1+mL−mρ −(m−1)/ 2
Current la yers
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BL−1ρ1/ 2V 2
Turbule nce
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B 5 / 3L−4 / 3R1 / 3
Heating scaling laws Heating scaling laws from Mandrini et al. 2000from Mandrini et al. 2000
€
B
L€
B
L2
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B2
L
€
B2
L2
Proportionality constant:
Match total active region emission
to observed emission
Heating rates are volumetric
Energy BalanceEnergy BalanceHeating scaling relationships
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation
• Fieldlines reaching outside of box are ignoredFieldlines reaching outside of box are ignored
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation
• Fieldlines reaching outside of box are ignoredFieldlines reaching outside of box are ignored
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation
• Fieldlines reaching outside of box are ignoredFieldlines reaching outside of box are ignored• Sensitivity to choice of fieldlines? Sensitivity to choice of fieldlines?
• Insensitive to doubling of # of fieldlines. Insensitive to doubling of # of fieldlines.
• May require more testing of different techniques.May require more testing of different techniques.
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation Magnetic field extrapolation discrepanciesMagnetic field extrapolation discrepancies
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation Magnetic field extrapolation discrepanciesMagnetic field extrapolation discrepancies
• Side and top boundaries from potential fieldSide and top boundaries from potential field• No information from nearby active regionsNo information from nearby active regions• May not be force freeMay not be force free
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation Magnetic field extrapolation discrepanciesMagnetic field extrapolation discrepancies Steady-state loop discrepanciesSteady-state loop discrepancies
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation Magnetic field extrapolation discrepanciesMagnetic field extrapolation discrepancies Steady-state loop discrepanciesSteady-state loop discrepancies
• Compare temperature and EM from filter ratio: Compare temperature and EM from filter ratio: • Temperature too low Temperature too low
• EM too high EM too high
(observations under-dense vs. steady loops)(observations under-dense vs. steady loops)
AR 8210 Observations B/L B/L 2 B2/L B2/L 2
Log(T) 6.70 6.22 6.06 6.13 6.09Log(EM) 48.36 49.64 50.28 50.03 50.42
(Perhaps abundance differences?)(Perhaps abundance differences?)
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation Magnetic field extrapolation discrepanciesMagnetic field extrapolation discrepancies Steady-state loop discrepanciesSteady-state loop discrepancies Simplified heating parametrizationsSimplified heating parametrizations
Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation Magnetic field extrapolation discrepanciesMagnetic field extrapolation discrepancies Steady-state loop discrepanciesSteady-state loop discrepancies Simplified heating parametrizationsSimplified heating parametrizations
• Variables left out (velocity, density, etc.)Variables left out (velocity, density, etc.)• Heat distribution along loop (now uniform)Heat distribution along loop (now uniform)
ConclusionsConclusions
Forward modeling is possible and useful -- Forward modeling is possible and useful -- don’t assume we’ll get it right don’t assume we’ll get it right
Scaling relationships dramatically affect Scaling relationships dramatically affect the distribution of synthetic emissionthe distribution of synthetic emission
Many sources of discrepancy Many sources of discrepancy • These show which physics is most significantThese show which physics is most significant
A promising observational constraintA promising observational constraint