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?

Method OverviewMethod Overview

Non-constant alpha FFF model of

McTiernan, using method of

Wheatland et al. 2000

Photospheric magnetogra

m

Fieldline ExtrapolationFieldline Extrapolation

Associate fieldlines with loops

Fieldline ExtrapolationFieldline Extrapolation

Solve steady-state energy/momentum

equations along each fieldline

Energy BalanceEnergy Balance

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

€

B 2L−2V 2τCritica l ang le

€

B 2L−1V 2 tan θCritica l twis t

€

B2L−2VRφReconne ction ∝vA

€

BL−2ρ1/ 2V 2RReconne ction ∝vA⊥

€

B3 / 2L−3 / 2ρ1/ 4V 3 / 2R1/ 2

Current La yers ( 1)

€

B2L−2V 2τ logRφ (2)

€

B 2L−2V 2τ S 0.1

(3)

€

B 2L−2V 2τCurrent Sh eets

€

B2L−1R−1Vph2 τ

Taylor re laxation

€

B2L−2Vph2 τ

Turbule nce with: Clos ure

€

B5 / 3L−4 / 3ρ1/ 6V 4 / 3R1/ 3

Clos ure + s pect rum

€

Bs+1L−1−sρ (1−s) / 2V 2−sRs

Consta nt dis s ipat ion coefficients

€

B3 / 2L−3 / 2ρ1/ 4V 3 / 2R1/ 2

Resonan ce

€

B1+mL−3−mρ−(1+m ) / 2

Resonant abso rption (1)

€

B1+mL−1−mρ−(1+m ) / 2

(2)

€

B1+mL−mρ −(m−1)/ 2

Current la yers

€

BL−1ρ1/ 2V 2

Turbule nce

€

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

€

B2

L

€

B2

L2

Proportionality constant:

Match total active region emission

to observed emission

Heating rates are volumetric

Energy BalanceEnergy BalanceHeating scaling relationships

Interpolate to a 3-D data

cube

InterpolationInterpolation

Image ReconstructionImage Reconstruction

Satellite line of sight

Image ReconstructionImage Reconstruction

Satellite line of sight

Convolve with instrument response

Image ReconstructionImage Reconstruction

Synthetic image

Image ReconstructionImage Reconstruction

Ready to compare with observations!

Image ReconstructionImage Reconstruction

Results: AR 8210Results: AR 8210

€

B

L2

€

B2

L2

€

B2

L

€

B

L

Observed Emission

€

B

L2

€

B2

L2

€

B2

L

€

B

L

Results: AR 8651Results: AR 8651

Observed Emission

€

B

L2

€

B2

L2

€

B2

L

€

B

L

Results: AR 9017Results: AR 9017

Observed Emission

Sources of DiscrepancySources of Discrepancy Fieldline representationFieldline representation

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