Transcript Free Energy in the Solar Corona

Mapping Free Energy in the Solar Atmosphere
What can we learn from HMI & AIA?
Brian Welsch, Space Sciences Lab, UC Berkeley
What kinds of observations are required to compute and
understand the creation and dissipation of free energy?
How can we best make use of the joint AIA and HMI dataset?
What jobs need to get done before launch to allow proper
analysis and use of the SDO data?
This last point, in particular, is the focus of this session;
consequently, my talk is meant to engender discussion!
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Free energy U(F) is the actual magnetic energy
minus the potential magnetic energy.
8U(F) =  dV [ (B · B) - (B(P) · B(P))]
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Both B(x1,x2,x3) and B(P) (x1,x2,x3) match the distribution of normal flux, Bn(x1,x2), at corona’s base.
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Nonpotential part of field is B (x1,x2,x3) = B - B(P)
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B(P) carries no currents, or, equivalently, is curl free.
1. For any Bn|S , B(P) has minimal energy.
2. B(P) = - , with 2  Laplace’s eqn. gives B(P)
3. For any Bn|S , B(P) is unique.
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HMI data can be used in several ways to
quantify free magnetic energy.
1.
Use B(x1,x2,0) to extrapolate B & B(P) (McTiernan, Thurs. a.m.)
– can compare model fields to AIA data
2.
Magnetic Virial Theorem (Wheatland & Metcalf 2005)
– novel application to photospheric magnetograms
3.
Free Energy Flux (FEF) through photosphere (Welsch, 2006)
– gives photospheric loci of energy injection
4.
Magnetic charge topology (MCT, e.g., Barnes et al. 2005).
– can give coronal loci of departures from potential field
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3) ILCT (Welsch et al. 2004) & other methods can
determine flows from pairs of magnetograms.
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3) From B(x1,x2,0) and v(x1,x2), maps of the free
energy flux can be computed (Welsch et al. 2006)
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4) From B(P)(t1), B(P)(t2), MCT calculates changes in flux ij
connecting photospheric sources i & j to estimate U(F).
Each magnetogram in a sequence is partitioned into fluxes i.
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4) [Lifted from Longope’s talk, TRACE-RHESSI-SOHO meeting, Dec. 2004]
Role(s) of Current Sheets
W
Energy RELEASE:
W accumulates
prior to reconn’
burst: latency
Wfce
W






W 
2
W 
Wpot
2
22LL
Rapidly released
via local E field
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C4: Coronal Energy Inputs I.
Here are a few random (and arguable!) thoughts that
didn’t fit anywhere else.
• Mapping free energy using AIA data will
require new techniques – not so with HMI.
• Techniques that can be automated would be
good – AIA will generate a lot of data!
• AIA will tell us about non-potentiality from
emergence – something HMI probably
won’t do so well.
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How can we use coronal observations to determine
how much and where B differs from B(P)?
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Qualitative differences?
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Canfield et al. (1999) – X-ray sigmoids
Schrijver, Title, & De Rosa (2005)
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Schrijver, Title, & DeRosa (2005) found that free
energy can be detected qualitatively.
similarities
differences
Comparisons of TRACE EUV observations
with B(P) revealed similarities & differences.
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How can we use coronal observations to determine
how much and where B differs from B(P)?
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Qualitative differences?
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Canfield et al. (1999) – X-ray sigmoids
Schrijver, Title, & De Rosa (2005)
Quantitative differences?
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Can we infer B directly?
C4: Coronal Energy Inputs I.
Can we infer B directly from coronal morphology?
1. Gary & Alexander (1999) distorted of a model
B to match coronal observations.
– assumed an initial topology in model B
– distortions were non-force-free (but perhaps this is OK)
2. De Rosa (2004, unpublished?) investigated
automated loop identification algorithms.
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Punchline: This is not easy to do!
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How can we use coronal observations to determine
how much and where B differs from B(P)?
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Qualitative differences?
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–
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Canfield et al. (1999) – X-ray sigmoids
Schrijver, Title, & De Rosa (2005)
Quantitative differences?
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Can we infer B directly?
If we cannot infer B, then what?
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Can we quantify departures from B(P)?
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How can AIA observations be used to quantify
departures from B(P)?
Aside - The corona exhibits ~two modes of emission:
a) steady state – perhaps averaged over weak fluctuations
b) highly intermittent – “impulsive,” stronger fluctuations
What gives rise to EUV/SXR emissivity?
I.) Local emissivity  steady heating?
 B? or ? independent of B - B(P) (at large scales)?
II.) Local emissivity  intermittent magnetic reconnection?
 B = B - B(P).
Can we distinguish between these?
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If steady emissivity is a function of B (or ), then
what can AIA tell us about magnetic connections?
Can Pevtsov’s Law (2003), relating photospheric magnetic flux
to coronal SXR emission, be extended to EUV observations?
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Does each EUV loop correspond, on average, to a certain
amount of coronal (or photospheric) flux?
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Study Idea: Quantify how many EUV/SXR loops connect
photospheric sources (Voronoi regions?) of with varying
flux.
Applicable to MCT, which estimates free energy by estimating
flux ij linking photopheric sources i and  j.
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From Pevtsov et al. (2003):
X-ray spectral radiance LX vs. total unsigned magnetic flux for solar and stellar
objects. Dots: Quiet Sun. Squares: X-ray bright points. Diamonds: Solar active regions.
Pluses: Solar disk averages. Crosses: G, K, and M dwarfs. Circles: T Tauri stars. Solid
line: Power-law approximation LX  1.15 of combined data set.
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If emissivity  B = B - B(P), can models predict loci
of reconnection-driven emission in AIA?
Several models predict (to varying degrees)
reconnection sites:
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Extrapolations (NLFFF & potential)
MCT – separators
FEF – corona above free energy injection sites
Longcope et al. 2005: 4 x 1018 Mx per reconnection
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Which observations might we pursue? A “starter” list:
1. Avg. reconnected flux, , per reconnection event?
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avg. reconnected flux per DN?
avg. reconnected flux per coronal loop? (vs. ?)
2. Avg. reconnection rate, / t?
3. Avg. “latency time” vs. spatial scale?
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
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Separatrices/ QSLs, during emergence are thin.
Does this mean reconnection happens quickly?
How about during cancellations?
How about shear flows ?
4. What can we learn from “simulated emission”
forward models? (Lundquist/Schrijver/Mok et al.’s)
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References
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Barnes et al., 2005: Implementing a Magnetic Charge Topology Model for Solar Active Regions,
Barnes, G., Longcope, D.W., & Leka, K.D., ApJ, v. 629, 561.
Canfield et al. 1999: Sigmoidal morphology and eruptive solar activity, Canfield, R. C., Hudson, H.S.,
& McKenzie, D.E., GRL, v. 26, 627
Démoulin & Berger, 2003: Magnetic Energy and Helicity Fluxes at the Photospheric Level,
Démoulin, P., and Berger, M. A. Sol. Phys., v. 215, # 2, p. 203-215.
Fletcher et al., 2003: Tracking of TRACE Ultraviolet Flare Footpoints, Fletcher, L., Pollock, J.A.., &
Potts, H.E. Sol Phys, v. 222, 279
Gary & Alexander, 1999: Constructing the Coronal Magnetic Field By Correlating Parameterized
Magnetic Field Lines With Observed Coronal Plasma Structures, Gary, G.A., & Alexander, D., Sol
Phys., v. 186, 123
Longcope et al., 2005: Observations of Separator Reconnection to an Emerging Active Region,
Longcope, D. W.; McKenzie, D. E.; Cirtain, J.; Scott, J. ApJ, v. 630, # 1, p. 596.
Lundquist et al., 2005: Predicting Coronal Emissions with Multiple Heating Rates, Lundquist, L.L.,
Fisher, G.H., Leka, K.D., Metcalf, T.R., & McTiernan, J.M., AGU Spring Meeting Abstracts, A2
Metcalf et al., 2005: Magnetic Free Energy in NOAA Active Region 10486 on 2003 October 29,
Metcalf, T. R., Leka, K. D., Mickey, D. L., ApJ, 623, # 1, pp. L53-L56.
Mok et al., 2005: Calculating the Thermal Structure of Solar Active Regions in Three Dimensions,
Mok, Y., Miki\'c, Z., Lionello, R., & Linker, J.A., ApJ, v. 621, 1098
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References, cont’d
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Metcalf et al., 1995: Is the solar chromospheric magnetic field force-free? Metcalf, T. R., Jiao, L.,
McClymont, A. N., Canfield, R. C., Uitenbroek, H. , ApJ, v. 439, #1, p. 474- 481.
Pevtsov et al., 2003:: The Relationship Between X-Ray Radiance and Magnetic Flux, Pevtsov,
A.A., Fisher, G.H., Acton, L.W., Longcope, D.W., Johns-Krull, C.M., Kankelborg, C.C., & Metcalf,
T.R., ApJ, v. 598, 1387.
Schrijver et al., 2005: The Nonpotentiality of Active-Region Coronae and the Dynamics of the
Photospheric Magnetic Field, Schrijver, C. J, DeRosa, M. L., Title, A. M., and Metcalf, T. R., ApJ,
v. 628, #1, p. 501.
Schrijver et al., 2004: The Coronal Heating Mechanism as Identified by Full-Sun Visualizations,
Schrijver, C. J, Sandman, A. W.; Aschwanden, M. J., DeRosa, M. L., ApJ, v. 615, #1, p. 512.
Welsch et al., 2004: ILCT: Recovering Photospheric Velocities from Magnetograms by Combining
the Induction Equation with Local Correlation Tracking, Welsch, B. T., Fisher, G. H., Abbett, W.P.,
and Regnier, S., ApJ, v. 610, #2, p. 1148-1156.
Welsch, 2006: Magnetic Flux Cancellation and Coronal Magnetic Energy, ApJ, in press.
Wheatland et al., 2000: An Optimization Approach to Reconstructing Force-free Fields,
Wheatland, M. S., Sturrock, P. A., Roumeliotis, ApJ, v. 540, #2, p. 1150-1155.
Wheatland & Metcalf, 2005: An improved virial estimate of solar active region energy,
Wheatland, M.S. and Metcalf, T.R. , ApJ, in press. (v. 636, #2, 10 Jan. 2006) [on astro-ph]
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