Preliminary Results from Nonlinear Field Extrapolations using Hinode Boundary

Data

Marc DeRosa (LMSAL), on behalf of the NLFFF Team*

WG1 ~ SHINE 2007

*Karel Schrijver, Tom Metcalf, Graham Barnes, Bruce Lites, Ted Tarbell,

Aad van Ballegooijen, Jim McTiernan, Gherardo Valori, Thomas Wiegelmann, Mike Wheatland, Tahar Amari, Guillaume Aulanier,

Pascal Démoulin, Kanya Kusano, Stéphane Régnier, Julia Thalmann, Marcel Fuhrmann

Marc DeRosa (LMSAL), on behalf of the NLFFF Team*

WG1 ~ SHINE 2007

*Karel Schrijver, Tom Metcalf, Graham Barnes, Bruce Lites, Ted Tarbell,

Aad van Ballegooijen, Jim McTiernan, Gherardo Valori, Thomas Wiegelmann, Mike Wheatland, Tahar Amari, Guillaume Aulanier,

Pascal Démoulin, Kanya Kusano, Stéphane Régnier, Julia Thalmann, Marcel Fuhrmann

RationaleRationale

Understanding the structure and evolution of the solar corona requires a quantitative understanding of the quantitative understanding of the coronal magnetic field and its currentscoronal magnetic field and its currents.

Nonlinear force-free fields (NLFFFs) provide a useful Nonlinear force-free fields (NLFFFs) provide a useful modelmodel. These are computed by extrapolating upward from a surface (usually photospheric) vector magnetogram.

Three popular methods:

OptimizationOptimization [minimize a metric containing ( B) B and B ]

Current-field iterationCurrent-field iteration [compute field, apply currents, recompute field,…]

Magneto-frictionalMagneto-frictional [solves a MHD-like system of equations that include an ad-hoc friction term that drives the system toward a force-free state]

Understanding the structure and evolution of the solar corona requires a quantitative understanding of the quantitative understanding of the coronal magnetic field and its currentscoronal magnetic field and its currents.

Nonlinear force-free fields (NLFFFs) provide a useful Nonlinear force-free fields (NLFFFs) provide a useful modelmodel. These are computed by extrapolating upward from a surface (usually photospheric) vector magnetogram.

Three popular methods:

OptimizationOptimization [minimize a metric containing ( B) B and B ]

Current-field iterationCurrent-field iteration [compute field, apply currents, recompute field,…]

Magneto-frictionalMagneto-frictional [solves a MHD-like system of equations that include an ad-hoc friction term that drives the system toward a force-free state]

Recap of previous workRecap of previous work

We have previously used analytic solutions as blind test We have previously used analytic solutions as blind test cases, and found that these algorithms are viable.cases, and found that these algorithms are viable. However, the fields from these test cases do not resemble solar fields. [Schrijver et al. 2006]

We also tested the methods on a solar-like modelWe also tested the methods on a solar-like model, and found: [Metcalf et al. 2008]

Correct solution is largely recovered by all methods when a Correct solution is largely recovered by all methods when a “chromospheric” vector magnetogram is used“chromospheric” vector magnetogram is used (i.e., a magnetogram containing no net Lorentz force or magnetic torque).

Correct solution is not recovered when a “photospheric” vector Correct solution is not recovered when a “photospheric” vector magnetogram is usedmagnetogram is used (i.e., a magnetogram containing forces and torques).

““Photospheric” boundary data can be pre-processedPhotospheric” boundary data can be pre-processed to remove forces and torques. However, gettinggetting accurate measurements of accurate measurements of physical quantities (such as free energies) remains difficultphysical quantities (such as free energies) remains difficult.

We have previously used analytic solutions as blind test We have previously used analytic solutions as blind test cases, and found that these algorithms are viable.cases, and found that these algorithms are viable. However, the fields from these test cases do not resemble solar fields. [Schrijver et al. 2006]

We also tested the methods on a solar-like modelWe also tested the methods on a solar-like model, and found: [Metcalf et al. 2008]

Correct solution is largely recovered by all methods when a Correct solution is largely recovered by all methods when a “chromospheric” vector magnetogram is used“chromospheric” vector magnetogram is used (i.e., a magnetogram containing no net Lorentz force or magnetic torque).

Correct solution is not recovered when a “photospheric” vector Correct solution is not recovered when a “photospheric” vector magnetogram is usedmagnetogram is used (i.e., a magnetogram containing forces and torques).

““Photospheric” boundary data can be pre-processedPhotospheric” boundary data can be pre-processed to remove forces and torques. However, gettinggetting accurate measurements of accurate measurements of physical quantities (such as free energies) remains difficultphysical quantities (such as free energies) remains difficult.

Hinode datasetHinode dataset

Two vector magnetograms derived from Hinode/SOT-SP scans bracketing X flare on 2006 Dec 13 from AR10930:

native spatial sampling is 0.16″×0.16″

slit is 164″ long (1024 pixels)

~90min for a 160″-wide scan

binned 4×4 for our purposes

SOT-SP magnetogram embedded in MDI magnetogram

resulting cutout is 320×320 pixels (205″×205″)

Links to Ca H flare movie, and to Hinode/XRT flare movie

Two vector magnetograms derived from Hinode/SOT-SP scans bracketing X flare on 2006 Dec 13 from AR10930:

native spatial sampling is 0.16″×0.16″

slit is 164″ long (1024 pixels)

~90min for a 160″-wide scan

binned 4×4 for our purposes

SOT-SP magnetogram embedded in MDI magnetogram

resulting cutout is 320×320 pixels (205″×205″)

Links to Ca H flare movie, and to Hinode/XRT flare movie

Pre-flare magnetogramPre-flare magnetogram

Hinode/SOT-BFI

Pre-flare magnetogramPre-flare magnetogramcutout forextrapolation

Hinode/SOT-BFI

2006.12.12 2030 case2006.12.12 2030 case

2006.12.12_2030

Comparison with observationsComparison with observations

(example from 2003.03.13)

Start with an image with prominent loops (e.g., TRACE).

Trace some loops by hand.

Draw fieldlines in the model that interesect midpoint of each hand-traced line.

Determine the best-fit fieldline for each hand-traced fieldline.

Start with an image with prominent loops (e.g., TRACE).

Trace some loops by hand.

Draw fieldlines in the model that interesect midpoint of each hand-traced line.

Determine the best-fit fieldline for each hand-traced fieldline.

Comparison with observationsComparison with observations

“Best match” determined by evaluating length of several spokes in vicinity of crossing point.

Minimum aggregate length wins.

“Best match” determined by evaluating length of several spokes in vicinity of crossing point.

Minimum aggregate length wins.

Hinode/XRT overlay - preflareHinode/XRT overlay - preflare

fieldlines contained within a 320×320×128 pixel volume2006.12.12_2030

Volume renderings of currentVolume renderings of currentpre-flare post-flare

E/Epot=1.32 E/Epot=1.14

Volume renderings of currentVolume renderings of currentpre-flare post-flare

E/Epot=1.32 E/Epot=1.14

SummarySummary

NLFFF algorithms do not reach a consensus for this caseNLFFF algorithms do not reach a consensus for this case.

Still, we can determine a best-matching modelwe can determine a best-matching model by comparing model fieldlines to observations in the EUV (from TRACE) and/or in x-rays (from Hinode/XRT).

In the best-matching model, free energy drops from 32% to free energy drops from 32% to 14% of potential energy, corresponding to a drop in free 14% of potential energy, corresponding to a drop in free energy of 3energy of 310103232 erg erg, even as total field energy increased by ~1032 erg during this time.

Issue #1: EUV and x-ray coverage was not optimalEUV and x-ray coverage was not optimal for this for this regionregion, making it hard to determine best-fit model. (TRACE had only 285 binned 22, and x-ray images not the best for identifying loops.)

Issue #2: Lower boundary did not fully contain both flare Lower boundary did not fully contain both flare ribbons.ribbons. We are currently enlarging the lower boundary footprint and will repeat the analysis.

NLFFF algorithms do not reach a consensus for this caseNLFFF algorithms do not reach a consensus for this case.

Still, we can determine a best-matching modelwe can determine a best-matching model by comparing model fieldlines to observations in the EUV (from TRACE) and/or in x-rays (from Hinode/XRT).

In the best-matching model, free energy drops from 32% to free energy drops from 32% to 14% of potential energy, corresponding to a drop in free 14% of potential energy, corresponding to a drop in free energy of 3energy of 310103232 erg erg, even as total field energy increased by ~1032 erg during this time.

Issue #1: EUV and x-ray coverage was not optimalEUV and x-ray coverage was not optimal for this for this regionregion, making it hard to determine best-fit model. (TRACE had only 285 binned 22, and x-ray images not the best for identifying loops.)

Issue #2: Lower boundary did not fully contain both flare Lower boundary did not fully contain both flare ribbons.ribbons. We are currently enlarging the lower boundary footprint and will repeat the analysis.