“How can we improve the coronal fieldmodeling and sciences enhanced with
the improved modeling?”
Karel Schrijver (LMSAL)
and the NLFFF working group*
after five annual meetings
Solar-C Science Definition Meeting ~ Sagamihara ~ 20 Nov. 2008

*Karel Schrijver, Marc DeRosa, Tom Metcalf, Graham Barnes, KD Leka, Bruce Lites, Markus Aschwanden, TaharAmari, Aurélien Canou, Jim McTiernan, Stéphane Régnier, Julia Thalmann, Gherardo Valori, Mike Wheatland,Thomas Wiegelmann, Mark Cheung, Paul Conlon, Marcel Fuhrmann, Bernd Inhester, Tilaye Tadesse, Aad vanBallegooijen, Kanyo Kusano, Pascal Demoulin, Guillaume Aulanier, Bill Abbett, …

Rationale

Algorithms

Solar study I We performed 14 extrapolations for each of two Hinode

SOT-SP vector-magnetogram maps bracketing the X flareon 13 Dec. 2006 in AR 10930.
[ApJ 675, 1637 (2008)]"

Ca II H from Hinode/SOT-BFI

Hinode/XRT overlay - preflare

Field lines contained within a 320×320×128-pixel volume

2006.12.12_2030

Volume renderings of current density
pre-flarepost-flaredifference in free energy = 3 × 1032 erg

isosurface of |J| shown in red
E/Epot=1.32

E/Epot=1.14

Free energies for AR 10930
pre-flare

E/Epot=1.32

pre-flare E/Epot1.32
1.10
1.09
1.10
1.04
1.04
0.88
0.95
1.05
1.01
1.03
1.04
1.05
0.95
1.00

From Table 1 of Schrijver et al. (2008)

isosurface of |J| shown in red

Model
Wh+pp
Wh+np
Wiewp
Valpp
Wh0pp
Wiens
Valnp
Wienp
Wiepp
McTpp
Wh0np
Wh–np
Wh–pp
McTnp
Potential

Table of metrics for AR 10930

Schrijver et al. (2008)

Summary for AR 10930

Solar study II We performed extrapolations based on Hinode/SOT-SPvector magnetogram scan of AR 10953 on 30 Apr. 2007.
[DeRosa et al, submitted to ApJ on 13 Nov. 2008.]

AR 10953
FDMG from SOHO/MDISTEREOscopic imaging available
 STEREO A&B data were used for a quantitative

comparison of the models with the coronal loop traces:

Best fit to STEREO data: The best fit model to the STEREO loop traces matches nobetter than the potential field, and does not contain a fluxrope or arcade-like filament configuration.

Table of metrics for AR 10953

Comparison with STEREO We compared model field lines to three-dimensional loop

trajectories determined using stereoscopic analysis ofSTEREO/SECCHI-EUVI observations.
 Alignment: φ < 5° (yellow), φ > 45° (red)Appearances XRT (soft X-ray) images do not have enough structure to differentiatequantitatively, while EUV images show few (or no) loops in AR cores.
 Appearance of Amari&Canou’s FEMQ (and XTRAPOL) solutions
have a flux rope-like configuration near the site of a small filament(seen in Hα) which lies largely outside the vector-field map.

Potential field overlay

Wheatland-negative solutionAmari-FEMQ solution

Line-of-sight integrated currents

“Censoring” the observations
 Observed vector magnetic field is inconsistent with basic requirementsof force-freeness and alpha-flux balance. Preprocessing removes net
force and torque, but does not remove these two inconsistencies.
 The algorithms deal with this in different ways: some select/censor thedata, others introduce sources of flux and current, some modify/ignore
the top and side boundaries.

Net flux between α and α+dα should bezero. This is not true for observed (purple)
or pre-processed (black) vector field.

“Censoring” is one way to deal withinconsistency: Wh only uses α in the blackareas, setting α =0 in white regions, disregarding the oppositepolarity (gray).

The ideal solution would connect points
with matching α values. A poor model, or ahighly-structured α map, shows scatter.

Forces near the lower boundary: Forcing the field can significantly alter the solution of thefield. See linear magnetostatic field model by Low (1992)
Potential field

Forced: a = 1.0

2.0

3.0

4.0; at fixed α Some NLFFF models work quite well for a force-freeboundary field (see Metcalf et al., Solar Physics 247, 269 [2008])

Low (1992)

Reference model

From “chromosphere”

From “photosphere”

Critical problem areas in NLFFF modeling
1.

2.

No quantitative metric for goodness-of-fit available for the core domainof active regions.
Observed magnetic field is inconsistent with the NLFFF model:
Photosphere has Lorentz and buoyancy forces.
 Observations are inconsistent with model assumption.
 All codes have trouble converging/optimizing when applied toforced boundary data.
 Some codes performed well when applied to force-free cases withknown solar-like solutions.
Preprocessing is an attempt to mitigate this inconsistency Boundary (substantially) altered to minimize net force and torque.
 Laplacian smoothing is applied.
 Results are better with preprocessing than without.
 Including directional information on chromospheric fibrils does
not suffice (although it did in a numerical test case).
 The “pre-processing” is only one of many possible suchmanipulations - needs work.

Status of NLFFF modeling Active, committed globe-spanning NLFFF team.
 Increased appreciation of the magnitude of the problem.
 (Some, perhaps all) NLFFF algorithms work in principle, but- not surprisingly - they are very sensitive to boundary (andinitial) conditions.
Several models improved incorporation of boundaryconditions.
During the NLFFF-team project, resolutions advanced from
643 to over 3203.
Some spherical-coordinate versions are being tested.
Provided guidance for observations: Large fov at high resolution [see next page]; X-ray and EUV observations for model validation.

Improving the modelinga) We need a physically realistic description (and measurements)of the photosphere-corona interface, ideally with guidancefrom chromospheric (vector-)magnetic observations. Hα fibril
directions only appears to be insufficient, although we may
still find them helpful with chromospheric l.o.s. field.
b) Vector-magnetic maps need to include all substantialconnections (for flux and currents) of an active region to its
surroundings at least every few hours, and for flux emergenceat least every ~0.5h. A large fov is likely as critical as highresolution: f.o.v. >10 × AR area, resolution <1”.
c) Codes need to accommodate uncertainties in the boundaryfield.
d) e)

f) …

Improving the modelinga) b)c) …

b) We need more inter-comparisons of NLFFF algorithms tobetter understand their responses to inconsistent, incomplete,imperfect boundary and initial conditions; and to understand if
model-field differences point to algorithm problems, tointrinsic limitations to extrapolations, or forces, or non-uniqueness.
c) Use high-fidelity radiative-MHD simulations of active regions

and associated polarization signals to perform NLFFF
experiments to understand impacts of various effects.
d) We need a quantitative metric for the goodness-of-fit ofNLFFF models to the observed corona to enable iterative
improvement of NLFFF models. Stereoscopic imaging at
3-5MK emissions would help.

Recommendations for Solar-C(B) In my opinion:
 If the science focus is primarily coronal (e.g., field instability,coronal heating, coronal seismology, …), then Solar-C
instrumentation should enable: Large area spectro-polarimetric observations, large-area highresolution (photospheric and chromospheric), narrow bandcoronal imaging, plus question-specific instrumentation.
 If the science focus is primarily surface-to-corona coupling, thenSolar-C instrumentation should focus on High-resolution (space, time, and “depth”) spectropolarimetric observations, and rapid (E)UV/optical
spectrography, plus low coronal imaging and perhaps
spectrography.
 If both, Solar-C instrumentation should have both sets ofcapabilities rather than a compromising compromise.