Newark, 31.03.2008 Wiegelmann et al.: Coronal magnetic fields 1

Solar coronal magnetic fields:Source of Space weather

Thomas Wiegelmann, Julia Thalmann, Bernd Inhester, Li Feng, Peng Ruan

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Usually we see the solar corona only during an eclipse

11. August 1999 total solar eclipse

• Solar corona is about 200times hotter as photosphere.

• But only 10-12 as dense.• Corona is very faint and

produces only about 10-6 the visible brightness compared with photosphere.

• Observations from spaceallow us to observe thecorona all the time in different wavelength.

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Observation fromSpace with SOHO/EIT

Coronalactivity

is driven by magnetic

fields!

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Space weather

-Solar Storms

-Charged particlesimpact Earth

-Aurora Question:Origin of coronal

eruptions

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Coronal mass ejectionsand flares are assumed to occur due toinstabilities in thecoronal magnetic field configuration.

It is importantto investigatethe coronal

magnetic field

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Solar magneticfield measured

routinely only inphotosphere

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Effect of magnetic field visible in corona

• We cannot measure the 3D-coronal magnetic field accurately direct.

• Measurements of photospheric B-field.(Line-of-sight and vector magnetograms).

• Extrapolate photospheric field into corona.

• Extrapolation method depends on assumptions about coronal plasma.

Magnetic ‘field lines’ observed with TRACE

=> Coronal magnetic field models

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Model Mathematics Observationsneeded

Validity

Potential

Fields

Line of sightmagnetogram

(Global) currentfree regions,quiet sun

Linear

Force-Free

LOS mag.

+ observations ofplasma structures

Local in activeregions, low-betaplasma

Nonlinear Force-Free

Vectormag.

(Noise, ambiguity

Preprocessing)

Active regions,low beta plasmain low corona

MHS

Equilibrium

Vectormag.

+ Tomography

Helmet streamer,finite beta plasma,full solar corona

0

)()( 0

B

pBB

0

)(

B

BrB

0

B

BB 0

0

B

B

Coronal magnetic field models

Better Models More Challenging

Computational + Observational

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Mathematicalsimple and requiresonly Line-of-sightmagnetograms

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-Minimize L numerically.-Boundary condition: Photospheric B-field vector.-Noise and inconsistencies in vector magnetograms require preprocessing.

NLFFF-consortium:Most accurate and

fastest method.

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Ground based Vector magnetographSolar Flare Telescope, Tokyo, (Sakurai et al.1995)

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CoronalMagnetic Field

Nonlinear Force-free code

Preprocessing tool

Vectormagnetogram

H-AlphaImage

ChromosphericMagnetic Field

Optional

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Flare seen in Trace and H-Alpha, Jan. 20. 2004,(from Goff, van Driel-Gesztelyi, Demoulin, Sol. Phys. 2007)

Evolution of Flaring Active Region NOAA 10540 (Thalmann and Wiegelmann, A&A 2008, in press)

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SOHO/MDINAO/SFT, Time cadence about 1 day

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Evolution of AR10540

For movie the spatial resolution was reduced (factor 2) and from 4 magnetograms with a time cadence of (28h, 22h, 21h) we interpolated to15 min [movie is only illustrative and not for data analysis].

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Flaring Active Region Quiet Active Region

Solar X-ray flux. Vertical blue lines: vector magnetograms available

Magnetic field extrapolationsfrom Solar Flare telescope

Extrapolated from SOLISvector magnetograph

M6.1 FlareMagneticenergy builds

up and isreleases during

flareFuture plans:Study flaring

ARs with highertime cadence

with Solar Dynamics Observatory.

M6.1 Flare

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Future: Combine magnetic field extrapolation with vector tomographic methods based on coronal

Faraday and Hanle measurements.(feasibility study by Kramar and Inhester 2006)

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Coronal plasma and magnetic field

Lorentz force

pressure gradient

gravity

B

for vertical scales < 0.1 RS

(gravitational scale height) => Pressure constant on field lines

Plasma outlinesmagnetic field lines

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Force-free equilibria and coronal plasma

smallsmall

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Coronal magnetic field Plasma in EUV

SOHO/EIT, Traceetc. show 2D projections of

coronal plasma

3D Structure?

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The STEREO-mission within the NASA/STP program

Two almost identical spacecrafts observe the Sun and heliosphere

• Launched October 2006• Aim: 3D view of

Solar corona.• Spacecraft have

different orbits due to swing-by at moon.

• The two STEREO spacecraft seperate about 44o every year.

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Stereoscopic Reconstruction of 3D coronal loop structures

(Li Feng et al. 2007)

EUVI_B EUVI_AJune 8, 2007Angle 11.8o

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Coronal loops in NOAA 10960

EUVI_AEUVI_BLoops identified from unsharp mask filtered images.

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MDI : 2007-06-08T03:12:00 UT 2007-06-08T03:12:00 UT

Linear force-free extrapolation

3D magnetic field lines :

a guide to the loop correspondence

Loop correspondence

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Loop reconstruction

3D loop is the intersection of two back-projection surfaces generated from two view directions.

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3D Loop reconstruction

Yellow: reconstructed 3D loops

Red: best fit magnetic field lines

view from STEREO_A Northeast of AR

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Loop parameters

1. The linear force-free assumption is often not adequate.

2. Most of the loops cannot be approximated by planar curve segments .

3. Most of the loops are not circular.

Still to do:Reconstruct

density, temperature,plasma flowalong loops

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Outlook: Self-consistentB-Field and Plasma model

Force-free code

Vectormagnetogram

MHS code

Force-freemagnetic field

-Length+shape of loops-Magnetic field strength -Electric current density

com

pare

STEREOimages

Plasma along magnetic

loops

Scaling laws

Artificialimages

LOS-integration

Tomography

Self-consistentequilibrium

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