Solar stereoscopy where we are and which developments do we require to progress
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Solar stereoscopy - where we are and which developments do we require to progress?. Thomas Wiegelmann, Bernd Inhester, Li Feng, Judith de Patoul. How?. What do we have and what we want?. 3D geometry/physics of e.g. coronal loops and polar plumes. EUV-images from 2 viewpoints.

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Solar stereoscopy where we are and which developments do we require to progress
Solar stereoscopy - where we are and which developments do we require to progress?

Thomas Wiegelmann, Bernd Inhester,

Li Feng, Judith de Patoul


What do we have and what we want

How?

What do we have and what we want?

3D geometry/physics

of e.g. coronal loops

and polar plumes

EUV-images from

2 viewpoints

1. Extract curve-like objects

2. Associateobjects in bothimages

3. GeometricStereoscopy

4. Estimatereconstruction error in 3D

5. Derive physical

quantities


1 extract curve like objects
1. Extract curve-like objects

Processed image: A 7x7 boxcar smoothed image was subtracted from original

Original Trace-image

(from Aschwanden,Sol. Phys. 2008)


Extract curve like objects a manual loop tracing
Extract curve-like objectsa) Manual loop tracing

Can we teach the

computer to trace

loops automatically?

Trace-image, central part

(Aschwanden, 2008)

210 manually traced loops.


1 extract curve like objects b automatic loop tracing
1. Extract curve-like objectsb) Automatic loop tracing

Ridge detection

Definition of a ridge

Image intensity I (x, y) satisfies:

Inhester et al, Sol. Phys. 2008


1. Extract curve-like objectsb) Automatic loop tracing






Merging and cleaning

Done by hand until now


solar rotation:

two viewpoints

2. Associate objects in both images

Correspondence problem:Which two loops in the two images are the projections of the same loop in the real 3D case?

Two-view TRACE images mimicking the EUVI image pair

(Feng et al., Sol. Phys. 2007)


Magnetic field and EUV-images

Plasma outlines magnetic field lines

Can we use coronal magnetic field models

as a proxy for 3D plasma loops?


Single viewpoint soho eit trace use b field for feature recognition wiegelmann et al sol phys 2005
Single viewpoint: SOHO/EIT, TRACEUse B-Field for feature-recognition(Wiegelmann et al., Sol. Phys. 2005)

  • Extrapolate coronal magnetic field from photosphere.

  • Project 3D field lines onto an EUV-image.

  • Emissivity and gradient along projected field lines.

  • Alternative-1:Compare field lines and plasma.How well are they aligned?

  • Alternative-2: Extract 1-D loops out of the EUV-images and compare with projections of magnetic field lines thereafter.


Linear force-free field with α=-0.01 [Mm-1]

3D-magnetic field lines,

linear force-free α=-0.01 [Mm-1].

Used in Marsch et. al. 2005 tostudy plasma flows with Sumer.

Alternative-1: Compare projected field lines direct with EUV-image


Alternative-2: Compare projected field

lines with extracted EUV-loops

Loops extracted from

EUVI-image with automatic

feature recognition tool.

Dotted lines:Projection of best-fit

linear force-free field lines.


Can we extend this method to solve the

correspondence problem of STEREO-images?

  • A 3D magnetic field lines is unique.

  • Project field lines onto EUVI-images[or loops extracted from EUVI].

  • Measure distance of loops and projectedmagnetic field lines in both images.

  • Loops close to the same field line inboth images are very likely associated.


3. GeometricStereoscopy

  • Epipolar geometry reduces 3D-reconstructionproblem to several 2D problems.

  • Coordinate system is defined by spacecraft locations and rotation axis of the Sun.

From Inhester,

ISSI 2006


  • Epipolar geometry provides necessary criteriumfor loop association: Related loops in bothimages must intersect with same epipolar lines.

  • Epipolar range often not easy to specify,because ends of loops can be very faint=> Parts of loops not visible in one orboth images.

From Inhester,

ISSI 2006


Reconstruction ambiguity
Reconstruction ambiguity

3. GeometricStereoscopy

Reconstruction of east-west orientation loops has two solutions, which one is correct?

Two-viewpoint images are not sufficient


4. Estimatereconstruction error in 3D

curve segment in-clined to epipolar line

  • Features tangential to epipolar lines have highestreconstruction error.

  • For east-west coronal loops this means that largest reconstruction errors occur at the loop top.

From Inhester,

ISSI 2006

curve segment par-rallel to epipolar line


4. Estimatereconstruction error in 3D

From Inhester,

ISSI 2006

  • 3D reconstruction error depends on the resolution w of EUVI-images and on the angle between projection planes.

  • Projection angle is smaller or equal as angle between STEREO-A or B.

  • For loop segments in the epipolarplane the projection angle is zeroand the error infinite.


4. Estimatereconstruction error in 3D

2. Associateobjects in bothimages

  • Small separation angle between spacecraft:Association problem easy to solve,Large 3D reconstruction error.

  • Large separation angle:Association problem difficult to solve,Small 3D reconstruction error.


Magnetic stereoscopy

Artificial STEREO-images from a model Active Region.

(Wiegelmann & Inhester, Solar Phys. 2006)



Magnetic modeling with different models (c) potential,

d) linear force-free, e) nonlinear force-free). Yellow

dotted lines show the original exact loops.

We used (artificial) EUV-images from two different viewpoints to constrain the magnetic loops.


Geometric stereoscopy. We removed ambiguities (multiple

solutions) in the stereoscopic reconstruction by choosing the

solution which is closest to a given magnetic field model.

(Here we used the worst model, a potential field, which was,however, sufficient to remove the ambiguities.)


Magnetic stereoscopy

Wiegelmann&Inhester 2006


Compare real + artificial images,

Loops + B-lines

Modeling,Tomography

5. Derive physical

quantities

  • Rigorous Test of B-field models.

  • Obtain free model parameters.

  • Test scaling laws.

  • Get plasma parameters along loops- Temperature- Density- Pressure



1. Extract curve-like objects

EUVI_B

EUVI_A

Loops identified from unsharp mask filtered images.


2. Associateobjects in bothimages

Loop correspondence

Linear force-free extrapolation 

3D magnetic field lines :

a guide to the loop correspondence

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


Loop correspondence

2. Associateobjects in bothimages

correspondence in the northern active region


3. GeometricStereoscopy

Loop reconstruction

Yellow: reconstructed 3D loops

Red: best fit magnetic field lines

Northeast of AR

view from STEREO_A


4. Estimatereconstruction error in 3D

Yellow: Reconstructed loop with error bars.Red: Best fit linear force-free field line.


5. Derive physical

quantities

Loop parameters

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

2. Most of the loops cannot be approximated by planarcurve segments .

3. Most of the loops are not circular.


Example-2: Polar Plumes (Feng et al., ApJ, submitted)

1. Extract curve-like objects.Here: straight lines,intensity maximum.

4

EUVI_A

0

1

2

3

2. Associateobjects in both images.Easy for smallseparation angle.

EUVI_B

4

0

1

2

3


solar limb as seen from STEREO A

Side View

3. GeometricStereoscopy

4. Estimatereconstruction error in 3D

dotted lines: 3D reconstruction results

solid lines: extrapolations back to the solar surface.

Small separation angle: Correspondenceproblem easy to solve, no reconstruction ambiguity.

But: Large 3D reconstruction error.


Project 3D plumes onSUMER observations

5. Derive quantities

Density, Temperature,

Plasma flow

(1)Doppler Shift map: No obvious outflows detected in plume regions.

(2) Ne

measured from density sensitive Si VIII line ratio

(3) Te

measured from Mg IXtemperaturesensitive

line pair.


Polar plumes feng et al 2009
Polar Plumes, Feng et al. 2009

5. Derive quantities

Density, Temperature,

Plasma flow

  • Outflow velocity along plumes is to small to make it a dominant contributor to the fast solar wind.

  • 3D plumes are more horizontal than a dipole field.

  • Plumes are in hydrostatic equilibrium.

  • Temperature derived from the density scale height is higher than electron temperature.


Stereoscopy vs coronal field extrapolation
Stereoscopy vs. coronal field extrapolation

Hinode FOV

From DeRosa et al. 2009: Blue lines are stereoscopic reconstructed

loops (Aschwanden et al 2008), Red lines nonlinear force-free

extrapolated field lines from Hinode/SOT.


Stereoscopy vs coronal field extrapolation1
Stereoscopy vs. coronal field extrapolation

  • Vector magnetogram data(Hinode/SOT) areessential for nonlinear force-free field modeling.

  • Unfortunately Hinode-FOV covered only a smallfraction (about 10%) of area spanned by loopsreconstructed from STEREO-SECCHI images.

  • Quantitative comparison was unsatisfactory.

  • Plan: Compare magnetic field extrapolationsfrom SDO/HMI and stereoscopy with STEREO/SECCHI and SDO/AIA.

  • Can we combine extrapolations from photosphericmeasurements with stereoscopy?


Where to go in stereoscopy where to go in corona modeling

3D field

lines

3D EUV

loops

Scaling

laws

Stereoscopy

Tomography

Plasma

along magnetic

loops

Artificial

images

3D Force-free

magnetic field

LOS-integration

Self-consistent

equilibrium

Where to go in stereoscopy?Where to go in corona modeling?

SDO/HMI

magnetogram

STEREO

images

Force-free

code

consistent?

compare

MHS

code


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