Observational Test of Coronal Magnetic Field Models I. Comparison with Potential Field Model

SHINE 2008, June 23-27, Utah

Observational Test of Coronal Magnetic Field Models

I. Comparison with Potential Field Model

Hao-Sheng Lin & Yu Liu

Institute for Astronomy

University of Hawaii


‘Vector’ Coronal Magnetogramof AR 10581 and AR 10582, 2004

Contour plot of the line-of-sight magnetogram over-plotted on the EIT Fe XVI 284 A image. The contours are 5G, 3G, and 1G.

Transverse field orientation Longitudinal Field Strength


Current Status of IR Coronal Magnetometry

Instrumentation• We can (almost) make routine coronal magnetic

field measurements…– SOLARC is working…– CoMP is been relocated to Haleakala…

Capabilities• Linear polarization can be obtained easily…even

during solar minimum.• Neither has the sensitivity for longitudinal magnetic

field measurement during solar minimum.


SOLARC: Off-Axis Mirror Coronagraph

SOLARC on the summit of Haleakala, Maui.

LCVR Polarimeter

Input array of fiber optics bundle

Re-imaging lens

Prime focus inverse occulter/field stop

Secondary mirror

Primary mirror

Optical Configuration of SOLARC and OFIS

Fiber Bundle

Collimator

Echelle GratingCamera Lens

NICMOS3 IR camera

50 cm aperture


Light Trap

Collimating Lens

Pre-Filter Wheel

Filter/Polarimeter

Detector

Occulting Disk

Re-Imaging Lens

Calibration Polarizer Stage

Coronal Multi-channel Polarimeter (CoMP) – S. Tomczyk, HAO

20-cm coronagraph, National Solar Observatory, Sac Peak


March 9, 2004


Coronal Magnetometry 101Polarization Mechanism• The forbidden coronal emission lines in the visible and IR are

polarized by the Saturated Hanle Effect.Information Content• Linear Polarization (easy to measure):

– The direction of the linear polarization yields the direction of the magnetic field projected in the plane of the sky containing sun center.

– Linear polarization does not yield information about the strength of the magnetic fields.

– The magnetic field direction intepretation is subjected to a 90 degree ambiguity--- the van Vleck effect.

• Circular Polarization (difficult to measure):– Similar to the photospheric Zeeman effect, yields line-of-

sight magnetic field strength,– with an alignment effect correction.


What Can we Do with these Coronal Magnetic Field Measurements?

1. Build a Coronal Magnetic Field Model.


Can we invert the polarization measurements to derive the 3d magnetic field structure of the corona?


The Full Inversion Problem

• The coronal atmosphere is optically thin, and the observed coronal polarization signals may not originate from a single localized source along the line of sight.

• There are many independent parameters in the model, but only a few observables…

The inversion problem is severely under constrained!

There are currently no tested, reliable inversion methods for reconstruction of the 3D magnetic field structure of corona using polarization measurements…

If inversion is not possible, what can we do?


What Can we Do with these Coronal Magnetic Field Measurements?

1. Build a Coronal Magnetic Field Model

2. Check extrapolation/simulation Models

Given a coronal magnetic field model derived from extrapolation or MHD simulation of observed photospheric magnetic fields, can we verify the validity of this model?


Forward Modeling…

Yes! In principle…If we know the 3-dimensional • magnetic field, • density, and • temperature

structure of the corona, then we can calculate what the emergent linear and circular polarization signals should look like, and compare them with the observed polarization signals…


In reality…• Extrapolations only yield the magnetic field

configuration. – There are no information about n and T. n and T has to be derived, inferred, assumed, or

guessed by other means…• The photospheric and coronal magnetic field

observations are not co-temporal…– Uncertainties due to evolution of the active region.

• Potential and force-free assumption may not be valid.


Limitations of Forward Modeling…

• If the observed and synthesized polarization signals match…The model may be good,– But we don’t know if this is the best model…

• If the observed and synthesized polarization signals don’t match…– The magnetic field model may be good, but – The density and temperature model is not good,– The corona may have changed…– Can be anything…


Can we reproduces these Fe XIII 1075 nm polarization measurements from a coronal magnetic field model derived from potential field extrapolation of observed photospheric magnetogram?

Testing Potential Field Extrapolation of AR 10582


About AR 10581 AND 10582…

• Flaring activities in AR10582 ceased about 5 days before our coronal B observation… Potential field

extrapolation may be OK?

Time of coronal magnetic field observation…


Potential Field Model of AR 10581 and 10582


Density and Temperature…

Make some educated guesses…• The coronal is bright in the active regions,• The density falls off exponentially.

1. Assume a uniform temperature through out the corona…

2. For density: assume four empirical models:

1. Uniform density, ne = constant.

2. Gravitationally stratified, ne ~ e-h/0.15, Sn ~ ne2.

3. Sn weighted by B: S ~ e-2h/0.15 B.

4. Sn weighted by B2: S ~ e-2h/0.15 B2.


Line-

of-S

ight d

irect

ion


LOS direction (Lower Panels)Photospheric Magnetic flux


None of the empirical models have produced synthesized linear polarization maps that agree with the observed one.

However…• The source function weighted by B2, with the

most narrow width gave the best result. Should we try source function with even

narrower width (along the LOS direction)?


TRACE images have demonstrated long ago that the coronal intensity structures have characteristics scale much smaller than the 200 ~ 300 km width we used… Try using the loop width

of ~ 56 km (7 times Fe XVI 284 A characteristic loop width, Aschwanden et al., 2000) as the width of the source function.


• Since the thickness of the new source function is small, we computed the synthesized LP map as a function of position along the Line of Sight…



p: rms error in degree of linear polarization,

: rms error of azimuth angle of LP,

LP: combined rms error of the degree of polarization and the azimuth angle of the LP.

Lin’s synthesis code

Judge’s code

LOS direction

Source function of the best-fit layer


Comparison with Judge’s Synthesis Code

• Phil Judge’s code includes collisional depolarization effect…

• We really can’t tell which code is better from this comparison. But Judge’s code includes more physics…


Circular Polarization

• The sensitivity of this dataset is not sufficient for a point-to-point comparison within the FOV. We only compared the averaged LOS magnetic

field strength as a function of height.


• The longitudinal B as a function of height h, as well as the height of reversal of B(h) are calculated for each layer.

• The height of B reversal agrees with the observed value at two layers.

• B(h) at layer 130 fits the observed one better.



Is this a coincidences?

• Two independent parameters – the degree of linear polarization, and– azimuth angle of linear polarizationhave minimum at about the same location…

• Two other independent parameter/function– the height of Stokes V reversal, and– B(h)

match the observed circular polarization signals at the same location…


Conclusions

• Potential field extrapolation of AR 10582 has reproduced the observed coronal linear and circular polarization maps. – The inferred source functions of the linear and circular

polarization are fairly localized!Single-source inversion (Judge 2007) might be possible…

– The LP and CP source functions are close to the location of the sunspot of the active region.

– The locations of the source function of the linear and circular polarization are not the same…

– This potential field model may be OK!

Liu & Lin, 2008, ApJ, 680, 1496


What’s Next?

More observations (if the Sun cooperates) and more comparisons with models…• Is potential-field extrapolation really OK?• Does force-free extrapolations provide better

model? • MHD models should come with information about

n and T… Direct comparison can be performed without

guessing where the source is located.


Please Help!

• A future SHINE Session?

Observational Test of

Coronal Magnetic Field Models

Construct the coronal magnetic field model of AR 10582 using your favorite extrapolation/MHD code, and we can start testing these models vigorously…





Testing Coronal B Model by Forward Modeling

1. Construct a coronal magnetic field model,• Potential field extrapolation,• Force-free field extrapolation,• MHD simulation,from photospheric magnetic field observation several days before or after the coronal observation…

2. Construct a thermodynamic model,• Density n• Temperature Twe don’t really have reliable measurement of n and T!

3. Calculate the emergent Stokes vector,4. Compare the observed and synthesized polarization signals.

Documents

Observational Test of Coronal Magnetic Field Models I. Comparison with Potential Field Model