1. 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

2. SHINE 2008, June 23-27, Utah ‘Vector’ Coronal Magnetogram of 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 orientationLongitudinal Field Strength

3. SHINE 2008, June 23-27, Utah 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.

4. SHINE 2008, June 23-27, Utah 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 Grating Camera Lens NICMOS3 IR camera 50 cm aperture

5. SHINE 2008, June 23-27, Utah 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

6. SHINE 2008, June 23-27, Utah March 9, 2004

7. SHINE 2008, June 23-27, Utah Coronal Magnetometry 101 Polarization 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.

8. SHINE 2008, June 23-27, Utah What Can we Do with these Coronal Magnetic Field Measurements? 1. Build a Coronal Magnetic Field Model.

9. SHINE 2008, June 23-27, Utah Can we invert the polarization measurements to derive the 3d magnetic field structure of the corona?

10. SHINE 2008, June 23-27, Utah 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?

11. SHINE 2008, June 23-27, Utah 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?

12. SHINE 2008, June 23-27, Utah 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…

13. SHINE 2008, June 23-27, Utah 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.

14. SHINE 2008, June 23-27, Utah 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…

15. SHINE 2008, June 23-27, Utah 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

16. SHINE 2008, June 23-27, Utah 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…

17. SHINE 2008, June 23-27, Utah Potential Field Model of AR 10581 and 10582

18. SHINE 2008, June 23-27, Utah 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, n e = constant. 2.Gravitationally stratified, n e ~ e -h/0.15, S n ~ n e 2. 3.S n weighted by B: S ~ e -2h/0.15 B. 4.S n weighted by B 2 : S ~ e -2h/0.15 B 2.

19. SHINE 2008, June 23-27, Utah Line-of-Sight direction

20. SHINE 2008, June 23-27, Utah LOS direction (Lower Panels) Photospheric Magnetic flux

21. SHINE 2008, June 23-27, Utah None of the empirical models have produced synthesized linear polarization maps that agree with the observed one. However… The source function weighted by B 2, with the most narrow width gave the best result.  Should we try source function with even narrower width (along the LOS direction)?

22. SHINE 2008, June 23-27, Utah 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.

23. SHINE 2008, June 23-27, Utah 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…

24. SHINE 2008, June 23-27, Utah

25.  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

26. SHINE 2008, June 23-27, Utah 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…

27. SHINE 2008, June 23-27, Utah 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.

28. SHINE 2008, June 23-27, Utah 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.

29. SHINE 2008, June 23-27, Utah

30. Is this a coincidences? Two independent parameters –the degree of linear polarization, and –azimuth angle of linear polarization have 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…

31. SHINE 2008, June 23-27, Utah 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

32. SHINE 2008, June 23-27, Utah 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.

33. SHINE 2008, June 23-27, Utah 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…

34. SHINE 2008, June 23-27, Utah

37. 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 T we don’t really have reliable measurement of n and T! 3.Calculate the emergent Stokes vector, 4.Compare the observed and synthesized polarization signals.