1. High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer. Techniques for Measuring Coronal Magnetic Fields

2. Steven Tomczyk Solar in Sonoma 11/28/12 Motivation The Corona is a Magnetically Dominated System Coronal Magnetism is the Source of Space Weather  Coronal Mass Ejections  Energetic Particle Acceleration  Coronal Heating  Solar Wind Acceleration are not currently understood and will remain so until we are able to obtain routine measurements of coronal magnetic fields LASCO

3. Steven Tomczyk Solar in Sonoma 11/28/12 Approach  Must Measure Coronal Magnetic Field Strength and Direction - On Solar Disk and Above Limb  Need Complementary Observations of Coronal Plasma  Chromosphere / Transition Region Magnetic Field Observations Observations Over a Large Range of Spatial and Temporal Scales >> Large Field-of-View and Synoptic Need Systems Approach to Study the Coupled Solar Atmosphere

4. Steven Tomczyk Solar in Sonoma 11/28/12 Review Methods to Measure Coronal Magnetic Fields Illustrate with Example Data Discuss Future Prospects  In situ  UV / EUV, Visible / IR Zeeman, Hanle Effects  Radio Gyroresonance  Seismology Strengths and Limitations Talk Outline

5. Steven Tomczyk Solar in Sonoma 11/28/12 In Situ Measurements “Radio observations provide the most direct means of measuring coronal magnetic fields” D. Gary, 2012 S&H Decadal Survey White Paper In situ measurements provide the ONLY direct means of measuring the coronal magnetic field Pioneer, Mariner, Helios, ACE, Messenger spacecraft (r ≥ 0.29 AU) (Mariani & Neubauer, 1990) Solar Probe Plus / Fields (r ≥ 8.5 R sun ) All other methods are indirect

6. Steven Tomczyk Solar in Sonoma 11/28/12 Circular Polarization (Stokes V) Determines B LOS Stokes V scales as R Wavelength dependence of Zeeman Effect favors Long Wavelengths - Visible and Especially IR Zeeman signals difficult to measure for UV and Shorter Wavelengths - Need 100-1000 G for UV lines Zeeman Effect

7. Steven Tomczyk Solar in Sonoma 11/28/12 Judge et al. (2001) FeXIII 1074.7 nm has the best expected Zeeman S/N based on line intensity, magnetic sensitivity and sky background Visible / IR Coronal Zeeman Candidate Emission Lines UV / EUV C IV 155 nm, Mg II 280 nm

8. Steven Tomczyk Solar in Sonoma 11/28/12 UV/EUV and Vis/IR methods are the same, except that At visible and IR wavelengths, the solar disk is MUCH brighter than the coronal emission Observations are confined to above the limb only For all techniques talked about today, the corona above the limb is optically thin Line of sight integration issues Visible / IR Emission Lines

9. Steven Tomczyk Solar in Sonoma 11/28/12 UV Zeeman Effect Future Prospects Peter (2012)

10. Steven Tomczyk Solar in Sonoma 11/28/12 Near IR Coronal Zeeman Example Solar-C OFIS, FeXIII 1074.7 nm (Lin, et al., 2004) 46 cm aperture, integration time 70 mins, 20 arcsec fiber V/I ~10 -4 / G

11. Steven Tomczyk Solar in Sonoma 11/28/12 Near IR Coronal Zeeman Example CoMP, FeXIII 1074.7 nm (Tomczyk et al., 2007) Intensity, LOS velocity, Field Direction, LOS Field Strength, from 10/20/05, 2.5 hours integration, 10 arcsec resolution Errors of Several Gauss in Bright Corona

12. Steven Tomczyk Solar in Sonoma 11/28/12 Future Prospects for Zeeman Measurements ATST 4-m aperture 5 arcminute field-of-view High Spatial Resolution Operation into Far-IR Photon Noise from Corona and Background

13. Steven Tomczyk Solar in Sonoma 11/28/12 COSMO Large Coronagraph Future Prospects for Zeeman Measurements 1.5-m refractive coronagraph 1º field-of-view < 5ppm scattered light Synoptic operation

14. Steven Tomczyk Solar in Sonoma 11/28/12 Reduction of Linear Polarization by Magnetic Field (Depolarization) Linear Polarization produced by anisotropy of Radiation Field Works on disk as well as above limb Lines to use: Lyman series (TR; Bommier & Sahal-Brechot,1982) O VI 103.2 nm (Raouafi, et al., A&A, 1999) Interpretation depends on atmospheric model, scattering geometry, velocity field, LOS integration Hanle Effect

15. Steven Tomczyk Solar in Sonoma 11/28/12 Hanle Effect Hanle Effect is due to Quantum coherences between atomic states Effective over a restricted range of field strength - where Zeeman Splitting is approximately equal to Natural Line Width A[10 7 s -1 ] ~ 0.88 g B[G] (Fineschi, 2001) Works with UV/EUV permitted lines For Forbidden lines (Vis/IR) - Hanle effect is saturated for very small field strengths and linear polarization contains no information on magnetic field strength - POS direction only

16. Steven Tomczyk Solar in Sonoma 11/28/12 Hanle Effect Range Peter, 2011 Fineschi, 2001

17. Steven Tomczyk Solar in Sonoma 11/28/12 SUMER Observation of Linear Polarization in O IV 103.2 nm (Raouafi, et al., A&A, 1999) Hanle Effect Example Interpreted by (Raouafi, et al., A&A, 2002) to yield B 3-6 G

18. Steven Tomczyk Solar in Sonoma 11/28/12 Hanle Measurement Prospects Ly-α Trujillo Bueno (2011)

19. Steven Tomczyk Solar in Sonoma 11/28/12 Radio Methods Gyroresonance: Opacity formed in thin layer - Maps at a given frequency provide iso-gauss surface Circular Polarization proportional to B (not B los ) Observed on solar disk, B > 200 G Physical height not known; need to assume harmonic order AR6615 observed with VLA (5, 8 15 GHz) Lee (2007)

20. Steven Tomczyk Solar in Sonoma 11/28/12 Future Radio Assets Frequency Agile Solar Radiotelescope Factor of 420 in frequency and spatial resolution High Time Resolution www.fasr.org

21. Steven Tomczyk Solar in Sonoma 11/28/12 Gyroresonance Uncertainty Difficuly to quantify Gyrofrequency:f(MHz) = 2.8 B(G) Then,σ f (MHz) = 2.8 σ B (G) For FASR, Frequency Resolution is 5 MHz Setting σ f = 5 MHz, gives σ B ~ 2 G

22. Steven Tomczyk Solar in Sonoma 11/28/12 Near Future Radio Assets Owens Valley Solar Array Upgrade www.ovsa.njit.edu Underway now Many fewer dishes than FASR - reduced imaging capability Very high time resolution

23. Steven Tomczyk Solar in Sonoma 11/28/12 TRACE July 14, 1998 Oscillation Amplitude ~100 km/s Coronal Waves and Seismology Developed over the past decade (Aschwanden, Nakariakov, Vervichte, Schrijver, deMoortel and others Impulsively excited, strongly damped oscillations Seen in intensity images from e.g. Trace Can use to infer strength of coronal magnetic field Application is limited

24. Steven Tomczyk Solar in Sonoma 11/28/12 Ubiquitous Waves Velocity Amplitude ~0.3 km/s rms  Perturbations seen in velocity, not intensity  Wave propagation is aligned with magnetic field  Phase speeds 0.3-2 Mm/s CoMP Instrument

25. Steven Tomczyk Solar in Sonoma 11/28/12 Phase Speed Map Phase Speeds 0.3-2 Mm/s Potential for Coronal Seismology

26. Steven Tomczyk Solar in Sonoma 11/28/12 Waves provide the POS component of the phase speed - Transverse Component of Coronal Magnetic Field Zeeman Effect provides LOS component Which can be combined to give the Vector Magnetic Field Coronal Vector Magnetic Field

27. Steven Tomczyk Solar in Sonoma 11/28/12 Potential for Coronal Seismology (Aschwanden, 2004) Then, An uncertainty in the phase speed of 60 km/s, and an electron density of 10 9 cm -3 results in a 1 G magnetic field uncertainty Sensitive Method – But Need Coronal Density Need n e /σ ne > ~3

28. Steven Tomczyk Solar in Sonoma 11/28/12 On the solar disk: Gyroresonance and Zeeman Effect in UV/EUV provide B LOS Strong Fields > 200 G only Hanle Effect of UV/EUV permitted lines Weak Fields in restricted B range Above the limb: Visible/IR Zeeman UV/EUV Hanle Radio Bremsstrahlung All Sensitive to Weak and Strong Fields but have LOS integration issues Summary and Prospects

29. Steven Tomczyk Solar in Sonoma 11/28/12 Radio Measurements offer the best prospects for High Time Resolution (1 s) - Flare Observations Visible/IR Zeeman B los combined with Wave Seismology B trans offer the possibility of Coronal Vector Magnetic Field Measurement Summary and Prospects

30. Steven Tomczyk Solar in Sonoma 11/28/12 Inversion techniques development Hanle Effect LOS Integration Issues - Tomographic Reconstruction Radio 3d Coronal Image Synthesis Need density measurements to exploit seismology All techniques will have significant systematic errors - probably larger than random errors Required for Progress

31. Steven Tomczyk Solar in Sonoma 11/28/12 SolMex - 5 Polarimeters!

32. Steven Tomczyk Solar in Sonoma 11/28/12