1. -1- Coronal Faraday Rotation of Occulted Radio Signals M. K. Bird Argelander-Institut für Astronomie, Universität Bonn International Colloquium on Scattering and Scintillation in Radio Astronomy Pushchino, Russia Monday, 19 June 2006

2. -2- Outline  Coronal Faraday Rotation – Definition  Coronal FR using Various Radio Sources –Pulsars –Extended Continuum Sources –Spacecraft (Helios E12: 1975-1984)  FR Variations over Different Time Scales –Background Coronal Magnetic Field –FR Signature of Coronal Mass Ejections –FR Fluctuations: Alfvén Waves & Quasi-harmonic Oscillations  Coronal FR Mapping – the Future?  Summary

3. -3- Coronal Faraday Rotation - Definition

4. -4- Faraday Rotation  : Definition radians 2.36∙10 4 in MKS or cgs units radio frequency (Helios: 2.3 GHz) electron density mag field proj. along ray path with

5. -5- Interplanetary Electron Column Density from Earth “Dispersion Measure” Units: hexems 1 hexem = 10 16 el/m 2 Earth Sun analogous plot for Faraday Rotation does not exist! I = ∫N e (s) ds

6. -6- Polarization Angle Measurement Electric Vectors (semi-major axis of polarization ellipse): E 0 = Source (transmitted) E = Measured (received) Angle definitions: q = locally measured polarization angle p = parallactic angle  = Faraday rotation

7. -7- Rotation Measure RM: A rotation measure of RM = 1 rad m -2 yields:  = 0.97° at 2.3 GHz ( =0.13 m)  = 57.3° at 300 MHz ( =1.0 m)  = 1432° at 60 MHz ( =5.0 m)

8. -8- Coronal Faraday Rotation Measurement 1.  can be positive or negative (from polarity of interplanetary magnetic field) 2.Angle ambiguity (    ± m·180°) 3.Contributions from electron density and magnetic field cannot be separated without independent measurements 4.Correction for variable ionosphere necessary if solar offset R > 10 R S

9. -9- Ionospheric Faraday Rotation

10. -10- Coronal FR using Various Radio Sources

11. -11- Coronal FR with Pulsars

12. -12- Pulsars at Conjunction 1978-79 [Bird et al., Nature 283, 459-460, 1980]

13. -13- Pulsar Pulse Profiles: Measurement Technique Pulsar Pulse Profiles: Measurement Technique PSR 0525+21 PSR 0540+23 intrinsic profile modified profile p-angle: intrinsic & modified

14. -14- Coronal FR of PSR 0525+21 (1978-79)

15. -15- Solwind Images during 1979 Occultation of PSR 0525+21

16. -16- Coronal Magnetic Field from RM & DM: 1979 Coronal Magnetic Field from RM & DM: 1979

17. -17- Coronal FR with Extended Continuum Sources 3C228 [Spangler, 2005] A B C 1'1'

18. -18- Coronal FR at VLA: 21 Aug 2003  RM: 62.5 rad/m 2 3C228 R = 7.1…6.2 R S

19. -19- SOHO/LASCO: 16 AUG 2003 3C228 Jupiter Venus

20. -20- Coronal FR with Helios  Helios – 1 –Launch: 10 Dec 1974 –EOM: 15 Mar 1986 –q = 0.31 AU (P = 190 d) –i = 0°, "spin up"  Helios – 2 –Launch: 15 Jan 1976 –EOM: 08 Jan 1981 –q = 0.29 AU (P = 186 d) –i = 0°, "spin down"

21. -21- Earth-Sun Line Fixed: Helios-1

22. -22- Coronal Faraday Rotation: Helios Observations = 35.4°  FR = 2.1°

23. -23- Helios FR: Effelsberg/Goldstone

24. -24- Coronal FR: Helios-1, Dec 1981 180  ambiguity

25. -25- FR Variations over Different Time Scales …Background Coronal Magnetic Field

26. -26- Ballerina Model of HCS

27. -27- Radio Ray Path Geometry in the Corona

28. -28- Coronal Faraday Rotation from Sector Structure

29. -29- Mean Absolute FR: 1975-1976 |  max |  R -4.15

30. -30- Coronal Electron Density: Radial Profiles

31. -31- Mean Coronal Magnetic Field 1975-76 3 R S < R < 10 R S : B r = 7.9 R -2.7 G (17) or B r = 6 R -3 + 1.2 R -2 G (18) [Pätzold et al., Solar Phys. 109, 91, 1987]

32. -32- FR Variations over Different Time Scales … FR Fluctuations: Alfvén Waves & Quasi-harmonic Oscillations

33. -33- FR Fluctuations: Standard Deviation vs. Solar Offset

34. -34- FR Spectra for Various Solar Offset Distances Andreev et al., [1996]

35. -35- FR Spectral Index vs Solar Offset

36. -36- Two-Station Coronal Sounding Measurements

37. -37- Measuring Coronal Velocities

38. -38- Coronal Velocities from FR Correlations

39. -39- Two-Station FR Measurements Two-Station FR Measurements

40. -40- Simultaneous FR Spectra with QHC

41. -41- Rapid Sequence of FR Spectra QHC comes… … and goes! [Chashei et al., 1999]

42. -42- FR Variations over Different Time Scales … FR Signature of Coronal Mass Ejections

43. -43- CME Passing through Helios-2 Ray Path Solwind Coronagraph Images recorded during Helios Solar Occultations In Oct/Nov 1979 [Bird et al., 1985]

44. -44- CME Height-Time Diagram, 24 Oct 1979

45. -45- CME Magnetic Field Estimates, 24 Oct 1979 UTSolar Offset (R S )  I (hexems)  (deg) (mG) 08:005.11.8±10±2 08:305.11.8+20+4 09:005.01.9+40+8 09:305.01.9+55+11 10:004.92.0+35+7 10:304.92.0±5±1 11:004.82.0-45-9

46. -46- Coronal FR Mapping – the Future?

47. -47- One line of sight to a linearly polarized source

48. -48-

49. -49- Simulated Coronal FR for CR 1751 [J. Kasper, priv. comm, 2004.]

50. -50- Transient Simulations: October 2003 CMEs CME not yet detected Large FR in  20 sources CME!

51. -51- FR Mapping – Conclusions regarding LOFAR  Expected density of suitably polarized sources:  1 deg -2  FR maps could be used to test models of coronal magnetic topology  FR maps of transient flux ropes could be used to predict the geoeffectivity of the ensuing CME impact at Earth

52. -52- Coronal Faraday Rotation: Summary  Faraday Rotation measurements provide a unique tool for investigating coronal magnetic structure… –Emperical model for the magnitude and radial dependence of the background coronal magnetic field –Evidence for outward (and inward) propagating Alfvén waves –Evidence for dominance of magnetic fluctuations over density fluctuations  FR Mapping of CMEs is a difficult, but not hopeless, task.