Helioseismology (III)

1. Probing Magnetic Fields and Flows in the Solar Convection Zone with Helioseismology Helioseismology (III) 周定一 Dean-Yi Chou 台灣清華大學，物理系 (2010.08, 北京)

2. Helioseismolgy Using solar p-mode oscillations (waves) measured on the solar surface to probe the solar interior.

3. Basic Principle to probe Solar Interiors Different modes penetrate into different depths.

4. Observations in Helioseismology Using solar p-mode oscillations (waves) measured on the solar surface to probe the solar interior. Observations setr = R But it still gives the same dispersion relation:

5. How to Probe Magnetic Fields Deep in the Solar Convection Zone? Interaction of acoustic waves with magnetic fields. changes in rotation, sound speed, and flow. Look for: 1. Solar-cycle variations of rotation 1. Solar-cycle variations of sound speed 2. Solar-cycle variations of meridional flows

7. Probing Subsurface Magnetic Fields 0.96 R < r < R Ring diagram Time-Distance Acoustic Imaging 0.8 R < r < R Time-Distance r  0.7 R ???

9. Differential Rotation

10. Temporal Variations of Rotation (Howe et a. 2000)

11. Probing Magnetic Fields with Multiple-Bounce Travel Time (Chou & Serebryanskiy 2002)

13. Phase Velocity Filter

14. Change in Travel Time (max-min)

15. Another Approach: Solar Cycle Variations of Frequencies (Chou & Serebryanskiy 2005)

18. Maximum (2000) - Minimum (1996+1997)

19. Perturbation at BCZ Perturbation at surface

20. Perturbation at BCZ Perturbation at surface

21. Perturbations at BCZ and surface Error added

22. Perturbations at BCZ and surface Error added

23. Data & Analysis • MDI frequencies (72-day data). • GONG frequencies (36-day data). • Average over minimum (1996.06 - 1997.07) as the reference frequency. • Compute the frequency shift relative to the reference frequency.

24. Minimum as reference

26. δΓ/Γ = 2 – 6 x 10^-5 , if FWHM = 0.05R • r = 0.65 – 0.67 R • B = (8πP δΓ/Γ)^(-1/2) = 0.17 – 0.29 M Gauss Upper limit set by inversion (Eff-Darwich et al. 2002) δc/c = 3 x 10^-5 (δΓ/Γ = 1.5 x 10^-5 ) Why don’t we see the signals in the inversion study?

27. Meridional Flows in Convection Zone

28. Meridional flow with time-distance (Giles et al. 1997) • Cross-correlation is computed for pairs in the north-south direction. • Cross-correlation functions are averaged over longitude. • Determine travel time from cross-correlation function. different distances different depths latitude longitude

29. relates to the flow velocity in the north-south direction. from TON data 2- 6 deg. r = 0.962 – 0.987 R 1 sec ～ 10 m/s The sine-shape time shift corresponds to the one-cell pole ward circulation pattern in each hemisphere.

31. Solar-Cycle Variations of Meridional Flows • Use data taken with Taiwan Oscillation Network(TON) • K-line full-disk images (1994-2004) • Time series of each site each day (~ 512 images) is analyzed separately. • 1676 time series (~ 0.8M images) are analyzed.

32. Solar-Cycle Variations of Meridional Flows (chou & Dai 2001) Δ= 2 – 6 deg r = 0.962 – 0.987 R 1 sec ≈ 10 m/s

33. Solar-Cycle Variations of Meridional Flows (chou & Dai 2001) Δ= 6 – 10 deg r = 0.938 – 0.962 R 1 sec ≈ 10 m/s

34. Solar-Cycle Variations of Meridional Flows (chou & Dai 2001) Δ= 6 – 10 deg r = 0.938 – 0.962 R 1 sec ≈ 10 m/s

35. Solar-Cycle Variations of Meridional Flows (chou & Dai 2001) 2000 - 1997 2- 6 deg, r = 0.962 – 0.987 R 6-10 deg, r = 0.938 – 0.962 R 10-16 deg, r = 0.900 – 0.938 R 1 sec ≈ 10 m/s

36. Solar-Cycle Variations of Meridional Flows (chou & Dai 2001) Giles et al. 1997 solar minimum max - min solar maximum additional component created at maximum

37. Beck et al. (2002) • Confirm the result of Chou & Dai (2001). • The location of the divergent flow coincides with magnetic field and torsional oscillations. Δ= 17 deg r = 0.9 R meridional flow torsional oscillations from time-distance torsional oscillations from f-modes magnetic field

38. Questions: • Does the divergent flow decrease as activities decrease? • How deep does it go? • How is it created?

39. Chou & Ladenkov (2005) • Improve data analysis to go deeper. • Study the decline phase of cycle 23. Findings: • The divergent flow decreases with activities. • It extends at least down to 0.8 R. • It amplitude peaks at about 0.9 R.

40. Declining Phase of Cycle 23(Chou & Ladenkov 2005)

42. Temporal variations of divergent flows Correlation between divergent flow & sunspot number 6-16 deg

43. Depth Variations 2- 6 deg, r = 0.962 – 0.987 R 6-10 deg, r = 0.938 – 0.962 R 10-16 deg, r = 0.901 – 0.938 R 16-22 deg, r = 0.864– 0.901R 22-32 deg, r = 0.793– 0.864R

44. Conclusion on Meridional Flow • Meridional flows extend through the entire CZ (Giles et al. 1999). • A divergent flow is generated in each hemisphere as activities develop. • The location of the divergent flow coincides with active latitude and torsional oscillations. • The magnitude of the divergent flow correlates with activities. • The divergent flow peaks at about 0.9 R. • It could be a tool to probe the magnetic field deep in the CZ.

45. The End