1. Global Helioseismology NSO/LPL Summer School June 11-15, 2007 fhill@noao.edu

2. History Discovered in 1960 that the solar surface is rising and falling with a 5-minute period Many theories of wave physics postulated: –Gravity waves or acoustic waves or MHD waves? –Where was the region of propagation? A puzzle – every attempt to measure the characteristic wavelength on the surface gave a different answer

3. The puzzle solved Acoustic waves trapped within the internal temperature gradient predicted a specific dispersion relation between frequency and wavelength A wide range of wavelengths are possible, so every early measurement was correct – result depended on aperture size Observationally confirmed in 1975 5,000,000 modes, max amplitude 20 cm/s

4. Three types of modes G(ravity) Modes – restoring force is buoyancy – internal gravity waves P(ressure) Modes – restoring force is pressure F(undamental) Modes – restoring force is buoyancy modified by density interface – surface gravity waves

5. Wave trapping G modes exist where ω < N 2 (Brunt-Väisälä frequency) P modes exist where ω S (Lamb frequency) F modes are analogous to surface water waves

6. The essential frequencies

7. Frequency units ν = 1/(Period in seconds), units are Hertz (Hz) ω = 2π/(Period in seconds), units are radians/sec P = 5 min = 300 sec, ν = 3.33 mHz or 3333.33 μHz; ω = 2.1  10 -2 rad/s

8. Acoustic-Gravity Waves UnstratifiedStratified

9. Ray Paths Turning points

12. Quantization Vertical quantization: Horizontal quantization: Modes must live long enough to travel around circumference and self-interfere. Average interior sound speed is 70-100 km/s, thus requires lifetime longer than 0.5 days (Q > 20000).

13. Spherical Harmonics n – radial order: 0  n  80 – spherical harmonic degree: 0   4000 m – azimuthal degree: -  m 

14. Duvall law Modes turn at depth where sound speed = horizontal phase speed = ν/ℓ So, all modes with same ν/ℓ must take same time to make one trip between reflections

15. Rotational Splitting In absence of rotation, have standing wave pattern and degenerate case – the frequency 0 ( =  /2  ) is independent of m In presence of rotation, prograde and retrograde waves have different Observed frequency = m δ where δ is the splitting frequency Exactly analogous to a spinning bell

16. Observing Time Series X X X = = = Σ

17. An Observational Problem The sun sets at a single terrestrial site, producing periodic time series gaps The solar acoustic spectrum is convolved with the temporal window spectrum, contaminating solar spectrum with many spurious peaks

18. Solutions Antarctica – max 6 month duration Network – BiSON, IRIS, GONG – needs data merging, but maintainable Space – SoHO+MDI, GOLF – no merging but fragile.

19. Modern experiments GONGSOHO

20. Observing & processing challenges Image geometry is paramount Image scale affects ℓ-scale Angular orientation mixes m-states Fitting of spectral features not trivial Can only view portion of solar surface, so have spatial leakage

21. Solar Acoustic Spectra - Diagramm- Diagram -m- Diagram

25. Inversions 1

27. Eigenfunctions & Kernels G Modes – in the core, not observed (but maybe…) P Modes – throughout entire sun, but primarily in convection zone F Modes – at the surface Inversion kernels constructed from eigenfunctions weighted by density

28. Resolution kernels Trade-off between depth resolution and error magnification Trade-off curve Res kernels Trade-off curve

29. Internal Rotation Tachocline Near-surface shear layer

30. Temporal Evolution of Zonal Flows

31. Temporal Evolution

32. Tachocline oscillation Fig. 2 shows the rotation residual in the tachocline, and Fig. 3 shows the power spectrum over different periods. Panels a and d are in the ascending and descending phases of cycle 23, respectively, and show a dramatic difference in the character of the variation. Will this be repeated in cycle 24? Rachel Howe

33. G modes? Simulation Observation Analysis uses: very long time series (10 years) to take advantage of phase coherency even period spacing of g modes assumed internal rotation estimated observational SNR Intriguing, but needs verification Garcia et al, Science, June 15, 2007

34. Oscillations and the Solar Activity Cycle As the activity increases: –The frequencies increase –The energy decreases –The lifetimes decrease All of these changes are associated with the surface magnetic field

35. Oscillations & magnetic field Mode width (1/lifetime) Energy

36. Constraining solar structure & models Neutrino experiment solved All exotic models inconsistent with measured frequencies Standard model pretty good, but still discrepancy below CZ Near surface poorly understood

37. Sound Speed Variations Magnetic field? Thermal perturbations?

38. Observed-computed frequencies

39. Sound Source - Granulation Generates a randomly excited field of damped Helmholtz oscillators

40. Excitation Puzzles Line asymmetry V-I frequency offset

41. Acoustic Emission Lines

42. The sun as a star Low-degrees (ℓ = 0, 1, 2, 3) Large and small separations –Large: frequency separation between ℓ and ℓ + 1 –Small: frequency separation between ℓ and ℓ + 2 Echelle diagrams –Cut spectrum into 136 μHz segments and stack Core rotation Asteroseismology

43. Separations

44. Echelle diagram

45. Next topic Local Helioseismology