1. Local Helioseismology LPL/NSO Summer School June 11-15, 2007

2. Global vs Local Global: 1.Horizontal interference selects integer values of ℓ 2.Entire sun is sampled 3.Spherical harmonics describe waves 4.Cannot get structure as function of longitude 5.Cannot get non-symmetric latitudinal structure 6.One basic technique 7.Valid for ℓ < ~180 Local 1.No horizontal interference, can have any wavelength 2.Localized volume is sampled 3.Sinusoids or Hankel functions describe waves 4.Longitudinal structure can be determined 5.Non-symmetric latitudinal structure can be determined 6.Several techniques 7.Valid for ℓ > ~180

3. History 1987: Sunspots are observed to absorb p-modes 1988: Ring diagram method is invented 1990: Acoustic holography is invented 1993: Time-distance method is invented

4. Sunspot p-mode absorption Decompose observed velocity field in polar coordinates into Hankel functions: H m (1,2) (kr) = J m (kr) ± i Y m (kr) J m (kr): Bessel fnctn of 1 st kindY m (kr): Bessel fnctn of 2 nd kind

5. Sunspot p-mode absorption The quantities A m (k,ω) and B m (k,ω) are complex numbers containing the power and phase of the ingoing (A) and outgoing waves (B). Here m is the polar azimuthal order. Compute absorption: α = [P in – P out ] / P in

6. Results

7. Underlying physics P-modes are scattered by magnetic field into shorter (unobserved) wavelengths or other regimes P-mode energy is absorbed by magnetic field and transformed into MHD waves

8. Ring Diagrams Based on local plane-wave representation of oscillations (The “Flat-Sun society”) Approximation good for high degrees (ℓ > ~180) and shallow depths Allows analysis of wave properties in small regions Allows inference of sub-surface flows as function of position and depth

9. 3-D power spectrum

10. Rings

11. Effect of a flow

12. An extreme flow observed No tracking, solar rotation rate of 2000 m/s With tracking to remove rotation

13. Horizontal flows from rings

15. Deriving divergence & curl

16. Deriving vertical velocity

17. Vertical velocity

18. Divergence

19. Kinetic Helicity

20. Vorticity below strong flare producers AR 10486 AR 10069

21. Helicity before a large flare

22. Dashed – 0.9 Mm depthSolid – 7 Mm depth

23. Time-distance Sound is emitted from a location, travels down, and comes back up at some time later and some distance away from the source. The time and distance is influenced by the conditions of the plasma that the wave travels through.

24. Constructing a T-D plot At a given time T, compute the cross-correlation between a point and annuli centered on the point with different radii D. Repeat for many values of T, plot cross- correlation amplitude as a function of T and D. Can be done approximately by taking the power spectrum of a filtered oscillation power spectrum.

25. Observed time- distance diagram Cross-correlation function is well described by a Gabor wave packet T (min) Distance (°) T (min) Correlation

26. T-D diagnostics Changes in travel time are related to subsurface conditions (sound speed, flows) Can be inverted to infer the conditions

27. Sound speed below a spot

28. Meridonal flow from TD D=30 Mm D=200 MmD=130 Mm D=65 Mm 1 s = 10 m/s

29. Acoustic Holography in five easy (?) steps 1.Observe wave field in pupil areas 2.Compute a Green’s function describing how a single impulse at (r,z,t) forms an expanding ring at the surface (r′,0,t′). 3.Convolve Green’s function with the observed wave field (egression, H + blue) 4.Convolve time-reversed Green’s function with observed wave field (ingression, H - red) 5.Build maps of H + and H - over all r, z, t.

30. Green’s functions

31. Holography can view the farside of the Sun 8/29/05 8/30/05 8/31/05 9/01/05 9/02/05 9/03/05 AR10808

32. Farside maps

33. Farside Calibration

34. Farside puzzle The same “noise” structure appears in both MDI & GONG data, and in both holography & TD farside analyses. Thus, must be solar in origin. What are they? –Magnetic field concentrations that do not reach the surface? –Large velocity structures?

35. Comparison of methods Rings: easy; low spatial resolution and shallow depth range TD: harder; higher spatial resolution and greater depth range Holography: hardest All methods have a trade-off between depth range and spatial resolution

36. For more information http://www.hao.ucar.edu/summerschool/program.html Has links to very detailed lecture notes on helioseismology and solar internal dynamics