Local Helioseismology

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Local Helioseismology

• LPL/NSO Summer School
• June 11-15, 2007

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Global vs Local

• Global
• Horizontal interference selects integer values of
  l
• Entire sun is sampled
• Spherical harmonics describe waves
• Cannot get structure as function of longitude
• Cannot get non-symmetric latitudinal structure
• One basic technique
• Valid for l lt 180

• Local
• No horizontal interference, can have any
  wavelength
• Localized volume is sampled
• Sinusoids or Hankel functions describe waves
• Longitudinal structure can be determined
• Non-symmetric latitudinal structure can be
  determined
• Several techniques
• Valid for l gt 180

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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

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Sunspot p-mode absorption

• Decompose observed velocity field in polar
  coordinates into Hankel functions

Hm (1,2) (kr) Jm(kr) i Ym(kr)
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Sunspot p-mode absorption

• The quantities Am(k,?) and Bm(k,?) 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
• a Pin Pout / Pin

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Results
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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

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Ring Diagrams

• Based on local plane-wave representation of
  oscillations (The Flat-Sun society)
• Approximation good for high degrees (l gt 180)
  and shallow depths
• Allows analysis of wave properties in small
  regions
• Allows inference of sub-surface flows as function
  of position and depth

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3-D power spectrum
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Rings
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Effect of a flow
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An extreme flow observed
No tracking, solar rotation rate of 2000 m/s
With tracking to remove rotation
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Horizontal flows from rings
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Deriving divergence curl
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Deriving vertical velocity
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Vertical velocity
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Divergence
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Kinetic Helicity
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Vorticity below strong flare producers
AR 10069
AR 10486
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Helicity before a large flare
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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.

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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.

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Observed time-distance diagram
Cross-correlation function is well described by a
Gabor wave packet
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T-D diagnostics

• Changes in travel time are related to subsurface
  conditions (sound speed, flows)
• Can be inverted to infer the conditions

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Sound speed below a spot
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Meridonal flow from TD
1 s 10 m/s
D30 Mm
D65 Mm
D200 Mm
D130 Mm
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Acoustic Holography in five easy (?) steps

• Observe wave field in pupil areas
• Compute a Greens function describing how a
  single impulse at (r,z,t) forms an expanding ring
  at the surface (r',0,t').
• Convolve Greens function with the observed wave
  field (egression, H blue)
• Convolve time-reversed Greens function with
  observed wave field (ingression, H- red)
• Build maps of H and H- over all r, z, t.

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Greens functions
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Holography can view the farside of the Sun
AR10808
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Farside maps
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Farside Calibration
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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?

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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

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For more information

• http//www.hao.ucar.edu/summerschool/program.html
• Has links to very detailed lecture notes on
  helioseismology and solar internal dynamics