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Local Helioseismology
LPL/NSO Summer School
June 11-15, 2007
Global vs Local
• Global: 1. Horizontal interference selects
integer values of ℓ 2. Entire sun is sampled3. Spherical harmonics describe
waves4. Cannot get structure as
function of longitude5. Cannot get non-symmetric
latitudinal structure6. One basic technique7. Valid for ℓ < ~180
• Local1. No horizontal interference, can
have any wavelength2. Localized volume is sampled3. Sinusoids or Hankel functions
describe waves4. Longitudinal structure can be
determined5. Non-symmetric latitudinal
structure can be determined6. Several techniques7. Valid for ℓ > ~180
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
Sunspot p-mode absorption• Decompose observed velocity field in polar
coordinates into Hankel functions:
Hm (1,2) (kr) = Jm(kr) ± i Ym(kr)
Jm(kr): Bessel fnctn of 1st kind Ym(kr): Bessel fnctn of 2nd kind
Sunspot p-mode absorption
• The quantities Am(k,ω) and Bm(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 = [Pin – Pout] / Pin
Results
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
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
3-D power spectrum
Rings
Effect of a flow
An extreme flow observed
No tracking, solar rotation rate of 2000 m/s
With tracking to remove rotation
Horizontal flows from rings
Deriving divergence & curl
Deriving vertical velocity
Vertical velocity
Divergence
Kinetic Helicity
Vorticity below strong flare producers
AR 10486
AR 10069
Helicity before a large flare
Dashed – 0.9 Mm depth Solid – 7 Mm depth
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.
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.
Observed time-distance diagram
Cross-correlation function is well described by a Gabor wave packet
T (min)
Dis
tanc
e (°
)
T (min)
Cor
rela
tion
T-D diagnostics• Changes in travel time are related to
subsurface conditions (sound speed, flows)
• Can be inverted to infer the conditions
Sound speed below a spot
Meridonal flow from TD
D=30 Mm
D=200 MmD=130 Mm
D=65 Mm
1 s = 10 m/s
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.
Green’s functions
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
Farside maps
Farside Calibration
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?
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
For more information
• http://www.hao.ucar.edu/summerschool/program.html• Has links to very detailed lecture notes on
helioseismology and solar internal dynamics
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