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