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 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

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: 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

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

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 AR 10069

Helicity before a large flare

Dashed – 0.9 Mm depthSolid – 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) Distance (°) T (min) Correlation

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 Has links to very detailed lecture notes on helioseismology and solar internal dynamics