Global Helioseismology

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Global Helioseismology

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

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History

• Discovered in 1960 that the solar surface is
  rising and falling with a 5-minute period
• Many theories of wave physics postulated
• Gravity waves or acoustic waves or MHD waves?
• Where was the region of propagation?
• A puzzle every attempt to measure the
  characteristic wavelength on the surface gave a
  different answer

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The puzzle solved

• Acoustic waves trapped within the internal
  temperature gradient predicted a specific
  dispersion relation between frequency and
  wavelength
• A wide range of wavelengths are possible, so
  every early measurement was correct result
  depended on aperture size
• Observationally confirmed in 1975
• 5,000,000 modes, max amplitude 20 cm/s

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Three types of modes

• G(ravity) Modes restoring force is buoyancy
  internal gravity waves
• P(ressure) Modes restoring force is pressure
• F(undamental) Modes restoring force is buoyancy
  modified by density interface surface gravity
  waves

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Wave trapping

• G modes exist where ? lt N2 (Brunt-Väisälä
  frequency)
• P modes exist where ? lt ?ac (acoustic cut-off
  frequency) and ? gt S (Lamb frequency)
• F modes are analogous to surface water waves

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The essential frequencies
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Frequency units

• ? 1/(Period in seconds), units are Hertz (Hz)
• ? 2p/(Period in seconds), units are radians/sec
• P 5 min 300 sec, ? 3.33 mHz or 3333.33 µHz
  ? 2.1 ? 10-2 rad/s

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Acoustic-Gravity Waves
Unstratified
Stratified
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Ray Paths
Turning points
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Turning points
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Quantization
Modes must live long enough to travel around
circumference and self-interfere. Average
interior sound speed is 70-100 km/s, thus
requires lifetime longer than 0.5 days (Q gt
20000).
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Spherical Harmonics
? spherical harmonic degree 0 ? ? ? 4000
m azimuthal degree -? ? m ? ?
n radial order 0 ? n ? 80
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Duvall law

• Modes turn at depth where sound speed
  horizontal phase speed ?/l
• So, all modes with same ?/l must take same time
  to make one trip between reflections

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Rotational Splitting

• In absence of rotation, have standing wave
  pattern and degenerate case the frequency ?0 (
  ?/2?) is independent of m
• In presence of rotation, prograde and retrograde
  waves have different ?
• Observed frequency ? m d? where d? is the
  splitting frequency
• Exactly analogous to a spinning bell

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Observing Time Series
S
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An Observational Problem

• The sun sets at a single terrestrial site,
  producing periodic time series gaps
• The solar acoustic spectrum is convolved with the
  temporal window spectrum, contaminating solar
  spectrum with many spurious peaks

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Solutions

• Antarctica max 6 month duration
• Network BiSON, IRIS, GONG needs data merging,
  but maintainable
• Space SoHOMDI, GOLF no merging but fragile.

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Modern experiments
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Observing processing challenges

• Image geometry is paramount
• Image scale affects l-scale
• Angular orientation mixes m-states
• Fitting of spectral features not trivial
• Can only view portion of solar surface, so have
  spatial leakage

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Solar Acoustic Spectra
?-? Diagram
m-? Diagram
?-m-? Diagram
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Inversions 1
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Eigenfunctions Kernels

• G Modes in the core, not observed (but maybe)
• P Modes throughout entire sun, but primarily in
  convection zone
• F Modes at the surface
• Inversion kernels constructed from eigenfunctions
  weighted by density

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Resolution kernels

• Trade-off between depth resolution and error
  magnification
• Trade-off curve

Res kernels
Trade-off curve
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Internal Rotation
Tachocline
Near-surface shear layer
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Temporal Evolution of Zonal Flows
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Temporal Evolution
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Tachocline oscillation
Fig. 2 shows the rotation residual in the
tachocline, and Fig. 3 shows the power spectrum
over different periods. Panels a and d are in the
ascending and descending phases of cycle 23,
respectively, and show a dramatic difference in
the character of the variation. Will this be
repeated in cycle 24?
Rachel Howe
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G modes?
Simulation

• Analysis uses
• very long time series (10 years) to take
  advantage of phase coherency
• even period spacing of g modes
• assumed internal rotation
• estimated observational SNR
• Intriguing, but needs verification
• Garcia et al, Science, June 15, 2007

Observation
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Oscillations and the Solar Activity Cycle

• As the activity increases
• The frequencies increase
• The energy decreases
• The lifetimes decrease
• All of these changes are associated with the
  surface magnetic field

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Oscillations magnetic field
Mode width (1/lifetime)
Energy
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Constraining solar structure models

• Neutrino experiment solved
• All exotic models inconsistent with measured
  frequencies
• Standard model pretty good, but still discrepancy
  below CZ
• Near surface poorly understood

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Sound Speed Variations
Magnetic field? Thermal perturbations?
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Observed-computed frequencies
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Sound Source - Granulation
Generates a randomly excited field of damped
Helmholtz oscillators
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Excitation Puzzles
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Acoustic Emission Lines
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The sun as a star

• Low-degrees (l 0, 1, 2, 3)
• Large and small separations
• Large frequency separation between l and l 1
• Small frequency separation between l and l 2
• Echelle diagrams
• Cut spectrum into 136 µHz segments and stack
• Core rotation
• Asteroseismology

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Separations
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Echelle diagram
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Next topic

• Local Helioseismology