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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
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
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
Wave trapping• G modes exist where ω < N2 (Brunt-Väisälä frequency)
• P modes exist where ω < ωac (acoustic cut-off frequency) and ω > S (Lamb frequency)
• F modes are analogous to surface water waves
The essential frequencies
Frequency units
• ν = 1/(Period in seconds), units are Hertz (Hz)
• ω = 2π/(Period in seconds), units are radians/sec
• P = 5 min = 300 sec, ν = 3.33 mHz or 3333.33 μHz; ω = 2.1 10-2 rad/s
Acoustic-Gravity Waves
Unstratified Stratified
Ray Paths
Turning points
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Turning points
Quantization
Vertical quantization:
Horizontal 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 > 20000).
Spherical Harmonics
n – radial order: 0 n 80
– spherical harmonic degree: 0 4000
m – azimuthal degree: - m
Duvall law• Modes turn at depth
where sound speed = horizontal phase speed = ν/ℓ
• So, all modes with same ν/ℓ must take same time to make one trip between reflections
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 δ where δ is the splitting frequency
• Exactly analogous to a spinning bell
Observing Time Series
X
X
X
=
=
=
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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
Solutions
• Antarctica – max 6 month duration
• Network – BiSON, IRIS, GONG – needs data merging, but maintainable
• Space – SoHO+MDI, GOLF – no merging but fragile.
Modern experiments
GONG SOHO
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
Solar Acoustic Spectra
- Diagram
m- Diagram-m- Diagram
Inversions 1
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
Resolution kernels
• Trade-off between depth resolution and error magnification
• Trade-off curve
Res kernels
Trade-off curve
Internal Rotation
Tachocline
Near-surface shear layer
Temporal Evolution of Zonal Flows
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
G modes?Simulation
Observation
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 verificationGarcia et al, Science, June 15, 2007
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
Oscillations & magnetic field
Mode width (1/lifetime)
Energy
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
Sound Speed Variations
Magnetic field?
Thermal perturbations?
Observed-computed frequencies
Sound Source - Granulation
Generates a randomly excited field of damped Helmholtz oscillators
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Excitation Puzzles
Line asymmetry V-I frequency offset
Acoustic Emission Lines
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
Separations
Echelle diagram
Next topic
• Local Helioseismology
