Transcript Helioseismology - National Optical Astronomy Observatory

An Introduction to Helioseismology
(Global)
2008 Solar Physics Summer School
June 16-20, Sacramento Peak Observatory, Sunspot, NM
Special Acknowledgments
Rachel Howe
Rudi Komm
Frank Hill
( National Solar Observatory )
Global Helioseismology
•What is helioseismology?
–A bit of early history
•Basics
–p-modes and g-modes
–Spherical harmonics
•Observations
–Instrumentation
–Networks and spacecraft
–Time series
–Spectra
•Methods
–Peak finding
–Inversions
•Results
–Internal Properties of the Sun
–Solar Cycle variations
The early “days” of helioseismology
• 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 k- (diagnostic) diagram
• 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
• Max amplitude 20 cm/s
Helioseismology: A window to the Sun’s Interior
What is helioseismology?
Helioseismology utilizes waves that
propagate throughout the Sun to
measure its invisible internal (and
external) structure and dynamics.
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
Sound Source - Granulation
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The P modes
• A p mode is a standing
acoustic wave.
• Each mode can be
described by a spherical
harmonic.
• Quantum numbers n
(radial order), l
(degree), and m
(azimuthal order)
identify the mode.
Spherical Harmonics
l=6 m=0
l=6 m=3
l=6 m=6
• The harmonic
degree, l, indicates
the number of node
lines on the surface,
which is the total
number of planes
slicing through the
Sun.
• The azimuthal
number m, describes
the number of planes
slicing through the
Sun longitudinally.
•Picture credits: Noyes, Robert, "The Sun", in _The New Solar
System_, J. Kelly Beatty and A. Chaikin ed., Sky Publishing
Corporation, 1990, pg. 23.
• -l≤m≤l
Temporal 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
Spatial Frequency units
• kh = √(l(l+1)/Rsun (Mm-1)
Turning points
Ray Paths
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Turning points
QuickTime™ and a
YUV420 codec decompressor
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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 n,l,m = 0 + δ where δ
is the splitting frequency
• IF the Sun rotated uniformly --> δ depend
linearly on m.
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,VIRGO
Networks
•
6-site network of single-pixel
instruments, data since 1976,
completed 1992.
•
Modes up to l=4
•
Run by University of
Birmingham, UK
Networks
• Six stations
around the
world for
continual
coverage.
• 256x256
pixels 19952001
• 1024 pixels
since 2001
• Run from NSO
Tucson.
Space Instruments
1996 - Present
MDI GOLF VIRGO
Coming Soon….
HMI
Observing Time Series
Σ
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X
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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
Solar Acoustic Spectra
- Diagram
-m- Diagram
m- Diagram
Fitting the Spectrum
Standard model is a Lorentzian profile
Fitting the Spectrum
Considerations:
– Observations in Velocity and Intensity
– Asymmetric Profile
– Leakage matrix
Inversions
•
•
•
•
Modes are reflected due to density
variations.
The lower the l, the fewer surface
reflections, and the deeper the mode
penetrates.
Combining information from different
modes lets us build up a picture of
properties at different depths.
Modes of different m cover different
latitude ranges, giving latitudinal
resolution.
The (rotation) inversion problem
Kernel
Coefficients to be found
Averaging Kernel
Eigenfunctions & Kernels
• Inversion kernels
constructed from
eigenfunctions
weighted by density
Internal Rotation
Tachocline
Near-surface
shear layer
Temporal Evolution
Temporal Evolution of Zonal Flows
Sound Speed and Density
Inversions
Good job constraining solar
structure & dynamo models
BUT
• ( Neutrino experiment solved )
• Solar abundances
• Standard model pretty good, but still discrepancy below
CZ
• Near surface poorly understood
• Very few p-modes propagate deep enough into the Sun -->
G-modes will be very welcome
Simulation
G modes?
Analysis uses:
• very long time series (10 years)
• even period spacing of g modes
• assumed internal rotation
• estimated observational SNR
Observation
Intriguing, but needs verification
Garcia et al, Science, June 15, 2007