helioseismology and asteroseismology: sounding stars · asteroseismology: sounding stars professor...
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Helioseismology and Asteroseismology:
Sounding Stars
Professor Bill Chaplin, School of Physics & Astronomy University of Birmingham, UK
Science on the Sphere Royal Society Meeting, 15 July 2014
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helioseismology, n. The study of the sun's interior by the observation and analysis of oscillations at its surface. Cf. asteroseismology n. [Oxford English Dictionary]
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The Birmingham Solar Oscillations Network BiSON
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Gary Larson
“Inside the Sun”
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asteroseismology, n. The study of the interior of stars by the observation and analysis of oscillations at their surface. Cf. helioseismology n. [Oxford English Dictionary]
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Solar-like oscillations Stochastically excited and intrinsically damped by near-surface convection
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Standing acoustic waves Internal acoustic
ray paths Surface displacement:
oscillation patterns in 3D
red waves give…
blue waves give…
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In rapidly rotating stars…
Island Chaotic “Whispering gallery”
Moo
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Spherical Harmonics (l,m) 1,0 1,1 2,0
2,1 2,2 3,0
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3,1 3,2 3,3
5,5 10,5 10,10
Spherical Harmonics (l,m)
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n Fundamental period of radial pulsation: 2/1−
∝Π ρ
n Estimate period from sound crossing time
n Period similar to dynamical timescale (‘free fall’ time)
Ritter 1880; Shapley, 1914
Pulsation timescale
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Courtesy D. Hathaway
Sun: fundamental radial-mode period
Π f ≈ 1 hour
ν f ≈ 250 µHz
Pulsation timescale
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Frequency spectrum of low-degree (low-l) modes (contains overtones of 0 ≤ l ≤ 3)
BiSON data
High-overtone (n ≈20) modes!
250 µHz
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l=2
l=0
l=2
l=0
l=2
l=1
l=0 l=1
l=1
l=3 l=3
BiSON data
How are overtones of different degree, l, arranged in frequency?
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Ridge
Overtone, n, increasing
Angular degree
Frequency
Overtones of given l
Frequency spectrum: l-ν diagram Consider the overtones of each degree, l
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Frequency spectrum:
l-ν diagram Data collected
by MDI instrument on board SOHO
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Frequency spectrum: uniform non-rotating sphere
)2/()2(4
lnlnRc
nl +Δ≈+≈ νν
Rc2
=Δν
Clamped boundary conditions: displacement fixed to zero at centre, edge
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Frequency spectrum: uniform non-rotating sphere
⎟⎠
⎞⎜⎝
⎛++Δ≈⎟
⎠
⎞⎜⎝
⎛++≈
412/
212
4lnln
Rc
nl νν
Rc2
=Δν
Free boundary conditions: edges free
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Frequency spectrum: uniform non-rotating sphere
General form
⎟⎠
⎞⎜⎝
⎛++Δ≈ ενν
2lnnl
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Frequency spectrum: Star Stratified interior
)1(2
+−⎟⎠
⎞⎜⎝
⎛++Δ≈ lDllnnl ενν
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Frequency spectrum: Rotating Star
Stratified interior, slow rotation approx.
rot)1(2
νενν Δ++−⎟⎠
⎞⎜⎝
⎛++Δ≈ mlDllnnlm
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l=2
l=0
l=2
l=0
l=2
l=1
l=0 l=1
l=1
l=3 l=3
BiSON data
How are overtones of different degree, l, arranged in frequency?
)1(2
+−⎟⎠
⎞⎜⎝
⎛++Δ≈ lDllnnl ενν
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Échelle frequency plot BiSON Sun-as-a-star + model frequencies
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Kepler’s “best in class” The A-component of the solar-type binary 16 Cyg
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Kepler’s “best in class” The A-component of the solar-type binary 16 Cyg
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Sun SOHO
6116048
6603624
6106415
8379927
8006161 Doris
Arthur
Perky
Sun??
Saxo
Nunny
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“Getting High⎯ Confessions of a Peak-Bagging
Junkie”
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Toward automated peak-bagging of Sun-like stars
Appourchaux et al., 2012, A&A, 543, A54
Homogeneous analysis of 61 solar-type stars
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Fractional sound-speed differences: observed minus model BiSON + MDI data
Basu et al., 2009, ApJ, 699, 1403
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Internal Solar Rotation
GONG data
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Rotation of the Deep Interior
Period of 26.6 days
Fractional radius
Rotational frequency
Ω/2π (nHz)
24.6 days
31.3 days
BiSON + SOI/MDI data
?
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Spin-orbit alignment Asteroseismology constrains inclination
of stellar spin axis
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The “transit method” Detection of extra-solar planets
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Inference on stellar inclination Example: dipole mode of oscillation
A. Miglio
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Kepler-50 and Kepler-65 Two stars with multiple small planets
Chaplin et al., 2013, ApJ, 766, 101
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Inference on stellar inclination
Chaplin et al., 2013, ApJ, 766, 101
Example: dipole oscillation mode
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Chaplin et al., 2013, ApJ, 766, 101
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Kepler-50 and Kepler-65 Two stars with multiple small planets
Chaplin et al., 2013, ApJ, 766, 101
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Internal rotation of a subgiant Core rotates five-times faster than surface
Deheuvels et al., 2012, ApJ, 756, 19
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Huber et al., 2013, Science, 342, 331
Kepler-56 A misaligned multi-planet system
with a red-giant host star
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