asteroseismology from solar-like oscillations · asteroseismology for exoplanet hosts • determine...
TRANSCRIPT
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Asteroseismology from solar-like
oscillations
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The playing
field
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Fitting surface term:
Legacy Kepler data for 16 Cyg A
l = 0
l = 1
l = 3
l = 2
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Original: Model S
Modified: replace convection zone
by polytrope with 1 = 5/3
Separation
ratios
Roxburgh & Vorontsov (2003;
A&A 411, 215) Otí Floranes et al. (2005;
MNRAS 356, 671)
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Kernels for separations
d02
r02
Otí Floranes et al. (2005; MNRAS 356, 671)
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α Centaruri
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α Centauri
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α Centauri A
(Butler et al, 2004; ApJ 600, L75)
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α Centauri B
UVES (VLT) and UCLES (AAT)
Kjeldsen et al. (2005; ApJ 635, 1281)
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An initial analysis
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Classical variables
(a) Pourbaix et al. (2002)
(b) Pijpers (2003)
(c) Kervella et al. (2003)
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α Centauri system
OPAL EOS, OPAL96 opacity, He, Z settling
(Teixeira et al.)
MA: 1.11111 M¯
MB: 0.92828 M¯
X0: 0.71045
Z0: 0.02870
Age: 6.9848 Gyr
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α Centauri A
Model
problems?
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α Centauri B
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A borderline case
Best-fit model
Model with
convective core
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16 Cyg
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16 Cyg A, full set of Kepler data
l = 0
l = 1
l = 3
l = 2
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16 Cyg A, full set of Kepler data
l = 0
l = 1
l = 3
l = 2
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16 Cyg A, full set of Kepler data
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16 Cyg B, full set of Kepler data
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16 Cyg B, full set of Kepler data
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16 Cyg B, full set of Kepler data
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Average quantities
16 Cyg A 16 Cyg B
𝑀/𝑀⨀ 1.059 ± 0.016 1.004 ± 0.014
𝑅/𝑅⨀ 1.220 ± 0.006 1.102 ± 0.005
Age (Gyr) 6.67 ± 0.39 7.02 ± 0.34
𝑋0 0.693 ± 0.008 0.696 ± 0.008
𝑍0 0.026 ± 0.001 0.023 ± 0.001
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Bootis
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The first observations of solar-
like oscillations in a distant star
Kjeldsen et al. (1995; AJ 109, 1313)
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Fit to first data
Christensen-Dalsgaard et al. (1995; ApJ 443, L29)
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Location in HR diagram
1.6 M¯
1.66 M¯
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C-D & Houdek (2010; ApSS 328, 51)
Characteristic
frequencies
N2 'g2½
p(rad ¡ r+r¹) ;
l = 1
l = 2
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l = 1
C-D & Houdek (2010;
ApSS 328, 51)
l = 1
l = 0
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l = 2
C-D & Houdek (2010;
ApSS 328, 51)
l = 2
l = 0
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Surface term for mixed modes
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Fit to more
recent data
No surface term
With surface term
Di Mauro & C-D
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SONG
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μ Hercules
200 nights of SONG observations
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μ Hercules
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Asteroseismology for exoplanet
hosts • Determine mass, radius (with some
dependence on stellar models)
• Constrain age
• Constrain rotation period and possibly
orientation of rotation axis
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Rotational
splitting
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Gizon & Solanki (2003; ApJ 589, 1009)
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Analysis of Kepler-65
Chaplin et al. (2013; ApJ 766, 101)
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Rotationally split peaks, l = 1
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Probability distributions
Rotational
splitting
Inclination
Rotation axis in the plane
of the sky
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Red giants
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Red-giant evolution
Central
hydrogen
burning
Shell hydrogen
burning
Shell hydrogen
burning, and
core helium
burning
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Evolution, 2.5 𝑀⊙
Teixeira et al.
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The first detection of solar-like
oscillations in a red giant
Frandsen et al. (2002; A&A 394, L5)
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Nonradial
oscillations in
red giants
De Ridder et al. (2009; Nature 459, 398)
CoRoT observations
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Ophiuchi
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MOST
photometry
Barban et al. (2007;
A&A 468, 1033)
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2.35 M¯ evolution sequence
+: 5 Myr steps
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2.35 M¯ evolution sequence
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N2 'g2½
p(rad ¡ r+r¹) ;
Characteristic
frequencies
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Mode inertia
+ l = 0
* l = 1
l = 2
l = 3
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Eigenfunctions
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The CoRoT and Kepler era
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A HR diagram in
terms of max
Huber (2012)
Red
clump
Kepler
CoRoT
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Beck et al.
Science (2011; 332, 205)
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Kepler observations of solar twin
Frequency(mHz)
Pow
er
1 1 1
1 1
0
0
0 0
2 2
2
2
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Kepler observations of red giant
Beck et al. (2011; Science 332, 205)
Pe
rio
d s
pa
cin
gs
(se
c)
Obs.
Model
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Two types of modes in one star
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An sdB star in the core of a red giant
sdB star in
the core of
the red giant
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N/2𝜋
𝑆𝑙/2𝜋
l = 2
1
p region g region
Characteristic frequencies, red
giant (1.3 𝑀⨀, 6.2 𝑅⨀)
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g-mode period spacings
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Mode inertia, red giant
(1.3 𝑀⨀, 6.2 𝑅⨀)
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Integrands of inertia, l = 1 (1.3 𝑀⨀, 6.2 𝑅⨀)
g-dominated mode
p-dominated mode
ν = 79.1 μHz
ν = 84.3 μHz
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Bedding et al. (Nature, 2011, 471, 608)
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Kepler observations
Hydrogen burning
Helium burning
Bedding et al. (Nature, 2011, 471, 608)
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Buoyancy frequencies
Red giant Early He burning
He burning
convective
core
2.5 M¯ , ~70 L¯
End of He burning
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Ensemble asteroseismology
Hydrogen shell burning
Helium flash
No helium flash
Bedding et al. (Nature, 2011, 471, 608)
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Red-giant and clump stars
Mosser et al. (2014; A&A 572, L5)
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Core rotation in red giants Fine structure
core structure
Hyperfine
structure
Core rotation
Beck et al.
(2012; Nature, 481, 55)
Frequency
Pow
er
l = 1 l = 1 l = 1 l = 0 l = 2
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Rotational weight functions
Beck et al.(2012; Nature, 481, 55)
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Rotational
splitting
weight
l = 2
l = 2
l = 1
l = 1
Beck et al.(2012; Nature, 481, 55)
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Fast rotation of the stellar core
• More g-dominated dipolar modes show
larger splitting
• More g-dominated dipolar modes have
smaller βnl
• For more g-dominated dipolar modes the
weight is dominated by the stellar core
[The data are] compatible with a core
rotating ten times faster than the surface
Beck et al.(2012; Nature, 481, 55)
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Ensemble rotation
Mosser et al. (2013; A&A 548, A10)
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Rotation evolution
With no angular momentum transport,
angular momentum J is locally conserved
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1.1 𝑀⊙
m/M = 1 .5
.3
.2
.1
.15
𝑟𝑠ℎ𝑒𝑙𝑙
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Modelling core rotation
No additional transport
Eggenberger et al. (2012; A&A 544, L4)
1.5 M¯
Evolved to 12.6 L¯
Bottom of
convective envelope He core
Observed value: ~ 0.5 μHz
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Angular-momentum transport
• Turbulence
• Circulation (driven by rotation)
• Magnetic fields (primordial or dynamo-
generated)
• Gravity waves
Not enough!
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Rotation evolution
Cantiello et al. (2014; ApJ 788, 93)
Observations
Core rotation period
TS: Tayler-Spruit dynamo
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Rotation evolution
Cantiello et al. (2014; ApJ 788, 93)
Observations
Core rotation period
TS: Tayler-Spruit dynamo