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Seismology of the Sun and solar-like stars
Jørgen Christensen-Dalsgaard
Institut for Fysik og Astronomi, Aarhus Universitet
Collaborators
• M. J. Thompson• R. Howe• J. Schou• S. Basu• R. M. Larsen• J. M. Jensen
• Hans Kjeldsen• Teresa Teixeira• Tim Bedding • Maria Pia Di Mauro• Andrea Miglio
Where it all started
Grec et al., Nature 288, 541; 1980
Basic properties of oscillations
•Behave like spherical harmonics: Plm(cos ) cos(m - t)
•kh = 2 / h = [l(l+1)]1/2/r
Asymptotics of frequenciesAcoustic-wave dispersion relation
Hence
Lower turning point rt where kr = 0:
Rays
Inversion with rays
Observing a Doppler image
VIRGO on SOHO (whole-disk):
Data on solar oscillationsObservations:
MDI on SOHO
Observed frequencies
m-averaged frequencies from MDI instrument on SOHO
1000 error bars
A reference solar modelModel S:
•OPAL96 equation of state
•OPAL 92 opacities
•Nuclear parameters from Bahcall & Pinsonneault (1994)
•Diffusion and settling of helium and heavy elements from Michaud & Proffitt (1993)
•Mixing-length theory of convection
Frequency differences, Sun - model
No settling
The solar internal sound speed
No settling
Including settling
Sun - model
The solar internal sound speedSun - model
Changes in composition
The evolution of stars is controlled by the changes in their interior composition:
• Nuclear reactions
• Convective mixing
• Molecular diffusion and settling
• Circulation and other mixing processes outside convection zones
Nuclear burning
Settling
No relativistic effectsIncluding relativistic effects
Relativistic electrons in the Sun
Elliot & Kosovichev (1998; ApJ 500, L199)
Improvements:
•Non-LTE analysis
•3D atmosphere models
Consistent abundance determinations for a variety of indicators
Revision of solar surface abundances
Asplund et al. (2004; A&A 417, 751):Pijpers, Houdek et al.
Model S
Z = 0.015
How do we correct the models?
Basu & Antia (2004; ApJ 606 L85): an opacity increase to compensate for lower Z is required
Seaton & Badnell (submitted): recent Opacity Project results do indicate such an increase over the OPAL values.
Rotational splitting
Kernels for rotational splitting
Inferred solar internal rotation
Base of convection
zone
TachoclineNear solid-
body rotation of
interior
Rotation of the solar interior
BiSON and LOWL data; Chaplin et al. (1999; MNRAS 308, 405)
Tachocline oscillations
See Howe et al. (2000; Science 287, 2456)
● GONG-RLS
▲MDI-RLS
∆ MDI-OLA
Zonal flowsRotation rate - average value at solar minimum
Vorontsov et al. (2002; Science 296, 101)
Radial development of zonal flows
Howe et al., in preparation
Observed and modelled dynamics
6 1/2 year MDI inversion, enforcing 11-yr periodicity
Vorontsov et al.
Non-linear mean-field solar dynamo models
Covas, Tavakol and Moss
Local helioseismology
• Time-distance helioseismology
• Ring-diagram analysis
• Helioseismic holography
Tomography of three-dimensional,
time-dependent properties of solar interior
Rays for local helioseismology
Kosovichev et al. (2000; Solar Phys. 192, 159)
Near-surface flows
Time-distance analysis; Beck et al. (2002; ApJ 575, L47)
Meridional component
Zonal component
16:00 11 Jan 98
00:00 12 Jan 98
08:00 12 Jan 98
Emerging active region
Kosovichev et al. (2000; Solar Phys. 192, 159
Far-side imaging
Lindsey & Braun (2000; Science 287, 1799)
Far-side monitoring
MDI on SOHO
From the Sun to the stars
What we expect:the solar case
Grec et al., Nature 288, 541; 1980
Asymptotics of p modes
Large frequency separation:
Small frequency separations
Frequency separations:
Asteroseismic HR diagram
The present situation
Bedding & Kjeldsen (2003)
α Centauri A
α Centauri A
Observations with UVES on VLT
(Butler et al, 2004; ApJ 600, L75)
α Centauri A
(Butler et al, 2004; ApJ 600, L75)
α Centauri A
VLT(UVES) and AAT(UCLES)
optimally combined
Bedding et al., ApJ, in press (astro-ph/0406471 )
α Centauri B
UVES (VLT) and UCLES (AAT)
Kjeldsen et al. (in preparation)
Classical variables
(a) Pourbaix et al. (2002)
(b) Pijpers (2003)
(c) Kervella et al. (2003)
Fitting the α Cen systemObservable quantities for the system
Model parameters:
Fit using Marquardt method, with centred differences, using an 8-processor Linux cluster, implemented by T. C. Teixeira
Choice of oscillation variables, from Bedding et al. fits to Butler et al. observations:
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
α Centauri system
: A: B
α Centauri A
Observations: use Bedding et al. fits
Models: surf = 0.75
α Centauri B
Observations: use Bedding et al. fits
Models: surf = 0.75
α Centauri A
Observations: use Bedding et al. fits
Models: surf = 0.75
α Centauri B
Observations: use Bedding et al. fits
Models: surf = 0.75
Procyon
Radial-velocity observations
Brown et al. (1991; ApJ 368, 599)
Martić et al. (2004; A&A 418, 295)
MOST results
Matthews et al. (2004; Nature 430, 51 – July 1)
An interpretation of the MOST results
Kjeldsen simulations:
• 1.5 times solar granulation
•Stochastic excitation
•1.9 days lifetime of modes
• Amplitude scaled from velocity observations
No noise
MOST signal level
ξ Hydrae
ξ Hydrae
Stello et al.
Evolutionary state
Teixeira et al.
Ticks for every 5 Myr
Core He burning
The future
COROT (France, ESA, ...); launch 2006
The future?????
Eddington: the obvious next step in asteroseismology