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Status of solar and stellar modelling
Jørgen Christensen-Dalsgaard
Stellar Astrophysics Centre
Aarhus University
What kind of models?
• Model of eclipsing-binary system
• Stellar atmospheric model
• Models of convection-zone dynamics
• Dynamo models of stellar activity
• Flare models
• Oscillation background model
• Models of stellar structure and evolution
• Models of stellar oscillations
SELECTED PROBLEMS
• Numerical accuracy of model computations
• Consistency between evolution codes
• Microphysics (equation of state, opacity, …)
SELECTED PROBLEMS • Numerical accuracy of model computations
• Consistency between evolution codes
• Microphysics (equation of state, opacity, …)
• Stellar hydrodynamics
– Near-surface convection
– Convective overshoot
– Rotational mixing
– Evolution of rotation
– Effects of rotation on oscillations
SELECTED PROBLEMS • Numerical accuracy of model computations
• Consistency between evolution codes
• Microphysics (equation of state, opacity, …)
• Stellar hydrodynamics
– Near-surface convection
– Convective overshoot
– Rotational mixing
– Evolution of rotation
– Effects of rotation on oscillations
• Stellar magneto-hydrodynamics!!
Can helio- and asteroseismology
help?
Probably!
Kawaler: Harmonious stars can upset the false harmony
of our models
Relevant data • Eclipsing binaries
• ‘Classical’ stellar data (log g, Teff, composition, …)
– Note: very well known for the Sun, including age (although composition??)
• Surface rotation
• Surface magnetic field
• Stellar ‘noise’ background
• Oscillation data
– Frequencies
– Frequency combinations
– Excitation
– Amplitude ratios, phase differences
Approach to diffusive equilibrium in sdB stars
log HB age
(years)
Stable modes
Unstable modes
Nonadiabatic
asteroseismology
Fontaine et al. (2006;
Mem. S. A. It. 77, 49)
5.25
Unstable modes in sdB star
Stable modes
Unstable modes
Fontaine et al. (2006;
Mem. S. A. It. 77, 49)
log HB age(years)
No relativistic effects Including relativistic effects
Relativistic electrons in the Sun
Elliot & Kosovichev (1998; ApJ 500, L199)
Inferred solar internal rotation
Base of
convection
zone
Tachocline
Near solid-
body
rotation of
interior
Required precision
Strassmeier: Signal amplitude Signal precision Asteroseismic equivalent: Effect on frequency Frequency error
Diagnostics of a small convective core
1.3 M¯
0.25 Gyr
5.25 Gyr
Cunha & Metcalfe (2007; ApJ 666, 413)
Beck et al.
(2012; Nature, 481, 55)
Frequency
Po
we
r
Into the heart of a giant Fine structure ¢P: core structure
l = 1 l = 2
l = 0
Red giants: adiabatic frequencies
Dziembowski et al. 2001; Christensen-Dalsgaard, 2004
Eggenberger et al. 2010; Dupret et al 2010; Mazumdar et al. 2010
Modes trapped in the envelope (low E)
acoustic dominant
character
Modes trapped in the center
(high E)
g dominant character
Montalbán
Period spacing in red giants
Core Helium
burning phase
H-shell burning
RGB
Bedding et al. 2011
Kepler
CoRoT Mosser et al. 2011
Montalbán
KIC7341231, an unevolved red giant
[Fe/H] = -1 M/M¯ = 0.836 R/R¯ = 2.62 Age = 12.2 Gyr
Deheuvels et al. (2012; ApJ 756, 19)
Fitted rotational splittings
Solid-body rotation /2¼= 328 nHz Two-zone model Convective envelope, radiative core c/2¼= 696 nHz e/2¼= 51 nHz
Deheuvels et al. (2012; ApJ 756, 19)
Into the heart of a giant Fine structure
core structure
Hyperfine
structure
Core rotation
Beck et al.
(2012; Nature, 481, 55):
Core rotates at least
at 10 times
the surface rate
Frequency
Pow
er
Fitting individual frequencies
• Characterize model by set of parameters
– P = {M, age, Z0, Y0, ®ML, ®OV, …}
• Compute frequencies
• Minimize
• If min(χ2) >> 1 something is wrong with
– Model: interesting
– Data errors: a little boring
Dealing with large χ2: inversion?
• No adequate model within the given set, specified by the parameters
• Determine corrections to best-fitting model
• Identify origin of discrepancies in physical terms
Challenges
• Improve stellar modelling
• Develop probes that are sensitive to potential problems with the stellar models
– Location of glitches
– Frequency region of unstable modes
• Test the significance of identified problems
• Provide additional observational data, further to constrain the models
Prospects
• Improved asteroseismic data: more accurate frequencies, modes at lower frequencies, broader range of stars – Further extend CoRoT and Kepler
– BRITE
– TESS?
– PlanetVision?
– PLATO?
– SONG
Prospects
• Improved asteroseismic data: more accurate frequencies, modes at lower frequencies, broader range of stars – Further extend CoRoT and Kepler
– BRITE
– TESS?
– PlanetVision?
– PLATO?
– SONG
2012
2013