Theory of solar and stellar oscillations II

1
Theory of solar and stellar oscillations - II
Jørgen Christensen-Dalsgaard Institut for Fysik
og Astronomi, Aarhus Universitet Danish
AsteroSeismology Centre High Altitude Observatory
2
Functional analysis
3
Consequences
4
Near-surface frequency effects

• Stellar structure and oscillation modelling deal
  inadequately with
• Treatment of convection in modelling (thermal
  structure, turbulent pressure)
• Mode damping excitation
• Dynamical effects of convection on oscillations
• Atmospheric structure
• These effects are concentrated very near the
  surface

5
Effects on frequencies
6
Mode inertia
7
Example surface opacity change
8
Observed solar frequencies
9
Linearized numerical differences
Linearizing around a reference model, ? ?nl ?nl
(obs) - ?nl(mod)
10
Inverse problem for EOS
11
Kernels
12
Rotational splitting
13
Simple rotational splitting
14
Perturbation analysis
15
Rotational-splitting kernels
16
Kernels for rotational splitting
17
Kernels for rotational splitting
(5,2)
(20,8)
(20,17)
(20,20)
18
Spherically symmetric rotation
19
Kernels for spherically symmetric rotation
20
Mode damping or excitation
Note Convection enters in F Fr Fc
Likely conclusion in solar case (Gough
Balmforth Houdek et al.) observed modes are
linearly damped. Hence externally driven. (Rast
lecture.)
For selected other types of stars heat engine
works
21
Pulsating stars in the HR diagram
22
Asymptotics of low-degree p modes
23
Small frequency separations
Frequency separations
24
Asteroseismic HR diagram
25
Echelle diagram
26
Selected solar-like oscillators
Bedding Kjeldsen (2003)
27
? Bootis
28
Observed power spectrum
Kjeldsen et al. (1995)
29
Evolutionary state
30
Mode trapping
31
Mixed modes
32
Echelle diagram
? 0 ? 1 ? 2 ? 3
Di Mauro et al. (2003)
33
? Hydrae
34
? Hydrae
Stello et al.
35
Evolutionary state
Teixeira et al.
36
Mode trapping
37
? Hydrae
38
? Hydrae
39
? Hydrae
A / E-1/2
40
Semiregular variables
41
Semiregular variables
AAVSO observations. Mattei et al. (1997)
42
Statistics of stochastically excited oscillators
Energy is exponentially distributed. Hence
amplitude distribution is
43
4 1/2