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Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
1
Driving mechanism and energetic aspects of pulsations
in Doradus stars
A. Miglio J. Montalban
Liège, Belgium
M.-A. DupretLESIA, Paris Observatory, France
A. Grigahcène
Algiers, Algeria
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
2
Driving mechanism and energetic aspects in Doradus stars
ExcitationAmplitudeand phases
Mode identification
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
3
Convection and partial ionization zones Doradus starsInternal physics:
•1 convective core•1 convective envelope
He an H partial ionization zonesare inside the convective envelope
Fc/F
rad = (Γ3-1) / 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
4
Driving mechanism Doradus stars
Main driving occurs in the transition region where the thermal relaxation time is of the same order as the pulsation periods
For a solar calibrated mixing-length, the transition region for the g-modes is near the convective envelope bottom.
Quasi-adiabaticregion
Non-adiabaticregion
g50
Log(th)
S 0
Coupling between
• the dynamical equations and
• the thermal equations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
5
Driving mechanism Doradus
Flux blocking at the base of the convective envelope
Motor thermodynamical cycle
t i tml e e )( Y)( )( ,rr t , , r,r
M
0 d
M
0 d
d d
2
1
22r
m r
mm
LTT
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
6
Driving mechanism Doradus
M = 1.6 M0 , Teff = 7000 K , = 2 , Mode =1, g50
Flux blocking at the base of the convective envelope
Motor thermodynamical cycle
Work integral Luminosityvariation
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
7
Driving mechanism DoradusM = 1.6 M0
Teff = 7000 K = 2Mode =1, g50
Role of time-dependent
convection
c : Life-time of convective elements: Angular frequency
Log ( c )
Fc / F
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
8
Convection – pulsation interaction
3-D hydrodynamic simulations
All motions are convective ones
In particular the p-modes(present in the solution)
Nordlund & SteinSamadi, Belkacem (Meudon)
Analytical approach
Separation between convection and pulsationin the Fourier space of turbulence
Convective motions:short wave-lengths
Oscillations:long wave-lengths
1. Static solution without oscillations
2. Stability study of this solution
Perturbation Oscillations
Gough´s theory Gabriel´s theory
MLT
Gabriel´s theory
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hydrodynamic equations
Mean equations Convective fluctuations equations
Equations of linear non-radial
non-adiabatic oscillationsCorrelation terms
PerturbationPerturbation
Convection – pulsation interaction: Gabriel´s theory
• Convective flux• Reynolds stress• Turbulent kinetic energy dissipation
Perturbation of
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
10
Radiative luminosity Convective luminosity
Turbulent pressure
Turbulent kineticenergy dissipation
Convection – pulsation interaction: Work integral
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
11
Driving mechanism Doradus
WFRr: Radial radiative
flux term
M = 1.6 M0
Teff = 7000 K = 2Mode =1, g50
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
12
Driving mechanism Doradus
WFRr: Radial radiative
flux term
WFcr: Radial convective
flux term
M = 1.6 M0
Teff = 7000 K = 2Mode =1, g50
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
13
Driving mechanism DoradusM = 1.6 M0
Teff = 7000 K = 2Mode =1, g50
WFRr: Radial radiative
flux term
WFcr: Radial convective
flux term
Wpt: Turbulent pressure
W2: Turbulent kinetic
energy dissipation
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
14
Driving mechanism DoradusM = 1.6 M0
Teff = 7000 K = 2Mode =1, g50
WFRr: Radial radiative
flux term
WFcr: Radial convective
flux term
WFh: Transversal convective
and radiative flux
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
15
Driving mechanism DoradusM = 1.6 M0
Teff = 7000 K = 2Mode =1, g50
WFRr: Radial radiative
flux term
WFcr: Radial convective
flux term
Wtot: Total work
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Instability strips Doradus
= 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Instability strips Doradus
= 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Unstable modes Doradus
Dor g-modes
Sct p-g modes
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Unstable modes Doradus
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Unstable modes Doradus
Period range decreases with
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
21
Unstable modes Doradus
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Unstable modes Doradus
Key point: Location of the convective
envelope bottom
Instability region verysensitive to the effective
temperature and thedescription of convection
(, …)
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct –
Dor
Comparison : Sct red edge (=0, p1) Dor instability strip (=1)
HD 209295 Handler et al.
(2002)Tidally excited ?
HD 8801Henry et al. (2005)Am star
HD 49434
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Dor g-modes
Sct p-g modes
Unstable modesHybrid Sct – Dor
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Unstable modes
Stableregions
Hybrid Sct – Dor
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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HD 49434
HD 49434
Hybrid Sct – Dor
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Unstable modes (HD 49434)
2 4 20 400.5
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral : = 1
p2
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
p2
p1
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
p2
p1
g1
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
31
Hybrid Sct – Dor Work integral
p2
p1
g1
g2
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
32
Hybrid Sct – Dor Work integral
p2
p1
g1
g2
g3
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
33
Hybrid Sct – Dor Work integral
p2
p1
g1
g2
g3
g4
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
p2
p1
g1
g2
g3
g4
g6
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
g6
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
g6
g8
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
g6
g8
g10
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
g6
g8
g10
g12
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
g6
g8
g10
g12
g15
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
40
Hybrid Sct – Dor Work integral
g6
g8
g10
g12
g15
g21
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
g21
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integral
g21
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
43
Hybrid Sct – Dor Work integral
g21
g30
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
44
Hybrid Sct – Dor Work integral
g21
g30
g35
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
45
Hybrid Sct – Dor Work integral
g21
g30
g35
g40
Work integral : = 1
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
46
Hybrid Sct – Dor Work integralWork integral
= 1 , g6
= 1 , g25
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Radiative damping mechanism
Growth-rate
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Radiative damping mechanism
Growth-rate
< 0
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralPropagation diagrams
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralPropagation diagrams
g-mode cavity Evanescent
g-mode p-mode
g-mode cavity
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralAsymptotic behaviour
In propagation regions : 2 < N2 , L2
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralAsymptotic behaviour
In evanescent regions : L2 < 2 < N2
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralEigenfunctions behaviour
= 1 , g25
Small amplitudeIn the g-mode cavity
Large amplitudeat the bottom of theconvective envelope
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralEigenfunctions behaviour
= 1 , g25
Radiative dampingnegligible
Significantdriving
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralEigenfunctions behaviour
= 1 , g6
Large amplitudein the g-mode cavity
Smaller amplitudeat the bottom of theconvective envelope
EVANESCENT
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
56
Hybrid Sct – Dor
= 1 , g6
Eigenfunctions behaviour
Significantradiative damping
Drivingnegligible
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralWork integral
= 1 , g6
= 1 , g25
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Unstable modes (HD 49434)
2 4 20 400.5
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralPropagation diagrams
= 1
= 2
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Hybrid Sct – Dor Work integralPropagation diagrams
=2, g25
= 1
= 2
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
61
Spectro-photometric amplitudes and phasesand mode identification
Doradus
Phase-lags
Line-profile variations
Moment method
Amplitude ratios
Very sensitive to the non-adiabatictreatment of convection
Mode identification
Spectroscopy Photometry
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
62
• Distortion of the stellar surface described by the lagrangian displacement of matter
• Temperature :
• Flux :
• Limb darkening :
lnln
lnln
lnln
e
e
eff
eff
eff
T
gg
gT
TT
TT
TT
e
e
eff
eff
eff ln
ln
ln
ln
g
g
g
F
T
T
T
F
F
F
lnln
lnln
lnln
e
e
eff
eff
eff
h
gg
gh
TT
Th
hh
• Thermal equilibrium in the local atmosphere
Hypotheses
Photometric amplitudes and phasesand mode identification
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
63
Non - adiabaticcomputations
Influence of the local effective temperature
variations
Influence of the localeffective gravity
variations
Equilibriumatmosphere models
Stellar surfacevariation
)( cos ln
ln
ln
ln
) ( cos ln
ln
ln
ln )( cos )2)(1(
)(cos 10ln
2.5
e
e
eff
eff
eff
eff
tg
g
g
b
g
F
tT
T
T
b
T
Ft
bi Pm
T
m
Filters Integration on the pass-band
Linear computations Amplitude ratios and phase differences
Dependence with the degree Identification of
Monochromatic magnitude variation
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Multi-colourphotometricObservations
Amplitude ratios& Phase lags
Range of frequencies
Mode identificationRange of frequencies
Non-adiabatic asteroseismology
Improving the fit
Stellar parameters
Scuti
Doradus
Cephei
SPB
Convection
Chemical composition
Atmosphere models - Limb darkening
Time-dependence
Mixing Length ()
Full spectrum
Non-adiabaticcomputations
Equilibrium models,Stellar evolution code
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
65
Spectro-photometric amplitudes and phasesand mode identification
Very sensitive to the non-adiabatictreatment of convection
Time-dependent convection
Frozen convection
Phase-lag
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Frozen convection Time-dependent convection
-mechanism Not allowed by time-dependent convection
Spectro-photometric amplitudes and phasesand mode identification
Very sensitive to the non-adiabatictreatment of convection
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Doradus
3 frequencies: f1=1.32098 c/d, f2=1.36354 c/d, f3=1.47447 c/d
Balona et al. 1994 Strömgren photometry
Balona et al. 1996Simultaneous photometryand spectroscopy
Spectroscopic mode identification: (1, m1) = (3, 3),(2, m2) = (1, 1),(3, m3) = (1, 1)
Spectro-photometric amplitudes and phasesand mode identification
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
68
Doradus
Balona et al. 1996Simultaneous photometryand spectroscopy
Phase-lag ( Vmagnitude – displacement ):
Observations: 1 = - 65° ± 5° 3 = - 29° ± 8°
Theory: Time-dependent convection Frozen convection( = 2) = - 30° = - 165°
Spectro-photometric phase differences
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Photometric mode identification Doradus
Fro
zen
= 2 - MLT = 1 - MLT
Tim
e-de
pend
ent
Best models: Time-dependent convection = 1 modes
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
70
Influence of the effective temperaturevariations
Influence of the effective gravity variations
)( cos ln
ln
ln
ln
) ( cos ln
ln
ln
ln )( cos )2)(1(
)(cos 10ln
2.5
e
e
eff
eff
eff
eff
tg
g
g
b
g
F
tT
T
T
b
T
Ft
bi Pm
T
m
Importance of ultraviolet observations(bracketing the Balmer discontinuity)
Gravity derivatives vary quickly in u-v
Changes the weight of Teff and ge terms
Helps for the mode identification and
gives constraints on | Teff/Teff|
Stromgren, Genevasystems are perfects
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Conclusions
• Driving mechanism:
Main driving due to convective blocking at the base of the convective envelope
Time-Dependent convection does not inhibits the mechanism
Driving mechanism and energetic aspects in Doradus stars
The size of the convective envelope is the key point) predictions very sensitive to the treatment of convection
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Conclusions
• Mode identification, multi-color amplitudes and phases:Time-Dependent Convection required, gives constrain on :
• Convective envelope• Interaction convection – oscillations• Atmosphere models
Mode identification and non-adiabaticasteroseismology of Doradus stars
• Hybrid Scuti - Doradus• Driving at the bottom of the convective envelope• Radiative damping, deep in the g-mode cavity
Instability ranges depend on:• Location of convective envelope• Spherical degree • Local wave-length ) Brunt-Vaisala, Lamb frequencies
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Doradus Stabilization mechanism
Radiative dampingin the g-modes cavity
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Doradus Stabilization mechanism
Radiative dampingin the g-modes cavity
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Comparison : Sct red edge (=0, p1) Dor instability strip (=1)
= 1.8
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Stabilization mechanism Doradus
WFRr: Radial radiative
flux term
M = 1.6 M0
Teff = 7000 K = 2Mode =1, g50
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Unstable modes Doradus
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Unstable modes Doradus
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Unstable modes Doradus
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Non-adiabatic stellar oscillations: utility
Excitation mechanisms Mode identification
Solar-like oscillations
Unstable modes: growth rates
Stable modes: damping rates Line-widths in the power spectrum
Observations
Stochastic excitation models Amplitudes
Stable modes: damping ratesStable modes: damping rates
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Radiative luminosity Convective luminosity
Turbulent pressure
Turbulent kineticenergy dissipation
Convection – pulsation interaction: Work integral
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Solar-type oscillations
Difficulties : 1. Treatment in the efficient part of convection
Very short wave-length oscillations of the eigenfunctions
Local treatment
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Difficulties: 1. Treatment in the efficient part of convection
Origin of the problem:
dm
LdsTi C
dssd
i
LLL
C
CC
1
0 (...) 2
sidr
sdi
lC2
2
C
)/exp( )/exp( 2 lriclric ... s cc1
Wavelength much shorter than the mixing-length !
Solar-type oscillations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Difficulties: 1. Treatment in the efficient part of convection
Non-local (Balmforth 1992) Local (Gabriel 2003)
Introduction of new free parameters
Solutions
Solar-type oscillations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Difficulties: 1. Treatment in the efficient part of convection
Solutions
1
22
RRC FF
VsTVsT
Ts
1
C
CC
CC ssss
0 (...) (
2
sidr
sdi
lC2
2
C
Local (Gabriel 2003)
Solar-type oscillations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Difficulties: 2. Treatment of turbulent pressure perturbation
Increases the order of the system
Very stiff problem at the boundaries
Numerical instabilities
Solar-type oscillations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Models of stochastic excitation
• The Sun is a vibrationally stable oscillator.• Excitation of the mode is due to stochastic forcing coming from turbulent convective motions.
IP
Vs 2
Non-adiabatic models
Damping rate:
Stochastic models
Acoustical noise generation rate: P
Velocity
Theory
ObservationsLine-widths Observed amplitudes
Solar-type oscillations: confrontation to observations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Theoretical damping rates ↔ line-widths observed by BiSON (Chaplin et al. 1997)
Solar-type oscillations: confrontation to observations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Theoretical damping rates ↔ line-widths observed by BiSON (Chaplin et al. 1997)
Solar-type oscillations: confrontation to observations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Theoretical damping rates ↔ line-widths observed by BiSON (Chaplin et al. 1997)
Solar-type oscillations: confrontation to observations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Theoretical damping rates ↔ line-widths observed by BiSON (Chaplin et al. 1997)
Solar-type oscillations: confrontation to observations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Scuti Stables and unstable modes
Time-dependent convection
p7
p6
p4
p5
p3
g1
f
p1
p2
g2g3g4 g6 g8
Frozen convection
p7
p6
p4
p5
p3
g1
f
p1
p2
g2g3g4 g6 g8
= 2 - 1.8 M0 - = 1.5
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Scuti Instability strips
Radial modes
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Scuti Instability strips
= 2 modes
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Photometric amplitudes and phases
=0=1
=3
=2
=2
=3
=0=1=2
=3
phase(b-y)-phase(y) (deg) phase(b-y)-phase(y) (deg)
Amplitude ratios vs. phase difference - Stroemgren photometry
= 0.5 = 1
Scuti
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Conclusions
Damping rates Line-widths
Convection-pulsation interaction in solar-like stars
Efficient part of convective envelope
Local treatment → Spatial oscillationsof the eigenfunctions→ Introduction of a freeparameter in the perturbationof the closure equations
Perturbation of turbulent pressure
→ Numerical instabilities
AmplitudesStochasticexcitation
We found a model fitting theobserved damping rates but …
Theoretical difficulties Confrontation to observations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Oscillations de type solaire
Taux de d´amortissement confrontables aux observations (largeurs de raie)
Mécanisme d´excitation : Excitation stochastique
Oscillateur vibrationellement stableforcé stochastiquement par la convection
Contrainte sur les modèles non-adiabatiquesd´intéraction convection-oscillations
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Oscillations de type solaire
Difficulté des modèles non-adiabatiques:intéraction convection-oscillations
Grande enveloppe convectiveConvection efficace ( tc >> tp )
Oscillations spatiales non-physiquesdes fonctions propres
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Oscillations de type solaire
Difficulté des modèles non-adiabatiques:intéraction convection-oscillations
Grande enveloppe convectiveConvection efficace ( tc >> tp )
Oscillations spatiales non-physiquesdes fonctions propres
Solutions
Non-locales (Balmforth 1992) Locales (Gabriel 2003)
Introduction de paramètres libres supplémentaires
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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1
22
RRC FF
VsTVsT
Ts
Oscillations de type solaire
Difficulté des modèles non-adiabatiques:intéraction convection-oscillations
Grande enveloppe convectiveConvection efficace ( tc >> tp )
Oscillations spatiales non-physiquesdes fonctions propres
Solutions
Locales (Gabriel 2003)
1
C
CC
CC ssss
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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Conclusions
Mécanismes d’excitation
Bandes d’instabilité
Amplitudes et phasesphotométriques
Identification des modes
Astérosismologienon-adiabatique
Astérosismologie“classique” (fréquences)
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Mécanismes d’excitation
Conclusions
Amplitudes et phasesphotométriques
Bandes d’instabilitéAstérosismologienon-adiabatique
Identification des modes
Mécanisme (Fe) Contraintes sur lamétallicité
Marchetrès bien
Idem Idem OK mais effetde la rotation ?
Cephei
Modes p
SPB
Modes g
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Mécanismes d’excitation
Conclusions
Amplitudes et phasesphotométriques
Bandes d’instabilitéAstérosismologienon-adiabatique
Identification des modes
Frontière bleue: mécanisme (HeII)Frontière rouge: convection
Contraintes sur lesmodèles de convection et d’intéractionconvection - pulsation
Bon accordavec solaire
IdemNettement mieuxavec l’intéraction convection-pulsation
OK mais restedifficile
Effet de larotation ?
Scuti
Modes p
Dor
Modes g
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Conclusions
Type solaire
Modes p
Mécanismes d’excitationAmplitudes et phases
photométriques
Excitation stochastique,modélisation difficile de l’intéraction convection – oscillations
Amplitudes données parles modèles d’excitation stochastique.
Grands espoirs futurs :
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Oscillations de type solaire
Difficulté des modèles non-adiabatiques:intéraction convection-oscillations:
Solutions
Non-locales (Balmforth 1992) Locales (Gabriel 2003)
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Scuti Taille de l´enveloppe convective pourdifférentes températures effectives
Teff=8345.5 K
Teff=6119.5 K
M=1.8 M0, α=1.5
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Teff / Teff|
Longueur de mélange - différents - convection gelée
Sensibilité à la structure de l´enveloppe convective
Scuti Amplitudes et phases photométriques
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Photométrie multi-couleur et astérosismologie non - adiabatique
Observations en photométrie
multi-couleur
Rapports d´amplitude& déphasages
Modèles d´équilibreCode d´évolution stellaire
Calculs non-adiabatiques
Identification de mode
Paramètres stellaires
Scuti
Doradus
Cephei
SPB
Convection
Metallicité (Z)
Modèles d´atmosphère - Limb darkening
Mixing length ()
Hydrodynamique
FST
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Full Spectrum of Turbulence Longueur de mélange
Teff / Teff|
Amplitudes et phases photométriques Scuti
Sensibilité à la structure de l´enveloppe convective
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Amplitudes et phases photométriques Scuti
Full Spectrum of Turbulence Longueur de mélange
= 3 = 3
= 2
= 2 = 1
= 1 = 0
= 0
Q = 0.015 d Q = 0.033 d
Rapport d´amplitude vs. Différences de phase - photométrie Stroemgren
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Doradus
• Types spectraux
F
• Masses
+/- 1.5 M0
• Périodes
0.3 à 3 jours
modes g
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Doradus Amplitudes et phases photométriques
Comparaison : convection gelée convection dépendant du temps
M = 1.5 M0 - Teff = 7000 K - = 1.8
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Type solaire
• Types spectraux
F et G
• Masses
1 M0 à 1.5 M0
• Périodes
Quelques minutes
Modes p élevés
Faibles amplitudes
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• Excitation mechanisms
Photometric amplitudesand phases in different filters
Identification of the degree
Non - adiabaticasteroseismology
Non adiabatic oscillationsat the photosphere
Need of a non - adiabatic codefor the confrontation between theoryand observations
Utility of our non - adiabatic code
• Multi-colour photometry
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Introduction
Stellar pulsations
• Pressure modes
Acoustic waves
• Gravity modes
Buoyancy force
Asteroseismology
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stellar oscillations Non - radial non - adiabatic
Splitting in spherical harmonics
Non - radial
p - modes Acoustic waves
g - modes Buoyancy force
1)
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stellar oscillations Non - radial non - adiabatic
S 0
non - adiabatic
Coupling between the dynamical thermaland equations
• Equation of momentum conservation
• Equation of mass conservation
• Poisson equation
dynamical
• Equations of transfer by radiation and convection
thermal
• Equation of energyconservation
1)
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)( cos ln
ln
ln
ln
) ( cos ln
ln
ln
ln )( cos )2)(1(
)(cos 10ln
2.5
e
e
eff
eff
eff
eff
tg
g
g
b
g
F
tT
T
T
b
T
Ft
bi Pm
T
m
Stellar surfacedistortion
Influence of the local effective temperature
variations
Influence of the localeffective gravity
variations
Equilibriumatmosphere models
(Kurucz 1993)
Monochromatic magnitude variation
Non - adiabaticcomputations
Filters Integration on the pass-band
Linear computations Amplitude ratios and phase differences
Dependence with the degree Identification of
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4.2 Scuti Time dependent convection - MLTTheory of M. Gabriel
Red edge of the instability strip
Time-dependent convectionFrozen convectionRadial modes – 1.8 M0 , = 1.5
p7
p6
p5
p4
p3
p2
p1
p8
p7
p6
p5
p4
p3
p2
p1
p8
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4.2 Scuti Red edge of the instability strip
Time-dependent convection = 2 modes – 1.8 M0 , = 1.5
Frozen convection
p7
p6
p5
p4
p3
p2
p1
fg1g2
g3 g4 g5 g6 g7 g8 g9 g10
p7
p6
p5
p4
p3
p2
p1
fg1g2
g3 g4 g5 g6 g7 g8 g9 g10
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p7
p2
p3
p4
p5
p6
g2
g1
fp1
g7 g8g6
g4
g3
g5
Frozen Convection Time-dependent convection
p7
p6
p4
p5
p3
g1
fp1
p2
g2g3g4g5 g6 g7 g8
Figure 5 Figure 6
III. Instability StripIII. 1. δ Scuti stars
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Scuti Bandes d´instabilité
p7
p1
1.4 M0
2 M0
1.8 M0
1.6 M0
2.2 M0
= 1 - = 0
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Scuti Bandes d´instabilité
p7
p1
1.4 M0
1.6 M0
1.8 M0
2 M0
2.2 M0
= 0.5 - = 0
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Scuti Bandes d´instabilité
p6
fB
g7
fR
1.4 M0
2 M0
2.2 M0
1.8 M0
1.6 M0
= 1.5 - = 2
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Plan de l’exposé
1. Introduction
2. Oscillations stellaires non-adiabatiques : utilité
5. Conclusions
4. Applications • Cephei• Slowly Pulsating B• Scuti• Doradus• Type solaire
3. Modélisation du problème • Atmosphère• Convection
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Z
Teff / Teff|
Multi-colour photometry
Cephei
16 Lacertae
High sensitivity of thenon - adiabatic resultsto the metallicity
L / L|
Z = 0.015Z = 0.02Z = 0.025
Z = 0.015Z = 0.02Z = 0.025
U
B
A
A
U
V
A
A
Johnsonphotometry
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Modes excitation
Z > 0.016
Non-adiabatic constraints on the metallicity
4.1 Cephei : HD 129929
Unstable
Stable
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Contraintes sismiques sur l´overshooting
ov = 0.1 ± 0.05
ov= 0.1ov= 0.2
ov= 0
Instable
Stable
Cephei : HD 129929
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Excitation mechanism
M = 4 M0
Teff = 13 955 K
Z = 0.02
Mode = 1 g22
Work integral and luminosity variation from the centerto the surface of the star
Slowly Pulsating B stars
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Identification photométrique des modes
HD 74560 = 1
= 2
= 3
Slowly Pulsating B stars
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Excitation mechanism
Transitionzone
mechanism of excitation
Partial ionization zone of Helium II =
Opacity and thermal relaxation time from the center to the surface
Scuti
PS
ad
log (th)
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M = 1.8 M0
Teff = 7480 K
Z = 0.02 , = 1
Radial fundamental mode
Work integral and luminosity variation from the centerto the surface of the star
Scuti
Excitation mechanism
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Modes stables et instables Scuti= 0 - 1.8 M0 - = 1.5
p1
p8
p7
p6
p5
p4
p3
p2
Convection dépendant du tempsConvection gelée
p1
p8
p7
p6
p5
p4
p3
p2
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Mécanisme d´excitation :
Doradus
?? Bloquage convectif ?? (Guzik et al. 2000)
Travail intégré
M = 1.6 M0
Teff = 7000 K = 2Mode =1 , g47
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1.6 M0 - = 1 - = 1.5
Modes instables Doradus
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0vρtρ
Pp--vvρt
vρ
v-vvρUt
ρU
PF RN
Convection – pulsation interaction: Gabriel´s theory
0vρt
ρ
PΦ-ρρt
)(ρ
vvv
vv
PF-ρερU
t
ρURN
P: Pressure tensor ; p : its diagonal component.
Radiative Flux
XXX
RG
RG
pP
ppp
PPP
1
RF
Hydrodynamic equations
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Mean equations
RG
RGNCR
TRGTRG
ppVV
dtd
ppVFFdtsd
T
pppdtud
uρdtρd
2
2
2
21
0
TTpVV 1
RG ppV
2 Dissipation of turbulent kinetic energy into heat
Reynolds stress tensor
2rT Vp Turbulent pressure
Convection – pulsation interaction: Gabriel´s theory
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ssV
dt
sd
dt
sd
T
T
uVV
ppdt
Vd
Vdt
d
C
C
1
3
8
0
1
C
Convective efficiency
Life time of the convective elements
s
T
FF
s
T
FFVsTVsT
V
RRR
C
RR
CTRGTRG
22
3
8
CR 1
R Characteristic frequency of radiative energy lost by turbulent eddies
In the static case, assuming constant coefficients (Hp>>l !), we have solutions which are plane waves identical to the ML solutions.
Approximations of Gabriel’s Theory
Convective fluctuations equations
Convection – pulsation interaction: Gabriel´s theory
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Linear pulsation equationsPerturbation of the mean equations
0)1(
1 2
2 rr
lldr
rrdr
H
jrTj
T
rr
rp
AA
gdr
pd
dr
pd
drd
r
1211 turbg2
Equation of mass conservation
Radial component of the equation of momentum conservation
Transversal component of the equation of momentum conservation
r
r
r
rp
A
AViscHrp
rr HT
H
1212
A : Anisotropy parameterA=1/2 for isotropic turbulence
: Angular pulsation frequency
Convection – pulsation interaction: Gabriel´s theory
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Convection – pulsation interaction: Gabriel´s theory
Equation of Energy conservation
RG
HCR
CRHN
ppVFCH
rll
rr
Lrr
drdTrT
Lr
ll
dmLd
dmLd
dmdL
rr
llsTi
2
3
1
/41
1
FCH : Amplitude of the horizontal
component of the convective flux
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VsVsTT
TFF CC
Convective Flux : VsTFC
Perturbation :
Convective flux perturbation
efficient is convection where1
1
1 a
CCRC
CR7
i i
dssd
ll
cs
rr
drrd
rr
F
F
v
H
rC
rC
7654321
a a a a a a a
Convection – pulsation interaction: Gabriel´s theory
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r
r
VV
P
P
2
turb
turb
dssd
ll
cs
rr
drrd
rr
VV
v
H
r
r
7654321 b b b b b b b
Turbulent pressure :2
rVP turb
Perturbation :
Convection – pulsation interaction: Gabriel´s theory
Turbulent pressure perturbation
surface near the a
bC
77
i
P
P
HH
ll
Perturbation of the mixing-length
Hp Pressure scale height
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Convection – pulsation interaction: the Solar case
Difficulties: 2. Treatment of turbulent pressure perturbation
Local analysis tireXtrX ),( 0
...
... /
... /
ggp
pgg
ppbs/c
s/cpp
Movement
Transfer
Characteristic polynomial 0 (( 40 PP3
New terms = 0
New root: = 1/(b) ∞ at the convective boundaries
The worse numerical case givesthe best fits with observations
Re(1/(b)) < 0 at the left boundaryRe(1/(b )) > 0 at the right boundary
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Convection – pulsation interaction: the Solar case
Difficulties: 2. Treatment of turbulent pressure perturbation
The worse numerical case givesthe best fits with observations
Re(1/(b)) < 0 at the left boundaryRe(1/(b )) > 0 at the right boundary
Example:
z )1(
)1(2 22
2
xxix
dxdz
22 11
1exp)(
xx
ix
cxz
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Convection – pulsation interaction: the Solar case
Difficulties: 2. Treatment of turbulent pressure perturbation
The worse numerical case givesthe best fits with observations
Re(1/(b)) < 0 at the left boundaryRe(1/(b )) > 0 at the right boundary
Example:
z )1(
)1(2 22
2
xxix
dxdz
22 11
1exp)(
xx
ix
cxz
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Plan de l’exposé
1. Introduction
2. Convection-pulsation interaction
Plan of the presentation
1. Introduction
3. Confrontation to observations
2.1. The MLT theory of Gabriel
2.2. The case of solar-like oscillations
4. Conclusions
2. Convection-pulsation interaction
2.1. The MLT theory of Gabriel
2.2. The case of solar-like oscillations
3. Confrontation to observations
4. Conclusions
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Non-adiabatic stellar oscillations
Quasi-adiabaticregion
Non-adiabaticregion
S 0
Coupling between
• the dynamical equations
• the thermal equations
Introduction
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Theoretical damping rates ↔ line-widths observed by GOLF
Confrontation to observations
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Problem:
This solution fitting very well the observationsis subject to numerical instabilities near the upper
boundary of the convective envelope.
They come from the turbulent pressure perturbation term.
Confrontation to observations
Theoretical damping rates ↔ line-widths observed by GOLF
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Theoretical work integrals for different (mode l=0, p22)
Confrontation to observations
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Amplitudes et phases photométriques Scuti
Convection dépendant du temps
M = 1.8 M0 - Teff = 7150 K - = 0.5
Teff / Teff|
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Amplitudes et phases photométriques Scuti
Convection dépendant du temps
M = 1.8 M0 - Teff = 7130 K - = 1
Teff / Teff|
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Amplitudes et phases photométriques Scuti
Convection dépendant du temps
M = 1.8 M0 - Teff = 7150 K - = 1.5
Teff / Teff|
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Propagation cavities Doradus starsInternal physics:
High inertia of the g-modes near the
convective core top2
2 r 4 r
Main displacement isin the transversal direction
Small radial displacement
g50
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rT
r
r
r
p
A
Ag
dr
pd
dr
pd
dr
dr
12
11 turbg2
r
r
r
rp
A
Arp
rr HTh
H
1212
Radial component of the equation of momentum conservation
Transversal component of the equation of momentum conservation
A : Anisotropy parameterA=1/2 for isotropic turbulence
: Angular pulsation frequency
Influence of turbulent Reynolds stress perturbation
TTpVV 1 ),(Y ),( Y m
lhhmlr rT
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Work integral
Influence of turbulent Reynolds stress perturbation
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Pturb 0 and d Pturb / dr discontinuous
at the bottom of the convective envelope
singularity of the equations
unphysical discontinuity of the eigenfunctions
r
rVV
V
VVVV
V
VVVVPr
rr
r
rhhr
r
rhhr
d
d C (...)
d
d
1 (...)
hh2
2turb3
3h
Influence of turbulent Reynolds stress perturbation
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Non-local treatments:
PeVVVVb
hh log d d ; d 0
L0NL
Improves the things (continuity) but problem still present
r
rVV
V
VVVV
V
VVVVPr
rr
r
rhhr
r
rhhr
d
d C (...)
d
d
1 (...)
hh2
2turb3
3h
Influence of turbulent Reynolds stress perturbation
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Influence of Reynolds stress: Work integral
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Doradus
- d W / d log T
|L / L|
FR / F
W
For hot or small models:very thin convective envelope
the transition region is in the
radiative zone
Small -driving (Fe, ~ SPBs)compensated by
large radiative dampingbelow and above
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9 Aurigae
3 frequencies: f1=0.795 c/d, f2=0.768 c/d, f3=0.343 c/d
Zerbi et al. 1994Simultaneous photometryand spectroscopy
Spectroscopic mode id. : (1, |m1|) = (3, 1), Aerts & Krisciunas (1996) (3, |m3|) = (3, 1)
Spectro-photometric amplitudes and phases
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Aurigae
Balona et al. 1996Simultaneous photometryand spectroscopy
Phase-lag ( Vmagnitude – displacement ):
Observations: 1 = - 77° ± 12° 3 = - 41° ± 10°
Theory ( = 2): TDC = - 22° = - 39°FC = - 156° = - 140°
Spectro-photometric phase differences