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. Dupret LESIA, Paris Observatory, France A. Grigahcène Algiers, Algeria
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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.
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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
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Driving mechanism and energetic aspects in Doradus stars
ExcitationAmplitudeand phases
Mode identification
Workshop: « Doradus stars in the COROT fields »Nice, 26-28 May, 2008
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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
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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
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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
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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
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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
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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
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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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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
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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
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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
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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
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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
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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
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
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Hybrid Sct – Dor Work integral
p2
p1
g1
g2
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
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
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
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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
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Hybrid Sct – Dor Work integral
g21
g30
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
g30
g35
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
g30
g35
g40
Work integral : = 1
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 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
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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
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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
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• 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
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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
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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