Excitation and damping of oscillation modes in red-giant stars Marc-Antoine Dupret, Université de...
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Transcript of Excitation and damping of oscillation modes in red-giant stars Marc-Antoine Dupret, Université de...
Excitation and damping of oscillation modes in
red-giant stars
Marc-Antoine Dupret,
Université de
Liège, Belgium
Workshop Red giants as probes of the structure and evolution of the milky way
Academia Belgica Roma15-17 November 2010
K. Belkacem, J. De Ridder, J. Montalban, A.Miglio, R. Samadi, P. Ventura, H-G. Ludwig, A.Grigahcène, A.
Noels
- Mode physics in red giant stars
- Predictions for specific models
- Conclusions
Plan of the presentation
Subgiants Intermediate High luminosity
How red giants differ from the Sun from an acoustic point of view ?
Simple p-modes(2 > N2 , L1
2)
Sun
How red giants differ from the Sun ?
= 0
= 1
= 2
Regular frequency pattern ~ Asymptotic
Small separation Large separation
Sun
Helium burning Red Giant
Mode physics in Red Giants
3 M⊙ , 12.6 R⊙
Teff = 5025 K , log(L/L⊙) = 1.96
Huge restoring forceby buoyancy
Non-radial modesare mixed modes
Mode trapping
Mode physics in Red Giants
Trapped in the core
Trapped in the envelope
See also Dziembowski et al. (2001) Christensen-Dalsgaard (2004)
ENERGY density
M=2 M¯, Log(L/L¯)=1.8, pre-He burning
Mode trapping
Mode physics in Red Giants
Trapped inthe envelope
Trapped inthe core
See also Dziembowski et al. (2001) Christensen-Dalsgaard (2004)
M=2 M¯, Log(L/L¯)=1.8, pre-He burning
Stochastic excitation (top of the convective envelope)
Mode physics in Red Giants
Stochasticpower
Damping rate
Inertia
Stochasticexcitation model
Amplitude (velocity)
Reynolds stress
Entropy
Samadi et al. (2003, …)Belkacem et al. (2006, …)
Two types of terms :
Outermost part of the convective envelope
Main uncertainties : Injection length scale, kinetic energy spectrum
Houdek et al.
Mode physics in Red Giants
Coherent interaction convection-oscillations
Convective damping in the envelope
Very complex because : Convective time-scale
~ thermal time-scale
~ oscillation periods
Damping of the modes
See e.g. Gabriel (1996), Grigahcène et al. (2005), Balmforth et al. (1992)
Large uncertainties but …only depend on mode physics in the outermost part of the convective envelope
Not affected by mode trapping
Radiative damping in the core
Mode physics in Red Giants
T> 0
T<0
Large variations of thetemperature gradient
Large radiative damping
In a cavity with shortwavelength oscillations :
Significant for models with huge N2 in the core huge core-envelope density contrast
Affected by mode trapping
Similar heights for radial and resolved non-radial modes
If / I-1 :
If the modesare resolved :
Mode profiles in the power spectrum
Mode physics in Red Giants
Amplitude
= area !
Mode profileHeight in thepower spectrum
If the modesare not resolved :
If / I-1 :
Smaller heights for very long lifetime unresolved modes !
Models considered
3 M¯
2 M¯
Stellar evolution code : ATON (Mazzitelli, Ventura et al.)
A : Model at the bottom of red giant branch
M=2 M¯, Log(L/L¯)=1.32, pre-He burningLifetimes
Lifetime =Oscillatory behaviourdue to mode trapping
No radiativedamping
Dupret et al. (2009)
Model at the bottom of red giant branch
M=2 M¯, Log(L/L¯)=1.32, pre-He burning
Resolved modes: same H
Height in power spectrum
Unresolved:
Complexspectrum for l=1 modes !
A : Model at the bottom of red giant branch
Dupret et al. (2009)
Model at the bottom of red giant branch
Predicted power spectrum
A : Model at the bottom of red giant branch
Complex spectrum for l=1 modes !
l = 0
l = 2
l = 1
3 M¯
2 M¯
B : Intermediate model in the red giant branch
Intermediate model in the red giant branch
Mode life-times
Mode life-times
M=2 M¯, Log(L/L¯)=1.8, pre-He burningLifetimes
Lifetime =
B : Intermediate model in the red giant branch
Dupret et al. (2009)
Intermediate model in the red giant branch
Trapped in the envelope
Trapped in the core
M=2 M¯, Log(L/L¯)=1.8, pre-He burningWork integrals
Convectivedamping nearthe surface
Radiativedamping inthe core
B : Intermediate model in the red giant branch
Intermediate model in the red giant branch
The detectable modes have p-modes asymptotic pattern
M=2 M¯, Log(L/L¯)=1.8, pre-He burningHeight in PS
B : Intermediate model in the red giant branch
Model at the bottom of red giant branchB : Intermediate model in the red giant branch
Predicted power spectrum
Regular for l=0 and 2« Fine structures » of l=1 mixed modes
l = 0
l = 2
l = 1
3 M¯
2 M¯
An Helium burning model
Predicted power spectrum
An Helium burning model
Regular for l = 0 and 2« Fine structures » of l=1 mixed modes
l = 0
l = 2
l = 1
3 M¯
2 M¯
C : High luminosity model in the red giant branch
High luminosity model in the red giant branch
Mode life-times
Mode life-times
M=2 M¯, Log(L/L¯)=2.1, pre-He burningLifetimes
C : High luminosity model in the red giant branch
High luminosity model in the red giant branch
Height in the power spectrum
Negligible height fornon-radial modes
Not detectable
M=2 M¯, Log(L/L¯)=2.1, pre-He burningHeight in PS
Huge radiativedamping of mostnon-radial modes
C : High luminosity model in the red giant branch
Predicted power spectrum
Regular spectrumsimilar to main sequence stars
C : High luminosity model in the red giant branch
l = 0
l = 2
l = 1
2 M¯
A. Model at the bottom of red giant branch
3 M¯
Conclusions:
Complex spectrum (for l=1 modes)
3 M¯
2 M¯
B. Intermediate model in the giant branch
Regular for l=0 and 2, « Fine structure » for l=1
Conclusions:
3 M¯
2 M¯
Regular spectrum ~ main sequence stars
C. Intermediate model in the giant branchConclusions:
Very high potential of asteroseismology to probe the deep layers of red giants
Conclusions of the conclusions
Depending on the evolutionary status, very different kinds of spectra are predicted
Interpretation
Damping rate=
1 / Kelvin-Helmholtz
time
Radiative damping
as starevolves
Most radiative damping occurs atthe top of the pure Helium core
Mode physics in Red Giants
Kinetic energy : |r|2
Huge number of nodes in the core
Gravity
EVANE Acoustic
SCENT
KINETIC ENERGY
M=2 M¯, Log(L/L¯)=1.8, pre-He burning
Very dense spectrum
of non-radial modes
Intermediate model in the red giant branch
Mode life-times
M=2 M¯, Log(L/L¯)=1.8, pre-He burning
Inertia
3 M¯
2 M¯
Pre-Helium versus Helium burning
M=3 M¯, Log(L/L¯)=2, pre-He burning
Mode life-times
Pre-Helium
M=3 M¯, Log(L/L¯)=2, He burning
Helium burning
Mode life-times
Pre-Helium
M=3 M¯, Log(L/L¯)=2, pre-He burning
Life-times/Inertia/ Height1/2
Helium burning
M=3 M¯, Log(L/L¯)=2, He burning
Life-times/Inertia/ Height1/2
Asymptotic treatment
Final numerically improved version of MAD :
Full numerical results close to asymptotic-numerical
Numerical improvements
Numeratorin the core
Denominatorin the core
Damping rate
Model at the bottom of red giant branch
Resolved
Not resolved
M=2 M¯, Log(L/L¯)=1.32, pre-He burning
Decreasing artificiallythe frequency resolutioncould be a tool allowingto filter the radial modes
Intermediate model in the red giant branch
Height in power spectrum
The detectable modes follow p-modes asymptotic relations
M=3 M¯, Log(L/L¯)=2, Helium burning
Model at the bottom of red giant branch
M=2 M¯, Log(L/L¯)=1.32, pre-He burning
Mode trapped in the core, = 201.3 Hz
Mode trapped in the envelope, = 208.5 Hz
d EK/d log T
Eigenfunctions with many nodes in the g-mode cavity
Very dense spectrum of non-radial modes !!
Huge !
Solar-type modes : ng ~ 100 – 1000 !!!
in the g-cavity
Mode physics in Red Giants
Trapping and radiative damping
Life-time =
Envelope : Convective dampingindependent of
Core : Radiative damping
depends on and mode
trapping
Inertia : depends on and mode
trapping
Radiative damping
Life-time ~
Huge radiative damping:
Life-time depends on
Independent of trapping
Mode trapping
Mode physics in Red GiantsSee also Dziembowski et al. (2001) Christensen-Dalsgaard (2004)
Intermediate model in the red giant branch
Life-times/Inertia/ Height1/2
M=2 M¯, Log(L/L¯)=1.8, pre-He burningI
Lifetimes/Inertia
Intermediate model in the red giant branch
M=2 M¯, Log(L/L¯)=1.8, pre-He burningAmplitude
Kinetic energy : |r|2
Mode physics in Red Giants
Huge number of nodes in the core
Dense spectrum of non-radial modes
GRAV ITY
EVANESCENT
ACOUST IC
Work integral
Huge radiative dampingof most non-radial modes
Mode nearly trapped in the envelope = 22.8 Hz
High luminosity model in the red giant branch
M=2 M¯, Log(L/L¯)=2.1, pre-He burning
Model at the bottom of red giant branch
Amplitude
M=2 M¯, Log(L/L¯)=1.32, pre-He burningAmplitudes
How red giants differ from the Sun ?
Sun
Mode lifetimesdo not depend
on
Pure acoustic modes, (radial component of displacement dominates everywhere)
(for small )
High luminosity model in the red giant branchOnly radial modescould be observed !
I
Lifetimes/Inertia
M=2 M¯, Log(L/L¯)=2.1, pre-He burning
Model at the bottom of red giant branch
M=2 M¯, Log(L/L¯)=1.32, pre-He burning
Lifetimes/Inertia/ Height1/2 (if resolved)
Lifetime =
I
A : Model at the bottom of red giant branch
Model at the bottom of red giant branch
M=2 M¯, Log(L/L¯)=1.32, pre-He burning
Lifetimes/Inertia/ Height1/2 (if resolved)
Lifetime =
I
A : Model at the bottom of red giant branch
Model at the bottom of red giant branch
M=2 M¯, Log(L/L¯)=1.32, pre-He burning
Life-times/Inertia/ Height1/2
Work integral
No radiative damping
Mode trapped in the core, = 201.3 Hz
M=2 M¯, Log(L/L¯)=1.32, pre-He burning
A : Model at the bottom of red giant branch
High luminosity model in the red giant branch
Mode life-times
Mode life-times
M=2 M¯, Log(L/L¯)=2.1, pre-He burningLifetimes
C : High luminosity model in the red giant branch
High luminosity model in the red giant branch
Amplitude
Very small amplitudesfor non-radial modes
Huge radiativedamping of mostnon-radial modes
M=2 M¯, Log(L/L¯)=2.1, pre-He burning
C : High luminosity model in the red giant branch
Very dense spectrum of non-radial modes !!
= 0
= 1
= 2
Pre-Helium burning Red Giant
Mode physics in Red Giants