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


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


Trapped inthe envelope

Trapped inthe core

See also Dziembowski et al. (2001) Christensen-Dalsgaard (2004)


Stochastic excitation (top of the convective envelope)


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.


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


T> 0

T<0

qq

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


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


Resolved modes: same H

Height in power spectrum

Unresolved:

Complexspectrum for l=1 modes !




Predicted power spectrum


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


Lifetime =




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



The detectable modes have p-modes asymptotic pattern

M=2 M¯, Log(L/L¯)=1.8, pre-He burningHeight in PS


Model at the bottom of red giant branchB : Intermediate model in the red giant branch


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


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




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



Regular spectrumsimilar to main sequence stars


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


Kinetic energy : |r|2

Huge number of nodes in the core

Gravity

EVANE Acoustic

SCENT

KINETIC ENERGY


Very dense spectrum

of non-radial modes


Mode life-times


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


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


Resolved

Not resolved


Decreasing artificiallythe frequency resolutioncould be a tool allowingto filter the radial modes


Height in power spectrum

The detectable modes follow p-modes asymptotic relations

M=3 M¯, Log(L/L¯)=2, Helium 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


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)



M=2 M¯, Log(L/L¯)=1.8, pre-He burningI

Lifetimes/Inertia


M=2 M¯, Log(L/L¯)=1.8, pre-He burningAmplitude

Kinetic energy : |r|2


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




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




Lifetimes/Inertia/ Height1/2 (if resolved)

Lifetime =

I





Work integral

No radiative damping

Mode trapped in the core, = 201.3 Hz




Mode life-times

Mode life-times




Amplitude

Very small amplitudesfor non-radial modes

Huge radiativedamping of mostnon-radial modes



Very dense spectrum of non-radial modes !!

= 0

= 1

= 2

Pre-Helium burning Red Giant


Excitation and damping of oscillation modes in red-giant stars Marc-Antoine Dupret, Université de...

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