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

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

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