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 Roma 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 > N 2, L 1 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 ⊙ T eff = 5025 K, log(L/L ⊙ ) = 1.96 Huge restoring force by buoyancy Non-radial modes are 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 in the envelope Trapped in the 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 Stochastic power Damping rate Inertia Stochastic excitation 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 q q Large variations of the temperature gradient Large radiative damping In a cavity with short wavelength oscillations : Significant for models with huge N 2 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 modes are resolved : Mode profiles in the power spectrum Mode physics in Red Giants Amplitude = area !  Mode profile Height in the power spectrum If the modes are 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 burning Lifetimes Lifetime = Oscillatory behaviour due to mode trapping No radiative damping 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: Complex spectrum 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 M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning Lifetimes 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 burning Work integrals Convective damping near the surface Radiative damping in the 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 burning Height 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 M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning Lifetimes C : High luminosity model in the red giant branch

High luminosity model in the red giant branch Height in the power spectrum Negligible height for non-radial modes Not detectable M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning Height in PS Huge radiative damping of most non-radial modes C : High luminosity model in the red giant branch

Predicted power spectrum Regular spectrum similar 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 branch Conclusions:

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 star evolves Most radiative damping occurs at the top of the pure Helium core

Mode physics in Red Giants Kinetic energy :  |  r| 2 Huge number of nodes in the core Gravity EVANEEVANE Acoustic SCENTSCENT 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 / Height 1/2

Helium burning M=3 M ¯, Log(L/L ¯ )=2, He burning Life-times/Inertia / Height 1/2

Asymptotic treatment Final numerically improved version of MAD : Full numerical results close to asymptotic-numerical Numerical improvements Numerator in the core Denominator in 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 artificially the frequency resolution could be a tool allowing to 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, =  Hz Mode trapped in the envelope, =  Hz d E K /d log T

Eigenfunctions with many nodes in the g-mode cavity Very dense spectrum of non-radial modes !! Huge ! Solar-type modes : n g ~ 100 – 1000 !!! in the g-cavity Mode physics in Red Giants

Trapping and radiative damping Life-time = Envelope : Convective damping independent 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 Giants See also Dziembowski et al. (2001) Christensen-Dalsgaard (2004)

Intermediate model in the red giant branch Life-times/Inertia / Height 1/2 M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning  I Lifetimes/Inertia

Intermediate model in the red giant branch M=2 M ¯, Log(L/L ¯ )=1.8, pre-He burning Amplitude

Kinetic energy :  |  r| 2 Mode physics in Red Giants Huge number of nodes in the core Dense spectrum of non-radial modes G R A V I T Y EVANESCENTEVANESCENT A C O U S T I C

Work integral Huge radiative damping of 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 burning Amplitudes

How red giants differ from the Sun ? Sun Mode lifetimes do not depend on Pure acoustic modes, (radial component of displacement dominates everywhere) (for small )

High luminosity model in the red giant branch Only radial modes could 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 / Height 1/2 (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 / Height 1/2 (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 / Height 1/2 Work integral No radiative damping Mode trapped in the core, =  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 M=2 M ¯, Log(L/L ¯ )=2.1, pre-He burning Lifetimes C : High luminosity model in the red giant branch

High luminosity model in the red giant branch Amplitude Very small amplitudes for non-radial modes Huge radiative damping of most non-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