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Theoretical Interpretation of Power Spectra of Stellar Oscillations

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1 Theoretical Interpretation of Power Spectra of Stellar Oscillations
H.Ando National Astronomical Observatory of Japan 9th, December, 2004

2 1. Observed Power Spectra of Stellar Oscillations
Procyon(F5 subg) Kambe (2000) Sun, αCen A, βHyi(G2 subg), η Boo(G0 subg), ξ Hya(G7 g) Bedding and Kjeldsen (2003) PASA, 20,

3 Spectrum of Procyon on 25,26,27,28, and 29, Dec., 2000

4 Summed spectrum of Procyon
on 25, 28, and 29, Dec., 2000

5 Power Spectra

6 Charactristics of Spectra
・shape of envelope (peak freq.) ・Asymptotic Formula Large separation Small Separation

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8 Newly recognized points
・Not a simple distribution of amplitudes ・Deviation from equal spacing pattern

9 2. Theoretical background of Oscillations
・Radial Pulsation (l=0) acoustic modes(n=0,1,2,....) fn(r) ・non-radial oscillation(l≠0) acoustic modes (p-mode) (n,l,m) gravity modes (g-mode)(n,l,m) fn(r)Ylm(θ,φ)

10 Propagation diagram in Stars
ex. Procyon M=1.42 M⦿ (Prieto et. al 2002) #1(ZAMS) #51 (Procyon; L=7L⦿, Te=6530) #211(giant; L=7.7L⦿, Te=4490) Observed parameters of Procyon L= 7.04L⦿ , Te= 6530

11 Propagation diagram for #1
E-07 E-07 E-07 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-05 E-05 E-04 E-04 E-01 E-01 P G P G

12 E-06 E-06 E-06 E-06 E-06 E-06 E-04 E-06 E-06 E-06 E-06 E-06 E-06 E-06 E-04 E-06 E-06 E-06 E-06 E-03 E-06 E-06 E-03 E-06 E-06 E-03 E-06 E-04 E-05 E-05 E-05 E-04 E-04 E-04 E-04 P G P G

13 E-05 E-06 E-05 E-04 E-05 E-05 E-04 E-05 E-05 E-04 E-04 E-05 E-05 E-04 E-04 E-05 E-04 E-04 E-04 E-05 E-05 E-04 E-03 E-04 E-05 E-04 E-03 E-03 E-04 E-05 E-04 E-03 E-03 E-04 E-04 E-04 E-03 E-03 E-03 E-03 E-04 E-04 G P G P

14 Interaction bet ween Two potential wells
・ZAMS: Almost independent

15 ・Advanced Evolution stage:
Mixed character Avoided Crossing

16 Mixed Mode

17 3. Prediction of Power Spectra
Basic assumptions ・Power ∝ (Input Energy)/(Kinetic Energy of mode), where KE is estimated with radial displacement, say(δr/r=1.0), at the surface. ・Input Energy Continuous spectrum by turbulent convection (Kolmogorov spectrum) We give Power ∝ f^n/(KE) n=2 : flat input energy (say, 1m/s at the surface) n=-2: Kolmogorov type input energy

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24 Summary ・There are pulsation modes (l=0) beyond Cut-off frequency
・There are practical cut-off in lower end due to existence of g-modes’ territory ・Larger interaction of p-modes and g-modes in l=1 -modes with smaller amplitudes in mixed modes -frequencies of modes(l=1) shifted to modes with l=0 in lower frequency region

25 A possible suggestion Quantitative analysis of the Oscillation spectrum of ηBoo Guenther AJ, 612, , 2004

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