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Theoretical Interpretation of Power Spectra of Stellar Oscillations

Explore power spectra characteristics and theoretical background of stellar oscillations, including radial and non-radial modes, with propagation diagrams and observed parameters. Predict power spectra based on basic assumptions.

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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, 203-212

  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

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

  8. 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)

  9. 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

  10. Propagation diagram for #1 36 36 0 2236.61 47.29 5.90E-07 35 35 0 2116.27 46.00 8.05E-07 34 34 0 1999.02 44.71 9.92E-07 33 33 0 1884.98 43.42 1.15E-06 32 32 0 1774.07 42.12 1.29E-06 31 31 0 1666.27 40.82 1.40E-06 30 30 0 1561.78 39.52 1.48E-06 29 29 0 1460.84 38.22 1.53E-06 28 28 0 1363.62 36.93 1.55E-06 27 27 0 1270.12 35.64 1.54E-06 26 26 0 1180.19 34.35 1.52E-06 25 25 0 1093.67 33.07 1.49E-06 24 24 0 1010.51 31.79 1.45E-06 23 23 0 930.78 30.51 1.42E-06 22 22 0 854.58 29.23 1.40E-06 21 21 0 781.89 27.96 1.40E-06 20 20 0 712.57 26.69 1.42E-06 19 19 0 646.44 25.43 1.46E-06 18 18 0 583.36 24.15 1.49E-06 17 17 0 523.35 22.88 1.51E-06 16 16 0 466.58 21.60 1.52E-06 15 15 0 413.22 20.33 1.50E-06 14 14 0 363.33 19.06 1.47E-06 13 13 0 316.95 17.80 1.41E-06 12 12 0 274.08 16.56 1.33E-06 11 11 0 234.74 15.32 1.25E-06 10 10 0 198.94 14.10 1.19E-06 9 9 0 166.66 12.91 1.23E-06 8 8 0 137.71 11.73 1.42E-06 7 7 0 111.79 10.57 1.91E-06 6 6 0 88.70 9.42 2.97E-06 5 5 0 68.21 8.26 5.43E-06 4 4 0 50.49 7.11 1.14E-05 3 3 0 35.37 5.95 2.91E-05 2 2 0 22.92 4.79 1.02E-04 1 1 0 12.80 3.58 7.99E-04 -1 0 1 4.23 2.06 6.11E-01 -2 0 2 1.97 1.41 7.14E-01 P G P G

  11. 25 25 0 1224.07 34.99 3.05E-06 24 24 0 1131.91 33.64 3.21E-06 23 23 0 1043.65 32.31 3.38E-06 22 22 0 959.17 30.97 3.48E-06 21 21 0 879.00 29.65 3.59E-06 20 20 0 802.57 28.33 3.83E-06 19 19 0 746.14 27.32 1.42E-04 18 19 1 728.52 26.99 4.35E-06 17 18 1 659.75 25.69 4.33E-06 16 17 1 593.52 24.36 4.72E-06 15 16 1 530.53 23.03 5.13E-06 14 15 1 470.90 21.70 5.54E-06 13 14 1 414.70 20.36 5.86E-06 12 13 1 362.18 19.03 6.03E-06 11 12 1 319.80 17.88 9.31E-04 10 12 2 313.30 17.70 6.11E-06 9 11 2 268.43 16.38 5.81E-06 8 10 2 227.25 15.07 5.51E-06 7 9 2 189.91 13.78 5.02E-06 6 8 2 167.35 12.94 6.05E-03 5 8 3 156.58 12.51 4.58E-06 4 7 3 127.08 11.27 4.37E-06 3 6 3 105.14 10.25 1.12E-03 2 6 4 101.36 10.07 4.58E-06 1 5 4 79.28 8.90 5.75E-06 0 4 4 73.00 8.54 1.80E-03 -1 4 5 60.86 7.80 9.30E-06 -2 3 5 53.57 7.32 5.26E-04 -3 3 6 47.92 6.92 2.70E-05 -4 3 7 41.58 6.45 6.67E-05 -5 2 7 39.04 6.25 8.00E-05 -6 2 8 32.63 5.71 1.70E-04 -7 2 9 30.25 5.50 1.39E-04 -8 2 10 26.37 5.14 2.36E-04 -9 1 10 24.17 4.92 4.53E-04 P G P G

  12. 211 1 -23 22 45 1097.25 33.12 2.65E-05 -24 22 46 1060.79 32.57 6.50E-06 -25 21 46 1046.33 32.35 1.15E-05 -26 21 47 1009.25 31.77 1.01E-04 -27 21 48 975.16 31.23 1.78E-05 -28 21 49 962.36 31.02 1.82E-05 -29 20 49 930.81 30.51 2.01E-04 -30 20 50 897.73 29.96 8.23E-05 -31 20 51 882.12 29.70 1.95E-05 -32 19 51 860.46 29.33 2.05E-04 -33 19 52 830.45 28.82 3.23E-04 -34 19 53 806.29 28.40 3.59E-05 -35 19 54 795.75 28.21 6.40E-05 -36 18 54 770.81 27.76 5.44E-04 -37 18 55 745.08 27.30 4.06E-04 -38 18 56 726.23 26.95 4.20E-05 -39 17 56 716.05 26.76 1.23E-04 -40 17 57 694.02 26.34 8.00E-04 -41 17 58 671.87 25.92 6.44E-04 -42 17 59 653.85 25.57 7.07E-05 -43 17 60 645.80 25.41 9.67E-05 -44 16 60 627.81 25.06 8.81E-04 -45 16 61 608.60 24.67 1.22E-03 -46 16 62 590.72 24.30 3.20E-04 -47 16 63 580.86 24.10 6.02E-05 -48 15 63 570.18 23.88 4.37E-04 -49 15 64 553.83 23.53 1.64E-03 -50 15 65 537.77 23.19 1.58E-03 -51 15 66 522.89 22.87 3.66E-04 -52 15 67 514.61 22.68 7.27E-05 -53 14 67 505.59 22.49 4.93E-04 -54 14 68 491.91 22.18 1.96E-03 -55 14 69 478.35 21.87 2.31E-03 -56 14 70 465.50 21.58 9.38E-04 -57 14 71 455.57 21.34 1.08E-04 -58 14 72 450.26 21.22 1.92E-04 -59 13 72 439.52 20.96 1.54E-03 -60 13 73 428.07 20.69 3.16E-03 -61 13 74 417.01 20.42 2.85E-03 -62 13 75 406.54 20.16 1.09E-03 -63 13 76 398.22 19.96 1.27E-04 -64 13 77 393.84 19.85 1.89E-04 G P G P

  13. Interaction bet ween Two potential wells ・ZAMS: Almost independent

  14. ・Advanced Evolution stage: Mixed character Avoided Crossing

  15. Mixed Mode

  16. 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

  17. 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

  18. A possible suggestion Quantitative analysis of the Oscillation spectrum of ηBoo Guenther AJ, 612, 454-462, 2004

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