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L IGHT AND RADIAL VELOCITY VARIATIONS DUE TO LOW FREQUENCY OSCILLATIONS

L IGHT AND RADIAL VELOCITY VARIATIONS DUE TO LOW FREQUENCY OSCILLATIONS IN ROTATING STARS. Jadwiga Daszy ń ska-Daszkiewicz Instytut Astronomic zny, Uni w ersy tet Wrocław ski, Poland Collaborators : W ojtek Dziembowski , A los h a Pamyatnykh.

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L IGHT AND RADIAL VELOCITY VARIATIONS DUE TO LOW FREQUENCY OSCILLATIONS

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  1. LIGHT AND RADIAL VELOCITY VARIATIONS DUE TO LOW FREQUENCY OSCILLATIONS IN ROTATING STARS Jadwiga Daszyńska-Daszkiewicz Instytut Astronomiczny, Uniwersytet Wrocławski, Poland Collaborators: Wojtek Dziembowski , Alosha Pamyatnykh 22November 2006, Porto Workshop

  2. INSTABILITY DOMAINS IN THE MAIN SEQUENCE A. A. Pamyatnykh

  3. for SPB pulsators often  ~ 

  4. Slow modes in the traditional approximation •  ~  << N(r) • not too fast rotation: ( / crit)2 << 1 • Cowling approximation

  5. Separation of the angular and radial dependences in eigenfunctions s= 2/l(l+1) (s) Ylm (cos)eim (cos) - the Hough functions Modes with >0 propagate in the radiative zone (N>0). The radial wave number

  6. Definition of mode degree, , for g-modes s = 2/ 0 then   l(l+1)

  7. Retrograde r-mode with g-modes properties at s>|m|+1 (Savonije 2005, Townsend 2005)

  8. the Hough function

  9. the Hough function

  10. (, /2) – the normalized driving rate For instability: • 2/ - should match the thermal time scale in the driving zone • /2 – determines the r-dependence of eigenfunctions The pressure eigenfunction should be large in the driving zone like (+1)/2 for high order g-modes in non-rotating stars

  11. Radial displacement Z = exp [i (m - t)] in co-rotating system m>0 - prograde modes m<0 - retrograde modes

  12. Oscillating atmospheric parameters f(, /2)

  13. Light variations in the x passband Fx(Teff, log g) hx(ns,Teff, log g)

  14. Pulsation velocity field

  15. Disc-averaged radial velocity rotational part pulsational part

  16. the rotational contribution to arises from r, n, Fbol, g

  17. An example: M=6 M8, MS star logTeff= 4.205 logL/L8= 3.204 Vrot=0, 50, 150, 250 km/s

  18. Selected modes: g-modes with l=1,2, most unstable at each (l,m) r-modes, most unstable with m= -1,-2 (only for Vrot ≥ 150 km/s)

  19. Hough functions for l=1 and r mode with m= -1

  20. Amplitudes of light and radial velocity variations g-mode l=1,m=0 and r-mode,m=-1

  21. Amplitudes of light and radial velocity variations g-modes: l=1,m= ±1

  22. Hough functions for l=2 and r-mode with m= -2

  23. Prospectsformodeidentification

  24. Diagnostic diagrams AVrad /AV vs. AU /AV

  25. fast rotation have a small effect on mode stability but a large effect on visibility  rotation impairs mode visibility in the light but not in the mean radial velocity variations  g-modes with the same  and different m do not form regular multiplets and they have different visibility and instability properties  there are large differences between modes in the light to radial velocity amplitude ratios  Good prospects for mode identification

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