1. LIGHT AND RADIAL VELOCITY VARIATIONS DUE TO LOW FREQUENCY OSCILLATIONS IN ROTATING STARS Jadwiga Daszy ń ska-Daszkiewicz Instytut Astronomiczny, Uniwersytet Wroc ł awski, Poland Collaborators: Wojtek Dziembowski, Alosha Pamyatnykh 22 November 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 not too fast rotation: (  /  crit ) 2 << 1 Cowling approximation  ~   ~  << N(r)

5. Separation of the angular and radial dependences in eigenfunctions s= 2  /  ( +1)   (s) Y m   (cos  )e im   (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    ( +1)

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

9. the Hough function

11.  ( , /  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

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

13. Oscillating atmospheric parameters f ( , /  2 )

14. F x ( T eff, log g ) h x (n s, T eff, log g ) Light variations in the x passband

15. Pulsation velocity field

16. Disc-averaged radial velocity pulsational part rotational part

17. the rotational contribution to arises from  r,  n,  F bol,  g

18. An example: M=6 M , MS star logT eff = 4.205 logL/L  = 3.204 V rot =0, 50, 150, 250 km/s

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

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

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

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

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

25. Prospects for mode identification

27. Diagnostic diagrams A Vrad /A V vs. A U /A V

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