1. Dynamical Origin of Wind Structure The effect of “velocity porosity” on P-Cygni line absorption strength Stan Owocki Bartol Research Institute Department of Physics & Astronomy University of Delaware

2. Key Issues What is effect of wind clumping on line-absorption? Velocity dispersion vs. Spatial Porosity What are relevant scaling parameters (cf. f , h=l/f)? In dynamical model, how important for, eg. PV?

3. Spatial Porosity Same amount of material More light gets through Less interaction between matter and light Incident light

4. Effective opacity porosity length=h

5. Porous envelopes h=0.5r h=r h=2r l=0.05rl=0.1rl=0.2r h  l/f

7. Profile-weighted line column depth Step function

8. Line absorption trough  =1      

9. Velocity vs. Mass

10. vv } } VV Velocity filling factor :

11. Velocity vs. Mass

12. “Velocity Porosity” Vorosity?

13. Absorption reduction 0.5 f = 1 xx RARA 0.2 0.1

14. Line absorption smooth,  =1     porous, f v = 1-v/2v    

15. Line-Driven Instabilty sim (SSF)

16. Instability model CAK init. cond. radius (R  ) 1 10 0 4 Time (days) 110 0 4 radius (R  ) Velocity Density

17. Profile-weighted line column depth Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

18. Profile-weighted line column depth Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

19. Dynamic absorption spectrum-weak line Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

20. Dynamic absorption spectrum-weak line Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

21. Dynamic absorption spectrum - med. line Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

22. Dynamic absorption spectrum - med. line Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

23. Dynamic absorption spectrum-strong line Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

24. Dynamic absorption spectrum-strong line Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

25. Weak Time-Averaged Absorption Profiles Wavelength (V  ) 0 I /I cont 0 1 Medium Strong

26. Weak Time-Averaged Absorption Profiles Wavelength (V  ) 0 I /I cont 0 1 Medium Strong

27. Dynamic absorption spectra StrongMediumWeak 0 0 0 00 Wavelength (V  )

28. Summary Spatial porosity for continuum opacity –characterized by “porosity length” h=l/f  But for line opacity, key is“velocity clumping” –characterized by f vel (and  Sob of smoothed wind) Line-driven instability suggests: – f vel ~= 0.7-0.8 (maybe 0.5 if seeded by low freq. pert) – Mdot misunderestimated by f vel, i.e. 0.5-0.8 – Maybe upto a factor 2 of the ca. 10 needed for PV

30. 2D Simulation of Co-rotating Interaction Regions local CAK model nonlocal smooth model nonlocal structured model c.  log(Density) b. a.

31. Profile-weighted line column depth Wavelength (V  ) 0 0 8 Time (days) CAK init. cond.

32. Dynamic absorption spectrum-med. line Wavelength (V  ) 0 0 8 Time (days) CAK init. cond.

33. Dyn. abs. spectrum - very strong line Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

34. Dyn. abs. spectrum - very strong line Wavelength (V  ) 0 0 4 Time (days) CAK init. cond.

35. Instability model: Mdot radius (R  )110 0 4 Time (days) CAK init. cond.