1. Modeling Disks of sgB[e] Stars Jon E. Bjorkman Ritter Observatory

2. Dusty Hot Star Winds Hot stars with dust: –B[e] –WR –Novae and Supernovae Wind must cool below condensation temperature Dust forms at large distances Problem: density must be large enough that reaction rates are faster than flow times Zickgraf, et al. 1986

3. Eta Carinae Morse & Davidson 1996

4. General Wind Kinematics Radial Momentum Equation Radial Motion

5. General Wind Kinematics Azimuthal Motion

6. Bi-Stability & Disks Lamers & Pauldrach 1991 Ionization shift at low latitudes –Higher mass loss –Lower terminal speed

7. Rotationally Induced Bi-Stability Pelupessy et al. 2000 Terminal SpeedMass Loss Need additional factor

8. Rotating Stellar Winds Bjorkman & Cassinelli, 1993 Low Density, High V ∞ High Density, Low V ∞

9. Ionization Structure Krauss & Lamers 2003

10. WCD Inhibition Radial Force OnlyNon-radial Force Effects Owocki, Cranmer, & Gayley 1996

11. WCDs and Be Stars Non-radial line forces (prevent disk formation) Outflow speed too large (~400 km/s) Density too small (to explain IR excess) –Disk “leaks” Material falls back onto star Material flows outward through disk Must put material into orbit Must remove radiative acceleration

12. Magnetic Channeling Owocki & ud-Doula 2003 Cassinelli et al. 2002

13. Asymmetric Mass Ejections Kroll’s gravity filter: –Point “explosion” –Material thrown backward falls onto star –Material thrown forward goes into orbit Stellar Bright Spot ModelOwocki 2003Spot + Line-Force Cutoff

14. Keplerian (Orbiting) Disks Fluid Equations Vertical scale height (Keplerian orbit) (Scale height) (Hydrostatic)

15. Viscosity in Keplerian Disks Viscosity Diffusion Timescale (eddy viscosity) Lynden-Bell & Pringle 1974

16. Viscous Decretion Disk Lee, Saio, Osaki 1991

17. Disk Temperature Flared Reprocessing DiskFlat Reprocessing Disk

18. Disk Winds Model for HD 87643 Oudmaijer et al. 1998

19. Power Law Approximations Keplerian Decretion Disk Flaring

20. Monte Carlo Radiation Transfer Divide stellar luminosity into equal energy packets Pick random starting location and direction Transport packet to random interaction location Randomly scatter or absorb photon packet When photon escapes, place in observation bin (frequency and direction) REPEAT 10 6 -10 9 times

21. MC Radiative Equilibrium Sum energy absorbed by each cell Radiative equilibrium gives temperature When photon is absorbed, reemit at new frequency, depending on T

22. T Tauri Envelope Absorption

23. T Tauri Disk Temperature Whitney, Indebetouw, Bjorkman, & Wood 2004

24. T Tauri Disk Temperature Snow Line Water Ice Methane Ice

25. Effect of Disk on Temperature Inner edge of disk –heats up to optically thin radiative equilibrium temperature At large radii –outer disk is shielded by inner disk –temperatures lowered at disk mid-plane Does not solve dust formation problem; requires –high density at condensation radius –additional opacity interior to condensation radius

26. Model of sgB[e] Star

27. Reaction network Timescales Condensation Condition Porter 2003 (Gail & Sedlmayr 1988) Dust Formation

28. SED Porter 2003 Bi-stability Viscous Decretion Bi-stability Viscous Decretion

29. NLTE Monte Carlo RT Gas opacity depends on: –temperature –degree of ionization –level populations During Monte Carlo simulation: –sample radiative rates Radiative Equilibrium –Whenever photon is absorbed, re-emit it After Monte Carlo simulation: –solve rate equations –update level populations and gas temperature –update disk density (solve hydrostatic equilibrium) determined by radiation field

30. sgB[e] Density (pure H model) Bi-stability Viscous Decretion

31. Gas (Electron) Temperature Bi-stability Viscous Decretion

32. Dust Temperature Bi-stabilityViscous Decretion

33. Mid-Plane Temp Bi-stability Viscous Decretion R dust = 400 R * R dust = 1300 R *

34. Density Bi-stability Viscous Decretion

35. sgB[e] Model SED Bi-stabilityViscous Decretion (  m)

36. IR Spectroscopy Roche, Aitken, & Smith 1993

37. Dust Properties Wood, Wolff, Bjorkman, & Whitney 2001 Large Dust Grains

38. YSO (GM Aur) SED Inner Disk Hole = 4 AU Rice et al. 2003

39. Line-Blanketed Disk Opacity Bjorkman, Bjorkman, & Wood 2000

40. Conclusions Bi-Stability: –Pros: Provides better shielding for dust formation –Cons: Requires small condensation radius Viscous Decretion –Pros: Slow outflow enables much larger condensation radius Disk wind may produce low velocity outflow –Cons: Dust optical depth is much too small Generally, –need to increase disk outflow rate (without increasing free-free excess) –Or provide more shielding to decrease condensation radius