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Modeling Disks of sgB[e] Stars

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

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Modeling Disks of sgB[e] Stars

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  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 • Ionization shift at low latitudes • Higher mass loss • Lower terminal speed Lamers & Pauldrach 1991

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

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

  9. Ionization Structure Krauss & Lamers 2003

  10. WCD Inhibition Radial Force Only Non-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 Cassinelli et al. 2002 Owocki & ud-Doula 2003

  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 Model Spot + Line-Force Cutoff Owocki 2003

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

  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 Flat Reprocessing Disk Flared 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 106-109 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 Water Ice Snow Line 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. Dust Formation • Reaction network • Timescales • Condensation Condition Porter 2003 (Gail & Sedlmayr 1988)

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

  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-stability Viscous Decretion

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

  34. Density Bi-stability Viscous Decretion

  35. sgB[e] Model SED Bi-stability Viscous Decretion l (mm) l (mm)

  36. IR Spectroscopy Roche, Aitken, & Smith 1993

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

  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

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