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Modeling the Structure of Hot Star Disks

Modeling the Structure of Hot Star Disks. Jon E. Bjorkman Ritter Observatory. Systems with Disks. Infall + Rotation Young Stellar Objects (T Tauri, Herbig Ae/Be) Mass Transfer Binaries Active Galactic Nuclei (Black Hole Accretion Disks) Outflow + Rotation

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Modeling the Structure of Hot Star Disks

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  1. Modeling the Structure of Hot Star Disks Jon E. Bjorkman Ritter Observatory

  2. Systems with Disks • Infall + Rotation • Young Stellar Objects (T Tauri, Herbig Ae/Be) • Mass Transfer Binaries • Active Galactic Nuclei (Black Hole Accretion Disks) • Outflow + Rotation • AGBs (bipolar planetary nebulae) • LBVs (e.g., Eta Carinae) • Oe/Be, B[e] • Rapidly rotating (Vrot = 350 km s-1) • Hot stars (T = 20000K) • Ideal laboratory for studying disks

  3. General Wind Considerations • Radial Momentum Equation • Radial Motion • Be disk line profiles • Widths and symmetry => (Dachs, Hanuschik, …) Disk probably is Keplerian

  4. General Wind Considerations • Azimuthal Motion

  5. Rotating (in/out) Flows • Fluid Equations (cylindrical coords: ) • Equation of State

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

  7. Disk Variability • Viscosity • Viscous Diffusion Timescale • too large, unless a ~ 0.1–1 (eddy viscosity)

  8. Viscous Decretion a-Disks (Keplerian orbit) (continuity eq.) (surface density) (hydrostatic) (scale height)

  9. Power Law Approximations • Keplerian Decretion Disk • Flaring

  10. Isothermal Keplerian Disk Density a = 3.5 b = 1.5

  11. 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

  12. MC Radiative Equilibrium • Sum energy absorbed by each cell • Radiative equilibrium gives temperature • When photon is absorbed, reemit at new frequency, depending on T • Problem: Don’t know Ta priori • Solution: Change T each time a photon is absorbed and correct previous frequency distribution avoids iteration

  13. Temperature Correction Frequency Distribution: Bjorkman & Wood 2001

  14. Model of B[e] Star Bjorkman 1998

  15. Disk Temperature Bjorkman 1998

  16. B[e] SED Bjorkman 1998

  17. T Tauri Envelope Absorption

  18. Disk Temperature Water Ice Snow Line Methane Ice

  19. 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 • Permits dust formation in outer disk • Requires a different opacity source at smaller radii

  20. 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

  21. Disk Temperature Carciofi & Bjorkman 2004

  22. Disk Density Carciofi & Bjorkman 2004

  23. NLTE Level Populations Carciofi & Bjorkman 2004

  24. SED and Polarization Carciofi & Bjorkman 2004

  25. IR Excess Carciofi & Bjorkman 2004

  26. LTE Line-Blanketed Polarization Observed Observed MC Simulation MC Simulation

  27. HAeBe Model • Inner Disk: • NLTE Hydrogen • Flared Keplerian • h0 = 0.07, b = 1.5 • R* < r < Rdust • Outer Disk: • Dust • Flared Keplerian • h0 = 0.017, b = 1.25 • Rdust < r < 10000 R* Flux Polarization Bjorkman & Carciofi 2003

  28. Summary • Viscous Timescale: • 20 years (a = 0.01) • probably a bit too long (but a may be larger) • NLTE Modeling of Keplerian Disk • Fully self-consistent 3-D model • determines radiative equilibrium temperature • vertical hydrostatic equilibrium • steady state disk surface density • Single parameter: (and inclination angle i) • Reproduces Polarization and SED • Temperature • Inner disk: falls as r -3/4 (like thin blackbody) • Outer disk: isothermal

  29. Acknowledgments • Rotating winds and bipolar nebulae • NASA NAGW-3248 • Ionization and temperature structure • NSF AST-9819928 • NSF AST-0307686 • Geometry and evolution of low mass star formation • NASA NAG5-8794 • Collaborators: A. Carciofi, K.Wood, B.Whitney, K. Bjorkman, J.Cassinelli, A.Frank, M.Wolff • UT Students: B. Abbott, I. Mihaylov, J. Thomas • REU Students: A. Moorhead, A. Gault

  30. Be Star Ha Profile i = 82º Carciofi and Bjorkman 2003

  31. Polarization vs IR Excess P ~ sin2i Edge-on Pole-on Coté & Waters 1987

  32. MC Polarization vs IR Excess Gault, Bjorkman & Bjorkman 2002

  33. Disk Orientation: Inclination Polarimetric sin2i Interferometric sin2i Quirrenbach et al. 1996

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