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 Problem: density must be large enough that reaction rates are faster than flow times Zickgraf, et al. 1986

Eta Carinae Morse & Davidson 1996

General Wind Kinematics Radial Momentum Equation Radial Motion

General Wind Kinematics Azimuthal Motion

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

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

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

Ionization Structure Krauss & Lamers 2003

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

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

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

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

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

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

Viscous Decretion Disk Lee, Saio, Osaki 1991

Disk Temperature Flared Reprocessing DiskFlat Reprocessing Disk

Disk Winds Model for HD Oudmaijer et al. 1998

Power Law Approximations Keplerian Decretion Disk Flaring

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 times

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

T Tauri Envelope Absorption

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

T Tauri Disk Temperature Snow Line Water Ice Methane Ice

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

Model of sgB[e] Star

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

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

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

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

Gas (Electron) Temperature Bi-stability Viscous Decretion

Dust Temperature Bi-stabilityViscous Decretion

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

Density Bi-stability Viscous Decretion

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

IR Spectroscopy Roche, Aitken, & Smith 1993

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

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

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

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