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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
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Tcond =1500 K << T* = 25000 K
Eta Carinae
Morse & Davidson 1996
General Wind Kinematics
• Radial Momentum Equation
• Radial Motion
v
dvdr
= -GM
r2+
vf2
r+ Fext
vr ~
Vesc (radiation-driven)
= a (Keplerian)
ÏÌÔÔ
ÓÔÔ
General Wind Kinematics
• Azimuthal Motion
vf µ
Vrotr- 1 (vr ? vf ; angular momentum-conserving)
Vrotr (magnetically dominated; solid body rotation)
Vcritr- 1/ 2 (vr = vf ; Keplerian)
Ï
Ì
ÔÔÔÔÔ
Ó
ÔÔÔÔÔ
Bi-Stability & Disks
Lamers & Pauldrach 1991
• Ionization shift at low latitudes
– Higher mass loss
– Lower terminal speed
Rotationally Induced Bi-Stability
Pelupessy et al. 2000
Terminal Speed Mass Loss
req
rpole
: 10
v• ,eq
v• ,pole
: 1/ 3
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 Only Non-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 2003Cassinelli 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 Model Owocki 2003Spot + Line-Force Cutoff
Keplerian (Orbiting) Disks
• Fluid Equations
• Vertical scale height
(Keplerian orbit)
(Scale height)
(Hydrostatic)
€
(vϖ << vφ;v z = 0)
€
fϖ
€
fz
€
Fgrav
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T = 15000K
P = a2r
Dq = 6∞ H / v = 0.1
Viscosity in Keplerian Disks
• Viscosity
• Diffusion Timescale
n = aaH
tn = v 2 / n
=Vcrit
aa2v R
(eddy viscosity)
Lynden-Bell & Pringle 1974
t +dt t
Viscous Decretion Disk
• Lee, Saio, Osaki 1991
Disk Temperature
sT 4 = I nmdWÚ: (R / v )3
Flared Reprocessing DiskFlat Reprocessing Disk
T : v - 3/ 4 T : v - 1/ 2
Disk Winds
Model for HD 87643
Oudmaijer et al. 1998
Power Law Approximations
• Keplerian Decretion Disk
• Flaring
b = 98
a = 198
(flat passive disk; T µ r - 3/ 4)
b = 54
a = 114
(flared passive disk; T µ r - 1/ 2)
b = 32
a = 72
(isothermal disk; T = const)
r = r0(R* / v )a exp -z
H(v )
Ê
ËÁÁÁ
ˆ
¯˜̃˜̃
2È
Î
ÍÍÍ
˘
˚
˙˙˙
H = H0(v / R*)b
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)
€
Eγ = LΔt / Nγ
€
τ =−lnξ (ξ is a random number)
REPEAT 106-109 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
€
Eabs = Eemit
nabsEγ = 4πmiκ PB(Ti )
T Tauri Envelope Absorption
T Tauri Disk Temperature
Whitney, Indebetouw, Bjorkman, & Wood 2004
T Tauri Disk Temperature
Snow LineWater 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)
Dtdust = 1/ (n1ai )
Dtflow = Rdustcon / v•
Dust Formation
SED
Porter 2003
Bi-stabilityViscous 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-stability Viscous Decretion
Mid-Plane Temp
Bi-stability Viscous Decretion
Rdust = 400 R* Rdust = 1300 R*
Density
Bi-stability Viscous Decretion
sgB[e] Model SED
Bi-stability Viscous Decretion
(m) (m)
IR Spectroscopy
Roche, Aitken, & Smith 1993
Dust Properties
Wood, Wolff, Bjorkman, & Whitney 2001
€
amax = 1μm
€
amax = 3μm
€
amax = 1mm
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
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