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Bok Globule: Isolated Cloud Core
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Primordial Disks: From Protostar to Protoplanet
Jon E. BjorkmanRitter Observatory
Cloud Cores
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Bok Globule: Isolated Cloud Core
Theorist’s Cloud Core
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Star Formation
• Within Cloud Cores – gravity overcomes gas pressure
• gas must be cold– cores collapse
• Free-fall• Inside out (Shu 1977)• Form protostars
– rotation• Cloud flattens into disk• material falls on disk
– protostar • accretes material from disk
Rotating Infall• Streamlines follow ballistic trajectories
– Ulrich (1976); Cassen & Moosman; Terebey, Shu, & Cassen (1984)
Keto
Keto
Accretion with Rotation• Accretion termination shock above/below disk surface• Material added at centrifugal radius (orbital periastron)
– Centrifugal radius grows with time
Young Stellar Objects
Circumstellar Disks
Disk Winds
Matt 2005
• Magneto-Centrifugal– Blandford & Payne (1982)– Pudritz & Norman (1983)
• Magnetospheric– X Wind (Shu et al. 1994)
T Tauri SED
Adams, Lada, & Shu 1987
• IR Excess– Starlight reprocessed
by disk (passively irradiated disk)
– Ldisk ~ 1/4 Lstar
– Shape determined by temperature vs radius
• UV excess– Disk-Star boundary
layer / accretion shock– Causes “veiling” of
spectral lines
SED Classification
• Class 0-III– Adams, Lada & Shu 1987
• Class 0:– Mostly sub-mm emission– Deeply embedded protostars
• Class I:– Rising SEDs from 2 to 100 m– Protostars still accreting from
infalling envelope• Class II (Classical T Tauri):
– Falling IR SEDs– Stars surrounded by disks
• Class III (Weak-lined T Tauri):– Little IR excess– Almost no circumstellar material
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Star/Disk Formation SequenceClass 0 Class I Class II
Class III Debris Disks
Keplerian (Orbiting) Disks
• Fluid Equations
• Vertical scale height
(Keplerian orbit)
(Scale height)
(Hydrostatic)
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(vϖ << vφ;v z = 0)
€
fϖ
€
fz
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Fgrav
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T = 15000K
P = a2r
Dq = 6∞ H / v = 0.1
Disk Temperature
sT 4 = I nmdWÚ: (R / v )3
Kenyon & Hartman 87Flared Reprocessing Disk
Adams, Lada, & Shu 88Flat Reprocessing Disk
T : v - 3/ 4 T : v - 1/ 2
Flaring Effects:Disk Temperature & SED
Kenyon & Hartmann 87log wavelength (micron)
Near IR
Far IR
Viscous Accretion Disk• Sources of Viscosity
– Eddy Viscosity (Shakura & Sunyaev 1977)
– Magneto-Rotational Instability (Balbus & Hawley 1991) requires slight ionization
• Possible dead zones in disk interior
Lee, Saio, Osaki 1991
n = aaH
Viscosity in Keplerian Disks
• Viscosity
• Diffusion Timescale n = aaH
tn = v 2 / n
=Vcritaa2 v R
(eddy viscosity)
Lynden-Bell & Pringle 1974
t +dt t
Steady State Accretion -Disks
vf =Vcrit R / v
vv =&M
2pv SS =
&MVcritR1/ 2
3paa2v 3/ 2Rmax
v- 1
È
ÎÍÍÍ
˘
˚˙̇˙
r = S2pH
e- 0.5(z/H )2
H = (a / vf )v
(surface density)
(scale height)
(Keplerian orbit)
(hydrostatic)
(continuity eq.)
Power Law Approximations
• Keplerian Accretion Disk
• Flaring
b = 98 a = 15
8 (flat passive disk; T µ r - 3/ 4)
b = 54 a = 9
4 (flared passive disk; T µ r - 1/ 2)
b = 32 a = 3 (isothermal disk; T = const)
r = r0(R* / v )a exp - zH(v )
ÊËÁÁÁ
ˆ¯˜̃̃˜2È
ÎÍÍÍ
˘
˚˙̇˙
H = H0(v / R*)b
3-D 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)
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Eγ = LΔt / Nγ
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τ =−lnξ (ξ is a random number)
REPEAT 106-109 times
T Tauri Model SED
MC Radiative Equilibrium• Sum energy absorbed by each cell• Radiative equilibrium gives temperature
• When photon is absorbed, reemit at new frequency, depending on T
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Eabs = Eemit
nabsEγ = 4πmiκ PB(Ti )
T Tauri Envelope Absorption
Monte Carlo Disk Temperature
Whitney, Indebetouw, Bjorkman, & Wood 2004
Radial Temperature Structure
Snow Line:Water Ice
Methane Ice
Optically thin T ~ r-0.4
Midplane
Surface
Vertical Temperature Structure
Dullemond
3-D Temperature Effects• At large radii
– outer disk is shielded by inner disk– temperatures lowered at disk mid-plane
• Surface layers– Heat up to optically thin dust temperature (Chiang & Goldreich
97)– Upper layers “puff up”
• Inner edge of disk– Heats up to optically thin dust temperature– Inner edge “puffed up” (relative to flat disk)– Shadows disk behind inner wall
Effect of Inner Wall
Dullemond, Dominik, & Nata 01
Disk Self-ShadowingDullemond, Dominik, & Nata 01
Dullemond 02
Protostar Evolutionary Sequence
i =80 i =30
Mid IR ImageDensitySpectrum
Whitney, Wood, Bjorkman, & Cohen 2003
Protostar Evolutionary Sequence
Mid IR ImageDensitySpectrum
i =80 i =30Whitney, Wood, Bjorkman, & Cohen 2003
Disk Evolution: Decreasing Mass
Wood, Lada, Bjorkman, Whitney & Wolff 2001
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Forming Planets: Standard Model
• Dust grains stick together – form rocks
• Grow into planetesimals– some still survive today
• Asteroids & comets
• Larger planetesimals attract smaller ones (gravity)
• Planetesimals accrete– form planet cores
Dust Processing in Disks• Gravity causes dust settling toward mid-plane
– ~104 yr• Grain Growth
– Grain size increases with disk age?• Ice Condensation
– dust may be coated with ice• Dust Removal
– Radiation Pressure• Poynting Robertson Effect
– Gas Drag• Accretion onto star (or planets)• Blown away by stellar / disk wind
– Evaporation (when dust gets too hot)
Dust Opacity
• Mie Scattering Opacity
• Dust has a particle size distribution
€
dn / da ∝ a− p (a < amax )
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κ =Qabsπa2 Qabs ~
1 (λ < a)a / λ (λ > a) ⎧ ⎨ ⎩
σ = Qscatπa2 Qscat ~
1 (λ < a)
(a / λ )4 (λ > a) ⎧ ⎨ ⎩
Dust Opacity
Wood, Wolff, Bjorkman, & Whitney 2001
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amax = 1μm
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amax = 3μm
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amax = 1mm
Evidence for Grain Growth
Wood, Wolff, Bjorkman, & Whitney 2001Bjorkman, Wood, & Whitney
ISM Dust Grains Large Dust Grains (1mm)
Evidence for Grain Growth
Wood et al. 1998Cotera et al. 2001
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h0 = 0.05
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h0 = 0.025
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h0 = 0.0025
Small Grain ModelLarge Grain ModelsHH30 Observations
Evidence for Dust Settling
• Observed scale height < thermal value• Self-Shadowed Disks?
– Dust settling reduces opacity in disk surface layers– Reduced absorption in surface layers reduces disk
heating– Causes outer disk collapse, producing fully self-
shadowed disk
Holes in Protoplanetary Disks
Transition Disks:GM AUR SED
• Inner Disk Hole Size = Jupiter’s Orbit
Rice et al. 2003
Planet Hole-Clearing Model
Rice et al. 2003
Planetary Gaps
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Kley 1999
Gap Structure
Bjorkman et al. 05
Predicted Gap Images
Bjorkman et al. 05
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Predicted Gap SED
Gap + Inner HoleGap Only
Varniere et al. 2004
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