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)

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fϖ

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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

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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