Dust evolution in protoplanetary disks: Effect on observations of - PowerPoint PPT Presentation

Workshop on Magneto-Rotational I nstability in Protoplanetary Disks Dust evolution in protoplanetary disks: Effect on observations of dust emission H. Nomura 1 , Y. Aikawa 2 , Y. Nakagawa 2 (1. Kyoto Univ., 2. Kobe Univ.)

§ 1 I ntroduction

From protoplanetary disk to planets Dust size growth (e.g., Hayashi et al. 1985) & settling ↓ Planetesimal formation ↓ Collisional growth, Planet formation ↓ Gas dispersal → Planetary ( 東工大H P より) system formation

Obs. of Dust Emission from PPDs (Furlan et al. 2006) Thermal dust emission 10 μ m S t a r D i s k Si feature Dust scattering (Kitamura et al. 2002) b y S u b a r u G G T a u I R D i s k O p t i c a l ・ S t a r ★ D u s t (Itoh et al. 2002)

Dust Evolution & SED Quiescent disk Dust evolution in disks → SED model calculation 10 4 yr Unable to reproduce observations especially 10 7 yr in turbulent disks Planet formation Turbulent disk (Tanaka et al. 2005) t= 0yr t= 0yr 10 7 yr 10 7 yr (Dullemond & Dominik 2005)

How to Supply Small Dust Grains? Turbulent disk , R= 1AU, t= 10 6 yr 1 μ m 1 μ m 1mm 1mm Δ v= 1km/ s Z= H 3.5H 0.25H Z= 0.25H Z= H Δ v= 1m/ s 2H a[ μ m] a[ μ m] → Fragmentation ? (Nomura et al. 2007) Supply of small dust grains to inner disk Vertical: cloud → disk midplane Radial: migrate with gas accretion flow

§ 2 Size growth, settling, & migration of dust particles and Disk model

Dust size growth, settling, migration Coagulation eq. for dust particles ∂ ∂ ∂ φ 1 (R φ v ) ( φ v ) + + i i R i z n out ∂ ∂ ∂ t R R z V ff V acc ・ z − i 1 N 1 ∑ ∑ = − m β φ φ m φ β φ ★ − − i i j, j i j j i i i, j j 2 = = j 1 j 1 β i-j,j = π (a i-j + a j ) 2 Δ v p s /m i-j m j R sticking a j a i a i-j Δ v ( ) ( ) = − − ∂ ∂ 2 V φ Ω z/D φ D φ / z Turbulent z i z i 0 i ( ) = = + D ρ c /a D α c H/ 1 Ω /D mixing 0 s K gas s

Velocity of Dust particles (V R &V Z ) Eq. of motion for dust a : dust radius d U GM = − − − ≈ D( U u ) * R 0 = D ρ c /a 3 dt R gas s Eq. of motion for gas ∇ P ∇ ⋅ d u ρ GM σ = − − − − gas + ≈ dust D( u U ) * R 0 3 dt ρ R ρ ρ gas gas gas ( ) Z V= U-v K 、 v= u-v K = − 2 V Ω /D z K ⎛ ⎞ ρ 2 2D Ω 2D ⎜ ⎟ = − gas + K V η ζ v ⎜ ⎟ R K + + + 2 2 2 2 ρ ρ D Ω D Ω ⎝ ⎠ gas dust K K ∂ ( ) 1 1 1 = − ζ R ρ α c h Ω gas s K ∂ 2 n out 2 ρ R R R Ω V ff z gas K V acc ・ ∂ p 1 1 1 gas = − η ∂ 2 2 ρ R R Ω ★ gas K R

Gas Density Profile Hydrostatic equilibrium in z-direction dP ρ GM z = − = − ρ g * z + 2 2 3/2 dz (x z ) z P= ρ kT/ μ m p , M * = 0.5 M s x ★ • ⎡ ⎤ 1 / 2 ⎛ ⎞ 9 3GM M R = − 2 ⎜ ⎟ Σα c Ω * ⎢ 1 * ⎥ s0 3 4 8 π x ⎝ x ⎠ ⎢ ⎥ ⎣ ⎦ ・ M acc = 1x10 -8 M s / yr (= const.), α = 0.01

Gas & Dust Temperature Profile Γ X + Γ pe + L gr - Λ line = 0 ) Gas : Thermal equi. ( Γ X : X-ray heating Λ line : Rad. cooling (Ly α , OI, CII, CO lines) (H, H 2 ionization) ★ Γ pe : FUV heating L gr : Gas-dust 中心星 (grain photoelectric) collisions ∞ ∞ ∫ ∫ ∫ = π d ν κ I d Ω 4 d ν κ B (T ) ν ν ν ν gr 0 0 Heating: Irradiation from central star Cooling: Dust thermal radiation

§ 3 Resulting Dust Size & Spatial Distributions

Dust size distribution (only V z ) 1 μ m 1 μ m 1mm Quiescent 1mm R= 1AU R= 1AU 4 cm -3 n out = 10 6 yr t= 10 Z~ H 2H z coag 2 yr t= 10 R= 10AU R= 100AU Z~ H V ff n out 2H ・ z z coag ★ a[ μ m] a[ μ m] R t= 10 6 yr: large dust → settle, R → φ i / ρ dust,0

Dust size distribution (only V z ) 1 μ m 1 μ m 1mm Turbulent 1mm R= 1AU R= 1AU 4 cm -3 n out = 10 6 yr t= 10 Z~ 0.25H H 2H 2 yr z coag t= 10 R= 10AU R= 100AU Z~ 0.25H H V ff n out 2H ・ z z coag ★ a[ μ m] a[ μ m] R Large grains exist due to turbulent mixing

Small-dust/ Gas Ratio (only V z ) 4 cm -3 dn(R, z) n out = 10 ∫ = 2 A(R, z) π a da Small dust da 100AU f dust (R, z) = A(R, z)/A 0 (R, z) z fric z coag f dust Vertical velocity of dust 10AU z coag z fric dV GM z coag = − − z DV * z z fric z dz r 6 yr gas drag gravity t= 10 R= 1AU = D ρ c /a gas s Z/ R dust infall Quiescent Turbulent n out z Surface layer ( z fric < z , ρ gas : small ) R ★ V z : free-fall (only graviry) → f ∝1 / ρ g d u s t a s Middle layer ( z coag < z< z fric ) GM → f ∝1 / z gravity~ gas drag z = V * z d u s t Dr

Small-dust/ Gas Ratio (only V z ) Small dust Total dust 100AU 100AU z fric z fric z coag z coag ρ dust f dust 10AU 10AU z coag z coag z fric z fric z coag z coag z fric z fric R= 1AU R= 1AU Z/ R Z/ R Quiescent Turbulent (Nomura et al. 2007) Midplane ( z< z coag , ρ dust : large ) ( ) , coag < τ ~ z/V τ τ , 2 τ ~ 1/ n π a Δ V sed z sed coag dust z → f dust : small (smaller in turbulent disk)

Effect of radial migration: V R vs. V Z ⎛ ⎞ ρ 2 2D Ω 2D ⎜ ⎟ = − gas + V K η ζ v = D ρ c /a ⎜ ⎟ R K + + + 2 2 2 2 ρ ρ D Ω D Ω gas s ⎝ ⎠ gas dust K K ∂ ( ) 1 1 1 = − ζ R ρ α c h Ω V R V Z gas s K ∂ 2 2 ρ R R R Ω 1 μ m 1mm 1m gas K ∂ p 1 1 1 gas = − η Z= 2H Z= H ∂ 2 2 ρ R R Ω Z= 0.5H gas K ( ) Z = − 2 V Ω /D α = 0.01 z K n out V ff z α = 0.001 V acc ・ α = 0.0001 ★ α = 0 R= 1AU R a[ μ m] Amount of small dust grains ⇔ dust inflow in vertical & radial directions ⇔ n out & α

Dust size distribution (V z & V z ) 4 cm -3 1 μ m n out = 10 1 μ m 1mm 1mm 6 yr V & V o n l y V R Z t= 10 R z= H R= 3AU α = 0.01 20AU 100AU o n l y V V & V R R Z R= 3AU α = 0.001 20AU 100AU a[ μ m] a[ μ m] n out = 10 4 cm -3 → accretion flow dominant if α > 10 -2~ -3

§ 4 Effects on Dust Continuum Emission

Effect of dust inflow on SED Disk temp. & density + Dust evolution + Dust opacity + Rad. transfer → SED 6 yr t= 1x10 λ F λ [ergs/ cm 2 / s] Dark clouds dust Quiescent Obs. towards Turbulent CTTSs (D’Alessio et al. 2006) No dust inflow λ [ μ m] (n out = 0, α = 0) No dust inflow → Model cannot reproduce observations

Effect of dust inflow on SED Disk temp. & density + Dust evolution + Dust opacity + Rad. transfer → SED 6 yr t= 1x10 λ F λ [ergs/ cm 2 / s] Dark clouds dust Quiescent Obs. towards Turbulent CTTSs (D’Alessio et al. 2006) dust inflow (n out = 10 4 cm -3 ) No dust inflow λ [ μ m] (n out = 0, α = 0) n out > 10 4 cm -3 or α > 10 -2~ -3 → consistent with observations

Spatial distri. of dust emission λ = 450 μ m w/ o dust evolution λ = 850 μ m with dust evolution (Quiescent disk) R [AU] R [AU] Dust evolution → ALMA 5 σ detection limit F 850 μ m / F 450 μ m 50 antennas, 0”.1, 600s @ inner disk Dependence of spatial distribution of dust flux ratio on dust evolution → Observable by ALMA

§ 5 Summary Dust size growth, settling, and radial migration in protoplanetary disks Supply of small dust grains to inner disk Vertical: cloud → disk midplane ⇔ n out Radial: migrate with gas accretion ⇔ α SED model calculations n out > 10 4 cm -3 or α > 10 -2~ -3 → consistent with observations Effects on spatial distri. of dust emission : F 850 μ m / F 450 μ m @ inner disk → Observational diagnostics by ALMA