Vertical Oscillation of Protoplanetary Disk (PP disk): 1D multi - PowerPoint PPT Presentation

Vertical Oscillation of Protoplanetary Disk (PP disk): 1D multi color Radiation Hydrodynammical Simulations Hot upper atmospheres and cold main disk oscillate in the opposite directions. Tomoyuki Hanawa Tetsuya Harada (Chiba U.) 1 13 年 7 月 4 日木曜日

PP disk@ 1.6 μ m(H)+345 GHz Lin+06 & Ohashi+07 taken with SMA overlaid on Fukagawa+02 (Subaru) Much better images will be taken with ALMA 2 13 年 7 月 4 日木曜日

Williams & Cieza ’11 3 13 年 7 月 4 日木曜日

Structure of Irradiated PP Disk Emission Scattered (mid IR) Star direct (optical) absorption Disk Two Layer Model Chiang & Goldreich ’97 4 Hot Surface Layer + Cool Main Disk T s >> T d 13 年 7 月 4 日木曜日

1D Grazing Recipe stellar scattered+emission z = E ′ ν + E ′′ E ν ν , F ′ ν + F ′′ = ν , F ν √ Z 1 r 2 + z 2 ! ν ( z ) = π R 2 ⇤ B ν ( T e ff ) − 2 E 0 ρ ( z 0 ) dz 0 exp κ ν r 2 + z 2 7 z z τ 00 ν τ 0 ν r ∂ E 00 + ∂ F 00  ✓ ν + 4 π B ν ◆ � − E 00 + κ ν ,s E 0 ν ν = ρ c κ ν ,a , ν ∂ t ∂ z c ∂ F ν ∂ t + ∂ � c 2 χ 00 � ν E 00 = − ρ c ( κ ν ,a + κ ν ,s ) F 00 ν , ν ∂ z M1 model Eq. 5 13 年 7 月 4 日木曜日

Radiation Hydrodynamics ∂ρ ∂ assumption : T gas = T dust ∂ t + ∂ z ( ρ v z ) = 0 , + 1 ∂ v z ∂ v z P GMz + v z ∂ z + ( r 2 + z 2 ) 3 / 2 = 0 , ∂ t ∂ t ρ Z ∞ T ds dt = κ ν ,a [ cE ν − 4 π B ν ( T )] d ν . 0 ∂ E 00 + ∂ F 00  ✓ ν + 4 π B ν ◆ � − E 00 + κ ν ,s E 0 ν ν = ρ c κ ν ,a , α ν ∂ t ∂ z c ∂ F ν ∂ t + ∂ c 2 χ 00 � � ν E 00 = − ρ c ( κ ν ,a + κ ν ,s ) F 00 α ν , ∂ z ν speed reduction : α = 10 − 4 → c = 30 km s − 1 We solve the above partial differential equations explicitly . Our finite difference scheme is designed so that all the physical variables approach to the equilibrium ones in the limit of Δ t = ∞ . 6 13 年 7 月 4 日木曜日

Upwind Reconstruction of the Radiation Field Kinetic Reconstruction (1 − β 2 ) 3 3 E ν (1 − β · n ) − 4 I ν ( n ) = 3 + β 2 8 π 3 f β = β F Kanno, Harada, & Hanawa = β 4 − 3 f 2 , � | F | 2 + 2013, PASJ in press 13 年 7 月 4 日木曜日

Absorption & Emission within Cell 1 − e − ∆ τ i / 2 � S ν F � (+) e − ∆ τ i / 2 F (+) � = ν ,x,i +1 / 2 ,j,k + ν ,x,i +1 / 2 ,j,k 4 Flux at boundary absorption Flux at center Emission � � e − ∆ τ i : optical depth e − ∆ τ i / 2 F approaching to diffusion limit e − ∆ τ i when is large MUSCL for 2nd order in space ν ,xx,i +1 / 2 ,j,k ν ,xx,i +1 / 2 ,j,k e − ∆ τ i 1 − e − ∆ τ i / 2 � S ν P � (+) e − ∆ τ i / 2 P (+) � = ν ,x,i +1 / 2 ,j,k + ν ,x,i +1 / 2 ,j,k 6 � S 8 � 13 年 7 月 4 日木曜日

41 colors M * = 2.2 M o 0 . 1 µ m ≤ λ ≤ 1 mm T eff = 6250 K ∆ log λ = ∆ log ν = 0 . 1 R * = 3.8 R o Opacity: Draine (2003) λ (µm) 9 13 年 7 月 4 日木曜日

Initial model (Equilibrium) Model 1: Σ = 7 g cm -2 Σ = 7 , 20 , 70 g cm − 2 r = 100 AU z max = 70AU, Δ z = 0.5 AU T ρ 10 13 年 7 月 4 日木曜日

Model 1: overview 11 13 年 7 月 4 日木曜日

Early density oscillation at z = 0.25 AU D 12 13 年 7 月 4 日木曜日

density fluctuation at various heights Period = 420 yr, e -folding growth timescale = 2,000 yr. 13 13 年 7 月 4 日木曜日

velocity perturbation node node Upper layers expands to receive more stellar light, when the disk main body is compressed. 14 13 年 7 月 4 日木曜日

z = 0.25 AU thermal engine Pressure I PdV > 0 rotates clockwise Volume 15 13 年 7 月 4 日木曜日

Variation in Radiative Flux @ z = 19.75 AU density min density max Z ∆ F ν d ν 16 13 年 7 月 4 日木曜日

Excitation Mechanism Expanded Surface + Compressed Main Disk Excess Heating Compressed Surface + Compressed Main Disk Heating Deficiency 17 13 年 7 月 4 日木曜日

Limit Cycle Oscillation 18 13 年 7 月 4 日木曜日

Mass Ejection 10 -13 g cm -3 10 -15 g cm -3 ρ = 10 -14 g cm -3 19 13 年 7 月 4 日木曜日

Light variation and mass ejection Doppler shift in CO lines The period is 2/3 of the Keplerian. 20 13 年 7 月 4 日木曜日

High Surface Density ( Σ = 70 g cm -2 ) 21 13 年 7 月 4 日木曜日

PV diagram Σ =70 g cm -2 Σ =7 g cm -2 almost adiabatic τ th � τ dyn 22 13 年 7 月 4 日木曜日

Summary and Implications • PP disks are overstable against vertical oscillation with a node, since they have hot cold inner disk and hot surface layers. • The vertical oscillation affects appearance and evolution of PP disks. • 2D RHD simulations are desired. Flaring of an annulus may result in a 23 13 年 7 月 4 日木曜日