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
(1. Kyoto Univ., 2. Kobe Univ.)
Workshop on Magneto-Rotational I nstability in Protoplanetary Disks
↓ Collisional growth, Planet formation ↓ Gas dispersal → Planetary system formation
Dust size growth & settling ↓ Planetesimal formation
(e.g., Hayashi et al. 1985)
( 東工大H P より)
S t a r D i s k
(Kitamura et al. 2002)
D u s t O p t i c a l
I R
★
S t a r D i s k
Thermal dust emission
(Furlan et al. 2006)
10 μm Si feature Dust scattering
b y S u b a r u G G T a u
(Itoh et al. 2002)
Planet formation
t= 0yr 107yr t= 0yr 107yr (Dullemond & Dominik 2005) (Tanaka et al. 2005) 107yr 104yr
Quiescent disk Turbulent disk
Dust evolution in disks
→ SED model calculation
Unable to reproduce
in turbulent disks
→ Fragmentation ?
(Nomura et al. 2007)
Turbulent disk,
R= 1AU, t= 106yr
1μm 1mm
a[μm]
2H Z= H 3.5H 0.25H Z= H Z= 0.25H 1μm 1mm Δv= 1m/ s
a[μm]
Δv= 1km/ s
Supply of small dust grains to inner disk Vertical: cloud → disk midplane Radial: migrate with gas accretion flow
Dust size growth, settling, migration
Coagulation eq. for dust particles
= − = − −
− = ∂ ∂ + ∂ ∂ + ∂ ∂
N 1 j j j i, i i 1 i 1 j j j i j j, i i z i R i i
φ β φ m φ φ β m 2 1 z ) v (φ R ) v (Rφ R 1 t φ
βi-j,j= π(ai-j+ aj)2Δv ps/mi-jmj Δv ai-j aj ai
Turbulent mixing
( )
( )
z / φ D φ z/D Ω φ V
i i 2 z i z
∂ ∂ − − =
( )
/D Ω 1 H/ αc D
K s
+ =
/a c ρ D
s gas
=
★
z
R sticking
Vacc Vff nout
R GM ) D( dt d
3 *
≈ − − − = R u U U
V= U-vK 、v= u-vK
ρ ρ P R GM ) D( ρ ρ dt d
gas gas gas 3 * gas dust
≈ ⋅ ∇ + ∇ − − − − = σ R U u u
a : dust radius
K 2 2 2 2 2 K dust gas gas R
v ζ Ω D 2D η Ω D 2DΩ ρ ρ ρ V
K K
⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + + + − =
2 K gas gas
RΩ 1 R p ρ 1 2 1 η ∂ ∂ − =
( )Z
/D Ω V
2 K z
− =
( )
2 K K s gas gas
RΩ 1 hΩ αc Rρ R R ρ 1 2 1 ζ ∂ ∂ − =
/a c ρ D
s gas
=
★
z
R
Vacc Vff nout
★
z
x
3/2 2 2 * z
) z (x z ρGM ρg dz dP + − = − = Hydrostatic equilibrium in z-direction
P= ρkT/ μmp , M* = 0.5 Ms
⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − =
/ 1 * 3 * 2 s0
x R 1 x 8π M 3GM Ω Σαc 4 9
Macc= 1x10-8Ms/ yr (= const.), α= 0.01
・
Gas: Thermal equi. ( ΓX+ Γpe+ Lgr-Λline= 0)
Heating: Irradiation from central star Cooling: Dust thermal radiation
ΓX : X-ray heating
(H, H2 ionization)
Γpe: FUV heating
(grain photoelectric)
Λline: Rad. cooling
(Lyα, OI, CII, CO lines)
Lgr: Gas-dust
collisions
中心星
∞ ∞
=
gr ν ν ν ν
) (T B κ dν 4 dΩ I κ dν π
2H Z~ H zcoag a[μm] a[μm]
t= 10
6yr
1μm 1μm 1mm 1mm
t= 106yr: large dust → settle, R → φi/ ρdust,0
nout= 10
4cm
R= 1AU
Quiescent
2H Z~ H zcoag
R= 10AU R= 100AU R= 1AU t= 10
2yr
★
z
R
Vff nout
a[μm] a[μm]
t= 10
6yr
1μm 1μm 1mm 1mm
Large grains exist due to turbulent mixing
nout= 10
4cm
R= 1AU
Turbulent
R= 10AU R= 100AU R= 1AU t= 10
2yr
2H H zcoag Z~ 0.25H 2H H zcoag Z~ 0.25H
★
z
R
Vff nout
Surface layer (
zfric< z, ρgas: small)
z r GM DV dz dV
* z z
− − =
gas drag gravity
Middle layer (
zcoag< z< zfric)
Vertical velocity of dust
z Dr GM V
* z =
R
★
z
dust infall nout zfric zcoag zcoag zcoag zfric zfric R= 1AU 10AU 100AU Z/ R
fdust
Small dust
= da da z) dn(R, πa z) A(R,
2
Vz : free-fall (only graviry) → f
d u s t
∝1 / ρg
a s
gravity~ gas drag → f
d u s t
∝1 / z
/a c ρ D
s gas
=
fdust(R, z) = A(R, z)/A0(R, z)
nout= 10
4cm
t= 10
6yr
Turbulent Quiescent
(Nomura et al. 2007)
Midplane (
z< zcoag, ρdust: large)
, τ τ
sed coag <
( ),
ΔV πa n 1/ ~ τ
z 2 dust coag
z sed
z/V ~ τ
zfric zcoag zcoag zcoag zfric zfric R= 1AU 10AU 100AU Z/ R
fdust
zfric zcoag zcoag zcoag zfric zfric R= 1AU 10AU 100AU Z/ R
ρdust
Small dust Total dust → fdust : small (smaller in turbulent disk)
Turbulent Quiescent
α= 0.01 Z= H α= 0.001 α= 0.0001 α= 0 Z= 0.5H Z= 2H
a[μm]
R= 1AU
1μm 1m 1mm
Amount of small dust grains ⇔ dust inflow in vertical & radial directions ⇔ nout &α
VZ VR
K 2 2 2 2 2 K dust gas gas R
v ζ Ω D 2D η Ω D 2DΩ ρ ρ ρ V
K K
⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + + + − =
/a c ρ D
s gas
=
2 K gas gas
RΩ 1 R p ρ 1 2 1 η ∂ ∂ − =
( )Z
/D Ω V
2 K z
− =
( )
2 K K s gas gas
RΩ 1 hΩ αc Rρ R R ρ 1 2 1 ζ ∂ ∂ − =
★
z
R
Vacc Vff nout
α= 0.01
20AU R= 3AU 100AU a[μm] a[μm]
l y V
R
t= 10
6yr
z= H
1μm 1μm 1mm 1mm
α= 0.001
nout= 10
4cm
V
R &
V
Z
l y V
R
V
R &
V
Z
20AU R= 3AU 100AU
nout= 104cm-3
→ accretion flow dominant if α > 10-2~ -3
No dust inflow
→ Model cannot reproduce observations
CTTSs
(D’Alessio et al. 2006)
λ [μm] λFλ [ergs/ cm2/ s]
t= 1x10
6yr
Disk temp. & density + Dust evolution + Dust opacity + Rad. transfer → SED
Turbulent Quiescent No dust inflow (nout= 0, α= 0) Dark clouds dust
nout> 104cm-3 or α > 10-2~ -3
→ consistent with observations
CTTSs
(D’Alessio et al. 2006)
λ [μm] λFλ [ergs/ cm2/ s]
t= 1x10
6yr
Disk temp. & density + Dust evolution + Dust opacity + Rad. transfer → SED
Turbulent Quiescent No dust inflow (nout= 0, α= 0) Dark clouds dust dust inflow
(nout= 104cm-3)
Dependence of spatial distribution of dust flux ratio on dust evolution → Observable by ALMA
R [AU]
ALMA 5σ detection limit
50 antennas, 0”.1, 600s
λ= 450μm λ= 850μm
R [AU]
w/ o dust evolution with dust evolution (Quiescent disk)
Dust evolution →
F850μm/ F450μm
@ inner disk
Dust size growth, settling, and radial migration in protoplanetary disks Supply of small dust grains to inner disk Vertical: cloud → disk midplane ⇔ nout Radial: migrate with gas accretion ⇔ α SED model calculations
nout> 104cm-3 or α > 10-2~ -3
→ consistent with observations Effects on spatial distri. of dust emission
: F850μm/ F450μm @ inner disk
→ Observational diagnostics by ALMA