Dust crystallinity andthe evolution of dusty
disks
C.P. Dullemond, D. Apai, A. Natta, L. Testi, C. Dominik, S. Walch
Two questions:
What is the origin of the observed M ~ M*
2 relation of protoplanetary disks?
What does crystallinity of dust tell us about the processes in disks?
One answer:
The process of disk formation andviscous evolution!
Model• Start with a molecular cloud core of
mass Mcore, effective sound speed cs, and rotation rate .
• Use cloud collapse model to compute infall rate, and the radius within which this matter falls onto disk (Rcentr).
• Use viscous evolution model to follow the disk evolution.
Initial conditions of collapse:
• Let’s take a simple Shu-type collapse:– Collapse starts from slowly rotating singular
isothermal sphere– Mass-radius relation:
– Infall rate constant:
– Centrifugal radius:€
rcore =GMcore
2cs2
€
˙ M infall =cs
3
G
€
rc =1
16Ω2cs t 3
Disk formation and spreading
Let’s make a numerical model of the disk evolution:
€
∂(ΣR)
∂t+
∂(ΣRvR )
∂R= R ˙ σ
Mass conservation:
€
∂(ΣΩK R3)
∂t+
∂(ΣΩK R3vR )
∂R=
∂
∂RΣνR3 ∂ΩK
∂R
⎛
⎝ ⎜
⎞
⎠ ⎟
Angular momentum conservation:
Disk formation and spreading
Disk formation and spreading
Disk formation and spreading
Disk formation and spreading
Disk formation and spreading
Evolution of disk parameters
(after Hueso & Guillot 2005)
Class O, I Class II
Correlation M - M*
Accretion rate versus star mass
Natta et al. 2005
€
˙ M ∝ M 2
Accretion rate versus star mass
• So let’s do an experiment:– Make numerical models for series of cores
with ascending mass– Define dimensionless (important!)
(i.e. fraction of breakup rotation of core)– We assume of the core NOT to depend
on Mcore.€
≡ / GM /Rcore3
Accretion rate versus star mass
Disk mass versus star mass
Crystallinity of dust
10-micron feature of crystalline dust
Bouwman et al. 2001
Radial mixingCrystalline silicates
produced here(thermal annealing)...
...but they areobserved here
Turbulent transport
Morfill & Völk (1984), Gail (2001)Wehrstedt & Gail (2002)
Accretion
New idea:
New idea:
New idea:
Disk formation and spreading
Disk formation and spreading
Disk formation and spreading
Disk formation and spreading
Disk formation and spreading
Evolution of crystallinity
Evolution of crystallinity
Evolution of crystallinity
Evolution of crystallinity
Evolution of crystallinity
Summary
• Self-consistent disk formation and evolution models:– can explain the M ~ M2 relation.– provide a new view to dust crystallinity
• New problem: Why are there no 100% crystalline disks observed?