dust crystallinity and the evolution of dusty disks
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Dust crystallinity and the 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?. - PowerPoint PPT PresentationTRANSCRIPT
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Dust crystallinity andthe evolution of dusty
disks
C.P. Dullemond, D. Apai, A. Natta, L. Testi, C. Dominik, S. Walch
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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?
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One answer:
The process of disk formation andviscous evolution!
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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.
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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
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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:
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Disk formation and spreading
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Disk formation and spreading
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Disk formation and spreading
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Disk formation and spreading
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Disk formation and spreading
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Evolution of disk parameters
(after Hueso & Guillot 2005)
Class O, I Class II
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Correlation M - M*
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Accretion rate versus star mass
Natta et al. 2005
€
˙ M ∝ M 2
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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
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Accretion rate versus star mass
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Disk mass versus star mass
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Crystallinity of dust
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10-micron feature of crystalline dust
Bouwman et al. 2001
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Radial mixingCrystalline silicates
produced here(thermal annealing)...
...but they areobserved here
Turbulent transport
Morfill & Völk (1984), Gail (2001)Wehrstedt & Gail (2002)
Accretion
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New idea:
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New idea:
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New idea:
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Disk formation and spreading
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Disk formation and spreading
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Disk formation and spreading
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Disk formation and spreading
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Disk formation and spreading
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Evolution of crystallinity
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Evolution of crystallinity
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Evolution of crystallinity
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Evolution of crystallinity
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Evolution of crystallinity
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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?