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?