Dust crystallinity and the evolution of dusty disks

Two questions: What is the origin of the observed M ~ M*2 relation of

One answer: The process of disk formation and viscous evolution!

Model • Start with a molecular cloud core of mass Mcore, effective sound speed

Initial conditions of collapse: • Let’s take a simple Shu-type collapse: – Collapse starts

Disk formation and spreading Let’s make a numerical model of the disk evolution: Mass

Evolution of disk parameters Class O, I Class II (after Hueso & Guillot 2005)

Accretion rate versus star mass Natta et al. 2005

Accretion rate versus star mass • So let’s do an experiment: – Make numerical

10 -micron feature of crystalline dust Bouwman et al. 2001

Radial mixing Crystalline silicates produced here (thermal annealing). . . but they are observed

Summary • Self-consistent disk formation and evolution models: – can explain the M ~

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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?

One answer: The process of disk formation and viscous 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:

Disk formation and spreading Let’s make a numerical model of the disk evolution: Mass conservation: Angular momentum conservation:

Disk formation and spreading

Evolution of disk parameters Class O, I Class II (after Hueso & Guillot 2005)

Correlation M - M*

Accretion rate versus star mass Natta et al. 2005

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.

Accretion rate versus star mass

Disk mass versus star mass

Crystallinity of dust

10 -micron feature of crystalline dust Bouwman et al. 2001

Radial mixing Crystalline silicates produced here (thermal annealing). . . but they are observed here Turbulent transport Accretion Morfill & Völk (1984), Gail (2001) Wehrstedt & Gail (2002)

New idea:

Disk formation and spreading

Evolution of crystallinity

Summary • Self-consistent disk formation and evolution models: – can explain the M ~ M 2 relation. – provide a new view to dust crystallinity • New problem: Why are there no 100% crystalline disks observed?