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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?.
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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 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:
Mass conservation: Angular momentum conservation: Disk formation and spreading Let’s make a numerical model of the disk evolution:
Class II Class O, I Evolution of disk parameters (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 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.
10-micron feature of crystalline dust Bouwman et al. 2001
Crystalline silicates produced here (thermal annealing)... ...but they are observed here Turbulent transport Radial mixing Accretion Morfill & Völk (1984), Gail (2001) Wehrstedt & Gail (2002)
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?