Protoplanetary disk structure and evolution

The masses, sizes, and overall structure of protoplanetary disks are important to quantify as they set the total amount and the distribution of planet-forming materials. However, over time disks evolve and the dust contained within is transported, processed, and accreted into larger bodies. This evolution plays a critical role in determining both the physical and chemical properties of the dust, and by extension, of the planets that will eventually form. 

1 Viscous evolution and mass accretion through the disk 

Protoplanetary disks are not static objects. In addition to the orbital motion of the gas, there is radial motion as well. It is this radial motion that causes matter from 

Modeling a disk by solving the full three-dimensional Navier-Stokes equations is a complicated task. Moreover, it is still not fully understood what is the cause of frictional forces in the disk. Molecular viscosity is by orders of magnitude too small to cause any appreciable accretion. Instead, the most widely accepted view is that instabilities within the disk drive turbulence that increases the effective viscosity of the gas (see Section 3.2.5). A powerful simplification of the problem is (a) to assume a parameterization of the viscosity, the so-called a-viscosity (Shakura Syunyaev 1973) ((3-viscosity in the case of shear instabilities, Richard Zahn 1999) and (b) to split the disk into annuli, each of which constitutes an independent one-dimensional (ID) vertical disk structure problem. This then constitutes a 1+1D model a series of ID vertical models glued together in radial direction. Many models go even one step further in the simplification by considering only the vertically integrated or representative quantities such as the surface density X(r) = p(r, z.)dz 

The dynamical evolution of the disk as it undergoes such viscous evolution is described by the equation  

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There is an extensive bibliography regarding protoplanetary disks and their evolution (Williams and Cieza 2011), structure (Dullemond and Monnier 2010) and composition (Wood 2008). For this reason, in Sect. 6.1 a brief introduction of the science behind the circumstellar disks focusing on the disk properties around the far infrared frequency range is given. In Sect. 6.2 a simulation of a circumstellar disk is presented. This simulated disk is fed to the instrument simulator FllnS, and the obtained results are described in Sect. 6.3 for both an ideal instrument and for a more realistic instrument. 

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