Viscous disk models evolution

Evolution of the Solar Nebula. 04.4.2.1 Viscous accretion disk models... 

Given that convective instabihty is no longer considered to be a possible driver of disk evolution, the Ruden and Pollack (1991) models are interesting, but not likely to be applicable to the solar nebula. Unfortunately, httle effort has gone into generating detailed viscous accretion models in the interim the theoretical focus seems... 

While the viscous model for the evolution of protoplanetary disks has had some success in matching some of the general properties of protoplanetary disks, such as the observed mass accretion rates and effective temperatures, the exact source of the viscosity remains the subject of ongoing studies. Currently, the most popular candidates for driving the mass transport in protoplanetary disks are the magneto-rotational instability (MRI) and gravitational instability. A third candidate, shear instability, has also been proposed based on laboratory experiments of rotating fluids (Richard Zahn 1999), but questions remain as to whether these results can be extended to the scale of protoplanetary disks. 

A comparison of disk-dispersal timescales, such as that presented in Fig. 1 of Hollenbach et al. (2000), suggests that viscous spreading and photoevaporafion are the major dispersal mechanisms. Models combining these two mechanisms were first developed by Clarke etal. (2001) and later refined by Alexander etal. (2006a,b). The evolution of an accreting and photoevaporating disk can be summarized as follows. In the first 106 7yr viscous evolution proceeds relatively unperturbed by photoevaporafion. Once the viscous accretion inflow rates fall below the photoevaporation rates a gap opens up close to rg and the inner disk rapidly ( 105 yr) drains onto the central star. At this point direct ionization of the disk inner edge (the flux is not anymore attenuated by the inner-disk atmosphere) disperses the... 

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