Protostars and Planets VI, Heidelberg, July 15-20, 2013
A SEMI-ANALYTICAL DESCRIPTION FOR THE FORMATION AND GRAVITATIONAL EVOLUTION OF PROTOPLANETARY DISKS
Takahashi, Sanemichi (Kyoto University / Nagoya University )
Inutsuka, Shu-ichiro (Nagoya University)
Machida , Masahiro (Kyushu University)
Since planets are expected to form in protoplanetary disks, planet-formation scenarios should depend on the structure of protoplanetary disks formed through realistic star formation processes. Recent three-dimensional numerical simulations suggest that protoplanetary disks are gravitationally unstable in their early formation stages because the masses of the disks remain very large. The angular momentum is redistributed by the action of gravitational torques in the massive disk. We investigate the formation process of self-gravitating protoplanetary disks in unmagnetized molecular clouds. We develop a simplified one- dimensional accretion disk model that takes into account the infall of gas from the envelope onto the disk and the transfer of angular momentum in the disk with an effective viscosity. First we evaluate the gas accretion rate from the cloud core onto the disk by approximately estimating the effects of gas pressure and gravity acting on the cloud core. We formulate the effective viscosity as a function of the Toomre Q parameter that measures the local gravitational stability of the rotating thin disk. We use a function for viscosity that changes sensitively with Q when the disk is gravitationally unstable. We find a strong self-regulation mechanism in the disk evolution. During the formation stage of protoplanetary disks, the evolution of the surface density does not depend on the other details of the modeling of effective viscosity, such as the prefactor of the viscosity coefficient. Next, to verify our model, we compare the time evolution of the disk calculated with our formulation with that of three-dimensional hydrodynamical simulations. The structures of the resultant disks from the one-dimensional accretion disk model agree well with those of the three-dimensional simulations. Our model is a useful tool for the further modeling of chemistry, radiative transfer, and planet formation in protoplanetary disks.
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