A Semi-Analytical Description for the Formation and Gravitational Evolution of Protoplanetary Disks

Abstract

We investigate the formation process of self-gravitating protoplanetary disks in unmagnetized molecular clouds. The angular momentum is redistributed by the action of gravitational torques in the massive disk during its early formation. 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.

11 pages, 17 figures, accepted for publication in ApJ

References in corpus (22)

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Cited by in corpus (21)

• One Hundred First Stars : Protostellar Evolution and the Final Masses
• A revised condition for self-gravitational fragmentation of protoplanetary disks
• Dispersal of protoplanetary disks by the combination of magnetically driven and photoevaporative winds
• From Birth to Death of Protoplanetary Disks: Modeling Their Formation, Evolution, and Dispersal
• Gravitational instability in protostellar disks at low metallicities
• Apparent disk-mass reduction and planetesimal formation in gravitationally unstable disks in Class 0/I YSOs
• Photoevaporative Dispersal of Protoplanetary Disks around Evolving Intermediate-mass Stars
• Rapid growth of seed black holes during early bulge formation
• Formation, orbital and thermal evolution, and survival of planetary-mass clumps in the early phase of circumstellar disk evolution
• Structure Formation in a Young Protoplanetary Disk by a Magnetic Disk Wind
• Early evolution of disk, outflow, and magnetic field of young stellar objects: Impact of dust model
• Dust clearing by radial drift in evolving protoplanetary discs
• Disc population synthesis: Decrease in the solid mass reservoir through pebble drift
• Formation of massive stars under protostellar radiation feedback: Very metal-poor stars
• Orbital Evolution of Moons in Weakly Accreting Circumplanetary Disks
• Transition of BH feeding from the quiescent regime into star-forming cold disk regime
• The Origin of the Rotation Profiles in Star Forming Clouds
• Growth of Massive Disk and Early Disk Fragmentation in the Primordial Star Formation
• Massive Protostellar Disks as a Hot Laboratory of Silicate Grain Evolution
• The evolution of the flux-size relationship in protoplanetary discs by viscous evolution and radial pebble drift
• A semi-analytical model of the outer structure of protoplanetary discs formed by the collapse of a rotating molecular cloud