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

TL;DR

This paper presents a semi-analytical, one-dimensional model for the formation and evolution of self-gravitating protoplanetary disks, incorporating gas infall and gravitational stability effects, validated against 3D simulations.

Contribution

It introduces a simplified disk model with a Q-dependent viscosity to describe early disk formation and evolution, aligning well with 3D hydrodynamical simulations.

Findings

Strong self-regulation in disk evolution.

Surface density evolution is insensitive to viscosity prefactors.

Model agrees with 3D simulation structures.

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.