Infall onto the Protoplanetary Disk during the Gravitational Collapse of a Molecular Cloud

Abstract

The development of models for matter infall from a collapsing molecular cloud is an essential part of numerical studies on the formation and evolution of protoplanetary disks. In this article, the widely used Nakamoto and Nakagawa (1994) model is analyzed and modifications are proposed to complement the initial model. These improvements include calculation for the outer boundary of a molecular cloud and refinement of the initial density distribution within. Also, due to the finite size of a cloud, the approach for computing the rate of mass infall onto the protoplanetary disk during collapse is modified. The proposed enhancements are aimed at eliminating the key limitations of the initial model, but do not affect its advantages, such as simplicity in numerical implementation. Using the modified model, we investigate the duration of the embedded phase of the evolution of young stellar objects and compare the modeling results with observational data. The results indicate a shorter duration of the embedded phase of the evolution of young stellar objects, especially in star-forming regions with a high amplitude of the initial density perturbation of prestellar condensation.