Analytic solutions to the accretion of a rotating finite cloud towards a central object I. Newtonian approach

TL;DR

This paper presents a steady, analytic model for the accretion of a finite rotating gas cloud onto a central object, generalizing previous models and accounting for diverse boundary conditions in protostellar environments.

Contribution

It introduces a new analytic solution for finite rotating clouds, extending Ulrich's model, with implications for understanding protostar formation in dense clusters.

Findings

Deviations from Ulrich's density profiles and streamlines.

Prediction of a distinct equatorial accretion disc radius.

Model accommodates various external physical boundary conditions.

Abstract

We construct a steady analytic accretion flow model for a finite rotating gas cloud that accretes material to a central gravitational object. The pressure gradients of the flow are considered to be negligible and so, the flow is ballistic. We also assume a steady flow and consider the particles at the boundary of the spherical cloud to be rotating as a rigid body, with a fixed amount of inwards radial velocity. This represents a generalisation to the traditional infinite gas cloud model described by Ulrich (1976). We show that the streamlines and density profiles obtained deviate largely from the ones calculated by Ulrich. The extra freedom in the choice of the parameters on the model can naturally account for the study of protostars formed in dense clusters by triggered mechanisms, where a wide variety of external physical mechanisms determine the boundary conditions. Also, as expected, the model predicts the formation of an equatorial accretion disc about the central object with a radius different from the one calculated by Ulrich (1976).