Equilibrium of Gravitating System of Spherical Gas-Dust Cloud

Mohammed Abobaker

doi:10.13189/ujme.2019.070407

Abstract

In this paper, we take several different analytical and numerical approaches to studying the equilibrium of a gravitating system of a gas-dust cloud. We consider one-dimensional self-gravitating spherically symmetric fluid flow of a gas-dust cloud. We discuss the equilibrium of the system of gas-dust cloud by using simplified analytic stellar, polytropic models. A condition for the equilibrium of the cloud in the form of a differential equation is used. Using mass density in the cloud as a given function, we obtained the corresponding pressure analytically within the cloud and determined the central pressure. In dealing with a polytropic model, we found the analytical and numerical solution of the Lane-Emden equation for the various values of the polytropic index after that, central density and central pressure were obtained. Finally, the density and pressure of the cloud for the various values of the polytropic index are calculated. The result found by the simplified analytical method and the polytropic method is compared.

Highlights

A fundamental problem in the theory of star and planet formation is the physical structure of gas-dust clouds
The theory of the structure and evolution of the stars and planets have been formulated in the first half of the twentieth century; it is connected with names like Lane, Emden, Eddington, Chandrasekhar, and Fowle [1]
The equilibrium stellar models have been built by many authors e.g. [1, 6,7,8]

Summary

Introduction

A fundamental problem in the theory of star and planet formation is the physical structure of gas-dust clouds. The theory of the structure and evolution of the stars and planets have been formulated in the first half of the twentieth century; it is connected with names like Lane, Emden, Eddington, Chandrasekhar, and Fowle [1]. In the second half of the twentieth century, theories about the formation star and planet were greatly refined; this is due in part to new observation techniques and to computer simulations of its structure and evolution. It is connected with names like Penston, Larson, Hunter, Shu, and Safronov [2,3,4,5,6]. In 1966 Stein [10] discussed some way in which one

Simplified analytical stellar models

Lane-Emden equation

Density and pressure as functions of radius

Results and discussion

Summary and conclusion