The stability of non-uniform self gravitating system in the presence of non-uniform CRs pressure

Abstract

In this paper, we try to study the equilibrium structure and stability of a non-uniform self gravitating gaseous slab in vertical direction and in the presence of Cosmic Rays (CRs). Two models have been presented to study the effect of CRs pressure. In the first model, it is assumed that the CRs pressure follows the power law spatial function in vertical direction, and in the second model, it is assumed that the CRs pressure follows an increasing exponential function of $z$. The results show that the equilibrium structure of the system is different in the presence of CRs and in its absence. Gaseous slab has smaller thickness and lower density in the presence of CRs. Also, the perturbative stability analysis show that a non uniform system without CRs effect is unstable at the regions near to mid-plan and system becomes stable in bigger height. However, in the presence of CRs effect, all regions of system can be unstable. CRs effect increases the growth rate of instability in the inner part of slab and the presence of CRs lead to the instability in outer part of slab. Also, it is found that the critical wave length for instability is dependent to $z/H$ and it is not a constant value in all regions of slab.