Self Gravitating Instability of a Compressible Fluid Cylinder

The self-gravitating instability of a compressible-inviscid fluid cylinder immersed into a self-gravitating tenuous medium of negligible motion is developed. The stability criterion is derived based on the linear perturbation technique. Some previous reported works are recovered. The effect of different factors on the fluid cylinder instability is discussed. The compressibility has a tendency for a stabilizing the model in particular as the sound speed $a$ is very large in the stable domains $1.0233928\leq x<\infty$ but comparatively small in the unstable domains $0<x<1.0233928$ where $x=k R_{_{0}}$ is the dimensionless longitudinal wavenumber with $k$ is the axial wavenumber and $R_{_{0}}$ is the radius of the cylinder. In the absence of the compressibility factor the unstable domain is found to be $0<x<1.0678$.