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 to stabilize the model, in particular as the sound speed a is very large in the stable domains 1.0233928 less than or equal to x < infinity but comparatively small in the unstable domains 0 < x < 1.0233928, where x = kR(0) is the dimensionless longitudinal wave number with k the axial wave number and R-0 the radius of the cylinder. In the absence of the compressibility factor the unstable domain is found to be 0 < x < 1.0678.