Jeans gravitational instability of a magnetized rotating collision-less anisotropic plasma using generalized laws of double polytropy

The problem of gravitational instability of an astrophysical magnetized rotating plasma with an anisotropic pressure tensor is investigated on the basis of the quasi-hydrodynamic Chew-Goldberger-Low (CGL) equations, modified by using generalized laws of dual polytropic theory. Using a general form of the dispersion relation obtained by the normal mode method, we discuss the propagation of oscillating magneto-hydrodynamic waves of small amplitude perturbation in an infinite homogeneous plasma medium for the transverse, longitudinal and inclined directions with respect to the magnetic field vector. A number of modified Jeans gravitational instability criteria obtained for isotropic MHD and anisotropic CGL equations of rarefied plasma and distinguished by different orientations of the vectors of propagation of the disturbing wave, magnetic field, and rotation axis of the hydromagnetic fluid are analyzed. It is shown that rotation and anisotropic pressure not only change the classical criterion of gravitational instability of astrophysical magnetized plasma, but also cause new unstable regions.