Propagation of magnetohydrodynamic waves and gravitational instability in the astrophysical anisotropic and heat conducting plasma

The hydrodynamic instability of a magnetised, self-gravitating rotating anisotropic plasma is analysed in the collisionless approximation and taking into account the heat flux vector on the basis of the modified Chew-Goldberger-Low equations. The dispersion relation is derived and simplified cases of propagation of small-amplitude perturbation waves are discussed, with modified analytical criteria for hydrodynamic instability obtained. In accordance with the general dispersion relation, three cases when the propagation of the perturbation wave passes across, along, and obliquely to the magnetic field vector are specifically considered. It is shown that anisotropic pressure and heat flux not only modify the classical Jeans instability criterion but also induce new unstable regions. It is found that the presence of uniform plasma rotation reduces the critical wave number and has a stabilising effect on the gravitational instability criterion for transverse propagation of the perturbation wave and has no effect in the case of its longitudinal propagation. The inclusion of thermal flows leads to the appearance of two additional wave modes. The results obtained are important for the construction of evolutionary magnetohydrodynamic models of collisionless astrophysical plasma.