Gravitational instability of a heat-conducting plasma

The gravitational instability of an infinite, anisotropic, heat-conducting plasma is studied in this paper. It is found that, for the case of parallel propagation, the inclusion of heat-conduction terms in the fluid equations, in general, leads to overstability of the system, whereas the transverse propagation remains unaffected. We have solved numerically the dispersion relation corresponding to the parallel propagation and find that except for a range of wave numbers, the system is overstable. We also found that in the limit of vanishing zeroth-order heat flux, the condition for gravitational instability is similar to the Jeans's condition for instability for an isotropic plasma.