We use linear analysis to examine the effect of cosmic rays (CRs) on the
Parker-Jeans instability of magnetized self-gravitating gaseous disks. We adopt
a slab equilibrium model in which the gravity (including self-gravity) is
perpendicular to the mid-plane, the magnetic field lies along the slab. CR is
described as a fluid and only along magnetic field lines diffusion is
considered. The linearised equations are solved numerically. The system is
susceptible to Parker-Jeans instability. In general the system is less unstable
when the CR diffusion coefficient is smaller (i.e., the coupling between the
CRs and plasma is stronger). The system is also less unstable if CR pressure is
larger. This is a reminiscence of the fact that Jeans instability and Parker
instability are less unstable when the gas pressure is larger (or temperature
is higher). Moreover, for large CR diffusion coefficient (or small CR
pressure), perturbations parallel to the magnetic field are more unstable than
those perpendicular to it. The other governing factor on the growth rate of the
perturbations in different directions is the thickness of the disk or the
strength of the external pressure on the disk. In fact, this is the determining
factor in some parameter regimes.Comment: 19pages, 14figures submitted to Ap
