On the Effect of Non-Uniform Magnetic field on the Jeans Instability of a Viscoelastic Medium

In the present paper the problem of Jeans instability of a self gravitating viscoelastic medium in the presence of nonuniform magnetic field for both longitudinal and transverse mode of wave propagation under the kinetic and hydrodynamic limits has been investigated, using the generalized hydrodynamic model. It is found that magnetic field has no effect on the Jeans criterion for the onset of gravitational instability in case of longitudinal mode of wave propagation, whereas it modifies the Jeans criterion in the case of transverse mode of wave propagation and has stabilizing effect on the onset of instability. Further, it is observed that the magnetic field has no effect on the growth rate of Jeans instability of a viscoelastic medium. The effects of shear viscosity, bulk viscosity and Mach number on the Jeans criterion and on the growth rate of Jeans instability have also been studied numerically and the obtained results are depicted graphically, for both strongly coupled plasma (SCP) and weakly coupled plasma (WCP).