Self-gravitational instability of dusty plasma with dissipative effects

The influence of resistivity and viscosity effects on Jeans self-gravitational instability of dusty plasma is studied. The governing equations are constructed using magnetohydrodynamic model for dusty plasma. The general dispersion relation and Jeans criteria for instability are obtained employing the plane wave solutions on linearized perturbation equations. The Jeans criterion is found to be unaffected due to resistivity and viscosity parameter. The dispersion relation is analyzed for various directions of propagation with respect to magnetic field. The numerical calculations have been performed to show the effects of resistivity and viscosity on the growth rate of Jeans instability. It is observed that the presence of resistivity has destabilizing influence while viscosity has stabilizing effects on the growth rate of the Jeans instability. The analytical results are verified by the numerical analysis using both real and normalized astrophysical parameters. The present work is applicable to various space and astrophysical plasma systems, particularly for molecular clouds, protostellar disks, interstellar & circumstellar clouds and the ionosphere of the earth, etc.