Radiative and Gravitational Modes and Instabilities in an Inhomogeneous Magneto Dusty Plasma with Charge Variation

The Jeans instability of collisional magnetized dusty plasmas is examined incorporating polarization force, charge variation of dust grains, and radiative cooling of ion and electron species. The collisional effects of dust grains with neutrals are considered with sufficient background of neutral particles. A general dispersion relation is obtained using normal mode analysis technique which is found to be modified due to polarization force, dust charge fluctuation, and radiative effects of electrons and ions. The analytical discussion of general dispersion relation is presented in parallel and perpendicular mode of propagation. The Routh Hurwitz criterion is applied to analyze the stability of the considered system. We report the existence of a modified cyclotron mode in parallel propagation and a purely collisional mode in perpendicular propagation along with the gravitational mode. These modes are discussed analytically, as well as numerically, to show the importance of different parameters considering different situations. The implications of the result have been discussed for the molecular clouds.