Jeans instability of partially-ionized self-gravitating viscous plasma with Hall effect FLR corrections and porosity

The problem of Jeans gravitational instability and radiative instability is investigated for partially ionized self-gravitating plasma which has connection in astrophysical condensations and formation of objects. A general dispersion relation has been derived with the help of relevant linearized perturbation equations, using the normal mode analysis method. Effects of FLR corrections, radiative heat-loss function and collisions with neutrals on the Jeans criterion of self-gravitational instability of the system are discussed. The conditions of instability are derived for a temperature-dependent and density-dependent heat-loss function with thermal conductivity and FLR corrections for some special case. The stability of the system is discussed by using Routh-Hurwitz's criterion. Numerical calculations have been performed to discuss the dependence of the growth rate of the Jeans gravitational instability on the various physical parameters. The FLR corrections, viscosity, porosity, magnetic field, and neutral collision have stabilizing influence while finite electrical resistivity and permeability have a destabilizing influence on the growth rate of the gravitational instability. Our results are helpful for understanding the formation of dense molecular clouds.