Gravitational instability of partially ionized molecular clouds

Stars are formed as a result of the gravitational (Jeans) collapse of dense clumps in interstellar clouds. These clouds are partially ionized by nearby ionizing sources. We investigate the gravitational instability in such molecular clouds considering the non-Boltzmannian distribution for electrons and ions, which is more realistic than the Boltzmannian distribution. Assuming the perturbation (fluctuation) response in a radial direction as a mathematical analogue of the x-direction in the plane geometry approximation in the form f ~ exp(ikx-iωt), the equations of motion for different species of the multi-fluid plasma are linearized. Jeans' swindle is used as a local approximation for the equilibrium and the dispersion relation is derived by usual normal mode analysis. Then, an analytical solution to the dispersion equation with an explanation of the effects on star formation is given.