Analysis of Self-gravitational Instability of Partially-ionized Molecular Cloud under Radiative Hesat-Loss Fun

Abstract

The problem of Jeans instability of an infinite homogeneous self-gravitating of partially-ionized gaseous plasma carrying a uniform
magnetic field in the presence of thermal conductivity and the arbitrary radiative heat-loss function has been investigated. With the help of relevant linearized perturbation MHD equations of the problem using normal mode analysis, a general dispersion relation is obtained and the dispersion relation is discussed for longitudinal propagation and transverse propagation separately. The condition of instability as well as stability of the fluid has been discussed. The stability of the system is discussed by applying Routh-Hurwitz criterion. We found that the effect of collision with neutrals and magnetic field have a stabilizing influence, while thermal conductivity has destabilizing influence on the Jeans  instability. In addition, the classical Jeans result regarding the rise of initial break up has been considerably modified due to the arbitrary radiative heat-loss functions.