International Scholarly Research Network ISRN Astronomy and Astrophysics Volume 2012, Article ID 420938, 14 pages doi:10.5402/2012/420938 Research Article Effect of Radiative Heat-Loss Function and Finite Larmor Radius Corrections on Jeans Instability of Viscous Thermally Conducting Self-Gravitating Astrophysical Plasma Sachin Kaothekar 1, 2 and R. K. Chhajlani 1 1 School of Studies in Physics, Vikram University, Madhya Pradesh, Ujjain 456010, India 2 Department of Physics, Mahakal Institute of Technology, Madhya Pradesh, Ujjain 456664, India Correspondence should be addressed to Sachin Kaothekar, sackaothekar@gmail.com Received 3 April 2012; Accepted 15 June 2012 Academic Editors: C. W. Engelbracht, A. Ferrari, F. Fraschetti, I. Goldman, and C. Meegan Copyright © 2012 S. Kaothekar and R. K. Chhajlani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The effect of radiative heat-loss function and finite ion Larmor radius (FLR) corrections on the self-gravitational instability of infinite homogeneous viscous plasma has been investigated incorporating the effects of thermal conductivity and finite electrical resistivity for the formation of a star in astrophysical plasma. The general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. Furthermore the wave propagation along and perpendicular to the direction of external magnetic field has been discussed. Stability of the medium is discussed by applying Routh Hurwitz’s criterion. We find that the presence of radiative heat-loss function and thermal conductivity modify the fundamental Jeans criterion of gravitational instability into radiative instability criterion. From the curves we see that temperature dependent heat-loss function, FLR corrections and viscosity have stabilizing effect, while density dependent heat-loss function has destabilizing effect on the growth rate of self-gravitational instability. Our result shows that the FLR corrections and radiative heat-loss functions affect the star formation. 1. Introduction The problem of self-gravitational instability is widely investi- gated due to its relevance to the fragmentation of interstellar medium and its role in star formation. Also, the self- gravitational instability of molecular clouds is connected to the cloud collapse and star formation. Hayashi [1] has dis- cussed the problem of evolution of protostars and discusses the different phase of formation of protostar in connection with variation of temperature and density. Shu et al. [2] have investigated the problem of star formation in molecular clouds and concluded that the star formation occurs mainly in four phases. In this problem, the self-gravitational insta- bility of dust and gas plays important role. Draine and Mckee [3] have studied the theory of interstellar shocks. Mckee and Ostriker [4] have discussed the theory of star formation. They concluded that the key dynamical processes involved in star formation are turbulence, magnetic fields, and self- gravity. In this connection, the gravitational instability of infinite homogeneous self-gravitating magnetized and rotating plasma is also discussed by Chandrasekhar [5]. Several authors (Pacholczyk and Stodolkiewicz [6], Nayyar [7], and Shaikh et al. [8]) have investigated the problem of gravitational instability of plasma with different physical parameters such as viscosity, finite electrical conductivity, Hall current, thermal conductivity, magnetic field, and rota- tion. Yang et al. [9] have investigated the problem of large- scale gravitational instability and star formation. Borah and Sen [10] have investigated the gravitational instability of partially ionized molecular clouds considering the effects of electrons, ions, and charged dust grains. Avinash et al. [11] have studied the dynamics of self-gravitating dust clouds and the formation of planetesimals. Thus we find that a large number of problems are discussed for self-gravitating dusty and nondusty plasma with different parameters under various assumptions due to its importance in star formation and in many astrophysical situations.