On the Jeans Criterion of a Stratified Heat Conducting Gaseous Medium in the Presence of Non-uniform Rotation and Magnetic Field

The problem of self-gravitational instability of an infinite, homogeneous stratified gaseous medium with finite thermal conductivity and infinite electrical conductivity, in the presence of non-uniform rotation and magnetic field in the Chandrasekhar’s frame of reference, is studied. It is found that the magnetic field, whether uniform or non-uniform, has no effect on the Jeans’ criterion for gravitational instability and remains essentially unaffected. However, the thermal conductivity has the usual stabilizing effect on the criterion that the adiabatic sound velocity occurring in the Jeans criterion is replaced by the isothermal sound velocity. Thus, the present analysis extends the results of Chandrasekhar for the case of heat conducting medium and for non-uniform rotation and magnetic field.