Modified Jeans instability of magnetized viscous spin 1/2 quantum plasma with resistive effects and Hall current

Abstract

The effect of Hall current on Jeans self-gravitational instability is examined for finitely conducting dense quantum viscous plasma in the presence of spin generated magnetization. The basic equations of the problem are constructed using quantum magneto hydrodynamic (QMHD) model. The Hall and resistivity terms are incorporated in the idealized Ohm’s law and spin induced magnetization and viscosity terms are incorporated to the momentum equations. The general dispersion relation is found to be modified due to the presence of Hall current, electrical resistivity and viscosity parameter along with the spin induced magnetization. The dispersion relation is further reduced for both transverse and longitudinal mode of propagations. In the transverse mode of propagation the Jeans condition of instability is modified due to Alfven velocity, magnetization parameter and quantum corrections, and the growth rate of instability is found to be modified due to the electrical resistivity, viscosity, magnetization parameter and quantum corrections but remains unaffected by the presence of Hall current. In longitudinal direction of propagation the gravitational mode is affected due to the viscosity and quantum parameter while the Jeans condition of instability depends only upon the quantum correction. The Alfven mode in longitudinal direction gets modified due to the electrical resistivity, Hall current, viscosity and magnetization parameter however, it is found to be independent of quantum corrections. The numerical observations are also presented to show the effect of electrical resistivity, magnetization and quantum corrections on the growth rate of instability.