Structure formation through self-gravitational instability in degenerate and non-degenerate anisotropic magnetized plasma

Abstract

The self-gravitational instability is examined for non-degenerate and degenerate magnetized plasma. In the case of non-degenerate collisionless magnetized plasma the pressure is considered as anisotropic while in the case of degenerate situations it is taken as isotropic. The effect of finite Larmor radius correction of non-degenerate ions and viscous dissipation is taken into account in both the cases. Firstly in non-degenerate anisotropic plasma the conventional magnetohydrodynamic model is used to construct basic set of equations within the framework of modified Chew–Goldberger and Low theory. Secondly, in the case of degenerate isotropic plasma, which is considered to be composed of degenerate electrons and non-degenerate ions, the model equations are constructed using quantum magneto hydrodynamic model. The dynamics of degenerate particles are governed by Bohm and exchange potentials. The general dispersion relations are derived for both degenerate and non-degenerate situations separately using linearized perturbation equations. The results are discussed analytically and numerically for various modes of propagation. In case of non degenerate strongly magnetized plasma the effects of stress tensor anisotropy dominate over the influence of FLR effects while the FLR effects prevail in the weak magnetic field region. In case of isotropic degenerate plasma the implications of exchange parameter on the Jeans mass have been estimated and it is found that the increase in exchange parameter increases the limit of Jeans mass. The Jeans length and Jeans mass have been estimated for the white dwarf stars as $L_{J} \approx 2.1 \times 10^{11}~\mbox{m}$ and $M_{J} \approx 5 \times 10^{39}~\mbox{kg}$ respectively assist the existence of super Chandrasekhar white dwarfs.