Effect of rotation on structure formation of degenerate anisotropic white dwarfs

Abstract

In the present work, the effect of rotation and finite Larmor radius (FLR) correction of ions on gravitational instability in the context of anisotropic white dwarf situation is investigated. The propagation dynamics of the various modes has been discussed using general dispersion relation which is obtained by quantum magnetohydrodynamic and Chew-Goldberger-Low (CGL) set of equations. The properties of dispersion relation are discussed for four different cases. The Alfven mode is modified with rotation and FLR correction while the gravitational mode remains unaffected by both the parameter for the case when rotation and wave vector both are parallel to magnetic field. Moreover, rotation (when longitudinal to magnetic field) becomes effective on gravitational mode in the perpendicular direction of propagation, as it modifies the condition of gravitational instability. The obtained analytical results are also discussed numerically. The implication of the present work is described for dense white dwarfs where the electrons are in a degenerate state with a strong magnetic field. The estimated value of Jeans length and Jeans mass are $L_{J1} = 5.5 \times 10^{7}~\mbox{m}$ and $M_{J1} = 3.5~M_{ \odot }$ respectively for rotating anisotropic plasma which corresponds to super Chandrashekhar white dwarfs while for non-rotating degenerate magnetized plasma, the Jeans length is $L_{J1}' = 4.7 \times 10^{7}~\mbox{m}$ and Jeans mass is $M_{J1}' = 2.1~M_{ \odot }$ . The presence of rotation effectively increases the critical mass of white dwarf.