Mechanical Stabilization of Magneto-Gravitational Instability in Rotating Viscoelastic Media through a Second Order Generalized Hydrodynamic Framework

A theoretical study of magneto-gravitational instability of a rotating, finitely conducting viscoelastic substance is presented in this paper by a second-order generalized hydrodynamic (GH) system. The given model integrates the effect of the viscoelastic relaxation time, shear viscosity, finite electrical resistivity, constant magnetic field, self-gravity and Coriolis forces because of rotation. Normal-mode analysis is used to derive and analyze linearized perturbation equations of both strongly coupled plasma (SCP) and weakly coupled plasma (WCP) regimes. The generalized complex dispersion relation is acquired and analysed on the basis of the Hurwitz stability criteria and dimensionless parameters. These findings reveal that rotation and finite resistivity have no effect on the modified threshold of the Jeans instability but greatly slow down the growth rate of unstable modes. Rotational forces make the system stable in the presence of Coriolis forces and the viscoelastic relaxation adds some elastic memory that slows the gravitational collapse. Higher viscosity and resistivity also inhibit more the short wavelength perturbations. The relative comparison shows that SCP media have lower growth rates compared to WCP regimes.