Thermal convective and rotational instability in dissipative magnetohydrodynamics

The thermal convective and magnetorotational instability is investigated by means of magnetohydrodynamic equations including anisotropic viscosity and resistivity dissipative effects. Magnetic force lines are assumed to be initially isothermal and the heat is restricted to being primarily transported along the magnetic force lines. To obtain the analytic expressions for the growth rate and instability criteria, we neglect the cross-field resistivity by applying our result to the weakly ionized environment. Under this assumption, the general dispersion relation describing the local thermal convective and magnetorotational instability is derived. The effects on the dispersion relation due to anisotropic resistivity and viscosity are discussed. Both the resistivity and viscosity show stabilizing effect on the thermal convective and rotational instability but do not affect the instability criterion. The analytic expression governing the growth rate is presented for Prandtl number Pm=1 case.