Structures in a class of magnetized scale-free discs

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamics (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density ∑₀ α r^-α, a coplanar azimuthal magnetic field B₀ α r^-γ, a consistent self-gravity and a power-law rotation curve ν₀ α r^-α, where ν₀ is the linear azimuthal gas rotation speed. The barotropic equation of state Π α ∑ⁿ is adopted for both MHD background equilibrium and coplanar MHD perturbations where Π is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among α, β, γ and n such that only one parameter (e.g. β) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For non-axisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e. fast and slow MHD density waves) can be derived once β is specified. To complement the magnetized singular isothermal disc analysis of Lou, we extend the analysis to a wider range of -1/ 4 < β< 1/2. As an illustrative example, we discuss specifically the β= 1/4 case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.