Structures in a class of magnetized scale-free discs

Abstract

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 Σ 0 r -α , a coplanar azimuthal magnetic field B 0 oc r -γ , a consistent self-gravity and a power-law rotation curve v 0 oc r -β , where v 0 is the linear azimuthal gas rotation speed. The barotropic equation of state n Σ n is adopted for both MHD background equilibrium and coplanar MHD perturbations where n is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among a, β, y 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.