Structures in a class of magnetized scale-free discs

Abstract

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamic (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density ${\Sigma }_0\propto r^{-\alpha }$, a coplanar azimuthal magnetic field $B_0\propto r^{-\gamma }$, a consistent self-gravity and a power-law rotation curve $v_0\propto r^{-\beta }$ where $v_0$ is the linear azimuthal gas rotation speed. The barotropic equation of state $\Pi \propto {\Sigma }^n$ is adopted for both MHD background equilibrium and coplanar MHD perturbations where $\Pi$ is the vertically integrated pressure and $n$ is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among $\alpha$, $\beta$, $\gamma$ and $n$ such that only one parameter (e.g., $\beta$) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For nonaxisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e., fast and slow MHD density waves) can be derived once $\beta$ is specified. To complement the magnetized singular isothermal disc (MSID) analysis of Lou, we extend the analysis to a wider range of $-1/4<\beta <1/2$. As an example of illustration, we discuss specifically the $\beta =1/4$ 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.

25 pages

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Cited by in corpus (7)

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• Correlations among Multi-Wavelength Luminosities of Star-Forming Galaxies
• Global Perturbation Configurations in a Composite Disc System with an Isopedic Magnetic Field
• Axisymmetric stability criteria for a composite system of stellar and magnetized gaseous singular isothermal discs
• Global structures in a composite system of two scale-free discs with a coplanar magnetic field
• Scale-Free Thin Discs with an Isopedic Magnetic Field
• Global non-axisymmetric perturbation configurations in a composite disc system with an isopedic magnetic field: relation between dark matter halo and magnetic field