### 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 ∑_{0} α r^{-α}, a coplanar azimuthal magnetic field B_{0} α r^{-γ}, a consistent self-gravity and a power-law rotation curve ν_{0} α r^{-α}, where ν_{0} 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.

Original language | English (US) |
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Pages (from-to) | 1333-1356 |

Number of pages | 24 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 356 |

Issue number | 4 |

DOIs | |

State | Published - Feb 1 2005 |

Externally published | Yes |

### Keywords

- Galaxies: Kinematics and dynamics
- Galaxies: Spiral
- Galaxies: Structure
- Ism: Magnetic fields
- MHD
- Stars: Formation

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Monthly Notices of the Royal Astronomical Society*,

*356*(4), 1333-1356. https://doi.org/10.1111/j.1365-2966.2004.08563.x