SIMBAD references

We construct both aligned and unaligned (logarithmic spiral) stationary configurations of non-axisymmetric magnetohydrodynamic (MHD) discs from either a full or a partial razor-thin power-law axisymmetric magnetized singular isothermal disc (MSID) that is embedded with a coplanar azimuthal magnetic field B_θof a non-force-free radial scaling r ^–1/2 and that rotates differentially with a flat rotation curve of speed aD, where a is the isothermal speed of sound and D is the dimensionless rotation parameter. Analytical solutions and stability criteria for determining D ² are derived. For aligned non-axisymmetric MSIDs, eccentric m = 1 displacements may occur at arbitrary D ² in a full MSID but are allowed only with a ² D ² = C ²_A/2 in a partial MSID (where C_Ais the Alfvén speed), while each case of|m |≥ 1 gives two possible values of D ² for purely azimuthal propagations of fast and slow MHD density waves (FMDWs and SMDWs) that appear stationary in an inertial frame of reference. For disc galaxies modelled by a partial MSID resulting from a massive dark matter halo with a flat rotation curve and a ² D ² ≫ C ²_A, stationary aligned perturbations of m = 1 are not allowed. For unaligned logarithmic spiral MSIDs with|m|≥ 1, there exist again two values of D ², corresponding to FMDWs and SMDWs that propagate in both radial and azimuthal directions relative to the MSID and that appear stationary in an inertial frame of reference. The larger D ² is always physically valid, while the smaller D ² is valid only for a > C_A/2 with a positive surface mass density Σ₀. For observational diagnostics, we examine the spatial phase relationships among enhancements of gas density and magnetic field, and velocity perturbations. These results are useful for probing magnetized bars, or lopsided, normal and barred spiral galaxies and for testing numerical MHD codes. In the case of NGC 6946, interlaced optical and magnetic field spiral patterns of SMDWs can persist in a disc with a flat rotation curve. Theoretical issues regarding the modal formalism and the MSID perspective are also discussed.