Stationary models for fast and slow logarithmic spiral patterns in disc galaxies

A recent wavelet analysis on multiwavelength image data of the nearby spiral galaxy NGC 6946 revealed a multi‐arm spiral structure that persists well into the outer differentially rotating disc region. The extended spiral arms in polarized radio‐continuum emission and in red light appear interlaced with each other, while the spiral arms in emissions of total radio continuum, of H α from H  ii regions, and of neutral hydrogen all trace the red‐light spiral arms, although to a somewhat lesser extent. The key issue now becomes how to sustain extended slow magnetohydrodynamic (MHD) density wave features in a thin magnetized disc with a flat rotation curve. We describe here a theoretical model to examine stationary non‐axisymmetric logarithmic spiral configurations constructed from a background equilibrium of a magnetized singular isothermal disc (MSID) with a flat rotation curve and with a non‐force‐free azimuthal magnetic field. It is found analytically that two types of stationary spiral MSID configurations may exist, physically corresponding to the two possibilities of fast and slow spiral MHD density waves. Such stationary MHD density waves are possible only at proper MSID rotation speeds. For the fast MSID configuration, logarithmic spiral enhancements of magnetic field and gas density are either in phase in the tight‐winding regime or shifted with a spatial phase difference ≳π/2 for open spiral structures. For the slow MSID configuration, logarithmic spiral enhancements of magnetic field and gas density are either out of phase in the tight‐winding regime or shifted with a spatial phase difference for open spiral structures and persist in a flat rotation curve. For NGC 6946, several pertinent aspects of the slow MSID scenario with stationary logarithmic spiral arms are discussed. The two exact solutions can be also utilized to test relevant numerical MHD codes.