Global Perturbation Configurations in a Composite Disc System with an Isopedic Magnetic Field

Abstract

We construct stationary global configurations of both aligned and unaligned logarithmic spiral perturbations in a composite disc system of stellar and isopedically magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. The thin gaseous SID is threaded across by a vertical magnetic field B_z with a constant ratio of the surface gas mass density to B_z. There exist two classes of stationary magnetohydrodynamic (MHD) solutions with in-phase and out-of-phase density perturbations. For both aligned and unaligned cases with azimuthal periodicities |m|\geq 2 (m is an integer), there may be two, one, and no solution situations, depending on the chosen parameters. For the transition criteria from an axisymmetric equilibrium to aligned secular bar-like instabilities, the corresponding T/|W| ratio can be much lower than the oft-quoted value of T/|W|\sim 0.14, where T is the total rotational kinetic energy and W is the total gravitational potential energy plus the magnetic energy. The T/|W| ratios for the two sets of solutions in different ranges are separated by m/(4m+4). For the unaligned cases, we study marginal stabilities for axisymmetric (m=0) and non-axisymmetric (m\neq 0) disturbances. The gravitational influence of an axisymmetric dark matter halo on the background is also examined. The global analytical solutions and their properties are valuable for testing and benchmarking numerical MHD codes. Our model analysis contains more realistic elements and offers useful insights into the structures and dynamics of disc galaxies consisting of stars and magnetized interstellar medium. In the presence of star burst activities, supernovae, hypernovae, superbubbles etc., our open magnetic field geometry in disc galaxies bears strong implications on circumnuclear and spiral galactic winds.