Global perturbation configurations in a composite disc system with an isopedic magnetic field

Yu-Qing Lou 0 1 2 3 Yue Wu 2 0 Department of Astronomy and Astrophysics, The University of Chicago , 5640 S. Ellis Ave, Chicago, IL 60637 , USA 1 Centre de Physique des Particules de Marseille (CPPM)/Centre National de la Recherche Scientifique (CNRS)/Institut National de Physique Nucle aire et de Physique des Particules (IN2P3) et Universite de la Me diterrane e Aix-Marseille II , 163, Avenue de Luminy F-13288 Marseille, Cedex 09 , France 2 Physics Department and Tsinghua Center for Astrophysics (THCA), Tsinghua University , Beijing 100084 , China 3 National Astronomical Observatories, Chinese Academy of Sciences , A20, Datun Road, Beijing 100012 , China A B S T R A C T 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. Earlier models are generalized to a more general theoretical framework. 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 . In reference to SID models of Shu & Li, Shu et al., Lou & Shen, Lou & Zou, Shen and Liu & Lou, there exist two classes of stationary magnetohydrodynamic (MHD) solutions with in-phase and out-of-phase density perturbations here. Relevant parameter regimes are explored numerically. For both aligned and unaligned cases with azimuthal periodicities |m| 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 | 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 = 0) disturbances. By including the gravitational influence of an axisymmetric dark matter halo on the background, the case of a composite partial magnetized singular isothermal discs (MSID) system is also examined. The global analytical solutions and their properties are valuable for testing and benchmarking numerical MHD codes. For astrophysical applications to large-scale galactic dynamics, 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 (ISM). In particular, 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. - The theoretical magnetohydrodynamic (MHD) disc model we set out to formulate in this paper is to explore possible large-scale global perturbation structures and stationary MHD density waves (Fan & Lou 1996; Lou & Fan 1998b) in a composite system of a stellar disc and an isopedicallly magnetized gaseous disc intended for the interstellar medium (ISM). These two gravitationally coupled discs are approximately treated as fluid and magnetofluid, respectively, and are both geometrically idealized as razor-thin singular isothermal discs (SIDs) with the gaseous SID being threaded across by an almost vertical magnetic field throughout. In astrophysical contexts of large-scale structures in disc galaxies, we also include gravitational effects of a massive axisymmetric dark matter halo and adopt a background composite system of two coupled partial SIDs (Syer & Tremaine 1996; Shu et al. 2000; Lou 2002; Lou & Shen 2003; Shen & Lou 2003; Lou & Zou 2004; Shen & Lou 2004a,b; Lou & Zou 2005; Shen, Liu & Lou 2005). Our motivation is to construct solutions with combined analytical and numerical techniques, to understand their basic properties, to provide observational diagnostics and to reveal or speculate physical implications. Chakrabarti, Laughlin & Shu (2003) studied substructures in grand-design spiral galaxies, such as branches, spurs and feathers, using a two-component disc model in which the gas component responds passively and non-linearly to the potential of a rigidly rotating spiral structure involving old stars and haloes. Here, we treat a dynamically coupled two-component disc system with or without a massive dark matter halo and focus on stationary global MHD density wave configurations. Specifically, we construct stationary MHD configurations for aligned and unaligned logarithmic spiral perturbations in a composite disc system of two SIDs with flat rotation curves. For observational diagnostics of nearby disc galaxies, we also examine phase relationships among perturbation patterns of the stellar surface mass density, the ISM surface mass density and the isopedic magnetic field. We now proceed to provide the more general background information relevant to the idealized MHD composite disc problem to be formulated and investigated here. In a pioneering work on a composite disc system of stellar and gaseous discs dynamically coupled by gravity, Lin & Shu (1966, 1968) proposed a combined approach involving a distribution function for the stellar disc and a fluid description for the gas disc to derive and analyse the local dispersion relation of coplanar galactic spiral density waves in the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation. The basic physical scenario is that stars form out of gas clouds in the ISM disc, leading to the coexistence of a stellar disc and a magnetized ISM disc at a later evolution stage of disc galaxy. Since the seminal work of Lin & Shu, there have been extensive theoretical researches on density wave oscillations, perturbation configurations and stability properties of a rotating composite disc system, mainly in the galactic context. Kato (1972) studied oscillations and overstabilites of density waves using a formalism similar to that of Lin & Shu (1966, 1968). Jog & Solomon (1984a,b) discussed the growth of local axisymmetric perturbations using a two-fluid formalism in a composite disc system. Bertin & Romeo (1988) investigated the role of a gas disc for spiral modes in a two-fluid model framework. The influence of interstellar gas on oscillations and stabilities of spheroidal galaxies was studied by Vandervoort (1991a,b). In order to account for the effects of the disc thickness, Romeo (1992) adopted a two-fluid approach to investigate a two-component disc system with finite disc thickness. Lowe et al. (1994) performed an extensive analysis for morphologies of disc galaxies. Different effective Qeff parameters (Safronov 1960; Toomre 1964) have been suggested for the axisymmetric stability of a composite disc system in a two-fluid formalism by Elmegreen (1995) and Jog ( (...truncated)