Global non-axisymmetric perturbation configurations in a composite disc system with an isopedic magnetic field: relation between dark matter halo and magnetic field

摘要

We study global non-axisymmetric stationary perturbations of aligned andunaligned logarithmic spiral configurations in an axisymmetric compositedifferentially rotating disc system of scale-free stellar and isopedicallymagnetized gas discs coupled by gravity. The gas disc is threaded across by avertical magnetic field $B_z$ with a constant dimensionless isopedic ratio$\lambda\equiv 2\pi\sqrt{G} \Sigma^{(g)}/B_z$ of surface gas mass density$\Sigma^{(g)}$ to $B_z$ with $G$ being the gravitational constant. Ourexploration focuses on the relation between $\lambda$ and the dark matteramount represented by a ratio $f\equiv\bar{\Phi}/\Phi$ in order to sustainstationary perturbation configurations, where $\bar{\Phi}$ is the gravitationalpotential of a presumed axisymmetric halo of dark matter and $\Phi$ is thegravitational potential of the composite disc matter. High and low $\lambda$values correspond to relatively weak and strong magnetic fields given the samegas surface mass density, respectively. The main goal of our model analysis isto reveal the relation between isopedic magnetic fields and dark matter halo inspiral galaxies with globally stationary perturbation configurations. Ourresults show that, fairly strong yet realistic magnetic fields require aconsiderably larger amount of dark matter in aligned and unaligned cases thanweak or moderate magnetic field strengths. We discuss astrophysical andcosmological implications of our findings. For examples, patterns and patternspeeds of galaxies may change during the course of galactic evolution.Multiple-armed galaxies may be more numerous in the early Universe. Flocculentgalaxies may represent the transitional phase of pattern variations ingalaxies.