The Parker Instability in a Thick Galactic Gaseous Disk. I. Linear Stability Analysis and Nonlinear Final Equilibria

A linear stability analysis of a multi-component and magnetized Galactic diskmodel is presented. The disk model uses the observed stratifications for thegas density and gravitational acceleration at the solar neighborhood and, inthis sense, it can be called a realistic model. The distribution of the totalgas pressure is defined by these observed stratifications, and the gaseous diskis assumed isothermal. The initial magnetic field is taken parallel to thedisk, with a midplane value of 5 $\mu$G, and its stratification along thez-axis is derived from the condition of magnetohydrostatic equilibrium in anisothermal atmosphere. The resulting isothermal sound speed is $\sim 8.4$ kms$^{-1}$, similar to the velocity dispersion of the main gas components within1.5 kpc from midplane. The thermal-to-magnetic pressure ratio decreases with$[z]$ and the warm model is Parker unstable. The dispersion relations show thatthe fastest growing mode has a wavelength of about 3 kpc, for both symmetricand antisymmetric perturbations, and the corresponding growth time scales areof about $3\times 10^7$ years. The structure of the final equilibrium stage isalso derived, and we find that the midplane antisymmetric (MA) mode gathersmore gas in the magnetic valleys. The resulting MA gas condensations havelarger densities, and the column density enhancement is a factor of about 3larger than the value of the initial stage. The unstable wavelengths and growthtimes for the multi-component disk model are substantially larger than those ofa thin disk model, and some of the implications of these results are discussed.Comment: Accepted for publication in ApJ, 18 text pages with 8 figure