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

Abstract

A linear stability analysis of a multi-component and magnetized Galactic disk model is presented. The disk model uses the observed stratifications for the gas density and gravitational acceleration at the solar neighborhood and, in this sense, it can be called a realistic model. The distribution of the total gas pressure is defined by these observed stratifications, and the gaseous disk is assumed isothermal. The initial magnetic field is taken parallel to the disk, with a midplane value of 5 µG, and its stratification along the z-axis is derived from the condition of magnetohydrostatic equilibrium in an isothermal atmosphere. The resulting isothermal sound speed is ∼ 8.4 km s −1 , similar to the velocity dispersion of the main gas components within 1.5 kpc from midplane. The thermal-to-magnetic pressure ratio decreases with [z] and the warm model is Parker unstable. The dispersion relations show that the fastest growing mode has a wavelength of about 3 kpc, for both symmetric and antisymmetric perturbations, and the corresponding growth time scales are of about 3×10 7 years. The structure of the final equilibrium stage is also derived, and we find that the midplane antisymmetric (MA) mode gathers more gas in the magnetic valleys. The resulting MA gas condensations have larger densities, and the column density enhancement is a factor of about 3 larger than the value of the initial stage. The unstable wavelengths and growth times for the multi-component disk model are substantially larger than those of a thin disk model, and some of the implications of these results are discussed.

Formation of interstellar clouds: Parker instability with phase transitions

“…, where g ( z ) =− g (− z ) = g = constant >0. More complicated gravitational fields have been considered analytically by Kellman (1972), Giz & Shu (1993), Kim, Hong & Ryu (1997), Kim & Hong (1998) and Kim et al (2000) and numerically by Santillán et al (2000) and Franco et al (2002). The main effect of a non‐constant gravitational acceleration is to increase the growth rate of the instability and shorten the separation of the magnetic valleys.…”

Incorporation of cosmic ray transport into the ZEUS MHD code

“…On the other hand, numerical studies of the Parker instability investigate the effects of uniform vertical gravity , realistic vertical gravity (Kim et al 2000), selfgravity (Chou et al 2000), the effects of spiral arms (Franco et al 2002), finite resistivity (Hanasz et al 2002;Tanuma 2003;Kowal et al 2003), partial ionization (Birk 2002) and coupling to other disk instabilities .…”

The influence of gravitational acceleration on the supernova-driven Parker instability

“…From this point of view, the structures built differ qualitatively from those which arise when the Parker instability is initiated by a non‐localized linear sinusoidal perturbation. In the latter case, a steady state appears to be reached and the loops extend up to ∼1 kpc with respect to the plane (Kim et al 1998, 2000). We can thus conclude that the origin of the large scale magnetic loops observed in haloes of edge‐on galaxies (Dettmar, private communiation) might likely be connected with explosions in the underlying discs with the explosion energy lying in the range .…”

“…Based on this model, they studied the effect of two values of the ratio of specific heats and different energy input for the explosion on the instability, but did not discuss the influence of different values of the gravitational acceleration on the growth of the instability (Horiuchi et al 1988; Matsumoto et al 1988; Giz & Shu 1993; Kamaya et al 1997; Kim et al 1997). The most recent results on the influence of a spatially dependent gravitational acceleration on the evolution of the Parker instability has been presented by Kim & Hong 1998; Kim et al 2000. The initial vertical density and gravitational acceleration distributions are chosen such that the system is in equilibrium under the assumption of isothermality.…”