The Parker Instability under a Linear Gravity

Abstract

A linear stability analysis has been done to a magnetized disk under a linear gravity. We have reduced the linearized perturbation equations to a second-order differential equation which resembles the Schrödinger equation with the potential of a harmonic oscillator. Depending on the signs of energy and potential terms, eigensolutions can be classified into ``continuum'' and ``discrete'' families. When magnetic field is ignored, the continuum family is identified as the convective mode, while the discrete family as acoustic-gravity waves. If the effective adiabatic index $\gamma$ is less than unity, the former develops into the convective instability. When a magnetic field is included, the continuum and discrete families further branch into several solutions with different characters. The continuum family is divided into two modes: one is the original Parker mode, which is a slow MHD mode modulated by the gravity, and the other is a stable Alfvén mode. The Parker modes can be either stable or unstable depending on $\gamma$. When $\gamma$ is smaller than a critical value ${\gamma }_{cr}$, the Parker mode becomes unstable. The discrete family is divided into three modes: a stable fast MHD mode modulated by the gravity, a stable slow MHD mode modulated by the gravity, and an unstable mode which is also attributed to a slow MHD mode. The unstable discrete mode does not always exist. Even though the unstable discrete mode exists, the Parker mode dominates it if the Parker mode is unstable. However, if $\gamma \ge {\gamma }_{cr}$, the discrete mode could be the only unstable one. When $\gamma$ is equal ${\gamma }_{cr}$, the minimum growth time of the unstable discrete mode is $1.3\times 10^8$ years with a corresponding length scale of 2.4 kpc. It is suggestive that the corrugatory features seen in the Galaxy and external galaxies are related to the unstable discrete mode.

Accepted for publication in ApJ, using aaspp4.sty, 20 text pages with 9 figures, also available upon request to [email protected] or [email protected]

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• Detection of a Corrugated Velocity Pattern in the Spiral Galaxy NGC 5427
• A Comparative Study of the Parker Instability under Three Models of the Galactic Gravity
• The Effect of the Random Magnetic Field Component on the Parker Instability
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• The Influence of the Gravitational Acceleration on the Supernova-Driven P arker Instability