THE PARKER INSTABILITY UNDER A LINEAR GRAVITY

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 that resembles the Schrodinge r equation with the potential of a harmonic oscillator. Depending on t he signs of energy and potential terms, eigensolutions can be classifi ed into ''continuum'' and ''discrete'' families. When the magnetic hel d is ignored, the continuum family is identified as the convective mod e, while the discrete family is identified 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 inc luded, 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 m ode modulated by the gravity, and the other is a stable Alfven mode. T he Parker modes can be either stable or unstable depending on gamma. W hen gamma is smaller than a critical value gamma(cr), the Parker mode becomes unstable. The discrete family is divided into three modes: a s table fast MHD mode modulated by the gravity, a stable slow MHD mode m odulated by the gravity, and an unstable mode that 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 dominat es it if the Parker mode is unstable. However, if gamma greater than o r equal to gamma(cr), then the discrete mode could be the only unstabl e one. When gamma is equal gamma(cr), the minimum growth time of the u nstable discrete mode is 1.3 x 10(8) yr, with a corresponding length s cale of 2.4 kpc. It is suggestive that the corrugated features seen in the Galaxy and external galaxies are related to the unstable discrete mode.