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 \geq \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 .