Three-dimensional evolution of the Parker instability under a uniform gravity

Using an isothermal MHD code, we have performed three-dimensional, high-res olution simulations of the Parker instability. The initial equilibrium syst em is composed of exponentially decreasing isothermal gas and a magnetic fi eld (along the azimuthal direction) under a uniform gravity. The evolution of the instability can be divided into three phases: linear, nonlinear, and relaxed. During the linear phase, the perturbations grow exponentially wit h a preferred scale along the azimuthal direction but with the smallest pos sible scale along the radial direction, as predicted from linear analyses. During the nonlinear phase, the growth of the instability is saturated and flow motion becomes chaotic. Magnetic reconnection occurs, which allows the gas to cross field lines. This, in turn, results in the redistribution of the gas and the magnetic field. The system approaches a new equilibrium in the relaxed phase, which is different from the one seen in two-dimensional works. The structures formed during the evolution are sheetlike or filament ary, whose shortest dimension is radial. Their maximum density enhancement factor relative to the initial value is less than 2. Since the radial dimen sion is too small and the density enhancement is too low, it is difficult t o regard the Parker instability alone as a viable mechanism for the formati on of giant molecular clouds.