Three-dimensional simulations of the parker instability in a uniformly rotating disk

We investigate the effects of rotation on the evolution of the Parker instability by carrying out three-dimensional numerical simulations with an isothermal magnetohydrodynamic code. These simulations extend our previous work on the nonlinear evolution of the Parker instability by J. Kim and coworkers. The initial equilibrium system is composed of exponentially stratified gas and a field (along the azimuthal direction) in a uniform gravity (along the downward vertical direction). The computational box, placed at the solar neighborhood, is set to rotate uniformly around the Galactic center with a constant angular speed. The instability has been initialized by random velocity perturbations. In the linear stage, the evolution is not much different from that without rotation, and the mixed (undular + interchange) mode regulates the system. The interchange mode induces alternating dense and rarefied regions with small radial wavelengths, while the undular mode bends the magnetic field lines in the plane of the azimuthal and vertical directions. In the nonlinear stage, flow motion overall becomes chaotic, as in the case without rotation. However, as the gas in higher positions slides down along field lines forming supersonic flows, the Coriolis force becomes important. As oppositely directed flows fall into valleys along both sides of the magnetic field lines, they experience the Coriolis force toward opposite directions, which twists the magnetic field lines there. Hence, we suggest that the Coriolis force plays a role in randomizing the magnetic field. The three-dimensional density structure formed by the instability is still sheetlike with the short dimension along the radial direction, as in the case without rotation. However, the long dimension is now slightly tilted with respect to the mean field direction. The shape of high-density regions is a bit rounder. The maximum enhancement factor of the vertical column density relative to its initial value is about 1.5, which is smaller than that in the case without rotation. We conclude that uniform rotation does not change our point of view that the Parker instability alone is not a viable mechanism for the formation of giant molecular clouds.