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

We investigate the effects of rotation on the evolution of the Parker insta bility by carrying out three-dimensional numerical simulations with an isot hermal magnetohydrodynamic code. These simulations extend our previous work on the nonlinear evolution of the Parker instability by J. Kim and coworke rs. 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 sol ar neighborhood, is set to rotate uniformly around the Galactic center with a constant angular speed. The instability has been initialized by random v elocity perturbations. In the linear stage, the evolution is not much diffe rent from that without rotation, and the mixed (undular + interchange) mode regulates the system. The interchange mode induces alternating dense and r arefied regions with small radial wavelengths, while the undular mode bends the magnetic field lines in the plane of the azimuthal and vertical direct ions. In the nonlinear stage, flow motion overall becomes chaotic, as in th e case without rotation. However, as the gas in higher positions slides dow n along field lines forming supersonic flows, the Coriolis force becomes im portant. As oppositely directed flows fall into valleys along both sides of the magnetic field lines, they experience the Coriolis force toward opposi te directions, which twists the magnetic field lines there. Hence, we sugge st 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 ca se without rotation. However, the long dimension is now slightly tilted wit h respect to the mean field direction. The shape of high-density regions is a bit rounder. The maximum enhancement factor of the vertical column densi ty relative to its initial value is about 1.5, which is smaller than that i n the case without rotation. We conclude that uniform rotation does not cha nge our point of view that the Parker instability alone is not a viable mec hanism for the formation of giant molecular clouds.