On the nature of buckling instability in galactic bars

Many strong simulated galactic bars experience buckling instability, which manifests itself as a vertical distortion out of the disk plane, and later dissipates. Using a simulation of an isolated Milky Way-like galaxy, I demonstrate that the phenomenon can be divided into two distinct phases. In the first one, the distortion grows and its pattern speed remains equal to the pattern speed of the bar, so that the distortion remains stationary in the reference frame of the bar. The growth can be described with the mechanism of a driven harmonic oscillator with time-dependent force, which decreases the vertical frequencies of the stars. At the end of this phase, most bar-supporting orbits have banana-like shapes with a resonant vertical-to-horizontal frequency ratio close to two. The increase of amplitudes of vertical oscillations leads to the decrease of the amplitudes of horizontal oscillations and the shrinking of the bar. The mass redistribution causes the harmonic oscillators to respond adiabatically and increase the horizontal frequencies. In the following second phase of buckling, the pattern speed of the distortion increases - reaching one third of the circular frequency - but it decreases with radius. The distortion propagates as a kinematic bending wave and winds up, leaving behind a pronounced boxy/peanut shape. The increased horizontal frequencies cause the weakening of the bar and the transformation of banana-like orbits into pretzel-like ones, except in the outer part of the bar, where the banana-like orbits and the distortion survive. The results strongly suggest that the buckling of galactic bars is not related to the fire-hose instability, but it can be fully explained by the mechanism of vertical resonance creating the distortion that later winds up.