How do the successive buckling events affect a galaxy bar and stellar disk? Potential Observable Signatures For Spotting the Buckling Action -- I

Until now, observations have caught up only a handful of galaxies in ongoing buckling action. Interestingly, N-body simulations over the past several decades show that almost every bar buckles or vertically thickens as soon as it reaches its peak strength during its evolution and leads to box$/$ peanut$/$ x (BPX) shapes. In order to understand the effect of multiple buckling events on the observable properties of galactic bar and disk, we perform an N-body simulation of a Milky Way-type disk. The axisymmetric galaxy disk forms a bar within a Gyr of its evolution and the bar undergoes two successive buckling events. We report that the time spans of these two buckling events are 220 Myr and 1 Gyr which have almost similar strengths of the bending modes. As a result of these two buckling events, the sizes of BPX shapes are around 5.8 kpc and 8.6 kpc which are around two-thirds of the bar length at the end of each buckling event. We find that the first buckling occurs at a smaller scale (radius less than 3 kpc) with a shorter time span affecting the larger length scales of the disk which is quantified in terms of changes in $m$ =2 and $m$ = 4 Fourier modes. While the second buckling occurs at larger scales (radius of around 6 kpc) affecting the inner disk the most. Finally, we provide observable kinematic signatures (for example quadrupolar patterns of the line-of-sight velocities) which can potentially differentiate the successive buckling events.