Boxy/peanut shaping of a mature galactic bar in action-angle space

We study vertical resonant trapping and resonant heating of orbits. These two processes both lead to the growth of a boxy/peanut-shaped bulge in a typical $N$-body model. For the first time, we study this by means of the action variables and resonant angles of the actual orbits that compose the model itself. We used the resonant angle instead of the frequency ratio, which allowed us to clearly distinguish between these two processes in numerical simulations. We show that trapping and heating occur simultaneously, at least at the stage of a mature bar, that is, some orbits quickly pass through vertical resonance while at the same time, a substantial number of orbits remains trapped into this stage for a long time. Half of all bar orbits spend more than 2.5 Gyr in vertical resonance over an interval of 4 Gyr. Half of the orbits trapped into the bar over the last 3 Gyr of simulation remain captured in vertical resonance for more than 2 Gyr. We conclude that in the later stages of the bar evolution, the process of vertical trapping dominates in the ongoing process that causes the boxy/peanut shape of a bar in a typical $N$-body model. This contradicts the results of several recent works.
Comment: Accepted for publication in A&A