Three Mechanisms for Bar Thickening
  We present simulations of bar-unstable stellar discs in which the bars
thicken into box/peanut shapes. Detailed analysis of the evolution of each
model revealed three different mechanisms for thickening the bars. The first
mechanism is the well-known buckling instability, the second is the vertical
excitation of bar orbits by passage through the 2:1 vertical resonance, and the
third is a gradually increasing fraction of bar orbits trapped into this
resonance. Since bars in many galaxies may have formed and thickened long ago,
we have examined the models for fossil evidence in the velocity distribution of
stars in the bar, finding a diagnostic to discriminate between a bar that had
buckled from the other two mechanisms.
