Orbital support and evolution of flat profiles of bars (shoulders)

Many barred spiral galaxies show excesses (shoulders) in an overall exponential surface-brightness profile along the bar major-axis. Recent studies using N-body simulations show that: i) these shoulders tend to appear in bars that are growing; ii) shoulders can also appear after bar buckling events, and be erased after a secondary buckling. The orbital support and main mechanism driving this evolution are not well understood. In this talk, I will show recent results I got performing frequency analyses of orbits integrated in frozen potentials of N-body simulations. I will show that shoulders are mostly built by orbits with loops at their ends and these are a subgroup of the Inner Lindblad Resonance (ILR) with typical ratios of vertical to radial frequencies 1 < Omega_z/Omega_R < 3/2 (warm ILR). I will also discuss how bars growth and thickening populates warm ILR orbits, with further bar thickening carrying the latter towards the vertical ILR (vILR), where orbits gain vertical energy at the cost of in-plane motion, become chaotic, kinematically hotter and less shoulder-supportive. Finally, I will show how this heating mechanism sheds light on the need for a growing bar and on why shoulders can be either created or erased soon after buckling events.