Using Commensurabilities and Orbit Structure to Understand Barred Galaxy
  Evolution
  We interpret simulations of secularly-evolving disc galaxies through orbit
morphology. Using a new algorithm that measures the volume of orbits in real
space using a tessellation, we rapidly isolate commensurate (resonant) orbits.
We identify phase-space regions occupied by different orbital families.
Compared to spectral methods, the tessellation algorithm can identify resonant
orbits within a few dynamical periods, crucial for understanding an evolving
galaxy model. The flexible methodology accepts arbitrary potentials, enabling
detailed descriptions of the orbital families. We apply the machinery to four
different potential models, including two barred models, and fully characterise
the orbital membership. We identify key differences in the content of orbit
families, emphasising the presence of orbit families indicative of the bar
evolutionary state and the shape of the dark matter halo. We use the
characterisation of orbits to investigate the shortcomings of analytic and
self-consistent studies, comparing our findings to the evolutionary epochs in
self-consistent barred galaxy simulations. Using insight from our orbit
analysis, we present a new observational metric that uses spatial and kinematic
information from integral field spectrometers that may reveal signatures of
commensurabilities and allow for a differentiation between models.
