The vertical profiles of disc galaxies are built by the material trapped
around stable periodic orbits, which form their ‘skeletons’. Therefore,
knowledge of the stability of the main families of periodic orbits in
appropriate 3D models enables one to predict possible morphologies for
edge-on disc galaxies. In a pilot survey we compare the orbital
structures that lead to the appearance of ‘peanut’- and ‘X’-like
features with the edge-on profiles of three disc galaxies (IC 2531, NGC
4013 and UGC 2048). The subtraction from the images of a model
representing the axisymmetric component of the galaxies reveals the
contribution of the non-axisymmetric terms. We find a direct
correspondence between the orbital profiles of 3D bars in models and the
observed main morphological features of the residuals. We also apply a
simple unsharp masking technique in order to study the sharpest features
of the images. Our basic conclusion is that the morphology of the boxy
‘bulges’ of these galaxies can be explained by considering disc material
trapped around stable 3D periodic orbits. In most models, these
building-block periodic orbits are bifurcated from the planar central
family of a non-axisymmetric component, usually a bar, at low-order
vertical resonances. In such a case, the boxy ‘bulges’ are parts of bars
seen edge-on. For the three galaxies we study, the families associated
with the ‘peanut’ or ‘X’-shape morphology are probably bifurcations at
the vertical 2/1 or 4/1 resonance
