On the nature of the barlens component in barred galaxies: what do
  boxy/peanut bulges look like when viewed face-on?
  Barred galaxies have interesting morphological features whose presence and
properties set constraints on galactic evolution. Here we examine barlenses,
i.e. lens-like components whose extent along the bar major axis is shorter than
that of the bar and whose outline is oval or circular. We identify and analyse
barlenses in $N$-body plus SPH simulations, compare them extensively with those
from the NIRS0S (Near-IR S0 galaxy survey) and the S$^4$G samples (Spitzer
Survey of Stellar Structure in Galaxies) and find very good agreement. We
observe barlenses in our simulations from different viewing angles. This
reveals that barlenses are the vertically thick part of the bar seen face-on,
i.e. a barlens seen edge-on is a boxy/peanut/X bulge. In morphological studies,
and in the absence of kinematics or photometry, a barlens, or part of it, may
be mistaken for a classical bulge. Thus the true importance of classical
bulges, both in numbers and mass, is smaller than currently assumed, which has
implications for galaxy formation studies. Finally, using the shape of the
isodensity curves, we propose a rule of thumb for measuring the barlens extent
along the bar major axis of moderately inclined galaxies, thus providing an
estimate of which part of the bar is thicker.
