On the observational diagnostics to separate classical and disk-like
  bulges
  Flattened bulges with disk-like properties are considered to be the end
product of secular evolution processes at work in the inner regions of
galaxies. On the contrary, classical bulges are characterized by rounder shapes
and thought to be similar to low-luminosity elliptical galaxies. We aim at
testing the variety of observational diagnostics which are commonly adopted to
separate classical from disk-like bulges in nearby galaxies. We select a sample
of eight unbarred lenticular galaxies to be morphologically and kinematically
undisturbed with no evidence of other components than bulge and disk. We
analyze archival data of broad-band imaging from SDSS and integral-field
spectroscopy from the ATLAS$^{\rm 3D}$ survey to derive the photometric and
kinematic properties, line-strength indices, and intrinsic shape of the sample
bulges. We argue that the bulge S\'ersic index is a poor diagnostics to
discriminate different bulge types. We find that the combination of
line-strength with either kinematic or photometric diagnostics does not provide
a clear separation for half of the sample bulges. We include for the first time
the intrinsic three-dimensional shape of bulges as a possible discriminant of
their nature. All bulges turn out to be thick oblate spheroids, but only one
has a flattening consistent with that expected for outer disks. We conclude
that bulge classification may be difficult even adopting all observational
diagnostics proposed so far and that classical and disk-like bulges could be
more confidently identified by considering their intrinsic shape.
