The Fundamental Manifold of spiral galaxies: ordered versus random
  motions and the morphology dependence of the Tully-Fisher relation
  (Abridged) We investigate the morphology dependence of the Tully-Fisher
relation, and the expansion of the relation into a three-dimensional manifold
defined by luminosity, total circular velocity and a third dynamical parameter,
to fully characterise spiral galaxies across all morphological types. We use a
semi-analytic hierarchical model of galaxy evolution to build the theoretical
TF relation. With this tool, we analyse a unique dataset of galaxies for which
we cross-match luminosity with total circular velocity and central velocity
dispersion. We provide a theoretical framework to calculate such measurable
quantities from semi-analytic models. We establish the morphology dependence of
the TF relation in both model and data. We analyse the dynamical properties of
the model galaxies and determine that the parameter 'sigma/Vc', i.e. the ratio
between random and total motions defined by velocity dispersion and circular
velocity, accurately characterises the varying slope of the TF relation for
different model galaxy types. We apply these dynamical cuts to the observed
galaxies and find that such selection produces a differential slope of the TF
relation. The TF slope in different ranges of 'sigma/Vc' is consistent with
that for the photometric classification in Sa, Sb, Sc. We conclude that
'sigma/Vc' is a good parameter to classify galaxy type, and we argue that such
classification based on dynamics more closely mirrors the physical properties
of the observed galaxies, compared to visual classification. We also argue that
dynamical classification is useful for samples where eye inspection is not
reliable or impractical. We conclude that 'sigma/Vc' is a suitable parameter to
characterise the hierarchical assembly history that determines the
disk-to-bulge ratio, and to expand the TF relation into a three-dimensional
manifold, defined by luminosity, circular velocity and 'sigma/Vc'.
