Formation and evolution of dwarf early-type galaxies in the Virgo
  cluster II. Kinematic Scaling Relations
  We place our sample of 18 Virgo dwarf early-type galaxies (dEs) on the V-K -
velocity dispersion, Faber-Jackson, and Fundamental Plane (FP) scaling
relations for massive early-type galaxies (Es). We use a generalized velocity
dispersion, which includes rotation, to be able to compare the location of both
rotationally and pressure supported dEs with those of early and late-type
galaxies. We find that dEs seem to bend the Faber-Jackson relation of Es to
lower velocity dispersions, being the link between Es and dwarf spheroidal
galaxies (dSphs). Regarding the FP relation, we find that dEs are significantly
offset with respect to massive hot stellar systems, and re-casting the FP into
the so-called kappa-space suggests that this offset is related to dEs having a
total mass-to-light ratio higher than Es but still significantly lower than
dSph galaxies. Given a stellar mass-to-light ratio based on the measured line
indices of dEs, the FP offset allows us to infer that the dark matter fraction
within the half light radii of dEs is on average >~ 42% (uncertainties of 17%
in the K band and 20% in the V band), fully consistent with an independent
estimate in an earlier paper in this series. We also find that dEs in the
size-luminosity relation in the near-infrared, like in the optical, are offset
from early-type galaxies, but seem to be consistent with late-type galaxies. We
thus conclude that the scaling relations show that dEs are different from Es,
and that they further strengthen our previous findings that dEs are closer to
and likely formed from late-type galaxies.
