  In this work we investigate the link between galaxy velocity dispersion, mass
and other properties (color, morphology) with the properties of dark matter
halos by comparing the clustering of galaxies at both fixed mass and velocity
dispersion. We use the Sloan Digital Sky Survey to define a volume limited
sample of massive galaxies complete in both stellar mass (>6e10 Msun) and
velocity dispersion (>75 km/s). Using this sample we show that at fixed
velocity dispersion there is no dependence of the clustering amplitude on
stellar or dynamical mass. Conversely when stellar or dynamical mass are fixed
there is a clear dependence of the clustering amplitude on velocity dispersion
with higher dispersion galaxies showing a higher clustering amplitude. We also
show that whilst when stellar or dynamical mass are fixed there remains a
dependence of clustering amplitude on morphology, there is no such dependency
when dispersion is fixed. However, we do see a dependence of the clustering
amplitude on color when both mass and dispersion are fixed. Despite this, even
when we restrict our samples to only elliptical or red galaxies the
relationship between dispersion and clustering amplitude at fixed mass remains.
It seems likely that the residual correlation with color is driven by satellite
galaxies in massive halos being redder at fixed dispersion. The lack of a
similar morphology dependence implies that the mechanism turning satellites red
is not changing their morphology. Our central result is that velocity
dispersion is more closely related to the clustering amplitude of galaxies than
either stellar or dynamical mass. This implies that velocity dispersion is more
tightly correlated with the halo properties that determine clustering, either
halo mass or age, and supports the notion that the star formation history of a
galaxy is more closely related to its halo properties than its overall mass.
