We investigate whether nuclear star clusters and supermassive black holes
follow a common set of mass scaling relations with their host galaxy's
properties, and hence can be considered to form a single class of central
massive object. We have compiled a large sample of galaxies with measured
nuclear star cluster masses and host galaxy properties from the literature and
fit log-linear scaling relations. We find that nuclear star cluster mass,
M_{NC}, correlates most tightly with the host galaxy's velocity dispersion: log
M_{NC} = (2.11 \pm 0.31) log (\sigma/54) + (6.63 \pm 0.09), but has a slope
dramatically shallower than the relation defined by supermassive black holes.
We find that the nuclear star cluster mass relations involving host galaxy (and
spheroid) luminosity and stellar and dynamical mass, intercept with but are in
general shallower than the corresponding black hole scaling relations. In
particular M_{NC} \propto {M}_{Gal,dyn}^{0.55 \pm 0.15}; the nuclear cluster
mass is not a constant fraction of its host galaxy or spheroid mass. We
conclude that nuclear stellar clusters and supermassive black holes do not form
a single family of central massive objects.Comment: 8 pages, 3 figure