Nuclear Star Clusters and the Stellar Spheroids of their Host Galaxies
  (Abridged) We combine published photometry for the nuclear star clusters
(NSCs) and stellar spheroids of 51 low-mass, early-type galaxies in the Virgo
cluster with empirical mass-to-light ratios, in order to complement previous
studies that explore the dependence of NSC masses (M_{NSC}) on various
properties of their host galaxies. We confirm a roughly linear relationship
between M_{NSC} and luminous host spheroid mass (M_{Sph}), albeit with
considerable scatter (0.57 dex). We estimate velocity dispersions from the
virial theorem, assuming all galaxies in our sample share a common DM fraction
and are dynamically relaxed. We then find that M_{NSC} \sim \sigma^{2.73\pm
0.29}, with a slightly reduced scatter of 0.54 dex.
  This confirms recent results that the shape of the M_{CMO} - \sigma relation
is different for NSCs and super-massive black holes (SMBHs). We discuss this
result in the context of the generalized idea of "central massive objects"
(CMOs).
  In order to assess which physical parameters drive the observed NSC masses,
we also carry out a joint multi-variate power-law fit to the data. In this, we
allow M_{NSC} to depend on M_{Sph} and R_{Sph} (and hence implicitly on
\sigma), as well as on the size of the globular cluster reservoir. When
considered together, the dependences on M_{Sph} and R_{Sph} are roughly
consistent with the virial theorem, and hence M_{NSC} \propto \sigma^2.
However, the only statistically significant correlation is a linear scaling
between M_{NSC} and M_{Sph}.
  We compare M_{NSC} with predictions for two popular models for NSC formation,
namely i) globular cluster infall due to dynamical friction, and ii) in-situ
formation during the early phases of galaxy formation that is regulated via
momentum feedback from stellar winds and/or supernovae. Neither model can
directly predict the observations, and we discuss possible interpretations of
our findings.
