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 on various properties of their host galaxies. We confirm a roughly linear relationship between NSC mass and luminous host spheroid mass, albeit with considerable scatter (0.57 dex). In order to translate this into an relation, we estimate velocity dispersions from the virial theorem, assuming that all galaxies in our sample share a common dark matter fraction and are dynamically relaxed. We then find that MNSC ∼ σ2.73 ± 0.29, with a slightly reduced scatter of 0.54 dex.
This confirms recent results that the shape of the relation is different for NSCs and super-massive black holes. 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 nuclear cluster masses, we also carry out a joint multivariate power-law fit to the data. In this, we allow the nuclear cluster mass to depend on spheroid mass and radius (and hence implicitly on velocity dispersion), as well as on the size of the globular cluster reservoir. When considered together, the dependences on MSph and RSph are roughly consistent with the virial theorem, and therefore MNSC ∝ σ2. However, the only statistically significant correlation appears to be a simple linear scaling between NSC mass and luminous spheroid mass.
We proceed to directly compare the derived NSC masses 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.