Nuclear star cluster formation in energy-space
  In a virialized stellar system, the mean-square velocity is a direct tracer
of the energy per unit mass of the system. Here, we exploit this to estimate
and compare root-mean-square velocities for a large sample of nuclear star
clusters and their host (late- or early-type) galaxies. Traditional
observables, such as the radial surface brightness and second-order velocity
moment profiles, are subject to short-term variations due to individual
episodes of matter infall and/or star formation. The total mass, energy and
angular momentum, on the other hand, are approximately conserved. Thus, the
total energy and angular momentum more directly probe the formation of galaxies
and their nuclear star clusters, by offering access to more fundamental
properties of the nuclear cluster-galaxy system than traditional observables.
We find that there is a strong correlation, in fact a near equality, between
the root-mean-square velocity of a nuclear star cluster and that of its host.
Thus, the energy per unit mass of a nuclear star cluster is always comparable
to that of its host galaxy. We interpret this as evidence that nuclear star
clusters do not form independently of their host galaxies, but rather that
their formation and subsequent evolution are coupled. We discuss how our
results can potentially be used to offer a clear and observationally testable
prediction to distinguish between the different nuclear star cluster formation
scenarios, and/or quantify their relative contributions.
