Importance of the Initial Conditions for Star Formation - III:
  Statistical Properties of Embedded Protostellar Clusters
  We investigate the formation of protostellar clusters during the collapse of
dense molecular cloud cores with a focus on the evolution of potential and
kinetic energy, the degree of substructure, and the early phase of mass
segregation. Our study is based on a series of hydrodynamic simulations of
dense cores, where we vary the initial density profile and the initial
turbulent velocity. In the three-dimensional adaptive mesh refinement
simulations, we follow the dynamical formation of filaments and protostars
until a star formation efficiency of 20%. Despite the different initial
configurations, the global ensemble of all protostars in a setup shows a
similar energy evolution and forms sub-virial clusters with an energy ratio
$E_\mathrm{kin}/|E_\mathrm{pot}|\sim0.2$. Concentrating on the innermost
central region, the clusters show a roughly virialised energy balance. However,
the region of virial balance only covers the innermost $\sim10-30%$ of all the
protostars. In all simulations with multiple protostars, the total kinetic
energy of the protostars is higher than the kinetic energy of the gas cloud,
although the protostars only contain 20% of the total mass. The clusters vary
significantly in size, mass, and number of protostars, and show different
degrees of substructure and mass segregation. Flat density profiles and
compressive turbulent modes produce more subclusters then centrally
concentrated profiles and solenoidal turbulence. We find that dynamical
relaxation and hence dynamical mass segregation is very efficient in all cases
from the very beginning of the nascent cluster, i.e., during a phase when
protostars are constantly forming and accreting.
