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 } } | \sim 0.2 .
Concentrating on the innermost central region , the clusters show a roughly virialised energy balance .
However , the region of virial balance only covers the innermost \sim 10 - 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 .