Hierarchical generative models for star clusters from hydro-dynamical
  simulations
  Star formation in molecular clouds is clumpy, hierarchically subclustered.
Fractal structure also emerges in hydro-dynamical simulations of star-forming
clouds. Simulating the formation of realistic star clusters with
hydro-dynamical simulations is a computational challenge, considering that only
the statistically averaged results of large batches of simulations are
reliable, due to the chaotic nature of the gravitational N-body problem. While
large sets of initial conditions for N-body runs can be produced by
hydro-dynamical simulations of star formation, this is prohibitively expensive
in terms of computational time. Here we address this issue by introducing a new
technique for generating many sets of new initial conditions from a given set
of star masses, positions and velocities from a hydro-dynamical simulation. We
use hierarchical clustering in phase space to learn a tree representation of
the spatial and kinematic relations between stars. This constitutes the basis
for the random generation of new sets of stars which share the same clustering
structure of the original ones but have individually different masses,
positions, and velocities. We apply this method to the output of a number of
hydro-dynamical star-formation simulations, comparing the generated initial
conditions to the original ones through a series of quantitative tests,
including comparing mass and velocity distributions and fractal dimension.
Finally, we evolve both the original and the generated star clusters using a
direct N-body code, obtaining a qualitatively similar evolution.
