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.