From the Top Down and Back Up Again: Star Cluster Structure from Hierarchical Star Formation

TL;DR

This paper demonstrates that the universal surface brightness profiles of young massive star clusters naturally result from hierarchical merging and relaxation processes, supported by analytical arguments and N-body simulations.

Contribution

It introduces a new analytical and simulation-based framework showing how hierarchical merging leads to observed cluster structures, linking formation processes to final profiles.

Findings

Hierarchical merging produces universal shallow profiles.

Simulations replicate observed surface density profiles.

Relaxation from hierarchical structures explains young cluster profiles.

Abstract

Young massive star clusters spanning $\sim 10^4 - 10^8 M_\odot$ in mass have been observed to have similar surface brightness profiles. Recent hydrodynamical simulations of star cluster formation have also produced star clusters with this structure. We argue analytically that this type of mass distribution arises naturally in the relaxation from a hierarchically-clustered distribution of stars into a monolithic star cluster through hierarchical merging. We show that arbitrary initial profiles will tend to converge to a universal profile under hierarchical merging, owing to phase-space mixing obeying certain conservation constraints. We perform $N$-body simulations of a pairwise merger of model star clusters and find that mergers readily produce the shallow surface brightness profiles observed in young massive clusters. Finally, we simulate the relaxation of a hierarchically-clustered mass distribution constructed from an idealized fragmentation model. Assuming only power-law spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus we provide physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This has important implications for the structure of nascent globular clusters.