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