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Young massive star clusters spanning $\sim 10^4 - 10^8 M_\odot$ in mass havebeen observed to have similar surface brightness profiles. Recenthydrodynamical simulations of star cluster formation have also produced starclusters with this structure. We argue analytically that this type of massdistribution arises naturally in the relaxation from a hierarchically-clustereddistribution of stars into a monolithic star cluster through hierarchicalmerging. We show that arbitrary initial profiles will tend to converge to auniversal profile under hierarchical merging, owing to phase-space mixingobeying certain conservation constraints. We perform $N$-body simulations of apairwise merger of model star clusters and find that mergers readily producethe shallow surface brightness profiles observed in young massive clusters.Finally, we simulate the relaxation of a hierarchically-clustered massdistribution constructed from an idealized fragmentation model. Assuming onlypower-law spatial and kinematic scaling relations, these numerical experimentsare able to reproduce the surface density profiles of observed young massivestar clusters. Thus we provide physical motivation for the structure of youngmassive clusters within the paradigm of hierarchical star formation. This hasimportant implications for the structure of nascent globular clusters.

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