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We perform a suite of hydrodynamic simulations to investigate how initialdensity profiles of giant molecular clouds (GMCs) affect their subsequentevolution. We find that the star formation duration and integrated starformation efficiency of the whole clouds are not sensitive to the choice ofdifferent profiles but are mainly controlled by the interplay betweengravitational collapse and stellar feedback. Despite this similarity, GMCs withdifferent profiles show dramatically different modes of star formation. Forshallower profiles, GMCs first fragment into many self-gravitation cores andform sub-clusters that distributed throughout the entire clouds. Thesesub-clusters are later assembled ``hierarchically'' to central clusters. Incontrast, for steeper profiles, a massive cluster is quickly formed at thecenter of the cloud and then gradually grows its mass via gas accretion.Consequently, central clusters that emerged from clouds with shallower profilesare less massive and show less rotation than those with the steeper profiles.This is because 1) a significant fraction of mass and angular momentum inshallower profiles is stored in the orbital motion of the sub-clusters that arenot able to merge into the central clusters 2) frequent hierarchical mergers inthe shallower profiles lead to further losses of mass and angular momentum viaviolent relaxation and tidal disruption. Encouragingly, the degree of clusterrotations in steeper profiles is consistent with recent observations of youngand intermediate-age clusters. We speculate that rotating globular clusters arelikely formed via an ``accretion'' mode from centrally-concentrated clouds inthe early Universe.

Effects of initial density profiles on massive star cluster formation in giant molecular clouds