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Centrally concentrated star formation in young clusters

The study of star cluster evolution necessitates modeling how their density profiles develop from their natal gas distribution. Observational evidence indicates that many star clusters follow a Plummer-like density profile. However, most studies have focused on the phase after gas ejection, neglecting the influence of gas on early dynamical evolution. We investigate the development of star clusters forming within gas clouds, particularly those with a centrally concentrated gas profile. Simulations were conducted using the \texttt{Torch} framework, integrating the \texttt{FLASH} magnetohydrodynamics code into \texttt{AMUSE}. This permits detailed modeling of star formation, stellar evolution, stellar dynamics, radiative transfer, and gas magnetohydrodynamics. We study the collapse of centrally concentrated, turbulent spheres with a total mass of $2.5\times 10^3\, M_\odot$, investigating the effects of varying numerical resolution and star formation scenarios. The free-fall time is shorter at the center than at the edges of the cloud, with a minimum value of $0.55\,\mathrm{Myr}$. The key conclusions from this study are: (1) the final stellar density profile is more centrally concentrated than analytically predicted, reflecting the role of global gas collapse and feedback; (2) sub-clusters can initially form even in centrally concentrated gas clouds; (3) gas collapses globally toward the center on the central free-fall time scale, contradicting the assumption in analytical models of local fragmentation and star formation; and (4) the mass of the most massive star formed is directly correlated with the cluster effective radius and inversely correlated with the velocity dispersion, while the duration of star formation correlates with the star formation efficiency.