Centrally concentrated star formation in young clusters

TL;DR

The study explores how centrally concentrated gas clouds influence the early formation and survival of young star clusters by self-consistently evolving gas, stars, radiation, and feedback with the Torch-AMUSE-Flash framework. It reveals that final stellar distributions tend toward greater central concentration than analytic local-collapse models predict, and that sub-clusters can emerge depending on the timing of massive-star formation and feedback. The mass of the most massive star strongly regulates gas expulsion and cluster morphology, with larger $M_{\max}$ yielding more extended and dynamically colder systems, while longer star-formation durations increase the global star-formation efficiency. These findings help explain the compact, Plummer-like cores observed in young clusters and underscore how resolution, IMF sampling, and feedback physics shape early cluster evolution.

Abstract

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.

Figures (11)

• Figure 1: The initial density and free-fall time $t_{\rm ff}$ of the cluster derived by Bek+2017 as a function of radius. The initial gas density (Eq. \ref{['eq:total_prfle']}) is shown in green, the final stellar density (Eq. \ref{['eq:plm']}) in red, and the final gas density (Eq. \ref{['eq:centrcon']}) in orange. The initial density profile is used directly in the simulation setup. The free-fall time $t_{\rm ff}$ of the initial gas density distribution as a function of radius is shown in (solid blue). The dashed blue horizontal line indicates the free-fall time corresponding to the average density, while the dotted blue vertical line marks the half-mass radius $r_{\rm h}$ of the initial gas distribution. The local value of $t_{\rm ff}$ is shortest in the central regions and increases significantly toward larger radii.
• Figure 2: Stellar density profiles at $4\,t_{\rm ff}$ (blue points) are compared with the analytically predicted Plummer profile for the stellar distribution (dashed orange line), as well as best-fit Plummer (dashed green) and EFF (dash-dotted magenta) models. The mass of the most massive star formed in each simulation is indicated in the lower-left corner of each panel. The panel marked with a $\star$ (n3s3) is shown at a slightly earlier time; see also the text for details on sub-cluster cases.
• Figure 3: Gas density slices and stellar distribution projections from the n3s6, n3s7, and n4s1 models. In these models sub-cluster formation occurs. For n3s6 and n3s7: (top row) onset of stellar feedback; (middle row) prior to the formation of the second cluster; (bottom row) after the formation of the second cluster. For n4s1: (top row) two clusters are present; (middle row) clusters merge into a single structure; (bottom row) the system separates again into two clusters. Ionization fronts are indicated by the cyan line. Black dots indicate individual stars, with massive stars shown in red. The symbol size of massive stars is proportional to their mass. Annotations in each panel include: (bottom left) scale bar; (bottom right) mass of the most massive star, total stellar mass within 5.5 pc, and total number of stars; (top left) simulation label; (top right) simulation time. The color scale represents the gas density in g cm$^{-3}$.
• Figure 4: Images of gas density and stellar distribution at different times for different maximum grid resolutions (higher refinement level $n$ corresponds to finer grid resolution). Each row corresponds to a level; each column, to a simulation time ($1.5~t_{\rm ff}$, $3~t_{\rm ff}$, $4.5~t_{\rm ff}$). The ionization fronts are marked with cyan lines. Stars are black dots; massive stars are red, with sizes proportional to their masses. In each panel, the notations are as follows: (bottom left) physical scale; (bottom right) the mass of the most massive star, total stellar mass, and number of stars; (top left) model label; (top right) simulation time. The color scale represents the gas density in g cm$^{-3}$
• Figure 5: Slices of gas density and projected stellar distribution at the formation time in each model of the most massive star with $M > 15\,M_{\odot}$(left column), and 1 Myr later (right column), for the n3s3, n3s9, n3s4, and n3s1 simulations. Ionization fronts are indicated by cyan lines. Black dots represent stars, while massive stars are shown in red; massive star symbol sizes are proportional to stellar mass. In n3s1, two most massive stars form: one with $50\,M_\odot$ at 891 kyr (triggering feedback), and a second with $53\,M_\odot$ at 1187 kyr. Annotations in each panel are (bottom left) physical scale; (bottom right) mass of the most massive star, total stellar mass within 5.5 pc, total gas mass within 5.5 pc, and number of stars; (top left) model; (top right) simulation time. The color scale represents the gas density.