Mergers all the way down: stellar collisions and kinematics of a dense hierarchically forming massive star cluster in a dwarf starburst

TL;DR

This study tackles how extremely dense GC progenitors form and imprint their internal structure during hierarchical assembly in a dwarf merger. It introduces a star-by-star hydrodynamical framework that couples galaxy-scale gas dynamics with collisional dynamics near massive stars and includes collisions and tidal disruption events. The simulation forms ~850 bound clusters, with the most massive reaching $M\sim 2\times10^5\,M_\odot$ and central densities $\Sigma_0>10^6\,M_\odot\,\mathrm{pc}^{-2}$, while a collisionally grown very massive star (~$1000\,M_\odot$) yields a BH remnant of order $6\times10^2$–$9\times10^2\,M_\odot$. Kinematically, younger stars are more centrally concentrated and rotation-dominated, whereas older stars are more isotropic, creating P2-like signatures akin to those observed in Galactic GCs, thereby linking early dense cluster formation to multiple populations; the results set a baseline for future long-term chemo-dynamical GC formation studies.

Abstract

Recent observations indicate that the progenitors of globular clusters (GCs) at high redshifts had high average stellar surface densities above $10^5\, \mathrm{M}_\odot\, \mathrm{pc}^{-2}$. The internal structure and kinematics of the clusters, however, remain out of reach. Numerical simulations are necessary to decipher the origin of spatio-kinematic features in present-day GCs. Here we study star cluster formation in a star-by-star hydrodynamical simulation of a low-metallicity starburst in a merger of two gas-rich dwarf galaxies. The simulation accounts for the multiphase interstellar medium, stellar radiation, winds and supernovae, and the accurate small-scale gravitational dynamics near massive stars. We also include prescriptions for stellar collisions and tidal disruption events by black holes. Gravitationally bound star clusters up to $\sim2\times10^5\, \mathrm{M}_\odot$ form dense with initial half-mass radii of $\sim0.1\unicode{x2013}1\, \mathrm{pc}$. The most massive cluster approaches the observed high-redshift surface densities throughout its hierarchical and dissipative assembly. The cluster also hosts a collisionally growing very massive star of $\sim1000\, \mathrm{M}_\odot$ that will eventually collapse, forming an intermediate mass black hole. The assembly leaves an imprint in the spatio-kinematic structure of the cluster. The youngest stars are more centrally concentrated, they show significant bulk rotation and have radially biased velocity components at outer radii. The older population is more round in shape, rotates slowly, its velocity distribution is isotropic and exhibits higher dispersion. If chemically enriched star formation proceeds mainly in the later stages of cluster assembly, these results provide a possible explanation for some of the multiple population features observed in dynamically young GCs.

Figures (6)

• Figure 1: The mass-size (left) and size-surface density (right) distributions of the simulated and observed young star clusters. The pink open circles show the general young star cluster population in the final snapshot. The squares indicate the evolution of the most massive cluster in $\sim0.1$ Myr steps starting when it had a bound mass equal to $25\%$ of its final mass (see Fig. \ref{['fig:2dmaps']}), coloured according to its mean stellar age from light to dark shade. The comparison data are observed young star clusters ($<10$ Myr) in the LEGUS survey (grey hexbins with the shade from light to dark indicating the number of clusters ranging from 1 to 38 clusters on the left and 1 to 28 clusters on the right; 2021MNRAS.508.5935B) and various surveys of strongly lensed clusters at redshifts $z\gtrsim2.4$ (filled symbols; 2022AA...659A...2V2022ApJ...940L..53V2023ApJ...945...53V2024Natur.632..513A2024Natur.636..332M2025AA...694A..59M), for which we have used the reported half-light radii to compute the effective surface densities. The solid line shows the compactness parameter $C_5=(M_\mathrm{cluster}/10^5\, \mathrm{M}_\odot)/(R_\mathrm{eff}/\mathrm{pc})=1$2016AA...587A..53K. The dotted lines on the left show sizes corresponding to a constant surface density for masses in the range $10^3$--$10^6$$\mathrm{M}_\odot$ pc$^{-2}$ from left to right and the dashed lines on the right show the surface densities for a constant mass in the range $10^3$--$10^6$$\mathrm{M}_\odot$ from left to right, in steps of 1 dex.
• Figure 2: Top: Colour composite images of the central 20 pc at four epochs along the formation of the most massive cluster (see text) in B (blue), V (green) and I (red) Johnson-Cousins broad-bands. The image resolution corresponds to that of the HST at the distance of LMC ($\sim 50$ kpc, 0.01 pc per pixel) degraded with a $\sim2$ pix Gaussian point spread function. The insets show the central 2 pc in an adjusted value range. Middle: V-band surface brightness maps of the stellar emission without dust attenuation. The white arrows show the centres of light (see text for details). The brightest spot close to the centre of the rightmost panel corresponds to the most massive star (see Section \ref{['section:VMSs']}) whose radiation properties are modelled as an initially 500 $\mathrm{M}_\odot$ star at an age of 1.2 Myr. This star, among others, is not visible in the top and bottom rows due to extinction. The insets in the middle and bottom rows show the central 2 pc in the same value range. Bottom: V-band surface brightness maps with attenuation, scattering and dust emission. The red arrows indicate the centres of light of the attenuated images measured similarly to the unattenuated one to highlight the offset in the direct and attenuated light.
• Figure 3: The radial projected profiles of stellar mass surface density (a), V-band surface brightness (b), 3D mass density (c) and stellar number density (d) of the most massive cluster at the four epochs shown in Fig. \ref{['fig:2dmaps']} and in the last snapshot when the cluster has a mean stellar age of 1.9 Myr. The solid lines in panels a, c and d indicate the gravitationally bound stellar component and the dashed lines show the total stellar mass in the region. In panel b the solid and dashed lines show the attenuated and the unattenuated surface brightness profiles, respectively. The power-law slopes of $-0.5$, $-1$, $-2$ and $-3$ are indicated in the panels. The best-fit surface density and brightness profiles of R136 from 2005ApJS..161..304M are shown in black in panels a and b, and the right-side y-axis in panel b shows the surface brightness scale in mag arcsec$^{-2}$. The vertical bars at the bottom of the panels show the projected half-mass radii of the bound component (panels a, c and d) and the projected half-light radii of the attenuated and unattenuated light profiles (b) with respective linestyles.
• Figure 4: The radial velocity distribution of the most massive cluster in 0.1 Myr steps. The lines are coloured with the mean stellar age of the cluster, increasing from light to dark. The panels show the 3D velocity dispersion (a), the velocity anisotropy (b), the rotation velocity along a $\pm 1$ pc slit along an inclined plane of rotation (c) and the tangential velocity (d). Each line is a mean of 100 bootstrapped samples oriented in a random inclination. The dashed line in panel b shows the final anisotropy profile without the removal of the bulk motion, $\beta_\mathrm{rot}$. The vertical bars in panel a show the projected $R_\mathrm{eff}$.
• Figure 5: The radial velocity distribution of the stars in the most massive cluster divided in to the younger (blue) and older (red) population in the final snapshot. The panels show the stellar number density (a); 3D velocity dispersion (b); radial and tangential velocity dispersion (c); velocity anisotropy excluding ($\beta$, solid) and including ($\beta_\mathrm{rot}$, dashed) the bulk velocities (d); the projected LOS rotation velocity in a $\pm 1$ pc slit and the tangential rotation velocity (solid and dashed lines, respectively; e); and the corresponding $V/\sigma$ of the tangential and LOS velocity components (f). The vertical gray line in the panels indicates the projected $R_\mathrm{eff}$, and the blue and red vertical lines in panel a shows the values of $R_\mathrm{eff}$ for the young and old populations, respectively.