Rapid formation of a very massive star >50000 $M_\odot$ and subsequently an IMBH from runaway collisions. Direct N-body and Monte Carlo simulations of dense star clusters

TL;DR

This study demonstrates that in an ultra-dense, massive star cluster, runaway collisions can rapidly assemble a very massive star (VMS) and lead to an IMBH within ~4.5–5 Myr. By directly comparing NBODY6++GPU (direct N-body) and MOCCA (Monte Carlo) simulations with updated SSE/BSE prescriptions and improved collision physics, the authors reveal that both methods produce broadly consistent VMS growth and IMBH formation, provided careful cross-calibration (e.g., disabling 3BBF for the VMS and reducing MOCCA timesteps). The work highlights the collisional channel as a plausible pathway for early BH seed formation in dense clusters and offers theoretical context for JWST observations of young, compact clusters at high redshift, while acknowledging substantial uncertainties in VMS internal structure, mass loss, and rejuvenation physics. These findings motivate further refinement of VMS stellar physics and invite multi-messenger observational tests (GW and EM signals) to distinguish IMBH formation channels in the early universe.

Abstract

Context. We present simulations of a massive young star cluster using \textsc{Nbody6++GPU} and \textsc{MOCCA}. The cluster is initially more compact than previously published models, with one million stars, a total mass of $5.86 \times 10^5~\mathrm{M}_{\odot}$, and a half-mass radius of $0.1~\mathrm{pc}$. Aims. We analyse the formation and growth of a very massive star (VMS) through successive stellar collisions and investigate the subsequent formation of an intermediate-mass black hole (IMBH) in the core of a dense star cluster. Methods. We use both direct \textit{N}-body and Monte Carlo simulations, incorporating updated stellar evolution prescriptions (SSE/BSE) tailored to massive stars and VMSs. These include revised treatments of stellar radii, rejuvenation, and mass loss during collisions. While the prescriptions represent reasonable extrapolations into the VMS regime, the internal structure and thermal state of VMSs formed through stellar collisions remain uncertain, and future work may require further refinement. Results. We find that runaway stellar collisions in the cluster core produce a VMS exceeding $5 \times 10^4~\mathrm{M}_{\odot}$ within 5 Myr, which subsequently collapses into an IMBH. Conclusions. Our model suggests that dense stellar environments may enable the formation of very massive stars and massive black hole seeds through runaway stellar collisions. These results provide a potential pathway for early black hole growth in star clusters and offer theoretical context for interpreting recent JWST observations of young, compact clusters at high redshift.

Figures (10)

• Figure 1: Initial mass of the cluster as a function of the half-mass radius. The color bar represents the number of particles. The dashed black line represents the relaxation time and the dotted black line corresponds to the collision time, when both are equals to a time evolution (i.e. age) of $\tau = 10\,$Gyr, which we consider as an upper limit for the typical evolutionary times of the clusters. Symbols indicate different simulations: N-body (squares), Monte Carlo (circles), hybrid N-body (diamonds), and this work (star).
• Figure 2: The figure shows the average mass in each shown Lagrangian shells $\langle M\rangle_{\mathrm{Lagr}}[\mathrm{M}_{\odot}]$ (Top) and, the Lagrangian radii $R_{\mathrm{Lagr}}~[\mathrm{pc}]$ (Bottom), both normalised by the cluster mass at the beginning of the simulation. We show both N-body and MOCCA results for the Lagrangian radii. In both plots, we show the shell representing 1 %, 10 %, 30%, 50%, 70% and 90 %. The differences between the Lagrangian radii in the N-body and MOCCA simulations arise from how escaping stars are treated. In the N-body simulations, stars with positive energy are not immediately removed from the system; instead, they remain until they cross a boundary set at ten times the half-mass radius. These stars are still included in the calculation of Lagrangian radii, which affects the results compared to MOCCA.
• Figure 3: The Figure shows the cumulative mass of escapers in the top panel and the cumulative number of collisions in the bottom panel. The total number of collisions is represented by a black solid line (N-body) and magenta solid line (MOCCA), while collisions involving the VMS are shown with a purple dot-dashed line (N-body) and cyan solid line (MOCCA). Binaries involving the VMS are shown with a red dotted line, and hyperbolic collisions with the VMS are shown by a blue dashed line.
• Figure 4: The Figure shows, in top panels: the mass of each escaping star. In bottom panels: the mass of the secondary star before colliding with the VMS, both in the case of hyperbolic and binary collisions. The color bar represents the density distribution of stars
• Figure 5: Histograms showing the contribution of colliding stars to VMS formation, divided into binary, hyperbolic, and total collisions. The mass ranges displayed are: $<0.1~\mathrm{M}_\odot$, $0.1$–$1~\mathrm{M}_\odot$, $1$–$10~\mathrm{M}_\odot$, $10$–$100~\mathrm{M}_\odot$, and $>100~\mathrm{M}_\odot$. Results are shown for both the N-body simulation (left column) and the MOCCA simulation (right column). The top panel displays the number of collisions, while the bottom panel shows the cumulative mass contributed by these collisions.