A cosmological framework for stellar collisions at high redshift in proto-globular clusters, nuclear star clusters, and Little Red Dots

Abstract

Observations and cosmological simulations indicate that the early Universe hosted numerous compact, high-density stellar systems, where close encounters and physical collisions between stars were likely common. We develop a bottom-up framework for stellar dynamics in such environments, spanning systems with and without intermediate- and supermassive black holes, and covering regimes where stellar collisions may or may not dominate the evolution. This radially-resolved analytic model connects dense star clusters in their cosmological context to observable outcomes mediated by stellar collisions. Initial conditions and environmental properties are drawn from high-resolution cosmological simulations, enabling exploration across a broad region of parameter space. The analytic predictions are validated against Monte Carlo simulations, demonstrating good agreement across key regimes. We find that stellar collisions are ubiquitous in many high-redshift environments, with runaway sequences naturally leading to the formation of very massive stars at early times. Finally, we show that high rates of destructive collisions can rapidly build up extremely dense gaseous environments around massive black holes, potentially providing an analogue to the observed population of Little Red Dots.

Figures (8)

• Figure 1: Cartoon schematic diagram of physical processes represented by our analytic model of (top) VMS formation and (bottom) clusters hosting black holes. In both models, we consider the regions of the star cluster that may host destructive versus constructive stellar collisions. For systems without a black hole (top), systems are typically constructive throughout, with massive merger products migrating to the center and contributing to the formation of a VMS. The inward migration is balanced by the effects of depletion and binary heating, as well as winds from the VMS. For systems with a black hole (bottom), we find that the inner regions are dominated by destructive collisions, leading to the buildup of dense gas, which may then accrete onto the black hole or be expelled from the cluster due to feedback, although we do not explicitly model these processes.
• Figure 2: Flowchart depicting the logic of the analytic model considered here. We consider two initial conditions on the left and right sides: a dense star cluster (left) and a dense star cluster that hosts a massive black hole (right). We are agnostic about the origin of the black hole, although some scenarios on the left hand side can lead to this initial condition. Tentative connections such as this are marked with grey dashed arrows. While the flowchart depicts binary either-or decisions, in our analytic calculation, we are able to track mixed outcomes--i.e., radial dependence of the criteria leading to a combination of the scenarios listed. The outcomes marked in grey (at choice (2) and (3)) do not occur for the parameters we consider here. The outcomes highlighted in yellow (choice (8) and below) only occur in systems that also experience destructive collisions in the interior (i.e., yes to choice (7)) and we do not explicitly consider these combined processes in this work.
• Figure 3: Top left panel: Number of collisions within radius $R$ per 50 Myr, following \ref{['eq:plNumberofCollisions']} and \ref{['eq:BHncolltot']} for three example cases where the presence and mass of a black hole is varied. In pink, a simple power law with no black hole is shown. In purple, the system has a black hole of $10^3M_\odot$ (dashed) and $10^6M_\odot$ (solid). In all three systems, the power law index $\alpha =1.2$. Bottom left panel: Number of collisions within 1 pc per 50 Myr vs power law index, following \ref{['eq:plNumberofCollisions']} and \ref{['eq:BHncolltot']} for three example cases where the presence and mass of a black hole is varied. In both panels, the cluster parameters are: $\rho_0 = 1e5 M_\odot \text{ pc}^{-3}$, $r_0 = 1$ pc, $f^{\rm IMF}_{M_*}=0.3$, $M_* = M_c =1M_\odot$, $r_{\rm min}=200 R_\odot$, $e=0.5$. At discontinuities, the expressions of \ref{['sec:exactsolutions']} are used. Right panels: timescale as a function of radius for systems considered in this work without (top) and with (bottom) a supermassive black hole of $10^6M_\odot$. The collision timescale assuming 1 $M_\odot$ stars is solid orange, the main sequence lifetime is pink dashed, the merger timescale (at $z=12$) is dark blue dot-dashed, and the relaxation time is shown in blue dotted. Shaded regions show the range for the systems considered in \ref{['tab:parameters']}.
• Figure 4: Left: Maximum very massive star (VMS) mass versus cluster half-mass density $\rho_h,*$, compared to theoretical predictions. The color bar depicts the total cluster mass. For comparison, we plot the fitting function of gonzalez_prieto_intermediate-mass_2024 in orange for a $10^6 M_\odot$ star cluster of varying density and the simulations of mestichelli_teen_2026 as red stars, vergara_rapid_2025 as the purple diamond, and pacucci_little_2025 as the orange plus, the simulations of katz_seeding_2015 as the black diamonds, the fit of katz_seeding_2015 as the dashed line, and the functions of gieles_concurrent_2018 for two normalizations in hollow orange and pink shapes. The orange (N1) shows a reference VMS mass of $10 M_\odot$ and $N= 1e5$, and the pink (N2) show a reference VMS mass of $10^{4.3}M_\odot$ and $N= 1e7$, both drawn from realizations in their study, with circles (squares, triangles) denoting the index $\delta=0.1 (0.5,0.9)$. Right: Black hole - stellar mass relation assuming 100% of VMS mass is converted to a black hole at the end of its life, compared to observational relation and theoretical models. The minimum black hole mass shown is $200M_\odot$. Pink circles show dwarf AGN from greene_2020_intermediate and down arrows show dynamical upper limits from the same work. Purple squares show JWST high-redshift AGN from harikane_jwstnirspec_2023 and maiolino_jades_2024. The yellow star denotes the Milky Way galactic center genzel_galactic_2010. The orange circles show local AGN from reines_relations_2015. The blue stars show possible IMBHs, including $\omega$ Centarui haberle_fast-moving_2024, NGC 205 nguyen_improved_2019, NGC 4395 woo_10000-solar-mass_2019, G1 gebhardt_20000_2002 and B023-G078 pechetti_detection_2022. The dark grey squares show the $M_{\rm BH}-M_{\rm *, galaxy}$ relation of kritos_supermassive_2024, while the lighter grey circles show the $M_{\rm BH}-M_{\rm *, NSC}$ relation of kritos_supermassive_2024. The grey lines show $M_{\rm BH}=0.1M_*, 0.01M_*,0.001M_*,0.0001M_*$ from top to bottom.
• Figure 5: Average density of gas within $10^{-5}$pc surrounding the massive black hole produced by destructive collisions versus cluster half-mass stellar density (left) and stellar mass (right). Four black hole masses are plotted: $10^4 M_\odot$ (blue rightward triangles), $10^5 M_\odot$ (beige leftward triangles), $10^6 M_\odot$ (orange squares), and $10^7 M_\odot$ (red stars). The average density within $10^{-4}$pc is shown in in the transparent points.