Star clusters and binaries in the first galaxies

Star cluster formation in metal-poor dwarf galaxies: the RIGEL framework

Beyond Pop III star clusters, I am generally interested in (metal-poor) star clusters in high-z galaxies. Since 2022, I have been collaborating with the group of Hui Li to develop a novel framework RIGEL (Realise Interstellar medium in Galactic Ecosystem and Lifecycle) of star formation and stellar feedback for the radiative hydrodynamic simulation code AREPO-RT (Kannan et al., 2019) that self-consistently models the radiative feedback, stellar winds, and supernovae from individual massive stars, taking into account the metallicity dependence of stellar evolution (Fig. 1). So far, the first version of RIGEL has been used to simulate star cluster formation during isolated evolution of metal-poor dwarf galaxies in the local Universe (Deng et al. 2024) and their mergers (Deng et al. 2025).

We found that early radiative feedback from massive stars has significant effects on star cluster properties. In particular, radiative feedback suppresses the formation of massive star clusters, thus steepening the cluster mass function (Fig. 2). We also found that cluster formation is mainly regulated by local stellar feedback rather than environmental factors, and the latter's effects only kick in through star-forming cloud properties. This can be seen by the invariant lifetime distribution of star-forming clouds across different galaxy merger stages (Fig. 3). The cloud-scale star formation efficiency for star clusters > 100 Msun (which account for 90% of stars formed) also hardly changes during galaxy mergers.

These findings highlight the pivotal roles of star-forming clouds and star clusters in galaxy evolution at the intermediate scale of 1 - 10 pc, as an interface for the complex crosstalk between smaller-scale processes (e.g., gravitational collapse, turbulence, amplification of magnetic fields, angular momentum transport, core/disk fragmentation, protostar formation and accretion, stellar evolution, dynamics, and feedback) and larger-scale processes (e.g., cosmic structure formation, radiation backgrounds, streaming motion of baryons relative to dark matter, and metal enrichment).

Fig. 1. Stellar lifetimes (left), production rates of photons in select energy bands considered by AREPO-RT (middle), and stellar wind mass loss rates and velocities (right) as functions of metallicity and initial stellar mass. In the middle panel, the curves of Opt., FUV, LW, and EUV0 bands are shifted by adding constants of 4, 3, 2, and 1, respectively, to reduce overlapping.

Fig. 2. Mass distribution of star clusters. The results for 3 high-resolution (with gas mass resolution ~ 1 Msun) simulations are shown, including two cases with full feedback for different metallicities, and a model without radiative feedback for the lower metallicity case. The dotted curves show the results from low-resolution runs (with gas mass resolution ~ 10 Msun).

Fig. 3. Cloud lifetime distributions at different merger stages. The dashed gray line denotes the maximum likelihood estimate fitting of the lifetime for all stages. The clouds in all merger stages follow the same exponentially decaying relation with a characteristic time of 1.48 Myr.

Characteristic masses for primordial star formation as functions of initial gas inflow rate (thin curves of different colors), which are combined to predict the final mass of Pop III stars (thick solid curve), assuming that only one star forms per cloud. Simulation results are shown for comparison (data points and a fit as the long-dashed line).

Initial mass functions of Pop III stars formed in the progenitors of typical luminous quasar host haloes (Li et at. 2021) under different degrees of fragmentation (denoted by the number of stars per cloud N), compared with the IMF predicted by Hirano et al. (2015) using 2D (single-star) simulations for Pop III star formation in unbiased regions (thick dashed).

Towards a universal analytical model for Population III star formation: interplay between feedback and fragmentation (2024, MNRAS, 534, 290)

JWST has brought us new insights into Cosmic Dawn with tentative detection of the unique signatures of metal-free Population III (Pop III) stars, such as strong HeII emission, extremely blue UV spectrum, and enhanced nitrogen abundance. Self-consistent theoretical predictions of the formation rates, sites, and masses of Pop III stars are crucial for interpreting the observations, but are challenging due to complex physical processes operating over the large range of length scales involved. One solution is to combine analytical models for small-scale star formation processes with cosmological simulations that capture the large-scale physics, such as structure formation, radiation backgrounds, and baryon-dark matter streaming motion that regulate the conditions of Pop III star formation.

We build an analytical model to predict the final masses of Pop III stars/clusters from the properties of star-forming clouds, based on the key results of small-scale star formation simulations and stellar evolution models. Our model for the first time considers the interplay between feedback and fragmentation and covers different modes of Pop III star formation, ranging from ordinary small (∼10−2000 M⊙) clusters in molecular-cooling clouds to massive (≳10^4 M⊙) clusters containing supermassive (∼10^4−3×10^5 M⊙) stars under violent collapse of atomic-cooling clouds.

As an example, the model is applied to the Pop III star-forming clouds in the progenitors of typical haloes hosting high-z luminous quasars, which shows that formation of Pop III massive clusters is common (∼20−70%) in such biased (∼4σ) regions, and the resulting heavy black hole seeds from supermassive stars can account for a significant fraction of observed luminous (≳10^46 erg s−1) quasars at z∼6.

For theoretical studies on Pop III remnants as seeds of high-z quasars in cosmic average conditions with cosmological simulations and semi-analytical models, see Jeon et al. (2023, 2024, 2025).

Dynamical evolution of Population III stellar systems and the resulting binary statistics (2020, MNRAS, 501, 643)

Population III (Pop III) stars are also expected to form in clusters according to simulations. The dynamical evolution of clusters determine the binary statistics, which is crucial for the feedback effect and observational signatures of Pop III stars.

In this work, we address this topic with N-body simulations. We design a physically-motivated model for the initial conditions of Pop III star clusters, based on small-scale hydrodynamic simulations and the scale-free nature of disk evolution during Pop III star formation. This novel model enables us to explore the dependence of binary statistics on initial condition parameters and make predictions for the signals of Pop III X-ray binaries (XRBs) and black hole binary (BHB) mergers.

We found that the binary properties are highly sensitive to the initial cluster size and distribution of binary separation, while the effect of initial mass function is relatively minor. Our simulations predict much (a factor of 10-10^4) lower efficiencies for the formation and accretion of Pop III XRBs than inferred/assumed in previous studies. We also estimate the efficiency of BBH mergers as a few per 10^4 to 10^5 Msun.

Application to the event GW190521 (2020, ApJ, 903, L40)

With these binary parameters, we also explore the Pop III origin of the BHB merger GW190521 recently reported by the LIGO collaboration, which involves BH masses in the mass gap of (pulsational) pair-instability supernovae (PPISNe) from standard stellar evolution models. Pop III stars are promising progenitors of the BHs found in GW190521, because Pop III stars, with small sizes and little mass loss, are likely to retain most of their hydrogen envelopes until the pre-supernova (SN) stage, avoid the PPISN regime and form BHs in the mass gap. We find that Pop III BBHs can naturally explain the observation, especially for the BBH evolution channel via dynamical hardening in nuclear star clusters. Our results are published in ApJ Letters.

Our Pop III scenario is further proved to be able to reproduce the observed merger rate density of GW190521-like events by more detailed modelling of the galactic dynamics and internal evolution of Pop III binary BHs, see the page Gravitational Waves & First Stars for details.

Binary statistics from 10000 runs for our fiducial model (histgrams), in terms of the distributions of primary mass, semi-major axis (separation), (secondary to primary) mass ratio and orbital eccentricity (clockwise). In the annotation of the bottom-right panel, f_B denotes the fraction of stars in (isolated) binaries, where the values in (out of) the brackets are derived with respect to number (mass) of stars. Select results from previous studies and trends in Pop I like binaries are also shown with contours of different linestyles for comparison.

Co-moving rate densities of PopIII BHB mergers similar to GW190521 from different evolution channels and environmental parameters (curves of different styles) based on our updated binary statistics, in comparison with the rate inferred from observation (shaded region).

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