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The formation of compact high-redshift star-forming clumps, along with the physical processes driving their evolution and their potential connection to present-day globular clusters (GCs), are key open questions in studies of galaxy formation. In this work, we aim to shed light on these aspects using the SImulating the Environment where Globular clusters Emerged (SIEGE) project, a suite of cosmological zoom-in simulations with subparsec resolution that is specifically designed to investigate the physical conditions behind the origin of compact stellar systems in high-redshift environments. The simulations analyzed in this study are focused on a dwarf galaxy with a virial mass of a few 10⁹M_⊙atz= 6.14, where the spatial resolution reaches 0.3 pc h⁻¹. Individual stars are formed directly by sampling the initial mass function, with a 100% star formation efficiency. This setup is designed to explore the impact of a high star formation efficiency under high-redshift conditions. The simulation reveals the emergence of numerous stellar clumps with sizes of 1–3 pc, stellar surface densities up to almost 10⁴M_⊙pc⁻², and masses predominantly spanning 10³M_⊙to several 10⁴M_⊙, with a few reaching 10⁵M_⊙and up to 10⁶M_⊙. All clumps form during intense, short bursts of star formation lasting less than a megayear, without noticeable signs of second peaks of star formation or accretion, often with negligible dark matter content (i.e., dark-to-stellar mass ratios below 1 within three times their effective radii). We measured a clear correlation between mass and size, with a clump mass function described by a power law with a slope of −2. Star formation conditions in the simulation reveal a behaviour that is similar to that of a feedback-free starburst scenario, where dense clumps form due to inefficient stellar feedback over small timescales. Notably, some clumps exhibit properties that closely resemble those of present-day globular clusters, highlighting their potential evolutionary connection. 

Star clusters stand at the crossroads between galaxies and single stars. Resolving the formation of star clusters in cosmological simulations represents an ambitious and challenging goal, since modelling their internal properties requires very high resolution. This paper is the third of a series within the SImulating the Environment where Globular clusters Emerged (SIEGE) project, where we conduct zoom-in cosmological simulations with sub-parsec resolution that include the feedback of individual stars, aimed to model the formation of star clusters in high-redshift proto-galaxies. We investigate the role of three fundamental quantities in shaping the intrinsic properties of star clusters, i.e., (i) pre-supernova stellar feedback (continuous or instantaneous ejection of mass and energy through stellar winds); (ii) star formation efficiency, defined as the fraction of gas converted into stars per freefall time, for which we test 2 different values (ϵ_ff= 0.1 and 1), and (iii) stellar initial mass function (IMF, standard vs top-heavy). All our simulations are run down toz= 10.5, which is sufficient for investigating some structural properties of the emerging clumps and clusters. Among the analysed quantities, the gas properties are primarily sensitive to the feedback prescriptions. A gentle and continuous feedback from stellar winds originates a complex, filamentary cold gas distribution, opposite to explosive feedback, causing smoother clumps. The prescription for a continuous, low-intensity feedback, along with the adoption of ϵ_ff= 1, also produces star clusters with maximum stellar density values up to 10⁴M_ʘpc⁻², in good agreement with the surface density-size relation observed in local young star clusters (YSCs). Therefore, a realistic stellar wind description and a high star formation effiency are the key ingredients that allow us to achieve realistic star clusters characterised by properties comparable to those of local YSCs. In contrast, the other models produce too diffuse clusters, in particular the one with a top-heavy IMF. 

ABSTRACT By means of 3D hydrodynamic simulations, we explore the effects of rotation in the formation of second-generation (SG) stars in globular clusters (GC). Our simulations follow the SG formation in a first-generation (FG) internally rotating GC; SG stars form out of FG asymptotic giant branch (AGB) ejecta and external pristine gas accreted by the system. We have explored two different initial rotational velocity profiles for the FG cluster and two different inclinations of the rotational axis with respect to the direction of motion of the external infalling gas, whose density has also been varied. For a low (10−24 g cm−3) external gas density, a disc of SG helium-enhanced stars is formed. The SG is characterized by distinct chemo-dynamical phase space patterns: it shows a more rapid rotation than the FG with the helium-enhanced SG subsystem rotating more rapidly than the moderate helium-enhanced one. In models with high external gas density ($$10^{-23}\, {\rm g\ cm^{-3}}$$), the inner SG disc is disrupted by the early arrival of external gas and only a small fraction of highly enhanced helium stars preserves the rotation acquired at birth. Variations in the inclination angle between the rotation axis and the direction of the infalling gas and the velocity profile can slightly alter the extent of the stellar disc and the rotational amplitude. The results of our simulations illustrate the complex link between dynamical and chemical properties of multiple populations and provide new elements for the interpretation of observational studies and future investigations of the dynamics of multiple-population GCs. 

ABSTRACT By means of 3D hydrodynamic simulations, we study how Type Ia supernovae (SNe) explosions affect the star formation history and the chemical properties of second-generation (SG) stars in globular clusters (GC). SG stars are assumed to form once first generation asymptotic giant branch (AGB) stars start releasing their ejecta; during this phase, external gas is accreted by the system and SNe Ia begin exploding, carving hot and tenuous bubbles. Given the large uncertainty on SNe Ia explosion times, we test two different values for the ‘delay time’. We run two different models for the external gas density: in the low-density scenario with short delay time, the explosions start at the beginning of the SG star formation, halting it in its earliest phases. The external gas hardly penetrates the system, therefore most SG stars present extreme helium abundances (Y > 0.33). The low-density model with delayed SN explosions has a more extended SG star formation epoch and includes SG stars with modest helium enrichment. On the contrary, the high-density model is weakly affected by SN explosions, with a final SG mass similar to the one obtained without SNe Ia. Most of the stars form from a mix of AGB ejecta and pristine gas and have a modest helium enrichment. We show that gas from SNe Ia may produce an iron spread of ∼0.14 dex, consistent with the spread found in about $$20{{\ \rm per\ cent}}$$ of Galactic GCs, suggesting that SNe Ia might have played a key role in the formation of this sub-sample of GCs. 

ABSTRACT We introduce a new set of zoom-in cosmological simulations with sub-pc resolution, intended to model extremely faint, highly magnified star-forming stellar clumps, detected at z = 6.14 thanks to gravitational lensing. The simulations include feedback from individual massive stars (in both the pre-supernova and supernova phases), generated via stochastic, direct sampling of the stellar initial mass function. We adopt a modified ‘delayed cooling’ feedback scheme, specifically created to prevent artificial radiative loss of the energy injected by individual stars in very dense gas (n ∼ 103–105 cm−3). The sites where star formation ignites are characterized by maximum densities of the order of 105 cm−3 and gravitational pressures Pgrav/k >107 K cm−3, corresponding to the values of the local, turbulent regions where the densest stellar aggregates form. The total stellar mass at z = 6.14 is 3.4$$\times 10^7~\rm M_{\odot }$$, in satisfactory agreement with the observed stellar mass of the observed systems. The most massive clumps have masses of $$\sim 10^6~\rm M_{\odot }$$ and half-mass sizes of ∼100 pc. These sizes are larger than the observed ones, including also other samples of lensed high-redshift clumps, and imply an average density one orders of magnitude lower than the observed one. In the size–mass plane, our clumps populate a sequence that is intermediate between the ones of observed high-redshift clumps and local dSph galaxies.