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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 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. 

ABSTRACT We discovered a strongly lensed (μ ≳ 40) Ly α emission at z = 6.629 (S/N ≃ 18) in the MUSE Deep Lensed Field (MDLF) targeting the Hubble Frontier Field (HFF) galaxy cluster MACS J0416. Dedicated lensing simulations imply that the Ly α emitting region necessarily crosses the caustic. The arc-like shape of the Ly α extends 3 arcsec on the observed plane and is the result of two merged multiple images, each one with a de-lensed Ly α luminosity L ≲ 2.8 × 1040 erg s−1 arising from a confined region (≲150 pc effective radius). A spatially unresolved Hubble Space Telescope(HST) counterpart is barely detected at S/N ≃ 2 after stacking the near-infrared bands, corresponding to an observed (intrinsic) magnitude m1500 ≳ 30.8 (≳35.0). The inferred rest-frame Ly α equivalent width is EW0 > 1120 if the IGM transmission is TIGM < 0.5. The low luminosities and the extremely large Ly α EW0 match the case of a Population III (Pop III) star complex made of several dozens stars (∼104 M⊙) that irradiate an H ii region crossing the caustic. While the Ly α and stellar continuum are among the faintest ever observed at this redshift, the continuum and the Ly α emissions could be affected by differential magnification, possibly biasing the EW0 estimate. The aforementioned tentative HST detection tends to favour a large EW0, making such a faint Pop III candidate a key target for the James Webb Space Telescope and Extremely Large Telescopes. 

We report the discovery of a complete Einstein ring around the elliptical galaxy NGC 6505, atz = 0.042. This is the first strong gravitational lens discovered inEuclidand the first in an NGC object from any survey. The combination of the low redshift of the lens galaxy, the brightness of the source galaxy (I_E = 18.1 lensed,I_E = 21.3 unlensed), and the completeness of the ring make this an exceptionally rare strong lens, unidentified until its observation byEuclid. We present deep imaging data of the lens from theEuclidVisible Camera (VIS) and Near-Infrared Spectrometer and Photometer (NISP) instruments, as well as resolved spectroscopy from theKeckCosmic Web Imager (KCWI). TheEuclidimaging in particular presents one of the highest signal-to-noise ratio optical/near-infrared observations of a strong gravitational lens to date. From the KCWI data we measure a source redshift ofz = 0.406. Using data from the Dark Energy Spectroscopic Instrument (DESI) we measure a velocity dispersion for the lens galaxy ofσ_⋆ = 303 ± 15 km s⁻¹. We model the lens galaxy light in detail, revealing angular structure that varies inside the Einstein ring. After subtracting this light model from the VIS observation, we model the strongly lensed images, finding an Einstein radius of 2.″5, corresponding to 2.1 kpc at the redshift of the lens. This is small compared to the effective radius of the galaxy,R_eff ∼ 12.″3. Combining the strong lensing measurements with analysis of the spectroscopic data we estimate a dark matter fraction inside the Einstein radius off_DM = (11.1_−3.5^+5.4)% and a stellar initial mass-function (IMF) mismatch parameter ofα_IMF = 1.26_−0.08^+0.05, indicating a heavier-than-Chabrier IMF in the centre of the galaxy.