Quantifying the timescales of star cluster emergence from their natal clouds remains one of the main challenges in understanding the star formation process. These timescales are fundamental measurements of the star formation cycle within galaxies, yet are difficult to constrain due to the complex interplay between stellar feedback and star formation across multiple physical scales. Here we present Hubble Space Telescope and James Webb Space Telescope observations of thousands of young star clusters in four nearby galaxies (M51, M83, NGC 628 and NGC 4449). A substantial fraction of these clusters are still embedded within their natal gas and remain invisible at optical wavelengths. We constrain their emergence process by measuring the timescales required to disperse the surrounding material. We find a strong correlation between dispersal timescale and cluster stellar mass, with massive clusters emerging faster than their lower-mass counterparts. This is a critical constraint on star formation and stellar feedback simulations, which struggle to fully reproduce star clusters formation and emergence. Our results emphasize the central role of massive clusters in driving the escape of ionizing radiation into the galactic medium. Finally, they impose time limitations for planet formation in massive cluster environments where disks get exposed to ultraviolet irradiation and further gas infall is halted.

This package provides the analysis products and raw simulation snapshots accompanying the paper "Centrally concentrated star formation in young clusters II: Jet feedback." It includes time‑history tables, per‑snapshot stellar particle catalogues, raw FLASH/Torch HDF5 snapshots at two reference epochs, and density‑slice movies for 14 hydrodynamic simulations of star cluster formation with and without protostellar jet feedback, spanning three AMR resolution levels.

Stellar surface abundances are records of the state of the gas from which stars formed, and thus trace how individual elements have mixed into the surrounding medium following their ejection from stars. In this work, we test the common assumption of instantaneous and homogeneous metal mixing during the formation of the first Population II stars by characterizing the chemical homogeneity of the gas in simulated star-forming environments enriched by Population III stellar feedback. Testing the homogeneity of metal mixing in this time period is necessary for understanding the spread of abundances in the most metal-poor stars, and the (in)homogeneity of individual sites of star formation. Using Aeos, a suite of star-by-star cosmological simulations, we quantify how gas abundances change over space and time relative to Population II stellar abundances using Mahalanobis distances, a measure of covariance-normalized dissimilarity. We find that the homogeneous mixing assumption holds only within ∼100 pc of a star-forming region and ∼ 7 Myr following the star formation event. Beyond this regime, deviations between stellar and gas abundances increase until they become indistinguishable from assuming a homogeneous mix of metals averaged over the initial mass function. This highlights the limited applicability of assuming instantaneous and homogeneous mixing in realistic halo environments at high redshift. We identify critical mixing scales that are necessary to explore chemical evolution in the early Universe. These scales can be applied to determine the precision needed for accurate chemical tagging of observed data and to explore parameter space with analytical models.

We present an extension of our semi-analytic model that follows the formation of Population III stars and their metal-enriched descendants, incorporating dark matter halo merger trees from cosmological $N$-body simulations and feedback from reionization. Our extended model is calibrated using two complementary cosmological hydrodynamical simulations: Aeos, which resolves individual Population III and II stars to $z\sim14.6$, and Renaissance, which is lower resolution but follows large-scale metal-enriched star formation to $z \sim 11$. With a combined calibration, we capture small-scale physics of primordial star formation over a large range in halo mass. We find good agreement between our calibrated model and Aeos, reproducing the evolution in number of star-forming halos and total stellar mass. Achieving this agreement requires increasing the normalization of, flattening the redshift dependence of, and adding scatter to the commonly used critical mass threshold $M_{\mathrm{crit}}$. Our treatment of the delay between Pop III stellar death and subsequent Pop II star formation emphasizes the need to account for halos that have yet to transition to Pop II, since incomplete sampling of this delay in simulations limits physically motivated calibrations. Finally, we apply our model to larger-volume dark matter only simulations and predict $\sim10$ active Pop III sources at $z = 10$ lie within the area strongly lensed by galaxy cluster MACS J0416 with a magnification exceeding $μ> 30$. These results demonstrate that semi-analytic approaches, when calibrated to hydrodynamical simulations, can provide accurate, computationally efficient predictions for the earliest stages of cosmic star formation.

The chemical abundances of stars in galaxies are a fossil record of the star formation and stellar evolution processes that regulate galaxy formation, including the stellar initial mass function, the fraction and timing of type Ia supernovae (SNeIa), and nucleosynthesis inside massive stars. In this paper, we systematically explore uncertainties associated with modeling chemical enrichment in dwarf galaxies. We repeatedly simulate a single EDGE-INFERNO dwarf (M-star approximate to 10(5) M-circle dot), varying the chemical yields of massive stars, the timing and yields of SNeIa, and the intrinsic stochasticity that arises from sampling individual stars and galaxy formation chaoticity. All simulations are high-resolution (3.6 pc), cosmological zoom-in hydrodynamical simulations that track the stellar evolution of all individual stars with masses of > 0.5 M-circle dot. We find that SNeIa make significant contributions to the iron content of low-mass, reionization-limited galaxies, with possible variations in mean abundance ratios and [Fe/H] related to minor changes in their evolutionary timescales. In contrast, different massive star yields, accounting (or not) for stellar rotation, result in mean abundance variations comparable to those arising from stochasticity, with the possible exception of extremely rapidly rotating stars. Nonetheless, massive stars significantly affect the shape of abundance trends with [Fe/H], for example, through the existence (or not) of a bimodality in the [X/Fe]-[Fe/H] planes, particularly in [Al/Fe]. Finally, we find that the variance arising from random sampling severely limits the interpretation of single galaxies. Our analysis showcases the power of star-by-star cosmological models to unpick how both systematic uncertainties (e.g., assumptions in low-metallicity chemical enrichment) and statistical uncertainties (e.g., averaging over enough galaxies and stars within a galaxy) affect the interpretation of chemical observables in ultra-faint dwarf galaxies.

Stars form in clusters from the gravitational collapse of giant molecular clouds, which is opposed by a variety of physical processes, including stellar feedback. The interplay between these processes determines the star formation rate of the clouds. To study how feedback controls star formation, we use a numerical framework that is optimized to simulate star cluster formation and evolution. This framework, called Torch, combines the magnetohydrodynamical code FLASH with N-body and stellar evolution codes in the Astrophysical Multipurpose Software Environment (AMUSE). Torch includes stellar feedback from ionizing and non-ionizing radiation, stellar winds, and supernovae, but, until now, did not include protostellar jets. We present our implementation of protostellar jet feedback within the Torch framework and describe its free parameters. We then demonstrate our new module by comparing cluster formation simulations with and without jets. We find that the inclusion of protostellar jets slows star formation, even in clouds of up to M = 2 × 10^4 M_⊙. We also find that the star formation rate of our lower mass clouds (M = 5 × 10^3 M_⊙) is strongly affected by both the inclusion of protostellar jets and the chosen jet parameters, including the jet lifetime and injection velocity. We follow the energy budget for each simulation and find that the inclusion of jets systematically increases the kinetic energy of the gas at early times. The implementation of protostellar jet feedback in Torch opens new areas of investigation regarding the role of feedback in star cluster formation and evolution.

Protostellar jets are one of the earliest forms of stellar feedback, but their impact on star formation and cluster assembly in centrally concentrated molecular clouds remains poorly understood. We study how protostellar jets affect the star formation efficiency, the temporal variability of star formation, star cluster structure, and the early dynamical state of centrally concentrated, newly forming star clusters using the Torch star cluster formation framework. We adopt a centrally concentrated initial cloud model with mass M = 2.5 x 10^3 solar masses and compare six pairs of simulations with and without protostellar jets, supplemented by one additional higher resolution pair of simulations. We analyze our simulations using global star formation diagnostics together with structural and dynamical measures of the stellar population. Models with jet feedback achieve star formation efficiencies of 12-16

Appel et al. 2025 describes the implementation of protostellar jets in the Torch code and this repository contains data from the simulation suite used in the paper to demonstrate the new implementation.

Interpretation of data from faint dwarf galaxies is made challenging by observations limited to only the brightest stars. We present a major improvement to tackle this challenge by undertaking zoomed cosmological simulations that resolve the evolution of all individual stars more massive than 0.5 M ⊙ , thereby explicitly tracking all observable stars for the Hubble time. For the first time, we predict observable color–magnitude diagrams and the spatial distribution of ≈100,000 stars within four faint ( M ⋆ ≈ 10 5 M ⊙ ) dwarf galaxies directly from their cosmological initial conditions. In all cases, simulations predict complex light profiles with multiple components, implying that typical observational measures of structural parameters can make the total V -band magnitudes appear up to 0.5 mag dimmer compared to estimates from simulations. Furthermore, when only small (⪅100) numbers of stars are observable, shot noise from realizations of the color–magnitude diagram introduces uncertainties comparable to the population scatter in, e.g., the total magnitude, half-light radius, and mean iron abundance measurements. Estimating these uncertainties with fully self-consistent mass growth, star formation, and chemical enrichment histories paves the way for more robust interpretation of dwarf galaxy data.

We investigate how stellar feedback from the first stars (Population III) distributes metals through the interstellar and intergalactic medium using the star-by-star cosmological hydrodynamics simulation, A eos . We find that energy injected from the supernovae (SNe) of the first stars is enough to expel a majority of gas and injected metals beyond the virial radius of halos with mass M _dm ≲ 10 ^7 M _⊙ , regardless of the number of SNe. This prevents self-enrichment and results in a nonmonotonic increase in metallicity at early times. Most minihalos ( M _dm ≳ 10 ^5 M _⊙ ) do not retain significant fractions of the yields produced within their virial radii until they have grown to halo masses of M _dm ≳ 10 ^7 M _⊙ . The loss of metals to regions well beyond the virial radius delays the onset of enriched star formation and extends the period that Population III star formation can persist. We also explore the contributions of different nucleosynthetic channels to 10 individual elements. On the timescale of the simulation (lowest redshift z = 14.3), enrichment is dominated by core-collapse supernovae for all elements, but with a significant contribution from asymptotic giant branch winds to the s -process elements, which are normally thought to only be important at late times. In this work, we establish important mechanisms for early chemical enrichment, which allows us to apply A eos in later epochs to trace the evolution of enrichment during the complete transition from Population III to Population II stars.

Context. Galaxy evolution is sensitive to how stars inject feedback into their surroundings. In particular, the stellar feedback from star clusters strongly affects gas motions and, consequently, the baryonic cycle. More massive clusters have stronger effects. Our previous results show that the star cluster mass distribution in dwarf galaxies depends on feedback because strong pre-supernova feedback, particularly ionizing radiation, results in fewer high-mass star clusters. Aims. We investigated the mass distribution of gas clouds in dwarf galaxies. Since star clusters form from the collapse of gas clouds, we expected similar feedback dependences in both their mass distributions; we thus hypothesized that pre-supernova feedback results in fewer high-mass gas clouds. Methods. To test our hypothesis, we used an isocontour analysis at three cutoff densities n = 10, 101.5, and 102 cm−3 to identify gas clouds from dwarf galaxy simulations performed with the RAMSES adaptive mesh refinement code. We calculated mass distributions for models that implement different combinations of the feedback modes: supernovae, stellar winds from massive stars, and ionizing radiation. Results. We find that the mass distribution for clouds with n > 100 cm−3 is independent of feedback, but that the mass distribution for cloud complexes with n > 10 cm−3 is more top-heavy in the presence of radiation. Winds do not affect the mass distribution at any of the scales we studied. Conclusions. This contradicts our hypothesis that the mass distribution of gas clouds would show a similar feedback dependence as the mass distribution of star clusters. Instead, our results show no feedback dependence in the mass function of dense clouds with n > 100 cm−3, suggesting their mass distribution is predominantly set by gravity. We conclude that the shape of the star cluster mass function must be determined by a combination of intra-cloud feedback regulation of star formation (i.e., regulation of star formation within a cloud due to the feedback of stars formed from that cloud itself) and, in the case of radiation, effects on the temperature of the parent gas clouds.

We present a new framework to incorporate feedback from massive interacting binaries in simulations of star cluster formation. Our new feedback model adds binary stellar evolution to the cluster formation code Torch , and couples it in Amuse to the preexisting modules for collisional stellar dynamics, magnetohydrodynamics, and mechanical and radiative feedback. Our model accounts for the effects of mass transfer on the stars’ mass-loss rates, their radiation spectra, and the timing of core-collapse supernovae. It also injects mass lost through nonconservative mass transfer and CE ejection into the interstellar medium (ISM). We demonstrate the use of our feedback model through simulations of isolated binaries in a gaseous medium, and of embedded clusters of massive binaries. Feedback from interacting binaries efficiently couples with the surrounding ISM. It increases the size of H ii regions, increases the kinetic and thermal energy of the gas, and increases the pressure within H ii regions compared to models that use single star stellar evolution. Those differences arise from the ionizing radiation, which increases by 3 orders of magnitude, resulting in H ii regions that expand due to thermal pressure rather than radiation pressure. The effects of stellar dynamics and the gravitational potential of the background gas cause the evolution of individual binaries to deviate from the predictions made by secular evolution, impacting the subsequent feedback from the binary. We conclude that massive interacting binaries are an important source of feedback in cluster-forming regions, and must be considered when studying the emerging timescales of young star clusters.

We explore the effect of variations in the Population III initial mass function (IMF) and star-by-star feedback on early galaxy formation and evolution using the Aeos simulations. We compare simulations with two different Population III IMFs: Mchar = 10 M circle dot and Mmax=100M circle dot (Aeos10) and Mchar = 20 M circle dot and Mmax=300M circle dot (Aeos20). Aeos20 produces significantly more ionizing photons, ionizing 30% of the simulation volume by z approximate to 14, compared to 9% in Aeos10. This enhanced ionization suppresses galaxy formation on the smallest scales. Differences in Population III IMF also affect chemical enrichment. Aeos20 produces Population II stars with higher abundances, relative to iron, of light and alpha-elements, a stronger odd-even effect, and a higher frequency of carbon-enhanced metal-poor stars. The abundance scatter between different Population II galaxies dominates the differences due to Population III IMF, though, implying a need for a larger sample of Population II stars to interpret the impact of Population III IMF on early chemical evolution. We also compare the Aeos simulations to traditional simulations that use single stellar population particles. We find that star-by-star modeling produces a steeper mass-metallicity relation due to less bursty feedback. These results highlight the strong influence of the Population III IMF on early galaxy formation and chemical evolution, emphasizing the need to account for IMF uncertainties in simulations and the importance of metal-poor Population II stellar chemical abundances when studying the first stars.

Globular clusters (GCs) are among the oldest and densest stellar systems in the Universe, yet how they form remains a mystery1. Here we present a suite of cosmological simulations in which both dark-matter-free GCs and dark-matter-rich dwarf galaxies naturally emerge in the Standard Cosmology. We show that these objects inhabit distinct locations in the size-luminosity plane and that they have similar ages, age spread, metallicity and metallicity spread to globulars and dwarfs in the nearby Universe. About half of our simulated globulars form by means of regular star formation near the centres of their host dwarf, with the rest forming further out, triggered by mergers. The latter are more tidally isolated and more likely to survive to the present day. Finally, our simulations predict the existence of a new class of object that we call 'globular-cluster-like dwarfs' (GCDs). These form from a single, self-quenching, star-formation event in low-mass dark-matter halos at high redshift and have observational properties intermediate between globulars and dwarfs. We identify several dwarfs in our Galaxy, such as Reticulum II (refs. 2-4), that could be in this new class. If so, they promise unprecedented constraints on dark-matter models and new sites to search for metal-free stars.

Mass segregation is seen in many star clusters, but whether massive stars form in the center of a cluster or migrate there dynamically is still debated. N-body simulations show that early dynamical mass segregation is possible when sub-clusters merge to form a dense core with a small crossing time. However, the effect of gas dynamics on both the formation and dynamics of the stars could inhibit the formation of the dense core. We aim to study the dynamical mass segregation of star cluster models that include gas dynamics and self-consistently form stars from the dense substructure in the gas. Our models use the torch framework, which is based on amuse and includes stellar and magnetized gas dynamics, as well as stellar evolution and feedback from radiation, stellar winds, and supernovae. Our models consist of three star clusters forming from initial turbulent spherical clouds of mass $10^4,,10^5,, 10^6 M_⊙$ and radius $11.7 pc$ that have final stellar masses of $3.6 M_⊙$, $6.5 M_⊙$, and $8.9 M_⊙$, respectively. There is no primordial mass segregation in the model by construction. All three clusters become dynamically mass segregated at early times via collapse confirming that this mechanism occurs within sub-clusters forming directly out of the dense substructure in the gas. The dynamics of the embedded gas and stellar feedback do not inhibit the collapse of the cluster. We find that each model cluster becomes mass segregated within 2 Myr of the onset of star formation, reaching the levels observed in young clusters in the Milky Way. However, we note that the exact values are highly time-variable during these early phases of evolution. Massive stars that segregate to the center during core collapse are likely to be dynamically ejected, a process that can decrease the overall level of mass segregation again.

The AEOS project introduces a series of high-resolution cosmological simulations that model star-by-star chemical enrichment and galaxy formation in the early Universe, achieving 1 pc resolution. These simulations capture the complexities of galaxy evolution within the first 300 Myr by modeling individual stars and their feedback processes. By incorporating chemical yields from individual stars, AEOS generates galaxies with diverse stellar chemical abundances, linking them to hierarchical galaxy formation and early nucleosynthetic events. These simulations underscore the importance of chemical abundance patterns in ancient stars as vital probes of early nucleosynthesis, star formation histories, and galaxy formation. We examine the metallicity floors of various elements resulting from Pop III enrichment, providing best-fit values for eight different metals (e.g., [O/H] = -4.0) to guide simulations without Pop III models. Additionally, we identify galaxies that begin star formation with Pop II after external enrichment and investigate the frequency of CEMP stars at varying metallicities. The AEOS simulations offer detailed insights into the relationship between star formation, feedback, and chemical enrichment. Future work will extend these simulations to later epochs to interpret the diverse stellar populations of the Milky Way and its satellites.

Nuclear Star Clusters (NSCs) are amongst the densest stellar systems in the Universe and are found at the centres of many bright spiral and elliptical galaxies, and up to ${\sim}$40% of dwarf galaxies. However, their formation mechanisms, and possible links to globular clusters (GCs), remain debated. This paper uses the EDGE simulations - a collection of zoom-in, cosmological simulations of isolated dwarf galaxies -- to present a new formation mechanism for NSCs. We find that, at a gas spatial and mass resolution of ${\sim}3\,$pc and ${\sim}161$ M$_\odot$, respectively, NSCs naturally emerge in a subset of our EDGE dwarfs with redshift-zero halo masses of $\rm{M}_{\rm{r}200\rm{c}} \sim 5 \times 10^9$ M$_\odot$. These dwarfs are quenched by reionisation, but retain a significant reservoir of gas that is unable to cool and form stars. Sometime after reionisation, the dwarfs then undergo a major (${\sim}$1:1) merger that excites rapid gas cooling, leading to a significant starburst. An NSC forms in this starburst that then quenches star formation thereafter. The result is a nucleated dwarf that has two stellar populations with distinct age: one pre-reionisation and one post-reionisation. Our mechanism is unique for two key reasons. Firstly, the low mass of the host dwarf means that NSCs, formed in this way, can accrete onto galaxies of almost all masses, potentially seeding the formation of NSCs everywhere. Secondly, our model predicts that NSCs should have at least two stellar populations with a large ($\gtrsim$1 billion year) age separation. This yields a predicted colour magnitude diagram for our nucleated dwarfs that has two distinct main sequence turnoffs. Several GCs orbiting the Milky Way, including Omega Centauri and M54, show exactly this behaviour, suggesting that they may, in fact, be accreted NSCs.

We present JWST NIRCam observations of the emerging young star clusters (eYSCs) detected in the nearby spiral galaxy M83. The NIRcam mosaic encompasses the nuclear starburst, the bar, and the inner spiral arms. The eYSCs, detected in Pa α and Br α maps, have been largely missed in previous optical campaigns of young star clusters (YSCs). We distinguish between eYSCI, if they also have compact 3.3 μ m polycyclic aromatic hydrocarbon (PAH) emission associated with them, and eYSCII, if they only appear as compact Pa α emitters. We find that the variations in the 3.3 μ m PAH feature are consistent with an evolutionary sequence where eYSCI evolve into eYSCII and then optical YSCs. This sequence is clear in the F300M​​​​​​−F335M (tracing the excess in the 3.3 μ m PAH feature) and the F115W−F187N (tracing the excess in Pa α ) colors, which become increasingly bluer as clusters emerge. The central starburst stands out as the region where the most massive eYSCs are currently forming in the galaxy. We estimate that only about 20% of eYSCs will remain detectable as compact YSCs. Combining eYSCs and YSCs (≤10 Myr), we recover an average clearing timescale of 6 Myr in which clusters transition from embedded to fully exposed. We see evidence of shorter emergence timescales (∼5 Myr) for more massive (>5 × 10 ^3 M _⊙ ) clusters, while star clusters of ∼10 ^3 M _⊙ about 7 Myr. We estimate that eYSCs remain associated with the 3.3 μ m PAH emission for 3–4 Myr. Larger samples of eYSC and YSC populations will provide stronger statistics to further test environmental and cluster mass dependencies on the emergence timescale.

We present a new suite of EDGE ('Engineering Dwarfs at Galaxy formation's Edge') cosmological zoom simulations. The suite includes 15 radiation-hydrodynamical dwarf galaxies covering the ultrafaint to the dwarf irregular regime (10 (4) <= M.(z = 0) <= 10 (8) M ((R))) to enable comparisons with observed scaling relations. Each object in the suite is evolved at high resolution ( R 3 pc ) and includes stellar radiation, winds, and supernova feedback channels. We compare with previous EDGE simulations without radiation, finding that radiative feedback results in significantly weaker galactic outflows. This generalizes our previous findings to a wide mass range, and reveals that the effect is most significant at low M-star. Despite this difference, stellar masses stay within a factor of two of each other, and key scaling relations of dwarf galaxies (size-mass, neutral gas-stellar mass, and gas-phase mass-metallicity) emerge correctly in both simulation suites. Only the stellar mass-stellar metallicity relation is strongly sensitive to the change in feedback. This highlights how obtaining statistical samples of dwarf galaxy stellar abundances with next-generation spectrographs will be key to probing and constraining the baryon cycle of dwarf galaxies.

The mode of star formation that results in the formation of globular clusters and young massive clusters is difficult to constrain through observations. We present models of massive star cluster formation using the TORCH framework, which uses the Astrophysical MUltipurpose Software Environment (AMUSE) to couple distinct multi-physics codes that handle star formation, stellar evolution and dynamics, radiative transfer, and magnetohydrodynamics. We upgraded TORCH by implementing the N-body code PETAR, thereby enabling TORCH to handle massive clusters forming from 10(6) M-circle dot clouds with >= 10(5) individual stars. We present results from TORCH simulations of star clusters forming from 10(4), 10(5), and 10(6) M-circle dot turbulent spherical gas clouds (named M4, M5, M6) of radius R = 11.7 pc. We find that star formation is highly efficient and becomes more so at a higher cloud mass and surface density. For M4, M5, and M6 with initial surface densities 2.325 x 10(1,2,3) M-circle dot pc(-2), after a free-fall time of t(ff) = 6.7,2.1,0.67 Myr, we find that similar to 30%, 40%, and 60% of the cloud mass has formed into stars, respectively. The end of simulation-integrated star formation efficiencies for M4, M5, and M6 are & varepsilon;(star) = M-star/M-cloud = 36%, 65%, and 85%. Observations of nearby clusters similar in mass and size to M4 have instantaneous star formation efficiencies of & varepsilon;(inst) <= 30%, which is slightly lower than the integrated star formation efficiency of M4. The M5 and M6 models represent a different regime of cluster formation that is more appropriate for the conditions in starburst galaxies and gas-rich galaxies at high redshift, and that leads to a significantly higher efficiency of star formation. We argue that young massive clusters build up through short efficient bursts of star formation in regions that are sufficiently dense (Sigma >= 10(2) M-circle dot pc(-2)) and massive (M-cloud >= 10(5) M-circle dot). In such environments, stellar feedback from winds and radiation is not strong enough to counteract the gravity from gas and stars until a majority of the gas has formed into stars.