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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. 

Supernova (SN) shocks that originate from stars on orbits embedded in dense active galactic nucleus (AGN) accretion disks evolve differently from those that occur in the interstellar medium. We aim to assess how shocks evolve in this dense stratified medium and understand where SNe are muffled and have their kinetic energy absorbed by an AGN disk versus escaping. We use Sirko–Goodman (SG) and Thompson–Quataert–Murray (TQM) AGN disk models for midplane radial profiles, generated with the pAGN code; we compare the disk pressure to the energy of a standard core-collapse SN (10^51 erg) to find radii where shock breakout can occur. For verification, we evolve three-dimensional hydrodynamic shearing box simulations of stratified Gaussian disks constructed from the midplane values that are injected with energy and mass from SNe placed at multiple radii and vertical locations, using the Athena code. We find SN shocks in SG disks around black holes with mass M_BH = 10^6 M⊙ become muffled beyond R ∼ 10^6 R_s, and that this muffling radius is inversely proportional to supermassive black hole mass with muffling occurring at R ∼ 10^2 R_s for M_BH = 10^9 M⊙. Around TQM disks, the muffling radius occurs at R ∼ 10^6 R_s, independent of M_BH. The largest determining factor for muffling an SN shock is the local scale height of the AGN disk. In conclusion, we developed a predictive analytic criterion to identify where AGN disks can muffle SN shocks depending on their density and vertical scale 

We investigate the structural evolution of young star clusters forming within centrally concentrated molecular clouds. Our simulations use the Torch framework, which integrates the FLASH magnetohydrodynamics code with the AMUSE environment, enabling a self-consistent treatment of gas dynamics, star formation, stellar evolution, radiative transfer, and gravitational interactions. We quantify cluster structure using the Q parameter for fractality and compute fractal dimensions via two methods: box-counting and correlation dimension. Our results show that clusters generally inherit fractal substructure from their parental clouds, which is typically erased within ∼2.5 t_ff through dynamical relaxation. Massive stars can induce the formation of secondary subclusters via feedback, with outcomes strongly dependent on stellar mass and formation timing. Interactions among subclusters, including mergers and dispersal, can extend fractal structure beyond 4 t_ff. We also find systematic correlations between the fractality parameter Q and the fractal dimension: fractality is positively correlated with both the correlation and box-counting dimensions, with the correlation dimension exhibiting a stronger correlation. These results demonstrate how stellar feedback and internal dynamics jointly shape the measurable fractal properties of embedded star clusters. 

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, 10^1.5, and 10^2 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 withn> 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. 

Magnetic fields are critical at many scales to galactic dynamics and structure, including multiphase pressure balance, dust processing, and star formation. Dynamo action determines their dynamical structure and strength. Simulations of combined large- and small-scale dynamos have successfully developed mean fields with strength and topology consistent with observations, but with turbulent fields much weaker than observed, while simulations of small-scale dynamos with parameters relevant to the interstellar medium yield turbulent fields 1 order of magnitude below the values observed or expected theoretically. We use the Pencil Code accelerated on GPUs with Astaroth to perform high-resolution simulations of a supernova-driven galactic dynamo, including heating and cooling in a periodic domain. Our models show that the strength of the turbulent field produced by the small-scale dynamo approaches an asymptote at only modest magnetic Prandtl numbers. This allows us to use these models to suggest the essential characteristics of this constituent of the magnetic field for inclusion in global galactic models. The asymptotic limit occurs already at a magnetic Prandtl number of only a few hundred, many orders of magnitude below physical values in the interstellar medium and consistent with previous findings for isothermal compressible flows. 

Abstract 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, calledTorch, combines the magnetohydrodynamical code FLASH with N-body and stellar evolution codes in the Astrophysical Multipurpose Software Environment (AMUSE).Torchincludes stellar feedback from ionizing and nonionizing radiation, stellar winds, and supernovae, but, until now, did not include protostellar jets. We present our implementation of protostellar jet feedback within theTorchframework 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 toM = 2 × 10⁴M_⊙. We also find that the star formation rate of our lower-mass clouds (M = 5 × 10³M_⊙) 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 inTorchopens new areas of investigation regarding the role of feedback in star cluster formation and evolution. 

Abstract 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. 

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 singleEDGE-INFERNOdwarf (M_★ ≈ 10⁵ M_⊙), 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_⊙. 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. 

We investigate the role of tidal forces in molecular cloud formation by examining how apparent boundedness, as diagnosed by the classical virial parameter, relates to the actual gravitational state of clouds subject to tidal forces from their environment. Clouds are identified by a dendrogram algorithm in zoom-in regions taken from a simulation of a Milky Way–mass galaxy with the Voronoi mesh code AREPO that resolves star-forming regions at subparsec resolution. To look at a range of environments, we use data from three different regions that evolve differently in the center, near the equivalent of the solar circle, and the outskirts of the modeled galaxy, at three different times, each spaced 2 Myr apart. We compute the importance of tidal forces on all identified clouds. We then compare the boundedness of clouds, including only their internal potentials, to boundedness also including the external gravitational potential. This comparison shows that tidal forces can unbind apparently bound clouds and bind apparently unbound clouds. We characterize the cloud population by comparing their virial parameters to their surface densities, finding the ratio of the maximum to the minimum eigenvalues of the tidal tensor, and determining the strength of gravitational instability in each examined region. We find that it is necessary to take the total gravitational potential into account rather than just the internal self-gravity of the clouds to have an accurate understanding of cloud dynamics. 

The study of star cluster evolution necessitates modeling how their density profiles develop from their natal gas distribution. Observational evidence indicates that many star clusters follow a Plummer-like density profile. However, most studies have focused on the phase after gas ejection, neglecting the influence of gas on early dynamical evolution. We investigate the development of star clusters forming within gas clouds, particularly those with a centrally concentrated gas profile. Simulations were conducted using the Torch framework, integrating the FLASH magnetohydrodynamics code into AMUSE. This permitted detailed modeling of star formation, stellar evolution, stellar dynamics, radiative transfer, and gas magnetohydrodynamics. We study the collapse of centrally concentrated, turbulent spheres with a total mass of 2.5 × 10^3 M⊙, investigating the effects of varying numerical resolution and star formation scenarios. The free-fall time is shorter at the center than at the edges of the cloud, with a minimum value of 0.55 Myr. The key conclusions from this study are: (1) the final stellar density profile is more centrally concentrated than was analytically predicted, reflecting the role of global gas collapse and feedback; (2) subclusters can initially form even in centrally concentrated gas clouds; (3) gas collapses globally toward the center on the central free-fall timescale, contradicting the assumption in analytical models of local fragmentation and star formation; and (4) the mass of the most massive star formed is directly correlated with the cluster effective radius and inversely correlated with the velocity dispersion, while the duration of star formation correlates with the star formation efficiency.