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We explore the relation between stellar surface density and gas surface density (the star–gas, or S-G, correlation) in a 20,000M_⊙simulation from the STAR FORmation in Gaseous Environments (starforge) project. We create synthetic observations based on the Spitzer and Herschel telescopes by modeling contamination by active galactic nuclei, smoothing based on angular resolution, cropping the field of view, and removing close neighbors and low-mass sources. We extract S-G properties such as the dense gas-mass fraction, the Class II:I ratio, and the S-G correlation (Σ_YSO/Σ_gas) from the simulation and compare them to observations of giant molecular clouds, young clusters, and star-forming regions, as well as to analytical models. We find that the simulation reproduces trends in the counts of young stellar objects and the median slope of the S-G correlation. This implies that the S-G correlation is not simply the result of observational biases, but is in fact a real effect. However, other statistics, such as the Class II:I ratio and dense gas-mass fraction, do not always match observed equivalents in nearby clouds. This motivates further observations covering the full simulation age range and more realistic modeling of cloud formation.

Most stars form in highly clustered environments within molecular clouds, but eventually disperse into the distributed stellar field population. Exactly how the stellar distribution evolves from the embedded stage into gas-free associations and (bound) clusters is poorly understood. We investigate the long-term evolution of stars formed in the starforge simulation suite – a set of radiation-magnetohydrodynamic simulations of star-forming turbulent clouds that include all key stellar feedback processes inherent to star formation. We use nbody6++gpu to follow the evolution of the young stellar systems after gas removal. We use HDBSCAN to define stellar groups and analyse the stellar kinematics to identify the true bound star clusters. The conditions modeled by the simulations, i.e. global cloud surface densities below 0.15 g cm−2, star formation efficiencies below 15 per cent, and gas expulsion time-scales shorter than a free fall time, primarily produce expanding stellar associations and small clusters. The largest star clusters, which have ∼1000 bound members, form in the densest and lowest velocity dispersion clouds, representing ∼32 and 39 per cent of the stars in the simulations, respectively. The cloud’s early dynamical state plays a significant role in setting the classical star formation efficiency versus bound fraction relation. All stellar groups follow a narrow mass-velocity dispersion power-law relation at 10 Myr with a power-law index of 0.21. This correlation result in a distinct mass–size relationship for bound clusters. We also provide valuable constraints on the gas dispersal time-scale during the star formation process and analyse the implications for the formation of bound systems.

Modelling self-gravity of collisionless fluids (e.g. ensembles of dark matter, stars, black holes, dust, and planetary bodies) in simulations is challenging and requires some force softening. It is often desirable to allow softenings to evolve adaptively, in any high-dynamic range simulation, but this poses unique challenges of consistency, conservation, and accuracy, especially in multiphysics simulations where species with different ‘softening laws’ may interact. We therefore derive a generalized form of the energy-and-momentum conserving gravitational equations of motion, applicable to arbitrary rules used to determine the force softening, together with consistent associated time-step criteria, interaction terms between species with different softening laws, and arbitrary maximum/minimum softenings. We also derive new methods to maintain better accuracy and conservation when symmetrizing forces between particles. We review and extend previously discussed adaptive softening schemes based on the local neighbour particle density, and present several new schemes for scaling the softening with properties of the gravitational field, i.e. the potential or acceleration or tidal tensor. We show that the ‘tidal softening’ scheme not only represents a physically motivated, translation and Galilean invariant and equivalence-principle respecting (and therefore conservative) method but also imposes negligible time-step or other computational penalties, ensuring that pairwise two-body scattering is small compared to smooth background forces and can resolve outstanding challenges in properly capturing tidal disruption of substructures (minimizing artificial destruction) while also avoiding excessive N-body heating. We make all of this public in the GIZMO code.

The current generation of galaxy simulations can resolve individual giant molecular clouds, the progenitors of dense star clusters. But the evolutionary fate of these young massive clusters, and whether they can become the old globular clusters (GCs) observed in many galaxies, is determined by a complex interplay of internal dynamical processes and external galactic effects. We present the first star-by-star N-body models of massive (N ∼ 105–107) star clusters formed in a FIRE-2 MHD simulation of a Milky Way-mass galaxy, with the relevant initial conditions and tidal forces extracted from the cosmological simulation. We select 895 (∼30 per cent) of the YMCs with >6 × 104 M⊙ from Grudić et al. 2022 and integrate them to z = 0 using the cluster Monte Carlo code, CMC. This procedure predicts a MW-like system with 148 GCs, predominantly formed during the early, bursty mode of star formation. Our GCs are younger, less massive, and more core-collapsed than clusters in the Milky Way or M31. This results from the assembly history and age-metallicity relationship of the host galaxy: Younger clusters are preferentially born in stronger tidal fields and initially retain fewer stellar-mass black holes, causing them to lose mass faster and reach core collapse sooner than older GCs. Our results suggest that the masses and core/half-light radii of GCs are shaped not only by internal dynamical processes, but also by the specific evolutionary history of their host galaxies. These results emphasize that N-body studies with realistic stellar physics are crucial to understanding the evolution and present-day properties of GC systems.

Formation of supermassive black holes (BHs) remains a theoretical challenge. In many models, especially beginning from stellar relic ‘seeds,’ this requires sustained super-Eddington accretion. While studies have shown BHs can violate the Eddington limit on accretion disc scales given sufficient ‘fuelling’ from larger scales, what remains unclear is whether or not BHs can actually capture sufficient gas from their surrounding interstellar medium (ISM). We explore this in a suite of multiphysics high-resolution simulations of BH growth in magnetized, star-forming dense gas complexes including dynamical stellar feedback from radiation, stellar mass-loss, and supernovae, exploring populations of seeds with masses $\sim 1\!-\!10^{4}\, \mathrm{M}_{\odot }$. In this initial study, we neglect feedback from the BHs: so this sets a strong upper limit to the accretion rates seeds can sustain. We show that stellar feedback plays a key role. Complexes with gravitational pressure/surface density below $\sim 10^{3}\, \mathrm{M}_{\odot }\, {\rm pc^{-2}}$ are disrupted with low star formation efficiencies so provide poor environments for BH growth. But in denser cloud complexes, early stellar feedback does not rapidly destroy the clouds but does generate strong shocks and dense clumps, allowing $\sim 1{{\ \rm per\ cent}}$ of randomly initialized seeds to encounter a dense clump with low relative velocity and produce runaway, hyper-Eddington accretion (growing by orders of magnitude). Remarkably, mass growth under these conditions is almost independent of initial BH mass, allowing rapid intermediate-mass black hole (IMBH) formation even for stellar-mass seeds. This defines a necessary (but perhaps not sufficient) set of criteria for runaway BH growth: we provide analytic estimates for the probability of runaway growth under different ISM conditions.

The properties of young star clusters formed within a galaxy are thought to vary in different interstellar medium conditions, but the details of this mapping from galactic to cluster scales are poorly understood due to the large dynamic range involved in galaxy and star cluster formation. We introduce a new method for modelling cluster formation in galaxy simulations: mapping giant molecular clouds (GMCs) formed self-consistently in a FIRE-2 magnetohydrodynamic galaxy simulation on to a cluster population according to a GMC-scale cluster formation model calibrated to higher resolution simulations, obtaining detailed properties of the galaxy’s star clusters in mass, metallicity, space, and time. We find $\sim 10{{\ \rm per\ cent}}$ of all stars formed in the galaxy originate in gravitationally bound clusters overall, and this fraction increases in regions with elevated Σgas and ΣSFR, because such regions host denser GMCs with higher star formation efficiency. These quantities vary systematically over the history of the galaxy, driving variations in cluster formation. The mass function of bound clusters varies – no single Schechter-like or power-law distribution applies at all times. In the most extreme episodes, clusters as massive as 7 × 106 M⊙ form in massive, dense clouds with high star formation efficiency. The initial mass–radius relation of young star clusters is consistent with an environmentally dependent 3D density that increases with Σgas and ΣSFR. The model does not reproduce the age and metallicity statistics of old ($\gt 11\rm Gyr$) globular clusters found in the Milky Way, possibly because it forms stars more slowly at z > 3.

Barnard’s Loop is a famous arc of Hαemission located in the Orion star-forming region. Here, we provide evidence of a possible formation mechanism for Barnard’s Loop and compare our results with recent work suggesting a major feedback event occurred in the region around 6 Myr ago. We present a 3D model of the large-scale Orion region, indicating coherent, radial, 3D expansion of the OBP-Near/Briceño-1 (OBP-B1) cluster in the middle of a large dust cavity. The large-scale gas in the region also appears to be expanding from a central point, originally proposed to be Orion X. OBP-B1 appears to serve as another possible center, and we evaluate whether Orion X or OBP-B1 is more likely to have caused the expansion. We find that neither cluster served as the single expansion center, but rather a combination of feedback from both likely propelled the expansion. Recent 3D dust maps are used to characterize the 3D topology of the entire region, which shows Barnard’s Loop’s correspondence with a large dust cavity around the OPB-B1 cluster. The molecular clouds Orion A, Orion B, and Orionλreside on the shell of this cavity. Simple estimates of gravitational effects from both stars and gas indicate that the expansion of this asymmetric cavity likely induced anisotropy in the kinematics of OBP-B1. We conclude that feedback from OBP-B1 has affected the structure of the Orion A, Orion B, and Orionλmolecular clouds and may have played a major role in the formation of Barnard’s Loop.

Most observed stars are part of a multiple star system, but the formation of such systems and the role of environment and various physical processes is still poorly understood. We present a suite of radiation-magnetohydrodynamic simulations of star-forming molecular clouds from the STARFORGE project that include stellar feedback with varied initial surface density, magnetic fields, level of turbulence, metallicity, interstellar radiation field, simulation geometry and turbulent driving. In our fiducial cloud, the raw simulation data reproduces the observed multiplicity fractions for Solar-type and higher mass stars, similar to previous works. However, after correcting for observational incompleteness the simulation underpredicts these values. The discrepancy is likely due to the lack of disc fragmentation, as the simulation only resolves multiples that form either through capture or core fragmentation. The raw mass distribution of companions is consistent with randomly drawing from the initial mass function for the companions of $\gt 1\, \mathrm{M}_{\rm \odot }$ stars. However, accounting for observational incompleteness produces a flatter distribution similar to observations. We show that stellar multiplicity changes as the cloud evolves and anticorrelates with stellar density. This relationship also explains most multiplicity variations between runs, i.e. variations in the initial conditions that increase stellar density (increased surface density, reduced turbulence) also act to decrease multiplicity. While other parameters, such as metallicity, interstellar radiation, and geometry significantly affect the star formation history or the IMF, varying them produces no clear trend in stellar multiplicity properties.

One of the key mysteries of star formation is the origin of the stellar initial mass function (IMF). The IMF is observed to be nearly universal in the Milky Way and its satellites, and significant variations are only inferred in extreme environments, such as the cores of massive elliptical galaxies and the Central Molecular Zone. In this work, we present simulations from the STARFORGE project that are the first cloud-scale radiation-magnetohydrodynamic simulations that follow individual stars and include all relevant physical processes. The simulations include detailed gas thermodynamics, as well as stellar feedback in the form of protostellar jets, stellar radiation, winds, and supernovae. In this work, we focus on how stellar radiation, winds, and supernovae impact star-forming clouds. Radiative feedback plays a major role in quenching star formation and disrupting the cloud; however, the IMF peak is predominantly set by protostellar jet physics. We find that the effect of stellar winds is minor, and supernovae ‘occur too late’ to affect the IMF or quench star formation. We also investigate the effects of initial conditions on the IMF. We find that the IMF is insensitive to the initial turbulence, cloud mass, and cloud surface density, even though these parameters significantly shape the star formation history of the cloud, including the final star formation efficiency. Meanwhile, the characteristic stellar mass depends weakly on metallicity and the interstellar radiation field, which essentially set the average gas temperature. Finally, while turbulent driving and the level of magnetization strongly influence the star formation history, they only influence the high-mass slope of the IMF.

As they grow, galaxies can transition from irregular/spheroidal with ‘bursty’ star formation histories (SFHs), to discy with smooth SFHs. But even in simulations, the direct physical cause of such transitions remains unclear. We therefore explore this in a large suite of numerical experiments re-running portions of cosmological simulations with widely varied physics, further validated with existing FIRE simulations. We show that gas supply, cooling/thermodynamics, star formation model, Toomre scale, galaxy dynamical times, and feedback properties do not have a direct causal effect on these transitions. Rather, both the formation of discs and cessation of bursty star formation are driven by the gravitational potential, but in different ways. Disc formation is promoted when the mass profile becomes sufficiently centrally concentrated in shape (relative to circularization radii): we show that this provides a well-defined dynamical centre, ceases to support the global ‘breathing modes’ that can persist indefinitely in less-concentrated profiles and efficiently destroy discs, promotes orbit mixing to form a coherent angular momentum, and stabilizes the disc. Smooth SF is promoted by the potential or escape velocity Vesc (not circular velocity Vc) becoming sufficiently large at the radii of star formation that cool, mass-loaded (momentum-conserving) outflows are trapped/confined near the galaxy, as opposed to escaping after bursts. We discuss the detailed physics, how these conditions arise in cosmological contexts, their relation to other correlated phenomena (e.g. inner halo virialization, vertical disc ‘settling’), and observations.