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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.

 

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.

 

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.

 

Stars form in dense, clustered environments, where feedback from newly formed stars eventually ejects the gas, terminating star formation and leaving behind one or more star clusters. Using the STARFORGE simulations, it is possible to simulate this process in its entirety within a molecular cloud, while explicitly evolving the gas radiation and magnetic fields and following the formation of individual, low-mass stars. We find that individual star-formation sites merge to form ever larger structures, while still accreting gas. Thus clusters are assembled through a series of mergers. During the cluster assembly process, a small fraction of stars are ejected from their clusters; we find no significant difference between the mass distribution of the ejected stellar population and that of stars inside clusters. The star-formation sites that are the building blocks of clusters start out mass segregated with one or a few massive stars at their centre. As they merge the newly formed clusters maintain this feature, causing them to have mass-segregated substructures without themselves being centrally condensed. The merged clusters relax to a centrally condensed mass-segregated configuration through dynamical interactions between their members, but this process does not finish before feedback expels the remaining gas from the cluster. In the simulated runs, the gas-free clusters then become unbound and breakup. We find that turbulent driving and a periodic cloud geometry can significantly reduce clustering and prevent gas expulsion. Meanwhile, the initial surface density and level of turbulence have little qualitative effect on cluster evolution, despite the significantly different star formation histories.

 

Simulations of isolated giant molecular clouds (GMCs) are an important tool for studying the dynamics of star formation, but their turbulent initial conditions (ICs) are uncertain. Most simulations have either initialized a velocity field with a prescribed power spectrum on a smooth density field (failing to model the full structure of turbulence) or ‘stirred’ turbulence with periodic boundary conditions (which may not model real GMC boundary conditions). We develop and test a new GMC simulation setup (called turbsphere) that combines advantages of both approaches: we continuously stir an isolated cloud to model the energy cascade from larger scales, and use a static potential to confine the gas. The resulting cloud and surrounding envelope achieve a quasi-equilibrium state with the desired hallmarks of supersonic ISM turbulence (e.g. density PDF and a ∼k−2 velocity power spectrum), whose bulk properties can be tuned as desired. We use the final stirred state as initial conditions for star formation simulations with self-gravity, both with and without continued driving and protostellar jet feedback, respectively. We then disentangle the respective effects of the turbulent cascade, simulation geometry, external driving, and gravity/MHD boundary conditions on the resulting star formation. Without external driving, the new setup obtains results similar to previous simple spherical cloud setups, but external driving can suppress star formation considerably in the new setup. Periodic box simulations with the same dimensions and turbulence parameters form stars significantly slower, highlighting the importance of boundary conditions and the presence or absence of a global collapse mode in the results of star formation calculations.

 

We analyse the first giant molecular cloud (GMC) simulation to follow the formation of individual stars and their feedback from jets, radiation, winds, and supernovae, using the STARFORGE framework in the GIZMO code. We evolve the GMC for $\sim 9 \rm Myr$, from initial turbulent collapse to dispersal by feedback. Protostellar jets dominate feedback momentum initially, but radiation and winds cause cloud disruption at $\sim 8{{\ \rm per\ cent}}$ star formation efficiency (SFE), and the first supernova at $8.3\, \rm Myr$ comes too late to influence star formation significantly. The per-free-fall SFE is dynamic, accelerating from 0 per cent to $\sim 18{{\ \rm per\ cent}}$ before dropping quickly to <1 per cent, but the estimate from YSO counts compresses it to a narrower range. The primary cluster forms hierarchically and condenses to a brief ($\sim 1\, \mathrm{Myr}$) compact ($\sim 1\, \rm pc$) phase, but does not virialize before the cloud disperses, and the stars end as an unbound expanding association. The initial mass function resembles the Chabrier (2005) form with a high-mass slope α = −2 and a maximum mass of 55 M⊙. Stellar accretion takes $\sim 400\, \rm kyr$ on average, but $\gtrsim 1\,\rm Myr$ for >10 M⊙ stars, so massive stars finish growing latest. The fraction of stars in multiples increase as a function of primary mass, as observed. Overall, the simulation much more closely resembles reality, compared to previous versions that neglected different feedback physics entirely. But more detailed comparison with synthetic observations will be needed to constrain the theoretical uncertainties.

 

Abstract We present STARFORGE (STAR FORmation in Gaseous Environments): a new numerical framework for 3D radiation MHD simulations of star formation that simultaneously follow the formation, accretion, evolution, and dynamics of individual stars in massive giant molecular clouds (GMCs) while accounting for stellar feedback, including jets, radiative heating and momentum, stellar winds, and supernovae. We use the GIZMO code with the MFM mesh-free Lagrangian MHD method, augmented with new algorithms for gravity, timestepping, sink particle formation and accretion, stellar dynamics, and feedback coupling. We survey a wide range of numerical parameters/prescriptions for sink formation and accretion and find very small variations in star formation history and the IMF (except for intentionally-unphysical variations). Modules for mass-injecting feedback (winds, SNe, and jets) inject new gas elements on-the-fly, eliminating the lack of resolution in diffuse feedback cavities otherwise inherent in Lagrangian methods. The treatment of radiation uses GIZMO’s radiative transfer solver to track 5 frequency bands (IR, optical, NUV, FUV, ionizing), coupling direct stellar emission and dust emission with gas heating and radiation pressure terms. We demonstrate accurate solutions for SNe, winds, and radiation in problems with known similarity solutions, and show that our jet module is robust to resolution and numerical details, and agrees well with previous AMR simulations. STARFORGE can scale up to massive (>105M⊙) GMCs on current supercomputers while predicting the stellar (≳ 0.1M⊙) range of the IMF, permitting simulations of both high- and low-mass cluster formation in a wide range of conditions. 

ABSTRACT The initial mass function (IMF) of stars is a key quantity affecting almost every field of astrophysics, yet it remains unclear what physical mechanisms determine it. We present the first runs of the STAR FORmation in Gaseous Environments project, using a new numerical framework to follow the formation of individual stars in giant molecular clouds (GMCs) using the gizmo code. Our suite includes runs with increasingly complex physics, starting with isothermal ideal magnetohydrodynamics (MHD) and then adding non-isothermal thermodynamics and protostellar outflows. We show that without protostellar outflows the resulting stellar masses are an order of magnitude too high, similar to the result in the base isothermal MHD run. Outflows disrupt the accretion flow around the protostar, allowing gas to fragment and additional stars to form, thereby lowering the mean stellar mass to a value similar to that observed. The effect of jets upon global cloud evolution is most pronounced for lower mass GMCs and dense clumps, so while jets can disrupt low-mass clouds, they are unable to regulate star formation in massive GMCs, as they would turn an order unity fraction of the mass into stars before unbinding the cloud. Jets are also unable to stop the runaway accretion of massive stars, which could ultimately lead to the formation of stars with masses ${\gt}500\, \mathrm{M}_{\rm \odot }$. Although we find that the mass scale set by jets is insensitive to most cloud parameters (i.e. surface density, virial parameter), it is strongly dependent on the momentum loading of the jets (which is poorly constrained by observations) as well as the temperature of the parent cloud, which predicts slightly larger IMF variations than observed. We conclude that protostellar jets play a vital role in setting the mass scale of stars, but additional physics are necessary to reproduce the observed IMF.