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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 ($N\sim10^5-10^7$) 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 ($\sim 30\%$) of the YMCs with $ > 6\times10^4M_{\odot}$ from Grudić et al.~2022 and integrate them to $z=0$ using the Cluster Monte Carlo Code, \texttt{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., 24 pages, 16 figures, matches version accepted by MNRAS

Increasingly, uncertainties in predictions from galaxy formation simulations (at sub-Milky Way masses) are dominated by uncertainties in stellar evolution inputs. In this paper, we present the full set of updates from the FIRE-2 version of the Feedback In Realistic Environments (FIRE) project code, to the next version, FIRE-3. While the transition from FIRE-1 to FIRE-2 focused on improving numerical methods, here we update the stellar evolution tracks used to determine stellar feedback inputs, e.g. stellar mass-loss (O/B and AGB), spectra (luminosities and ionization rates), and supernova rates (core-collapse and Ia), as well as detailed mass-dependent yields. We also update the low-temperature cooling and chemistry, to enable improved accuracy at $T \lesssim 10^{4}\,$K and densities $n\gg 1\,{\rm cm^{-3}}$, and the meta-galactic ionizing background. All of these synthesize newer empirical constraints on these quantities and updated stellar evolution and yield models from a number of groups, addressing different aspects of stellar evolution. To make the updated models as accessible as possible, we provide fitting functions for all of the relevant updated tracks, yields, etc, in a form specifically designed so they can be directly 'plugged in' to existing galaxy formation simulations. We also summarize the default FIRE-3 implementations of 'optional' physics, including spectrally-resolved cosmic rays and supermassive black hole growth and feedback., Comment: 26 pages, 12 figures. Submitted to MNRAS. Comments welcome

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 under-predicts these values. The discrepancy is likely due to the lack of disk 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 $>1\,\mathrm{M_\odot}$ stars, however, accounting for observational incompleteness produces a flatter distribution similar to observations. We show that stellar multiplicity changes as the cloud evolves and anti-correlates 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) 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., 20 pages, 21 figures, submitted to MNRAS

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. In this work we present simulations from the STARFORGE project that are the first cloud-scale RMHD 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 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. 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. The characteristic stellar mass depends weakly on metallicity and the interstellar radiation field. Finally, while turbulent driving and the level of magnetization strongly influences the star formation history, they only influence the high-mass slope of the IMF., Comment: 24 pages, 20 figures, extra figures at https://github.com/guszejnovdavid/STARFORGE_IMF_paper_extra_plots

We analyze 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 $\sim 8\%$ star formation efficiency (SFE), and the first supernova at $8.3 \rm Myr$ comes too late to influence star formation significantly. The per-freefall SFE is dynamic, accelerating from 0 to $\sim 18\%$ before dropping quickly to 10 M_\odot$ stars, so massive stars finish growing latest. The fraction of stars in multiples increases as a function of primary mass, as observed. Overall, the simulation much more closely resembles reality, compared to variations which neglect different feedback physics entirely. But more detailed comparison with synthetic observations is necessary to constrain the theoretical uncertainties., Accepted for publication in MNRAS. 17 pages, 10 figures. Comments welcome. Some data products and plotting code available at https://github.com/mikegrudic/StarforgeFullPhysics. Visit http://www.starforge.space to learn more about the STARFORGE Project. Simulation movie available at http://www.starforge.space/M2e4_fullphysics_flyaround.mp4

Barnard’s Loop is a famous arc of Hα emission 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 be the cause of 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 Orion λ reside 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 Orion λ molecular clouds and may have played a major role in the formation of Barnard’s Loop.

Many astrophysical hydrodynamics simulations must account for gravity, and evaluating the gravitational field at the positions of all resolution elements can incur significant cost. Typical algorithms update the gravitational field at the position of each resolution element every time the element is updated hydrodynamically, but the actual required update frequencies for hydrodynamics and gravity can be different in general. We show that the gravity calculation in hydrodynamics simulations can be optimised by only updating gravity on a timescale dictated by the already-determined maximum timestep for accurate gravity integration $\Delta t_{\rm grav}$, while staying well within the typical error budget of hydro schemes and gravity solvers. Our implementation in the GIZMO code uses the tidal timescale introduced in Grudi\'c & Hopkins 2020 to determine $\Delta t_{\rm grav}$ and the force update frequency in turn, and uses the jerk evaluated by the gravity solver to construct a predictor of the acceleration for use between updates. We test the scheme on standard self-gravitating hydrodynamics test problems, finding solutions very close to the na\"{i}ve scheme while evaluating far fewer gravity forces, optimising the simulations. We also demonstrate a $\sim 70\%$ speedup in a STARFORGE MHD GMC simulation, with larger gains likely in higher-resolution runs. In general, this scheme introduces a new tunable parameter for obtaining an optimal compromise between accuracy and computational cost, in conjunction with e.g. time-step tolerance, numerical resolution, and gravity solver tolerance., Comment: 8 pages, 6 figures. Resubmitted to MNRAS with revisions, including new merging polytropes test in 3.2

Intermediate-mass black holes (IMBHs) could form via runaway merging of massive stars in a young massive star cluster (YMC). We combine a suite of numerical simulations of YMC formation with a semi-analytic model for dynamical friction and merging of massive stars and evolution of a central quasi-star, to predict how final quasi-star and relic IMBH masses scale with cluster properties (and compare with observations). The simulations argue that inner YMC density profiles at formation are steep (approaching isothermal), producing some efficient merging even in clusters with relatively low effective densities, unlike models which assume flat central profiles resembling those of globular clusters (GCs) {\em after} central relaxation. Our results can be approximated by simple analytic scalings, with $M_{\rm IMBH} \propto v_{\rm cl}^{3/2}$ where $v_{\rm cl}^{2} = G\,M_{\rm cl}/r_{\rm h}$ is the circular velocity in terms of initial cluster mass $M_{\rm cl}$ and half-mass radius $r_{\rm h}$. While this suggests IMBH formation is {\em possible} even in typical clusters, we show that predicted IMBH masses for these systems are small, $\sim 100-1000\,M_{\odot}$ or $\sim 0.0003\,M_{\rm cl}$, below even the most conservative observational upper limits in all known cases. The IMBH mass could reach $\gtrsim 10^{4}\,M_{\odot}$ in the centers nuclear star clusters, ultra-compact dwarfs, or compact ellipticals, but in all these cases the prediction remains far below the present observed supermassive BH masses in these systems., Comment: 10 pages, 6 figures. Comments welcomed!

The properties of young star clusters formed within a galaxy are thought to vary in different interstellar medium (ISM) 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 modeling cluster formation in galaxy simulations: mapping giant molecular clouds (GMCs) formed self-consistently in a FIRE-2 MHD galaxy simulation onto 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 $\sim 10\%$ of all stars formed in the galaxy originate in gravitationally-bound clusters overall, and this fraction increases in regions with elevated $\Sigma_{\rm gas}$ and $\Sigma_{\rm SFR}$, 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 $7\times 10^6 M_\odot$ 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 $\Sigma_{\rm gas}$ and $\Sigma_{\rm SFR}$. The model does not reproduce the age and metallicity statistics of old ($>11\rm Gyr$) globular clusters found in the Milky Way, possibly because it forms stars more slowly at $z>3$., Comment: Accepted to MNRAS

Understanding the evolution of self-gravitating, isothermal, magnetized gas is crucial for star formation, as these physical processes have been postulated to set the initial mass function (IMF). We present a suite of isothermal magnetohydrodynamic (MHD) simulations using the GIZMO code, that resolve the formation of individual stars in giant molecular clouds (GMCs), spanning a range of Mach numbers found in observed GMCs. As in past works, the mean and median stellar masses are sensitive to numerical resolution, because they are sensitive to low-mass stars that contribute a vanishing fraction of the overall stellar mass. The {\em mass-weighted} median stellar mass $M_\mathrm{50}$ becomes insensitive to resolution once turbulent fragmentation is well-resolved. Without imposing Larson-like scaling laws, our simulations find $M_\mathrm{50} \propto M_\mathrm{0} \mathcal{M}^{-3} \alpha_\mathrm{turb} \mathrm{SFE}^{1/3}$ for GMC mass $M_\mathrm{0}$, sonic Mach number $\mathcal{M}$, virial parameter $\alpha_\mathrm{turb}$, and star formation efficiency $\mathrm{SFE}=M_\mathrm{\star}/M_\mathrm{0}$. This fit agrees well with previous IMF results from the RAMSES, ORION2, and SphNG codes. Although $M_\mathrm{50}$ has no significant dependence on the magnetic field strength at the cloud scale, MHD is necessary to prevent a fragmentation cascade that results in non-convergent stellar masses. For initial conditions and SFE similar to star-forming GMCs in our Galaxy, we predict $M_\mathrm{50}$ to be $>20 M_{\odot}$, an order of magnitude larger than observed ($\sim 2 M_\odot$), together with an excess of brown dwarfs. Moreover, $M_\mathrm{50}$ is sensitive to initial cloud properties and evolves strongly in time within a given cloud, predicting much larger IMF variations than are observationally allowed. We conclude that physics beyond MHD turbulence and gravity are necessary ingredients for the IMF., Comment: Note that this version has erratum at the end (does not affect results) 18 pages, 17 figures

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 center. 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 break up. 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., Comment: 18 pages, 15 figures, submitted to MNRAS

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 disk scales given sufficient "fueling" from larger scales, what remains unclear is whether or not BHs can actually capture sufficient gas from their surrounding ISM. We explore this in a suite of multi-physics 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 $\sim 1-10^{4}\,M_{\odot}$. 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 $\sim 10^{3}\,M_{\odot}\,{\rm pc^{-2}}$ 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 $\sim 1\%$ 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 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., Comment: Final version matching the publication

Barnard's Loop is a famous arc of H$\alpha$ emission 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/Brice\~{n}o-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 be the cause of 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 Orion $\lambda$ reside 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 Orion $\lambda$ molecular clouds and may have played a major role in the formation of Barnard's Loop., Comment: 25 pages, 10 figures. Submitted to ApJ

Previous studies of fueling black holes (BHs) in galactic nuclei have argued (on scales ~0.01-1000pc) accretion is dynamical with inflow rates $\dot{M}\sim\eta\,M_{\rm gas}/t_{\rm dyn}$ in terms of gas mass $M_{\rm gas}$, dynamical time $t_{\rm dyn}$, and some $\eta$. But these models generally neglected expulsion of gas by stellar feedback, or considered extremely high densities where expulsion is inefficient. Studies of star formation, however, have shown on sub-kpc scales the expulsion efficiency $f_{\rm wind}=M_{\rm ejected}/M_{\rm total}$ scales with the gravitational acceleration as $(1-f_{\rm wind})/f_{\rm wind}\sim\bar{a}_{\rm grav}/\langle\dot{p}/m_{\ast}\rangle\sim \Sigma_{\rm eff}/\Sigma_{\rm crit}$ where $\bar{a}_{\rm grav}\equiv G\,M_{\rm tot}(, Comment: 8 pages, 3 figures, updated to match published MNRAS version

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 $\sim k^{-2}$ 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., Comment: Submitted to MNRAS. 11 pages, 8 figures. See http://www.starforge.space/turbsphere_sigma_gas.mp4 for an animated version of Figure 2

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 ($>10^5 M_\odot $) GMCs on current supercomputers while predicting the stellar ($\gtrsim 0.1 M_\odot$) range of the IMF, permitting simulations of both high- and low-mass cluster formation in a wide range of conditions., Resubmitted to to MNRAS with revisions. Added Fig. 5 with useful mass-dependent stellar properties. 34 pages, 22 figures. Community feedback greatly appreciated. Visit http://starforge.space if you'd like to learn more about the STARFORGE Project, or if you like pretty movies

Pressure balance plays a central role in models of the interstellar medium (ISM), but whether and how pressure balance is realized in a realistic multiphase ISM is not yet well understood. We address this question using a set of FIRE-2 cosmological zoom-in simulations of Milky Way-mass disk galaxies, in which a multiphase ISM is self-consistently shaped by gravity, cooling, and stellar feedback. We analyze how gravity determines the vertical pressure profile as well as how the total ISM pressure is partitioned between different phases and components (thermal, dispersion/turbulence, and bulk flows). We show that, on average and consistent with previous more idealized simulations, the total ISM pressure balances the weight of the overlying gas. Deviations from vertical pressure balance increase with increasing galactocentric radius and with decreasing averaging scale. The different phases are in rough total pressure equilibrium with one another, but with large deviations from thermal pressure equilibrium owing to kinetic support in the cold and warm phases, which dominate the total pressure near the midplane. Bulk flows (e.g., inflows and fountains) are important at a few disk scale heights, while thermal pressure from hot gas dominates at larger heights. Overall, the total midplane pressure is well-predicted by the weight of the disk gas, and we show that it also scales linearly with the star formation rate surface density (Sigma_SFR). These results support the notion that the Kennicutt-Schmidt relation arises because Sigma_SFR and the gas surface density (Sigma_g) are connected via the ISM midplane pressure., 22 pages, 16 figures, accepted in MNRAS

We report the formation of bound star clusters in a sample of high-resolution cosmological zoom-in simulations of z>5 galaxies from the FIRE project. We find that bound clusters preferentially form in high-pressure clouds with gas surface densities over 10^4 Msun pc^-2, where the cloud-scale star formation efficiency is near unity and young stars born in these regions are gravitationally bound at birth. These high-pressure clouds are compressed by feedback-driven winds and/or collisions of smaller clouds/gas streams in highly gas-rich, turbulent environments. The newly formed clusters follow a power-law mass function of dN/dM~M^-2. The cluster formation efficiency is similar across galaxies with stellar masses of ~10^7-10^10 Msun at z>5. The age spread of cluster stars is typically a few Myrs and increases with cluster mass. The metallicity dispersion of cluster members is ~0.08 dex in [Z/H] and does not depend on cluster mass significantly. Our findings support the scenario that present-day old globular clusters (GCs) were formed during relatively normal star formation in high-redshift galaxies. Simulations with a stricter/looser star formation model form a factor of a few more/fewer bound clusters per stellar mass formed, while the shape of the mass function is unchanged. Simulations with a lower local star formation efficiency form more stars in bound clusters. The simulated clusters are larger than observed GCs due to finite resolution. Our simulations are among the first cosmological simulations that form bound clusters self-consistently in a wide range of high-redshift galaxies., 18 pages, 17 figures, accepted to MNRAS, high-quality images and/or animations for Figs 3,4,5,8,9 are available at http://www.tapir.caltech.edu/~xchma/HiZFIRE/globular/

Giant molecular clouds (GMCs) are well-studied in the local Universe, however, exactly how their properties vary during galaxy evolution is poorly understood due to challenging resolution requirements, both observational and computational. We present the first time-dependent analysis of giant molecular clouds in a Milky Way-like galaxy and an LMC-like dwarf galaxy of the FIRE-2 (Feedback In Realistic Environments) simulation suite, which have sufficient resolution to predict the bulk properties of GMCs in cosmological galaxy formation self-consistently. We show explicitly that the majority of star formation outside the galactic center occurs within self-gravitating gas structures that have properties consistent with observed bound GMCs. We find that the typical cloud bulk properties such as mass and surface density do not vary more than a factor of 2 in any systematic way after the first Gyr of cosmic evolution within a given galaxy from its progenitor. While the median properties are constant, the tails of the distributions can briefly undergo drastic changes, which can produce very massive and dense self-gravitating gas clouds. Once the galaxy forms, we identify only two systematic trends in bulk properties over cosmic time: a steady increase in metallicity produced by previous stellar populations and a weak decrease in bulk cloud temperatures. With the exception of metallicity we find no significant differences in cloud properties between the Milky Way-like and dwarf galaxies. These results have important implications for cosmological star and star cluster formation and put especially strong constraints on theories relating the stellar initial mass function to cloud properties., Comment: 15 pages, 11 figures accepted by MNRAS

Radiative feedback (RFB) from stars plays a key role in galaxies, but remains poorly-understood. We explore this using high-resolution, multi-frequency radiation-hydrodynamics (RHD) simulations from the Feedback In Realistic Environments (FIRE) project. We study ultra-faint dwarf through Milky Way mass scales, including H+He photo-ionization; photo-electric, Lyman Werner, Compton, and dust heating; and single+multiple scattering radiation pressure (RP). We compare distinct numerical algorithms: ray-based LEBRON (exact when optically-thin) and moments-based M1 (exact when optically-thick). The most important RFB channels on galaxy scales are photo-ionization heating and single-scattering RP: in all galaxies, most ionizing/far-UV luminosity (~1/2 of lifetime-integrated bolometric) is absorbed. In dwarfs, the most important effect is photo-ionization heating from the UV background suppressing accretion. In MW-mass galaxies, meta-galactic backgrounds have negligible effects; but local photo-ionization and single-scattering RP contribute to regulating the galactic star formation efficiency and lowering central densities. Without some RFB (or other 'rapid' FB), resolved GMCs convert too-efficiently into stars, making galaxies dominated by hyper-dense, bound star clusters. This makes star formation more violent and 'bursty' when SNe explode in these hyper-clustered objects: thus, including RFB 'smoothes' SFHs. These conclusions are robust to RHD methods, but M1 produces somewhat stronger effects. Like in previous FIRE simulations, IR multiple-scattering is rare (negligible in dwarfs, ~10% of RP in massive galaxies): absorption occurs primarily in 'normal' GMCs with A_v~1., Comment: 28 pages, 14 figures. Updated to match published MNRAS version

We present a large suite of MHD simulations of turbulent, star-forming giant molecular clouds(GMCs) with stellar feedback, extending previous work by simulating 10 different random realizations for each point in the parameter space of cloud mass and size. It is found that oncethe clouds disperse due to stellar feedback, both self-gravitating star clusters and unbound stars generally remain, which arise from the same underlying continuum of substructured stellar density, ie. the hierarchical cluster formation scenario. The fraction of stars that are born within gravitationally-bound star clusters is related to the overall cloud star formation efficiency set by stellar feedback, but has significant scatter due to stochastic variations in the small-scale details of the star-forming gas flow. We use our numerical results to calibrate a model for mapping the bulk properties (mass, size, and metallicity) of self-gravitating GMCs onto the star cluster populations they form, expressed statistically in terms of cloud-level distributions. Synthesizing cluster catalogues from an observed GMC catalogue in M83, we find that this model predicts initial star cluster masses and sizes that are in good agreement with observations, using only standard IMF and stellar evolution models as inputs for feedback. Within our model, the ratio of the strength of gravity to stellar feedback is the key parameter setting the masses of star clusters, and of the various feedback channels direct stellar radiation(photon momentum and photoionization) is the most important on GMC scales., Comment: Submitted to MNRAS. 20 pages, 14 figures. Feedback welcome :)

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 STARFORGE project, using a new numerical framework to follow the formation of individual stars in giant molecular clouds (GMCs) using the GIZMO code. Our suite include runs with increasingly complex physics, starting with isothermal ideal magnetohydrodynamic (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 $\mathrm{>500\,M_\odot}$. 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 the 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., 18 pages, 13 figures, submitted to MNRAS

The evolution of self-gravitating clouds of isothermal gas forms the basis of many star formation theories. Therefore it is important to know under what conditions such a cloud will undergo homologous collapse into a single, massive object, or will fragment into a spectrum of smaller ones. And if it fragments, do initial conditions (e.g. Jeans mass, sonic mass) influence the mass function of the fragments, as predicted by many theories of star formation? In this paper we show that the relevant parameter separating homologous collapse from fragmentation is not the Mach number of the initial turbulence (as suspected by many), but the infall Mach number $\mathcal{M}_{\rm infall}\sim\sqrt{G M/(R c_s^2)}$, equivalent to the number of Jeans masses in the initial cloud $N_J$. We also show that fragmenting clouds produce a power-law mass function with slopes close to the expected -2 (i.e. equal mass in all logarithmic mass intervals). However, the low-mass cut-off of this mass function is entirely numerical; the initial properties of the cloud have no effect on it. In other words, if $\mathcal{M}_{\rm infall}\gg 1$, fragmentation proceeds without limit to masses much smaller than the initial Jeans mass., Comment: 10 pages, 9 figures

We present a suite of 3D multi-physics MHD simulations following star formation in isolated turbulent molecular gas disks ranging from 5 to 500 parsecs in radius. These simulations are designed to survey the range of surface densities between those typical of Milky Way GMCs ($\sim 10^2 M_\odot\,pc^{-2}}$) and extreme ULIRG environments ($\sim 10^2 M_\odot\,pc^{-2}}$) so as to map out the scaling of the cloud-scale star formation efficiency (SFE) between these two regimes. The simulations include prescriptions for supernova, stellar wind, and radiative feedback, which we find to be essential in determining both the instantaneous per-freefall ($\epsilon_{ff}$) and integrated ($\epsilon_{int}$) star formation efficiencies. In all simulations, the gas disks form stars until a critical stellar surface density has been reached and the remaining gas is blown out by stellar feedback. We find that surface density is a good predictor of $\epsilon_{int}$, as suggested by analytic force balance arguments from previous works. SFE eventually saturates to $\sim 1$ at high surface density. We also find a proportional relationship between $\epsilon_{ff}$ and $\epsilon_{int}$, implying that star formation is feedback-moderated even over very short time-scales in isolated clouds. These results have implications for star formation in galactic disks, the nature and fate of nuclear starbursts, and the formation of bound star clusters. The scaling of $\epsilon_{ff}$ with surface density is not consistent with the notion that $\epsilon_{ff}$ is always $\sim 1\%$ on the scale of GMCs, but our predictions recover the $\sim 1\%$ value for GMC parameters similar to those found in sprial galaxies, including our own., Comment: 21 pages, 7 figures. Accepted to MNRAS

We describe a new adaptive timestep criterion for integrating gravitational motion, which uses the tidal tensor to estimate the local dynamical timescale and scales the timestep proportionally. This provides a better candidate for a truly general-purpose gravitational timestep criterion than the usual prescription derived from the gravitational acceleration, which does not respect the equivalence principle, breaks down when $\mathbf{a}=0$, and does not obey the same dimensional scaling as the true timescale of orbital motion. We implement the tidal timestep criterion in the simulation code GIZMO, and examine controlled tests of collisionless galaxy and star cluster models, as well as fully-dynamic galaxy merger and cosmological dark matter simulations. The tidal criterion estimates the dynamical time faithfully, and generally provides a more efficient timestepping scheme compared to an acceleration criterion. Specifically, the tidal criterion achieves order-of-magnitude smaller energy errors for the same number of force evaluations in potentials with inner profiles shallower than $\rho \propto r^{-1}$ (ie. where $\mathbf{a}\rightarrow 0$), such as star clusters and cored galaxies. For a given problem these advantages must be weighed against the additional overhead of computing the tidal tensor on-the-fly, but in many cases this overhead is small., Comment: Published in MNRAS

It has been established for decades that rotation curves deviate from the Newtonian gravity expectation given baryons alone below a characteristic acceleration scale $g_{\dagger}\sim 10^{-8}\,\rm{cm\,s^{-2}}$, a scale promoted to a new fundamental constant in MOND. In recent years, theoretical and observational studies have shown that the star formation efficiency (SFE) of dense gas scales with surface density, SFE $\sim \Sigma/\Sigma_{\rm crit}$ with $\Sigma_{\rm crit} \sim \langle\dot{p}/m_{\ast}\rangle/(\pi\,G)\sim 1000\,\rm{M_{\odot}\,pc^{-2}}$ (where $\langle \dot{p}/m_{\ast}\rangle$ is the momentum flux output by stellar feedback per unit stellar mass in a young stellar population). We argue that the SFE, more generally, should scale with the local gravitational acceleration, i.e. that SFE $\sim g_{\rm tot}g_\mathrm{crit} \equiv (G\,M_{\rm tot}/R^{2}) / \langle\dot{p}/m_{\ast}\rangle$, where $M_{\rm tot}$ is the total gravitating mass and $g_\mathrm{crit}=\langle\dot{p}/m_{\ast}\rangle = \pi\,G\,\Sigma_{\rm crit} \approx 10^{-8}\,\rm{cm\,s^{-2}} \approx g_{\dagger}$. Hence the observed $g_\dagger$ may correspond to the characteristic acceleration scale above which stellar feedback cannot prevent efficient star formation, and baryons will eventually come to dominate. We further show how this may give rise to the observed acceleration scaling $g_{\rm obs}\sim(g_{\rm baryon}\,g_{\dagger})^{1/2}$ (where $g_{\rm baryon}$ is the acceleration due to baryons alone) and flat rotation curves. The derived characteristic acceleration $g_{\dagger}$ can be expressed in terms of fundamental constants (gravitational constant, proton mass, and Thomson cross section): $g_{\dagger}\sim 0.1\,G\,m_{p}/\sigma_{\rm T}$., Comment: corrected MNRAS version

Most simulations of galaxies and massive giant molecular clouds (GMCs) cannot explicitly resolve the formation (or predict the main-sequence masses) of individual stars. So they must use some prescription for the amount of feedback from an assumed population of massive stars (e.g. sampling the initial mass function, IMF). We perform a methods study of simulations of a star-forming GMC with stellar feedback from UV radiation, varying only the prescription for determining the luminosity of each stellar mass element formed (according to different IMF sampling schemes). We show that different prescriptions can lead to widely varying (factor of ∼3) star formation efficiencies (on GMC scales) even though the average mass-to-light ratios agree. Discreteness of sources is important: radiative feedback from fewer, more-luminous sources has a greater effect for a given total luminosity. These differences can dominate over other, more widely recognized differences between similar literature GMC-scale studies (e.g. numerical methods, cloud initial conditions, presence of magnetic fields). Moreover the differences in these methods are not purely numerical: some make different implicit assumptions about the nature of massive star formation, and this remains deeply uncertain in star formation theory.

We study stellar-halo formation using six Milky Way-mass galaxies in FIRE-2 cosmological zoom simulations. We find that $5-40\%$ of the outer ($50-300$ kpc) stellar halo in each system consists of $\textit{in-situ}$ stars that were born in outflows from the main galaxy. Outflow stars originate from gas accelerated by super-bubble winds, which can be compressed, cool, and form co-moving stars. The majority of these stars remain bound to the halo and fall back with orbital properties similar to the rest of the stellar halo at $z=0$.In the outer halo, outflow stars are more spatially homogeneous, metal rich, and alpha-element-enhanced than the accreted stellar halo. At the solar location, up to $\sim 10 \%$ of our kinematically-identified halo stars were born in outflows; the fraction rises to as high as $\sim 40\%$ for the most metal-rich local halo stars ([Fe/H] $> -0.5$). We conclude that the Milky Way stellar halo could contain local counterparts to stars that are observed to form in molecular outflows in distant galaxies. Searches for such a population may provide a new, near-field approach to constraining feedback and outflow physics. A stellar halo contribution from outflows is a phase-reversal of the classic halo formation scenario of Eggen, Lynden-Bell $\&$ Sandange, who suggested that halo stars formed in rapidly $\textit{infalling}$ gas clouds. Stellar outflows may be observable in direct imaging of external galaxies and could provide a source for metal-rich, extreme velocity stars in the Milky Way., 19 pages, 20 figures, submitted to MNRAS

Measurements of the star formation efficiency (SFE) of giant molecular clouds (GMCs) in the Milky Way generally show a large scatter, which could be intrinsic or observational. We use magnetohydrodynamic simulations of GMCs (including feedback) to forward-model the relationship between the true GMC SFE and observational proxies. We show that individual GMCs trace broad ranges of observed SFE throughout collapse, star formation, and disruption. Low measured SFEs (<>10%) values are often artificially enhanced by rapid gas dispersal. Simulations including stellar feedback reproduce observed GMC-scale SFEs, but simulations without feedback produce 20x larger SFEs. Radiative feedback dominates among mechanisms simulated. An anticorrelation of SFE with cloud mass is shown to be an observational artifact. We also explore individual dense "clumps" within GMCs and show that (with feedback) their bulk properties agree well with observations. Predicted SFEs within the dense clumps are ~2x larger than observed, possibly indicating physics other than feedback from massive (main sequence) stars is needed to regulate their collapse., Fixed typo in the arXiv abstract