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Constraining the physical and chemical evolution of molecular clouds is essential to our understanding of star formation. These investigations often necessitate knowledge of some local representative number density of the gas along the line of sight. However, constraining the number density is a difficult endeavor. Robust constraints of the number density often require line observations of specific molecules along with radiation transfer modeling, which provides densities traced by that specific molecule. Column density maps of molecular clouds are more readily available, with many high-fidelity maps calculated from dust emission and extinction, in particular from surveys conducted with the Herschel Space Observatory. We introduce a new probabilistic model which is based on the assumption that the total hydrogen nuclei column density along a line of sight can be decomposed into a turbulent component and a gravitationally-dominated component. Therefore, for each pixel in a column density map, the line of sight is decomposed into characteristic diffuse (dubbed ``turbulent'') and dense (dubbed ``gravitational'') gas number densities from column density maps. The method thus exploits a physical model of turbulence to decouple the random turbulent column from gas in dense bound structures empirically using the observed column density maps. We find the model produces reasonable turbulent and gravitational densities in the Taurus L1495/B213 and Polaris Flare clouds. The model can also be used to infer an effective attenuating column density into the cloud, which is useful for astrochemical models of the clouds. We conclude by demonstrating an application of this method by predicting the emission of the [C II], [C I], and CO (J = 1-0) lines across the Taurus L1495/B213 region at the native resolution of the column density map utilizing a grid of photodissociation-region models., Comment: Resubmitted to A&A, comments welcome! Public GitHub with example lower resolution calculation here: https://github.com/AstroBrandt/GMCDensityEstimation

To date, JWST has detected the earliest known star clusters in our Universe (Adamo et al. 2024, Messa et al. 2024, Vanzella et al. 2024, Mowla et al. 2024). They appear to be relatively compact (~few pc, Adamo et al. 2024) and had only recently formed their stars. It was speculated that these clusters may be the earliest progenitors of globular clusters ever detected. Globular clusters are a relic of the initial stages of star formation in the Universe. However, because they contain little to no dark matter (e.g., Heggie & Hut 1996, Bradford et al. 2011, Conroy et al. 2011, Ibata et al. 2013), their formation mechanism poses a significant theoretical challenge. A recent suggestion pointed out that the relative velocity between the gas and the dark matter (Tseliakhovich & Hirata 2010) in the early Universe could naturally form potentially star-forming regions outside of dark matter halos. Here, for the first time, we follow the star formation process of these early Universe objects using high-resolution hydrodynamical simulations, including mechanical feedback. Our results suggest that the first dark matter-less star clusters are top-heavy, with a higher abundance of massive stars compared to today's clusters and extremely high stellar mass surface densities compared to the local Universe., Comment: 10 pages, 5 figures

Cosmic rays (CRs) are the primary driver of ionization in star forming molecular clouds (MCs). Despite their potential impacts on gas dynamics and chemistry, no simulations of star cluster formation following the creation of individual stars have included explicit cosmic ray transport (CRT) to date. We conduct the first numerical simulations following the collapse of a $2000 M_{\odot}$ MC and the subsequent star formation including CRT using the STARFORGE framework implemented in the GIZMO code. We show that when CR-transport is streaming-dominated, the CR energy in the cloud is strongly attenuated due to energy losses from the streaming instability. Consequently, in a Milky Way like environment the median CR ionization rate (CRIR) in the cloud is low ($ \zeta \lesssim 2 \times 10^{-19} \rm s^{-1}$) during the main star forming epoch of the calculation and the impact of CRs on the star formation in the cloud is limited. However, in high-CR environments, the CR distribution in the cloud is elevated ($\zeta \lesssim 6 \times 10^{-18}$), and the relatively higher CR pressure outside the cloud causes slightly earlier cloud collapse and increases the star formation efficiency (SFE) by $50 \%$ to $\sim 13 \%$. The initial mass function (IMF) is similar in all cases except with possible variations in a high-CR environment. Further studies are needed to explain the range of ionization rates observed in MCs and explore star formation in extreme CR environments., Comment: Accepted to The Astrophysical Journal

The dust grain size distribution (GSD) likely varies significantly across star-forming environments in the Universe, but its impact on star formation remains unclear. This ambiguity arises because the GSD interacts non-linearly with processes like heating, cooling, radiation, and chemistry, which have competing effects and varying environmental dependencies. Processes such as grain coagulation, expected to be efficient in dense star-forming regions, reduce the abundance of small grains and increase that of larger grains. Motivated by this, we investigate the effects of similar GSD variations on the thermochemistry and evolution of giant molecular clouds (GMCs) using magnetohydrodynamic simulations spanning a range of cloud masses and grain sizes, which explicitly incorporate the dynamics of dust grains within the full-physics framework of the \SF project. We find that grain size variations significantly alter GMC thermochemistry: with the leading-order effect is that larger grains, under fixed dust mass, GSD dynamic range, and dust-to-gas ratio, result in lower dust opacities. This reduced opacity permits ISRF and internal radiation photons to penetrate more deeply. This leads to rapid gas heating and inhibited star formation. Star formation efficiency is highly sensitive to grain size, with an order of magnitude reduction when grain size dynamic range increases from $10^{-3}$-0.1 $\rm\mu m$ to 0.1-10 $\rm\mu m$. Additionally, warmer gas suppresses low-mass star formation, and decreased opacities result in a greater proportion of gas in diffuse ionized structures., Comment: 13 pages, 5 figures, submitted to ApJ

Stellar feedback influences the star formation rate (SFR) and the interstellar medium of galaxies in ways that are difficult to quantify numerically, because feedback is an essential ingredient of realistic simulations. To overcome this, we conduct a feedback-halting experiment starting with a Milky Way-mass galaxy in the FIRE-2 simulation framework. Terminating feedback, and comparing to a simulation in which feedback is maintained, we monitor how the runs diverge. We find that without feedback, interstellar turbulent velocities decay. There is a marked increase of dense material, while the SFR increases by over an order of magnitude. Importantly, this SFR boost is a factor of $\sim$15-20 larger than is accounted for by the increased free fall rate caused by higher densities. This implies that feedback moderates the star formation efficiency per free-fall time more directly than simply through the density distribution. To probe changes at the scale of giant molecular clouds (GMCs), we identify GMCs using density and virial parameter thresholds, tracking clouds as the galaxy evolves. Halting feedback stimulates rapid changes, including a proliferation of new bound clouds, a decrease of turbulent support in loosely-bound clouds, an overall increase in cloud densities, and a surge of internal star formation. Computing the cloud-integrated SFR using several theories of turbulence regulation, we show that these theories underpredict the surge in SFR by at least a factor of three. We conclude that galactic star formation is essentially feedback-regulated on scales that include GMCs, and that stellar feedback affects GMCs in multiple ways., Comment: 20 pages, 10 figures, under ongoing review at ApJ

Stars form within dense cores composed of both gas and dust within molecular clouds. However, despite the crucial role that dust plays in the star formation process, its dynamics is frequently overlooked, with the common assumption being a constant, spatially uniform dust-to-gas ratio and grain size spectrum. In this study, we introduce a set of radiation-dust-magnetohydrodynamic simulations of star forming molecular clouds from the {\small STARFORGE} project. These simulations expand upon the earlier radiation MHD models, which included cooling, individual star formation, and feedback. Notably, they explicitly address the dynamics of dust grains, considering radiation, drag, and Lorentz forces acting on a diverse size spectrum of live dust grains. We find that once stars exceed a certain mass threshold ($\sim 2 M_{\odot}$), their emitted radiation can evacuate dust grains from their vicinity, giving rise to a dust-suppressed zone of size $\sim 100$ AU. This removal of dust, which interacts with gas through cooling, chemistry, drag, and radiative transfer, alters the gas properties in the region. Commencing during the early accretion stages and preceding the Main-sequence phase, this process results in a mass-dependent depletion in the accreted dust-to-gas (ADG) mass ratio within both the circumstellar disc and the star. We predict massive stars ($\gtrsim 10 M_{\odot}$) would exhibit ADG ratios that are approximately one order of magnitude lower than that of their parent clouds. Consequently, stars, their discs, and circumstellar environments would display notable deviations in the abundances of elements commonly associated with dust grains, such as carbon and oxygen., Comment: 14 pages, 9 figures, submitted to ApJ

Recently, we demonstrated self-consistent formation of strongly-magnetized quasar accretion disks (QADs) from cosmological radiation-magnetohydrodynamic-thermochemical galaxy-star formation simulations, including the full STARFORGE physics shown previously to produce a reasonable IMF under typical ISM conditions. Here we study star formation and the stellar IMF in QADs, on scales from 100 au to 10 pc from the SMBH. We show it is critical to include physics often previously neglected, including magnetic fields, radiation, and (proto)stellar feedback. Closer to the SMBH, star formation is suppressed, but the (rare) stars that do form exhibit top-heavy IMFs. Stars can form only in special locations (e.g. magnetic field switches) in the outer QAD. Protostars accrete their natal cores rapidly but then dynamically decouple from the gas and wander, ceasing accretion on timescales ~100 yr. Their jets control initial core accretion, but the ejecta are swept up into the larger-scale QAD flow without much dynamical effect. The strong tidal environment strongly suppresses common-core multiplicity. The IMF shape depends sensitively on un-resolved dynamics of protostellar disks (PSDs), as the global dynamical times can become incredibly short ($\ll$ yr) and tidal fields are incredibly strong, so whether PSDs can efficiently transport angular momentum or fragment catastrophically at $\lesssim 10$ au scales requires novel PSD simulations to properly address. Most analytic IMF models and analogies with planet formation in PSDs fail qualitatively to explain the simulation IMFs, though we discuss a couple of viable models., Comment: 39 pages, 23 figures, replaced with version accepted to the Open Journal of Astrophysics. Additional images and movies from the simulations available at http://www.tapir.caltech.edu/~phopkins/Site/animations/Movies_zoom.html

Stars are amongst the most fundamental structures of our Universe. They comprise most of the baryonic and luminous mass of galaxies, synthethise heavy elements, and injec\ t mass, momentum, and energy into the interstellar medium. They are also home to the planets. Since stellar properties are primarily decided by their mass, the so-called \ stellar initial mass function (IMF) is critical to the structuring of our Universe. We review the various physical processes, and theories which have been put forward as well as the numerical simulations which have been carried out to explain the origin of the stellar initial mass function. Key messages from this review are: (1) Gravity and turbulence most likely determine the power-law, high-mass part of the IMF. (2) Depending of the Mach number and the density distribution, several regimes are possible, including $\Gamma _{IMF} \simeq 0$, -0.8, -1 or -1.3 where $d N / d \log M \propto M^{\Gamma_{IMF}}$. These regimes are likely universal, however the transition between these regimes is not. (3) Protostellar jets can play a regulating influence on the IMF by injecting momentum into collapsing clumps and unbinding gas. (4) The peak of the IMF may be a consequence of dust opacity and molecular hydrogen physics at the origin of the first hydrostatic core. This depends weakly on large scale environmental conditions such as radiation, magnetic field, turbulence or metallicity. This likely constitutes one of the reason of the relative universality of the IMF., Comment: To appear in Annual Reviews of Astronomy and Astrophysics

After the nearly hundred gravitational-wave detections reported by the LIGO-Virgo-KAGRA Collaboration, the question of the cosmological origin of merging binary black holes (BBHs) remains open. The two main formation channels generally considered are from isolated field binaries or via dynamical assembly in dense star clusters. Here, we focus on understanding the dynamical formation of merging BBHs within massive clusters in galaxies of different masses. To this end, we apply a new framework to consistently model the formation and evolution of massive star clusters in zoom-in cosmological simulations of galaxies. Each simulation, taken from the FIRE project, provides a realistic star formation environment with a unique star formation history and hosts realistic giant molecular clouds that constitute the birthplace of star clusters. Combined with the code for star cluster evolution CMC, we are able to produce populations of dynamically formed merging BBHs across cosmic time in different environments. As the most massive star clusters preferentially form in dense massive clouds of gas, we find that, despite their low metallicities favourable to the creation of black holes, low-mass galaxies contain few massive clusters and therefore have a limited contribution to the global production of dynamically formed merging BBHs. Furthermore, we find that massive clusters can host hierarchical BBH mergers with clear identifiable physical properties. Looking at the evolution of the BBH merger rate in different galaxies, we find strong correlations between BBH mergers and the most extreme episodes of star formation. Finally, we discuss the implications for future LIGO-Virgo-KAGRA gravitational wave observations., Comment: 14 pages, 9 figures, 3 tables

We explore the relationship between stellar surface density and gas surface density (the star-gas or S-G correlation) in a 20,000 M$_{\odot}$ simulation from the STAR FORmation in Gaseous Environments (STARFORGE) Project. We create synthetic observations based on the Spitzer and Herschel telescopes by modeling active galactic nuclei contamination, smoothing based on angular resolution, cropping the field-of-view, and removing close neighbors and low-mass sources. We extract star-gas properties such as the dense gas mass fraction, the Class II:I ratio, and the S-G correlation ($\Sigma_{\rm YSO}/\Sigma_{\rm gas}$) 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., Comment: 25 pages, 16 figures. To be published in The Astrophysical Journal

In a companion paper, we reported the self-consistent formation of quasar accretion disks with inflow rates $\sim 10\,{\rm M_{\odot}\,yr^{-1}}$ down to <300 Schwarzschild radii from cosmological radiation-magneto-thermochemical-hydrodynamical galaxy and star formation simulations. We see the formation of a well-defined, steady-state accretion disk which is stable against star formation at sub-pc scales. The disks are optically thick, with radiative cooling balancing accretion, but with properties that are distinct from those assumed in most previous accretion disk models. The pressure is strongly dominated by (primarily toroidal) magnetic fields, with a plasma $\beta \sim 10^{-4}$ even in the disk midplane. They are qualitatively distinct from magnetically elevated or arrested disks. The disks are strongly turbulent, with trans-Alfvenic and highly super-sonic turbulence, and balance this via a cooling time that is short compared to the disk dynamical time, and can sustain highly super-Eddington accretion rates. Their surface and 3D densities at $\sim 10^{3}-10^{5}$ gravitational radii are much lower than in a Shakura-Sunyaev disk, with important implications for their thermo-chemistry and stability. We show how the magnetic field strengths and geometries arise from rapid advection of flux with the inflow from much weaker galaxy-scale fields in these 'flux-frozen' disks, and how this stabilizes the disk and gives rise to efficient torques. Re-simulating without magnetic fields produces catastrophic fragmentation with a vastly smaller, lower-$\dot{M}$ Shakura-Sunyaev-like disk., Comment: 46 pages, 30 figures. Updated to match accepted version from The Open Journal of Astrophysics. Part of a series with arXiv:2309.13115 . Animations of the simulations can be viewed at http://www.tapir.caltech.edu/~phopkins/Site/animations/Movies_zoom.html

It has recently become possible to zoom-in from cosmological to sub-pc scales in galaxy simulations to follow accretion onto supermassive black holes (SMBHs). However, at some point the approximations used on ISM scales (e.g. optically-thin cooling and stellar-population-integrated star formation [SF] and feedback [FB]) break down. We therefore present the first cosmological radiation-magnetohydrodynamic (RMHD) simulation which self-consistently combines the FIRE physics (relevant on galactic/ISM scales where SF/FB are ensemble-averaged) and STARFORGE physics (relevant on small scales where we track individual (proto)stellar formation and evolution), together with explicit RMHD (including non-ideal MHD and multi-band M1-RHD) which self-consistently treats both optically-thick and thin regimes. This allows us to span scales from ~100 Mpc down to <100 au (~300 Schwarzschild radii) around a SMBH at a time where it accretes as a bright quasar, in a single simulation. We show that accretion rates up to $\sim 10-100\,{\rm M_{\odot}\,yr^{-1}}$ can be sustained into the accretion disk at $\ll 10^{3}\,R_{\rm schw}$, with gravitational torques between stars and gas dominating on sub-kpc scales until star formation is shut down on sub-pc scales by a combination of optical depth to cooling and strong magnetic fields. There is an intermediate-scale, flux-frozen disk which is gravitoturbulent and stabilized by magnetic pressure sustaining strong turbulence and inflow with persistent spiral modes. In this paper we focus on how gas gets into the small-scale disk, and how star formation is efficiently suppressed., Comment: 38 pages, 18 figures. Replaced with accepted version

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 analyze 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%, and gas expulsion timescales shorter than a free fall time, primarily produce expanding stellar associations and small clusters. The largest star clusters, which have $\sim$1000 bound members, form in the densest and lowest velocity dispersion clouds, representing $\sim$32 and 39% 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 timescale during the star formation process and analyze the implications for the formation of bound systems., Comment: 20 Pages, 10 figures, submitted to MNRAS

The opacity limit is an important concept in star formation: isothermal collapse cannot proceed without limit, because eventually cooling radiation is trapped and the temperature rises quasi-adiabatically, setting a minimum Jeans mass $M_{\rm J}^{\rm min}$. Various works have considered this scenario and derived expressions for $M_{\rm J}^{\rm min}$, generally $\sim 10^{-3}-10^{-2}M_\odot$ in normal star-forming conditions, but with conflicting results about the scaling with ambient conditions and material properties. We derive expressions for the thermal evolution of dust-cooled collapsing gas clumps in various limiting cases, given a general ambient radiation field ($u_{\rm rad}$, $T_{\rm rad}$) and a general power-law dust opacity law $\sigma_{\rm d} = A_{\rm d} T^{\beta}$. By accounting for temperature evolution self-consistently we rule out a previously-proposed regime in which the adiabatic transition occurs while the core is still optically-thin. If the radiation field is weak or dust opacity is small, $M_{\rm J}^{\rm min}$ is insensitive to dust properties/abundance ($\sim A_{\rm d}^{-\frac{1}{11}}-A_{\rm d}^{-\frac{1}{15}}$), but if the radiation field is strong and dust is abundant it scales $\propto A_{\rm d}^{1/3}$. This could make the IMF less bottom-heavy in dust-rich and/or radiation-dense environments, e.g. galactic centers, starburst galaxies, massive high-$z$ galaxies, and proto-star clusters that are already luminous., Comment: To be submitted to the Open Journal of Astrophysics. Comments welcome

When a detailed model of a stellar population is unavailable, it is most common to assume that stellar masses are independently and identically distributed according to some distribution: the universal initial mass function (IMF). However, stellar masses resulting from causal, long-ranged physics cannot be truly random and independent, and the IMF may vary with environment. To compare stochastic sampling with a physical model, we run a suite of 100 STARFORGE radiation magnetohydrodynamics simulations of low-mass star cluster formation in $2000M_\odot$ clouds that form $\sim 200$ stars each on average. The stacked IMF from the simulated clouds has a sharp truncation at $\sim 28 M_\odot$, well below the typically-assumed maximum stellar mass $M_{\rm up} \sim 100-150M_\odot$ and the total cluster mass. The sequence of star formation is not totally random: massive stars tend to start accreting sooner and finish later than the average star. However, final cluster properties such as maximum stellar mass and total luminosity have a similar amount of cloud-to-cloud scatter to random sampling. Therefore stochastic sampling does not generally model the stellar demographics of a star cluster as it is forming, but may describe the end result fairly well, if the correct IMF -- and its environment-dependent upper cutoff -- are known., Comment: Accepted for publication in Open Journal of Astrophysics

As they grow, galaxies can transition from irregular/spheroidal with 'bursty' star formation histories (SFHs), to disky 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 disks and cessation of bursty star formation are driven by the gravitational potential, but in different ways. Disk 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 center, ceases to support the global 'breathing modes' which can persist indefinitely in less-concentrated profiles and efficiently destroy disks, promotes orbit mixing to form a coherent angular momentum, and stabilizes the disk. Smooth SF is promoted by the potential or escape velocity (not circular velocity) 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 disk 'settling'), and observations., Comment: Updated to match MNRAS accepted version. 45 pages, 32 figures

Modeling self-gravity of collisionless fluids (e.g. ensembles of dark matter, stars, black holes, dust, 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 multi-physics 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 timestep 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 neighbor 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 imposes negligible timestep or other computational penalties, ensures 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., Comment: 25 pages, 13 figures. Updated to match MNRAS accepted version. Six appendices with additional details and tests expanded

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

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

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., Comment: 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

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 Grudi\'c 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., Comment: 24 pages, 16 figures, matches version accepted by MNRAS

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

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

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

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 <1%, 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 $\alpha=-2$ and a maximum mass of $55 M_\odot$. Stellar accretion takes $\sim 400 \rm kyr$ on average, but $\gtrsim 1\rm Myr$ for $>10 M_\odot$ 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., Comment: 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

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

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}(

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

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., Comment: Fix error in Eq. 44 for wind mass loss rate

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., Comment: 18 pages, 13 figures, submitted to MNRAS

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!

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 :)

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., Comment: 22 pages, 16 figures, accepted in MNRAS

We explore the possibility that GW190412, a binary black hole merger with a non-equal-mass ratio and significantly spinning primary, was formed through repeated black hole mergers in a dense super star cluster. Using a combination of semi-analytic prescriptions for the remnant spin and recoil kick of black hole mergers, we show that the mass ratio and spin of GW190412 are consistent with a binary black hole whose primary component has undergone two successive mergers from a population of $\sim 10M_{\odot}$ black holes in a high-metallicity environment. We then explore the production of GW190412-like analogs in the CMC Cluster Catalog, a grid of 148 $N$-body star cluster models, as well as a new model, behemoth, with nearly $10^7$ particles and initial conditions taken from a cosmological MHD simulation of galaxy formation. We show that the production of binaries with GW190412-like masses and spins is dominated by massive super star clusters with high metallicities and large central escape speeds. While many are observed in the local universe, our results suggest that a careful treatment of these massive clusters, many of which may have been disrupted before the present day, is necessary to characterize the production of unique gravitational-wave events produced through dynamics., Comment: 9 pages, 4 figures, matches version accepted by ApJL

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

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., Comment: 19 pages, 20 figures, submitted 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

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

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., Comment: 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/

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

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 where and how massive stars form, and this remains deeply uncertain in star formation theory., Comment: Small metadata fix

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 (<<1%) are "real" but correspond to early stages, the true "per-freefall" SFE where most stars actually form can be much larger. Very high (>>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., Comment: Fixed typo in the arXiv abstract

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

A maximum stellar surface density $\Sigma_{max} \sim 3 \times 10^5\,{\rm M_\odot\,pc^{-2}}$ is observed across all classes of dense stellar systems (e.g. star clusters, galactic nuclei, etc.), spanning $\sim 8$ orders of magnitude in mass. It has been proposed that this characteristic scale is set by some dynamical feedback mechanism preventing collapse beyond a certain surface density. However, simple analytic models and detailed simulations of star formation moderated by feedback from massive stars argue that feedback becomes {\it less} efficient at higher surface densities (with the star formation efficiency increasing as $\sim \Sigma/\Sigma_{crit}$). We therefore propose an alternative model wherein stellar feedback becomes ineffective at moderating star formation above some $\Sigma_{crit}$, so the supply of star-forming gas is rapidly converted to stars before the system can contract to higher surface density. We show that such a model -- with $\Sigma_{crit}$ taken directly from the theory -- naturally predicts the observed $\Sigma_{max}$. $\Sigma_{max}\sim 100\Sigma_{crit}$ because the gas consumption time is longer than the global freefall time even when feedback is ineffective. Moreover the predicted $\Sigma_{max}$ is robust to spatial scale and metallicity, and is preserved even if multiple episodes of star formation/gas inflow occur. In this context, the observed $\Sigma_{max}$ directly tells us where feedback fails., Comment: 5 pages, 5 figures. Submitted to MNRAS. Comments welcome!

Young massive star clusters spanning $\sim 10^4 - 10^8 M_\odot$ in mass have been observed to have similar surface brightness profiles. Recent hydrodynamical simulations of star cluster formation have also produced star clusters with this structure. We argue analytically that this type of mass distribution arises naturally in the relaxation from a hierarchically-clustered distribution of stars into a monolithic star cluster through hierarchical merging. We show that arbitrary initial profiles will tend to converge to a universal profile under hierarchical merging, owing to phase-space mixing obeying certain conservation constraints. We perform $N$-body simulations of a pairwise merger of model star clusters and find that mergers readily produce the shallow surface brightness profiles observed in young massive clusters. Finally, we simulate the relaxation of a hierarchically-clustered mass distribution constructed from an idealized fragmentation model. Assuming only power-law spatial and kinematic scaling relations, these numerical experiments are able to reproduce the surface density profiles of observed young massive star clusters. Thus we provide physical motivation for the structure of young massive clusters within the paradigm of hierarchical star formation. This has important implications for the structure of nascent globular clusters., Comment: 16 pages, 10 figures

A large number of astronomical phenomena exhibit remarkably similar scaling relations. The most well-known of these is the mass distribution $\mathrm{d} N/\mathrm{d} M\propto M^{-2}$ which (to first order) describes stars, protostellar cores, clumps, giant molecular clouds, star clusters and even dark matter halos. In this paper we propose that this ubiquity is not a coincidence and that it is the generic result of scale-free structure formation where the different scales are uncorrelated. We show that all such systems produce a mass function proportional to $M^{-2}$ and a column density distribution with a power law tail of $\mathrm{d} A/\mathrm{d} \ln\Sigma\propto\Sigma^{-1}$. In the case where structure formation is controlled by gravity the two-point correlation becomes $\xi_{2D}\propto R^{-1}$. Furthermore, structures formed by such processes (e.g. young star clusters, DM halos) tend to a $\rho\propto R^{-3}$ density profile. We compare these predictions with observations, analytical fragmentation cascade models, semi-analytical models of gravito-turbulent fragmentation and detailed "full physics" hydrodynamical simulations. We find that these power-laws are good first order descriptions in all cases., Comment: 12 pages, 6 figures, 2 tables, submitted to MNRAS

Using a state-of-the-art cosmological simulation of merging proto-galaxies at high redshift from the FIRE project, with explicit treatments of star formation and stellar feedback in the interstellar medium, we investigate the formation of star clusters and examine one of the formation hypothesis of present-day metal-poor globular clusters. We find that frequent mergers in high-redshift proto-galaxies could provide a fertile environment to produce long-lasting bound star clusters. The violent merger event disturbs the gravitational potential and pushes a large gas mass of ~> 1e5-6 Msun collectively to high density, at which point it rapidly turns into stars before stellar feedback can stop star formation. The high dynamic range of the reported simulation is critical in realizing such dense star-forming clouds with a small dynamical timescale, t_ff <~ 3 Myr, shorter than most stellar feedback timescales. Our simulation then allows us to trace how clusters could become virialized and tightly-bound to survive for up to ~420 Myr till the end of the simulation. Because the cluster's tightly-bound core was formed in one short burst, and the nearby older stars originally grouped with the cluster tend to be preferentially removed, at the end of the simulation the cluster has a small age spread., Comment: 14 pages, 14 figures, Accepted for publication in the Monthly Notices of the Royal Astronomical Society, High-resolution version of this article also available at http://www.jihoonkim.org/index/research.html#gc

The Feedback In Realistic Environments (FIRE) project explores feedback in cosmological galaxy formation simulations. Previous FIRE simulations used an identical source code (FIRE-1) for consistency. Motivated by the development of more accurate numerics - including hydrodynamic solvers, gravitational softening, and supernova coupling algorithms - and exploration of new physics (e.g. magnetic fields), we introduce FIRE-2, an updated numerical implementation of FIRE physics for the GIZMO code. We run a suite of simulations and compare against FIRE-1: overall, FIRE-2 improvements do not qualitatively change galaxy-scale properties. We pursue an extensive study of numerics versus physics. Details of the star-formation algorithm, cooling physics, and chemistry have weak effects, provided that we include metal-line cooling and star formation occurs at higher-than-mean densities. We present new resolution criteria for high-resolution galaxy simulations. Most galaxy-scale properties are robust to numerics we test, provided: (1) Toomre masses are resolved; (2) feedback coupling ensures conservation, and (3) individual supernovae are time-resolved. Stellar masses and profiles are most robust to resolution, followed by metal abundances and morphologies, followed by properties of winds and circum-galactic media (CGM). Central (~kpc) mass concentrations in massive (L*) galaxies are sensitive to numerics (via trapping/recycling of winds in hot halos). Multiple feedback mechanisms play key roles: supernovae regulate stellar masses/winds; stellar mass-loss fuels late star formation; radiative feedback suppresses accretion onto dwarfs and instantaneous star formation in disks. We provide all initial conditions and numerical algorithms used., Comment: 64 pages, 40 figures. Simulation animations and visualizations available at http://www.tapir.caltech.edu/~phopkins/Site/animations and http://fire.northwestern.edu . Paper includes complete FIRE algorithms and public ICs (http://www.tapir.caltech.edu/~phopkins/publicICs). Updated to match published version