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Context. Turbulence is a key component of molecular cloud structure. It is usually described by a cascade of energy down to the dissipation scale. The power spectrum for subsonic incompressible turbulence is $k^{-5/3}$, while for supersonic turbulence it is $k^{-2}$. Aims. We aim to determine the power spectrum in an actively star-forming molecular cloud, from parsec scales down to the expected magnetohydrodynamic (MHD) wave cutoff (dissipation scale). Methods. We analyze observations of the nearby NGC 1333 star-forming region in three different tracers to cover the different scales from $\sim$10 pc down to 20 mpc. The largest scales are covered with the low density gas tracer $^{13}$CO (1-0) obtained with single dish, the intermediate scales are covered with single-dish observations of the C$^{18}$O (3-2) line, while the smallest scales are covered in H$^{13}$CO$^+$ (1-0) and HNC (1-0) with a combination of NOEMA interferometer and IRAM 30m single dish observations. The complementarity of these observations enables us to generate a combined power spectrum covering more than two orders of magnitude in spatial scale. Results. We derive the power spectrum in an active star-forming region spanning more than 2 decades of spatial scales. The power spectrum of the intensity maps shows a single power-law behavior, with an exponent of 2.9$\pm$0.1 and no evidence of dissipation. Moreover, there is evidence for the power-spectrum of the ions to have more power at smaller scales than the neutrals, which is opposite from theoretical expectations. Conclusions. We show new possibilities of studying the dissipation of energy at small scales in star-forming regions provided by interferometric observations., Comment: 6 pages (+2 appendix), 5 figures. Accepted to A&A Letters. GitHub repo with code available at https://github.com/jpinedaf/NGC1333_NOEMA_turbulence

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

We present Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 3 observations of 73 starless and protostellar cores in the Orion B North molecular cloud. We detect a total of 34 continuum sources at 106 GHz, and after comparisons with other data, 4 of these sources appear to be starless. Three of the four sources are located near groupings of protostellar sources, while one source is an isolated detection. We use synthetic observations of a simulation modeling a collapsing turbulent, magnetized core to compute the expected number of starless cores that should be detectable with our ALMA observations and find at least two (1.52) starless core should be detectable, consistent with our data. We run a simple virial analysis of the cores to put the Orion B North observations into context with similar previous ALMA surveys of cores in Chamaeleon I and Ophiuchus. We conclude that the Chamaeleon I starless core population is characteristically less bounded than the other two populations, along with external pressure contributions dominating the binding energy of the cores. These differences may explain why the Chamaeleon I cores do not follow turbulent model predictions, while the Ophiuchus and Orion B North cores are consistent with the model., Comment: 38 pages, 18 figures, accepted for publication in 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

The detection of narrow channels of accretion toward protostellar disks, known as streamers, have increased in number in the last few years. However, it is unclear if streamers are a common feature around protostars that were previously missed, or if they are a rare phenomenon. Our goals are to obtain the incidence of streamers toward a region of clustered star formation and to trace the origins of their gas, to determine if they originate within the filamentary structure of molecular clouds or from beyond. We used combined observations of the nearby NGC 1333 star-forming region, carried out with the NOEMA interferometer and the IRAM 30m single dish. Our observations cover the area between the IRAS 4 and SVS 13 systems. We traced the chemically fresh gas within NGC 1333 with HC3N molecular gas emission and the structure of the fibers in this region with N2H+ emission. We fit multiple velocity components in both maps and used clustering algorithms to recover velocity-coherent structures. We find streamer candidates toward 7 out of 16 young stellar objects within our field of view. This represents an incidence of approximately 40\% of young stellar objects with streamer candidates when looking at a clustered star forming region. The incidence increases to about 60\% when we considered only embedded protostars. All streamers are found in HC3N emission. Given the different velocities between HC3N and N2H+ emission, and the fact that, by construction, N2H+ traces the fiber structure, we suggest that the gas that forms the streamers comes from outside the fibers. This implies that streamers can connect cloud material that falls to the filaments with protostellar disk scales., Comment: 22 pages, 15 figures, accepted for publication in Astronomy and Astrophysics. GitHub repository with code available at https://github.com/tere-valdivia/propstar_gasflow

Electron fraction and cosmic-ray ionization rates (CRIR) in star-forming regions are important quantities in astrochemical modeling and are critical to the degree of coupling between neutrals, ions, and electrons, which regulates the dynamics of the magnetic field. However, these are difficult quantities to estimate. We aim to derive the electron fraction and CRIR maps of an active star-forming region. We combined observations of the nearby NGC 1333 star-forming region carried out with the NOEMA interferometer and IRAM 30-m single dish to generate high spatial dynamic range maps of different molecular transitions. We used the DCO$^+$ and H$^{13}$CO$^+$ ratio (in addition to complementary data) to estimate the electron fraction and produce cosmic-ray ionization rate maps. We derived the first large-area electron fraction and CRIR resolved maps in a star-forming region, with typical values of $10^{-6.5}$ and $10^{-16.5}$ s$^{-1}$, respectively. The maps present clear evidence of enhanced values around embedded young stellar objects (YSOs). This provides strong evidence for locally accelerated cosmic rays. We also found a strong enhancement toward the northwest region in the map that might be related either to an interaction with a bubble or to locally generated cosmic rays by YSOs. We used the typical electron fraction and derived a MHD turbulence dissipation scale of 0.054 pc, which could be tested with future observations. We found a higher cosmic-ray ionization rate compared to the canonical value for $N({\rm H_2})=10^{21}-10^{23}$ cm$^{-2}$ of $10^{-17}$ s$^{-1}$ in the region, and it is likely generated by the accreting YSOs. The high value of the electron fraction suggests that new disks will form from gas in the ideal-MHD limit. This indicates that local enhancements of $\zeta({\rm H_2})$, due to YSOs, should be taken into account in the analysis of clustered star formation., Comment: 13 pages, 13 Figures. Accepted to A&A. Abridged abstract. GitHub repo with code available at https://github.com/jpinedaf/NGC1333_NOEMA_Ions

Aims. We aim to study the structure and kinematics of the two filaments inside the subsonic core Barnard 5 in Perseus using high-resolution ($\approx$ 2400 au) NH3 data and a multi-component fit analysis. Methods. We used observations of NH3 (1,1) and (2,2) inversion transitions using the Very Large Array (VLA) and the Green Bank Telescope (GBT). We smoothed the data to a beam of 8'' to reliably fit multiple velocity components towards the two filamentary structures identified in B5. Results. Along with the core and cloud components, which dominate the flux in the line of sight, we detected two components towards the two filaments showing signs of infall. We also detected two additional components that can possibly trace new material falling into the subsonic core of B5. Conclusions. Following comparison with previous simulations of filament formation scenarios in planar geometry, we conclude that either the formation of the B5 filaments is likely to be rather cylindrically symmetrical or the filaments are magnetically supported. We also estimate infall rates of $1.6\times10^{-4}\,M_\odot\,yr^{-1}$ and $1.8\times10^{-4}\,M_\odot\,yr^{-1}$ (upper limits) for the material being accreted onto the two filaments. At these rates, the filament masses can change significantly during the core lifetime. We also estimate an upper limit of $3.5\times10^{-5}\,M_\odot\,yr^{-1}$ for the rate of possible infall onto the core itself. Accretion of new material onto cores indicates the need for a significant update to current core evolution models, where cores are assumed to evolve in isolation., Comment: 15 pages, 13 figures, accepted for publication on Astronomy and Astrophysics. The scripts used for the analysis presented in this paper can be found at https://github.com/SpandanCh/Barnard5_filaments

The internal velocity structure within dense gaseous cores plays a crucial role in providing the initial conditions for star formation in molecular clouds. However, the kinematic properties of dense gas at core scales (~0.01 - 0.1 pc) has not been extensively characterized because of instrument limitations until the unique capabilities of GBT-Argus became available. The ongoing GBT-Argus Large Program, Dynamics in Star-forming Cores (DiSCo) thus aims to investigate the origin and distribution of angular momenta of star-forming cores. DiSCo will survey all starless cores and Class 0 protostellar cores in the Perseus molecular complex down to ~0.01 pc scales with < 0.05 km/s velocity resolution using the dense gas tracer N$_2$H$^+$. Here, we present the first datasets from DiSCo toward the B1 and NGC 1333 regions in Perseus. Our results suggest that a dense core's internal velocity structure has little correlation with other core-scale properties, indicating these gas motions may be originated externally from cloud-scale turbulence. These first datasets also reaffirm the ability of GBT-Argus for studying dense core velocity structure and provided an empirical basis for future studies that address the angular momentum problem with a statistically broad sample., Comment: 17 pages, 12 figures, accepted by MNRAS

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

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

Accurately quantifying the impact of radiation feedback in star formation is challenging. To address this complex problem, we employ deep learning techniques, denoising diffusion probabilistic models (DDPMs), to predict the interstellar radiation field (ISRF) strength based on three-band dust emission at 4.5 \um, 24 \um, and 250 \um. We adopt magnetohydrodynamic simulations from the STARFORGE (STAR FORmation in Gaseous Environments) project that model star formation and giant molecular cloud (GMC) evolution. We generate synthetic dust emission maps matching observed spectral energy distributions in the Monoceros R2 (MonR2) GMC. We train DDPMs to estimate the ISRF using synthetic three-band dust emission. The dispersion between the predictions and true values is within a factor of 0.1 for the test set. We extended our assessment of the diffusion model to include new simulations with varying physical parameters. While there is a consistent offset observed in these out-of-distribution simulations, the model effectively constrains the relative intensity to within a factor of 2. Meanwhile, our analysis reveals weak correlation between the ISRF solely derived from dust temperature and the actual ISRF. We apply our trained model to predict the ISRF in MonR2, revealing a correspondence between intense ISRF, bright sources, and high dust emission, confirming the model's ability to capture ISRF variations. Our model robustly predicts radiation feedback distribution, even in complex, poorly constrained ISRF environments like those influenced by nearby star clusters. However, precise ISRF predictions require an accurate training dataset mirroring the target molecular cloud's unique physical conditions., Comment: Revised submission to ApJ following referee's comments

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

One of the most poorly understood aspects of low-mass star formation is how multiple-star systems are formed. Here we present the results of Atacama Large Millimeter/submillimeter Array (ALMA) Band-6 observations towards a forming quadruple protostellar system, G206.93-16.61E2, in the Orion B molecular cloud. ALMA 1.3 mm continuum emission reveals four compact objects, of which two are Class I young stellar objects (YSOs), and the other two are likely in prestellar phase. The 1.3 mm continuum emission also shows three asymmetric ribbon-like structures that are connected to the four objects, with lengths ranging from $\sim$500 au to $\sim$2200 au. By comparing our data with magneto-hydrodynamic (MHD) simulations, we suggest that these ribbons trace accretion flows and also function as gas bridges connecting the member protostars. Additionally, ALMA CO J=2-1 line emission reveals a complicated molecular outflow associated with G206.93-16.61E2 with arc-like structures suggestive of an outflow cavity viewed pole-on., Comment: The paper was accepted by APJL

We present Atacama Large Millimeter/submillimeter Array observations of the $\sim$10 kAU environment surrounding 21 protostars in the Orion A molecular cloud tracing outflows. Our sample is composed of Class 0 to flat-spectrum protostars, spanning the full $\sim$1 Myr lifetime. We derive the angular distribution of outflow momentum and energy profiles and obtain the first two-dimensional instantaneous mass, momentum, and energy ejection rate maps using our new approach: the Pixel Flux-tracing Technique (PFT). Our results indicate that by the end of the protostellar phase, outflows will remove $\sim$2 to 4 M$_\odot$ from the surrounding $\sim$1 M$_\odot$ low-mass core. These high values indicate that outflows remove a significant amount of gas from their parent cores and continuous core accretion from larger scales is needed to replenish core material for star formation. This poses serious challenges to the concept of ``cores as well-defined mass reservoirs", and hence to the simplified core-to-star conversion prescriptions. Furthermore, we show that cavity opening angles, and momentum and energy distributions all increase with the protostar evolutionary stage. This is clear evidence that even garden-variety protostellar outflows: (a) effectively inject energy and momentum into their environments on $10$ kAU scales, and (b) significantly disrupt their natal cores, ejecting a large fraction of the mass that would have otherwise fed the nascent star. Our results support the conclusion that protostellar outflows have a direct impact on how stars get their mass, and that the natal sites of individual low-mass star formation are far more dynamic than commonly accepted theoretical paradigms., Comment: 76 pages, 43 figures. Accepted by ApJ 2023.2.6

We define a sample of 200 protostellar outflows showing blue and redshifted CO emission in the nearby molecular clouds Ophiuchus, Taurus, Perseus and Orion to investigate the correlation between outflow orientations and local, but relatively large-scale, magnetic field directions traced by Planck 353 GHz dust polarization. At high significance (p~1e-4), we exclude a random distribution of relative orientations and find that there is a preference for alignment of projected plane of sky outflow axes with magnetic field directions. The distribution of relative position angles peaks at ~30deg and exhibits a broad dispersion of ~50deg. These results indicate that magnetic fields have dynamical influence in regulating the launching and/or propagation directions of outflows. However, the significant dispersion around perfect alignment orientation implies that there are large measurement uncertainties and/or a high degree of intrinsic variation caused by other physical processes, such as turbulence or strong stellar dynamical interactions. Outflow to magnetic field alignment is expected to lead to a correlation in the directions of nearby outflow pairs, depending on the degree of order of the field. Analyzing this effect we find limited correlation, except on relatively small scales < 0.5 pc. Furthermore, we train a convolutional neural network to infer the inclination angle of outflows with respect to the line of sight and apply it to our outflow sample to estimate their full 3D orientations. We find that the angles between outflow pairs in 3D space also show evidence of small-scale alignment., Comment: ApJ Accepted

Cosmic rays in star-forming galaxies are a dominant source of both diffuse $\gamma$-ray emission and ionisation in gas too deeply shielded for photons to penetrate. Though the cosmic rays responsible for $\gamma$-rays and ionisation are of different energies, they are produced by the same star formation-driven sources, and thus galaxies' star formation rates, $\gamma$-ray luminosities, and ionisation rates should all be linked. In this paper we use up-to-date cross-section data to determine this relationship, finding that cosmic rays in a galaxy of star formation rate $\dot{M}_*$ and gas depletion time $t_\mathrm{dep}$ produce a maximum primary ionisation rate $\zeta \approx 1\times 10^{-16} (t_\mathrm{dep}/\mbox{Gyr})^{-1}$ s$^{-1}$ and a maximum $\gamma$-ray luminosity $L_\gamma\approx 4\times 10^{39} (\dot{M}_*/\mathrm{M}_\odot\mbox{ yr}^{-1})$ erg s$^{-1}$ in the 0.1 - 100 GeV band. These budgets imply either that the ionisation rates measured in Milky Way molecular clouds include a significant contribution from local sources that elevate them above the Galactic mean, or that CR-driven ionisation in the Milky Way is enhanced by sources not linked directly to star formation. Our results also imply that ionisation rates in starburst systems are only moderately enhanced compared to those in the Milky Way. Finally, we point out that measurements of $\gamma$-ray luminosities can be used to place constraints on galactic ionisation budgets in starburst galaxies that are nearly free of systematic uncertainties on the details of cosmic ray acceleration., Comment: 19 pages, 8 figures, accepted for publication in MNRAS

Young stellar populations provide a record of past star formation, and by establishing their members' dynamics and ages, it is possible to reconstruct the full history of star formation events. Gaia has greatly expanded the number of accessible stellar populations, with one of the most notable recently-discovered associations being Cepheus Far North (CFN), a population containing hundreds of members spanning over 100 pc. With its proximity (d $\lesssim$ 200 pc), apparent substructure, and relatively small population, CFN represents a manageable population to study in depth, with enough evidence of internal complexity to produce a compelling star formation story. Using Gaia astrometry and photometry combined with additional spectroscopic observations, we identify over 500 candidate CFN members spread across 7 subgroups. Combining ages from isochrones, asteroseismology, dynamics, and lithium depletion, we produce well-constrained ages for all seven subgroups, revealing a largely continuous 10 Myr star formation history in the association. By tracing back the present-day populations to the time of their formation, we identify two spatially and dynamically distinct nodes in which stars form, one associated with $\beta$ Cephei which shows mostly co-spatial formation, and one associated with EE Draconis with a more dispersed star formation history. This detailed view of star formation demonstrates the complexity of the star formation process, even in the smallest of regions., Comment: Accepted to ApJ; 34 pages, 15 figures, 6 tables in two-column AASTEX63 format

High-resolution observations of the Perseus B5 "core" have previously revealed that this subsonic region actually consists of several filaments that are likely in the process of forming a quadruple stellar system. Since subsonic filaments are thought to be produced at the $\sim 0.1$ pc sonic scale by turbulent compression, a detailed kinematic study is crucial to test such a scenario in the context of core and star formation. Here we present a detailed kinematic follow-up study of the B5 filaments at a 0.009 pc resolution using the VLA and GBT combined observations fitted with multi-component spectral models. Using precisely identified filament spines, we find a remarkable resemblance between the averaged width profiles of each filament and Plummer-like functions, with filaments possessing FWHM widths of $\sim 0.03$ pc. The velocity dispersion profiles of the filaments also show decreasing trends towards the filament spines. Moreover, the velocity gradient field in B5 appears to be locally well ordered ($\sim 0.04$ pc) but globally complex, with kinematic behaviors suggestive of inhomogeneous turbulent accretion onto filaments and longitudinal flows towards a local overdensity along one of the filaments., Comment: 27 pages, 12 figures, published in The Astrophysical Journal

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

Observational advances over the last decade have enabled high-resolution, interferometric studies of forming multiple systems, statistical surveys of multiplicity in star-forming regions, and new insights into disk evolution and planetary architectures in these systems. In this review, we compile the results of observational and theoretical studies of stellar multiplicity. We summarize the population statistics spanning system evolution from the protostellar phase through the main-sequence phase and evaluate the influence of the local environment. In short, most stars are born in multiple stellar systems, most main sequence stars are members of multiple systems, but most star systems are single. We describe current models for the origin of stellar multiplicity and review the landscape of numerical simulations and assess their consistency with observations. We review the properties of disks and discuss the impact of multiplicity on planet formation and system architectures. Finally, we summarize open questions and discuss the technical requirements for future observational and theoretical progress., Comment: 36 pages, 9 figures, Protostars and Planets VII, Editors: Shu-ichiro Inutsuka, Yuri Aikawa, Takayuki Muto, Kengo Tomida, and Motohide Tamura

We present a new SOFIA/FORCAST mid-IR survey of luminous protostars and crowded star-forming environments in Cygnus X, the nearest million-solar mass molecular cloud complex. We derive bolometric luminosities for over 1000 sources in the region with these new data in combination with extant Spitzer and UKIDSS photometry, with 63 new luminous protostar candidates identified by way of the high quality SOFIA/FORCAST data. By including FORCAST data, we construct protostellar luminosity functions (PLFs) with improved completeness at the high luminosity end. The PLFs are well described by a power law function with an index of ~-0.5. Based on the Herschel temperature and column density measurements, we find no obvious dependence of the PLFs on the local gas temperature, but PLFs in regions of high stellar density or gas column density exhibit some excess at higher luminosities. Through the comparison between our observed PLFs and existing accretion models, both the turbulent core (TC) and the competitive accretion (CA) models are consistent with our results, while the isothermal sphere (IS) model is disfavored. The implications of these results on the star formation process are discussed., Comment: 20 pages, 21 figures, Accepted for publication in MNRAS

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

We adopt the deep learning method CASI-3D (Convolutional Approach to Structure Identification-3D) to systemically identify protostellar outflows in 12CO and 13CO observations of the nearby molecular clouds, Ophiuchus, Taurus, Perseus and Orion. The total outflow masses are 267 Msun, 795 Msun, 1305 Msun and 6332 Msun for Ophiuchus, Taurus, Perseus and Orion, respectively. We show the outflow mass in each cloud is linearly proportional to the total number of young stellar objects. The estimated total 3D deprojected outflow energies are 9e45 ergs, 6e46 ergs, 1.2e47 ergs and 6e47 ergs for Ophiuchus, Taurus, Perseus and Orion, respectively. The energy associated with outflows is sufficient to offset turbulent dissipation at the current epoch for all four clouds. All clouds also exhibit a break point in the spatial power spectrum of the outflow prediction map, which likely corresponds to the typical outflow mass and energy injection scale., Comment: ApJ Accepted

We characterize protostellar multiplicity in the Orion molecular clouds using ALMA 0.87~mm and VLA 9~mm continuum surveys toward 328 protostars. These observations are sensitive to projected spatial separations as small as $\sim$20~au, and we consider source separations up to 10$^4$~au as potential companions. The overall multiplicity fraction (MF) and companion fraction (CF) for the Orion protostars are 0.30$\pm$0.03 and 0.44$\pm$0.03, respectively, considering separations from 20 to 10$^4$~au. The MFs and CFs are corrected for potential contamination by unassociated young stars using a probabilistic scheme based on the surface density of young stars around each protostar. The companion separation distribution as a whole is double peaked and inconsistent with the separation distribution of solar-type field stars, while the separation distribution of Flat Spectrum protostars is consistent solar-type field stars. The multiplicity statistics and companion separation distributions of the Perseus star-forming region are consistent with those of Orion. Based on the observed peaks in the Class 0 separations at $\sim$100~au and $\sim$10$^3$~au, we argue that multiples with separations $<$500~au are likely produced by both disk fragmentation and turbulent fragmentation with migration, and those at $\ga$10$^3$~au result primarily from turbulent fragmentation. We also find that MFs/CFs may rise from Class 0 to Flat Spectrum protostars between 100 and 10$^3$~au in regions of high YSO density. This finding may be evidence for migration of companions from $>$10$^3$~au to $<$10$^3$~au, and that some companions between 10$^3$ and 10$^4$~au must be (or become) unbound., Comment: 76 pages, 20 Figures, 10 Tables, accepted by the Astrophysical Journal

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

Dynamical studies of dense structures within molecular clouds often conclude that the most massive clumps contain too little kinetic energy for virial equilibrium, unless they are magnetized to an unexpected degree. This raises questions about how such a state might arise, and how it might persist long enough to represent the population of massive clumps. In an effort to re-examine the origins of this conclusion, we use ammonia line data from the Green Bank Ammonia Survey and Planck-calibrated dust emission data from Herschel to estimate the masses and kinetic and gravitational energies for dense clumps in the Gould Belt clouds. We show that several types of systematic error can enhance the appearance of low kinetic-to-gravitational energy ratios: insufficient removal of foreground and background material; ignoring the kinetic energy associated with velocity differences across a resolved cloud; and over-correcting for stratification when evaluating the gravitational energy. Using an analysis designed to avoid these errors, we find that the most massive Gould Belt clumps harbor virial motions, rather than sub-virial ones. As a byproduct, we present a catalog of masses, energies, and virial energy ratios for 85 Gould Belt clumps., Comment: Submitted to ApJ

We investigate the effect of star formation on turbulence in the Orion A and Ophiuchus clouds using principal component analysis (PCA). We measure the properties of turbulence by applying PCA on the spectral maps in $^{13}$CO, C$^{18}$O, HCO$^+$ $J=$1$-$0, and CS $J=$2$-$1. First, the scaling relations derived from PCA of the $^{13}$CO maps show that the velocity difference ($\delta v$) for a given spatial scale ($L$) is the highest in the integral shaped filament (ISF) and L1688, where the most active star formation occurs in the two clouds. The $\delta v$ increases with the number density and total bolometric luminosity of the protostars in the sub-regions. Second, in the ISF and L1688 regions, the $\delta v$ of C$^{18}$O, HCO$^+$, and CS are generally higher than that of $^{13}$CO, which implies that the dense gas is more turbulent than the diffuse gas in the star-forming regions; stars form in dense gas, and dynamical activities associated with star formation, such as jets and outflows, can provide energy into the surrounding gas to enhance turbulent motions., Comment: 29 pages, 17 figures, 7 tables, accepted for publication in ApJ

Numerous spherical ``shells" have been observed in young star-forming environments that host low- and intermediate-mass stars. These observations suggest that these shells may be produced by isotropic stellar wind feedback from young main-sequence stars. However, the driving mechanism for these shells remains uncertain because the momentum injected by winds is too low to explain their sizes and dynamics due to their low mass-loss rates. However, these studies neglect how the wind kinetic energy is transferred to the ISM and instead assume it is instantly lost via radiation, suggesting that these shells are momentum-driven. Intermediate-mass stars have fast ($v_w \gtrsim 1000$ km/s) stellar winds and therefore the energy injected by winds should produce energy-driven adiabatic wind bubbles that are larger than momentum-driven wind bubbles. Here, we explore if energy-driven wind feedback can produce the observed shells by performing a series of 3D magneto-hydrodynamic simulations of wind feedback from intermediate-mass and high-mass stars that are placed in a magnetized, turbulent molecular cloud. We find that, for the high-mass stars modeled, energy-driven wind feedback produces $\sim$pc scale wind bubbles in molecular clouds that agree with the observed shell sizes but winds from intermediate-mass stars can not produce similar shells because of their lower mass-loss rates and velocities. Therefore, such shells must be driven by other feedback processes inherent to low- and intermediate-mass star formation., Comment: 17 pages, 5 figures. Submitted to the Astrophysical Journal

We have used the Taeduk Radio Astronomy Observatory to observe the Orion A and Ophiuchus clouds in the $J=$1$-$0 lines of $^{13}$CO, C$^{18}$O, HCN, HCO$^+$, and N$_2$H$^+$ and the $J=$2$-$1 line of CS. The fully sampled maps with uniform noise levels are used to create moment maps. The variations of the line intensity and velocity dispersion with total column density, derived from dust emission maps, are presented and compared to previous work. The CS line traces dust column density over more than one order of magnitude, and the N$_2$H$^+$ line best traces the highest column density regime ($\log(N_\mathrm{H_2}$) $>$ 22.8). Line luminosities, integrated over the cloud, are compared to those seen in other galaxies. The HCO$^+$-to-HCN luminosity ratio in the Orion A cloud is similar to that of starburst galaxies, while that in the Ophiuchus cloud is in between those of active galactic nuclei and starburst galaxies., Comment: 62 pages, 53 figures, 6 tables, accepted for publication in ApJS

Young stellar associations hold a star formation record that can persist for millions of years, revealing the progression of star formation long after the dispersal of the natal cloud. To identify nearby young stellar populations that trace this progression, we have designed a comprehensive framework for the identification of young stars, and use it to identify $\sim$3$\times 10^4$ candidate young stars within a distance of 333 pc using Gaia DR2. Applying the HDBSCAN clustering algorithm to this sample, we identify 27 top-level groups, nearly half of which have little to no presence in previous literature. Ten of these groups have visible substructure, including notable young associations such as Orion, Perseus, Taurus, and Sco-Cen. We provide a complete subclustering analysis on all groups with substructure, using age estimates to reveal each region's star formation history. The patterns we reveal include an apparent star formation origin for Sco-Cen along a semicircular arc, as well as clear evidence for sequential star formation moving away from that arc with a propagation speed of $\sim$4 km s$^{-1}$ ($\sim$4 pc Myr$^{-1}$). We also identify earlier bursts of star formation in Perseus and Taurus that predate current, kinematically identical active star-forming events, suggesting that the mechanisms that collect gas can spark multiple generations of star formation, punctuated by gas dispersal and cloud regrowth. The large spatial scales and long temporal scales on which we observe star formation offer a bridge between the processes within individual molecular clouds and the broad forces guiding star formation at galactic scales., Comment: Accepted to ApJ; 55 pages, 32 figures, 7 tables in two-column AASTEX63 format

Recent studies have suggested that low-energy cosmic rays (CRs) may be accelerated inside molecular clouds by the shocks associated with star formation. We use a Monte Carlo transport code to model the propagation of CRs accelerated by protostellar accretion shocks through protostellar cores. We calculate the CR attenuation and energy losses and compute the resulting flux and ionization rate as a function of both radial distance from the protostar and angular position. We show that protostellar cores have non-uniform CR fluxes that produce a broad range of CR ionization rates, with the maximum value being up to two orders of magnitude higher then the radial average at a given distance. In particular, the CR flux is focused in the direction of the outflow cavity, creating a 'flashlight' effect and allowing CRs to leak out of the core. The radially averaged ionization rates are less than the measured value for the Milky Way of $\zeta \approx 10^{-16} \rm s^{-1}$; however, within $r \approx 0.03$ pc from the protostar, the maximum ionization rates exceed this value. We show that variation in the protostellar parameters, particularly in the accretion rate, may produce ionization rates that are a couple of orders of magnitude higher or lower than our fiducial values. Finally, we use a statistical method to model unresolved sub-grid magnetic turbulence in the core. We show that turbulence modifies the CR spectrum and increases the uniformity of the CR distribution but does not significantly affect the resulting ionization rates.

One of the most important and well-established empirical results in astronomy is the Kennicutt-Schmidt (KS) relation between the density of interstellar gas and the rate at which that gas forms stars. A tight correlation between these quantities has long been measured at galactic scales. More recently, using surveys of YSOs, a KS relationship has been found within molecular clouds relating the surface density of star formation to the surface density of gas; however, the scaling of these laws varies significantly from cloud to cloud. In this Letter, we use a recently developed, high-accuracy catalog of young stellar objects from $\textit{Spitzer}$ combined with high-dynamic-range gas column density maps of twelve nearby ($<$1.5 kpc) molecular clouds from $\textit{Herschel}$ to re-examine the KS relation within individual molecular clouds. We find a tight, linear correlation between clouds' star formation rate per unit area and their gas surface density normalized by the gas free-fall time. The measured intracloud KS relation, which relates star formation rate to the volume density, extends over more than two orders of magnitude within each cloud and is nearly identical in each of the twelve clouds, implying a constant star formation efficiency per free-fall time $\epsilon_{\rm ff}\approx 0.026$. The finding of a universal correlation within individual molecular clouds, including clouds that contain no massive stars or massive stellar feedback, favors models in which star formation is regulated by local processes such as turbulence or stellar feedback such as protostellar outflows, and disfavors models in which star formation is regulated only by galaxy properties or supernova feedback on galactic scales., Comment: Accepted in ApJL. 16 pages, 4 figures

Stars form in cold dense cores showing subsonic velocity dispersions. The parental molecular clouds display higher temperatures and supersonic velocity dispersions. The transition from core to cloud has been observed in velocity dispersion, but temperature and abundance variations are unknown. We aim to study the transition from cores to ambient cloud in temperature and velocity dispersion using a single tracer. We use NH3 (1,1) and (2,2) maps in L1688 from the Green Bank Ammonia Survey, smoothed to 1', and determine the physical properties from fits. We identify the coherent cores and study the changes in temperature and velocity dispersion from cores to the surrounding cloud. We obtain a kinetic temperature map tracing the extended cloud, improving from previous maps tracing mostly the cores. The cloud is 4-6 K warmer than the cores, and shows a larger velocity dispersion (diff. = 0.15-0.25 km/s). Comparing to Herschel-based measurements, we find that cores show kinetic temperature $\approx$1.8 K lower than the dust temperature; while the gas temperature is higher than the dust temperature in the cloud. We find an average p-NH3 fractional abundance (with respect to H2) of $(4.2\pm0.2) \times 10^{-9}$ towards the coherent cores, and $(1.4\pm0.1) \times 10^{-9}$ outside the core boundaries. Using stacked spectra, we detect two components, one narrow and one broad, towards cores and their neighbourhoods. We find the turbulence in the narrow component to be correlated to the size of the structure (Pearson-r=0.54). With these unresolved regional measurements, we obtain a turbulence-size relation of ${\sigma}_{v,NT}\propto r^{0.5}$, similar to previous findings using multiple tracers. We discover that the subsonic component extends up to 0.15 pc beyond the typical coherent boundaries, unveiling larger extents of the coherent cores and showing gradual transition to coherence over ~0.2 pc., Comment: 37 pages, 33 figures, 1 table. Accepted for publication in A&A

We characterize in detail the two ~0.3 pc long filamentary structures found within the subsonic region of Barnard 5. We use combined GBT and VLA observations of the molecular lines NH$_3$(1,1) and (2,2) at a resolution of 1800 au, as well as JCMT continuum observations at 850 and 450 $\mu$m at a resolution of 4400 au and 3000 au, respectively. We find that both filaments are highly super-critical with a mean mass per unit length, $M/L$, of ~80 M$_\odot$ pc$^{-1}$, after background subtraction, with local increases reaching values of ~150 M$_\odot$ pc$^{-1}$. This would require a magnetic field strength of ~500 $\mu$G to be stable against radial collapse. We extract equidistant cuts perpendicular to the spine of the filament and fit a modified Plummer profile as well as a Gaussian to each of the cuts. The filament widths (deconvolved FWHM) range between 6500-7000 au (~0.03 pc) along the filaments. This equals ~2.0 times the radius of the flat inner region. We find an anti-correlation between the central density and this flattening radius, suggestive of contraction. Further, we also find a strong correlation between the power-law exponent at large radii and the flattening radius. We note that the measurements of these three parameters fall in a plane and derive their empirical relation. Our high-resolution observations provide direct constraints of the distribution of the dense gas within super-critical filaments showing pre- and protostellar activity., Comment: Accepted for publication in ApJ. 23 pages, 14 figures, 3 tables

We present ALMA (0.87~mm and 1.3~mm) and VLA (9~mm) observations toward the candidate intermediate-mass protostar OMC2-FIR3 (HOPS-370; L$_{bol}$~314~L$_{\odot}$) at $\sim$0.1" (40~au) resolution for the continuum emission and ~0.25" (100 au) resolution of nine molecular lines. The dust continuum observed with ALMA at 0.87~mm and 1.3~mm resolve a near edge-on disk toward HOPS-370 with an apparent radius of ~100 au. The VLA observations detect both the disk in dust continuum and free-free emission extended along the jet direction. The ALMA observations of molecular lines (H$_2$CO, SO, CH$_3$OH, $^{13}$CO, C$^{18}$O, NS, and H$^{13}$CN) reveal rotation of the apparent disk surrounding HOPS-370 orthogonal to the jet/outflow direction. We fit radiative transfer models to both the dust continuum structure of the disk and molecular line kinematics of the inner envelope and disk for the H$_2$CO, CH$_3$OH, NS, and SO lines. The central protostar mass is determined to be $\sim$2.5 M_sun with a disk radius of $\sim$94~au, when fit using combinations of the H$_2$CO, CH$_3$OH, NS, and SO lines, consistent with an intermediate-mass protostar. Modeling of the dust continuum and spectral energy distribution (SED) yields a disk mass of 0.035~M$_{\odot}$ (inferred dust+gas) and a dust disk radius of 62~au, thus the dust disk may have a smaller radius than the gas disk, similar to Class II disks. In order to explain the observed luminosity with the measured protostar mass, HOPS-370 must be accreting at a rate between 1.7 and 3.2$\times$10$^{-5}$~M$_{\odot}$~yr$^{-1}$., Comment: Accepted to ApJ; 51 pages, 12 Figures, 7 Tables

We adopt the deep learning method CASI-3D (Convolutional Approach to Structure Identification-3D) to identify protostellar outflows in molecular line spectra. We conduct magneto-hydrodynamics simulations that model forming stars that launch protostellar outflows and use these to generate synthetic observations. We apply the 3D radiation transfer code RADMC-3D to model 12CO (J=1-0) line emission from the simulated clouds. We train two CASI-3D models: ME1 is trained to predict only the position of outflows, while MF is trained to predict the fraction of the mass coming from outflows in each voxel. The two models successfully identify all 60 previously visually identified outflows in Perseus. Additionally, CASI-3D finds 20 new high-confidence outflows. All of these have coherent high-velocity structures, and 17 of them have nearby young stellar objects, while the remaining three are outside the Spitzer survey coverage. The mass, momentum and energy of individual outflows in Perseus predicted by model MF is comparable to the previous estimations. This similarity is due to a cancelation in errors: previous calculations missed outflow material with velocities comparable to the cloud velocity, however, they compensate for this by over-estimating the amount of mass at higher velocities that has contamination from non-outflow gas. We show outflows likely driven by older sources have more high-velocity gas compared to those driven by younger sources., Comment: Revised version submitted to ApJ, comments welcome

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

Context : Star formation takes place in cold dense cores in molecular clouds. Earlier observations have found that dense cores exhibit subsonic non-thermal velocity dispersions. In contrast, CO observations show that the ambient large-scale cloud is warmer and has supersonic velocity dispersions. Aims : We aim to study the ammonia ($\rm NH_3$) molecular line profiles with exquisite sensitivity towards the coherent cores in L1688 in order to study their kinematical properties in unprecedented detail. Methods : We used $\rm NH_3$ (1,1) and (2,2) data from the first data release (DR1) in the Green Bank Ammonia Survey (GAS). We first smoothed the data to a larger beam of 1' to obtain substantially more extended maps of velocity dispersion and kinetic temperature, compared to the DR1 maps. We then identified the coherent cores in the cloud and analysed the averaged line profiles towards the cores. Results : For the first time, we detected a faint (mean $\rm NH_3$(1,1) peak brightness $<$0.25 K in $T_{MB}$), supersonic component towards all the coherent cores in L1688. We fitted two components, one broad and one narrow, and derived the kinetic temperature and velocity dispersion of each component. The broad components towards all cores have supersonic linewidths ($\mathcal{M}_S \ge 1$). This component biases the estimate of the narrow dense core component's velocity dispersion by $\approx$28% and the kinetic temperature by $\approx$10%, on average, as compared to the results from single-component fits. Conclusions : Neglecting this ubiquitous presence of a broad component towards all coherent cores causes the typical single-component fit to overestimate the temperature and velocity dispersion. This affects the derived detailed physical structure and stability of the cores estimated from $\rm NH_3$ observations., Comment: Accepted for publication in Astronomy & Astrophysics on 06/07/2020. 15 pages, 16 figures, 1 table. Language edits from previous version

We study the formation, evolution and collapse of dense cores by tracking structures in a magnetohydrodynamic simulation of a star-forming cloud. We identify cores using the dendrogram algorithm and utilize machine learning techniques, including Neural Gas prototype learning and Fuzzy $c$-means clustering, to analyze the density and velocity dispersion profiles of cores together with six bulk properties. We produce a 2-d visualization using a Uniform Manifold Approximation and Projection (UMAP), which facilitates the connection between physical properties and three partially-overlapping phases: i) unbound turbulent structures (Phase I), ii) coherent cores that have low turbulence (Phase II), and iii) bound cores, many of which become protostellar (Phase III). Within Phase II we identify a population of long-lived coherent cores that reach a quasi-equilibrium state. Most prestellar cores form in Phase II and become protostellar after evolving into Phase III. Due to the turbulent cloud environment, the initial core properties do not uniquely predict the eventual evolution, i.e., core evolution is stochastic, and cores follow no one evolutionary path. The phase lifetimes are 1.0$\pm$0.1$\times$10$^5$ yr, 1.3$\pm$0.2$\times$10$^5$ yr, and 1.8$\pm$0.3$\times$10$^5$ yr for Phase I, II, and III, respectively. We compare our results to NH$_3$ observations of dense cores. Known coherent cores predominantly map into Phase II, while most turbulent pressure-confined cores map to Phase I or III. We predict that a significant fraction of observed starless cores have unresolved coherent regions and that $\gtrsim 20$% of observed starless cores will not form stars. Measurements of core radial profiles, in addition to the usual bulk properties, will enable more accurate predictions of core evolution., Comment: 26 pages, 16 figures. Accepted to MNRAS

In this chapter, we review some historical understanding and recent advances on the Initial Mass Function (IMF) and the Core Mass Function (CMF), both in terms of observations and theories. We focus mostly on star formation in clustered environment since this is suggested by observations to be the dominant mode of star formation. The statistical properties and the fragmentation behaviour of turbulent gas is discussed, and we also discuss the formation of binaries and small multiple systems., Comment: Review chapter published in Space Science Reviews

Star formation is a multi-scale, multi-physics problem ranging from the size scale of molecular clouds ($\sim$10s pc) down to the size scales of dense prestellar cores ($\sim$0.1 pc) that are the birth sites of stars. Several physical processes like turbulence, magnetic fields and stellar feedback, such as radiation pressure and outflows, are more or less important for different stellar masses and size scales. During the last decade a variety of technological and computing advances have transformed our understanding of star formation through the use of multi-wavelength observations, large scale observational surveys, and multi-physics multi-dimensional numerical simulations. Additionally, the use of synthetic observations of simulations have provided a useful tool to interpret observational data and evaluate the importance of various physical processes on different scales in star formation. Here, we review these recent advancements in both high- ($M \gtrsim 8 \, M_{\rm \odot}$) and low-mass star formation., Comment: 53 pages, 7 figures, To appear in Space Science Reviews (submitted January 31, 2020; accepted May 7, 2020), topical collection on Star formation

Star formation is a complex multi-scale phenomenon that is of significant importance for astrophysics in general. Stars and star formation are key pillars in observational astronomy from local star forming regions in the Milky Way up to high-redshift galaxies. From a theoretical perspective, star formation and feedback processes (radiation, winds, and supernovae) play a pivotal role in advancing our understanding of the physical processes at work, both individually and of their interactions. In this review we will give an overview of the main processes that are important for the understanding of star formation. We start with an observationally motivated view on star formation from a global perspective and outline the general paradigm of the life-cycle of molecular clouds, in which star formation is the key process to close the cycle. After that we focus on the thermal and chemical aspects in star forming regions, discuss turbulence and magnetic fields as well as gravitational forces. Finally, we review the most important stellar feedback mechanisms., Comment: 86 pages, 4 figures. To appear in Space Science Reviews, topical collection Star formation

We explore the relation between the stellar mass surface density and the mass surface density of molecular hydrogen gas in twelve nearby molecular clouds that are located at $<$1.5 kpc distance. The sample clouds span an order of magnitude range in mass, size, and star formation rates. We use thermal dust emission from $Herschel$ maps to probe the gas surface density and the young stellar objects from the most recent $Spitzer$ Extended Solar Neighborhood Archive (SESNA) catalog to probe the stellar surface density. Using a star-sampled nearest neighbor technique to probe the star-gas surface density correlations at the scale of a few parsecs, we find that the stellar mass surface density varies as a power-law of the gas mass surface density, with a power-law index of $\sim$2 in all the clouds. The consistent power-law index implies that star formation efficiency is directly correlated with gas column density, and no gas column density threshold for star formation is observed. We compare the observed correlations with the predictions from an analytical model of thermal fragmentation, and with the synthetic observations of a recent hydrodynamic simulation of a turbulent star-forming molecular cloud. We find that the observed correlations are consistent for some clouds with the thermal fragmentation model and can be reproduced using the hydrodynamic simulations., Comment: 39 pages, 10 figures, 3 tables. Accepted in ApJ

Star clusters form in dense, hierarchically collapsing gas clouds. Bulk kinetic energy is transformed to turbulence with stars forming from cores fed by filaments. In the most compact regions, stellar feedback is least effective in removing the gas and stars may form very efficiently. These are also the regions where, in high-mass clusters, ejecta from some kind of high-mass stars are effectively captured during the formation phase of some of the low mass stars and effectively channeled into the latter to form multiple populations. Star formation epochs in star clusters are generally set by gas flows that determine the abundance of gas in the cluster. We argue that there is likely only one star formation epoch after which clusters remain essentially clear of gas by cluster winds. Collisional dynamics is important in this phase leading to core collapse, expansion and eventual dispersion of every cluster. We review recent developments in the field with a focus on theoretical work., Comment: 53 pages, 7 figures, preprint of a review to appear in Space Science Reviews Topical collection "Star formation". Changes in this version: updated comments line to to acceptance of the paper by the journal

We investigate the time evolution of dense cores identified in molecular cloud simulations using dendrograms, which are a common tool to identify hierarchical structure in simulations and observations of star formation. We develop an algorithm to link dendrogram structures through time using the three-dimensional density field from magnetohydrodynamical simulations, thus creating histories for all dense cores in the domain. We find that the population-wide distributions of core properties are relatively invariant in time, and quantities like the core mass function match with observations. Despite this consistency, an individual core may undergo large (>40%), stochastic variations due to the redefinition of the dendrogram structure between timesteps. This variation occurs independent of environment and stellar content. We identify a population of short-lived (<200 kyr) overdensities masquerading as dense cores that may comprise ~20% of any time snapshot. Finally, we note the importance of considering the full history of cores when interpreting the origin of the initial mass function; we find that, especially for systems containing multiple stars, the core mass defined by a dendrogram leaf in a snapshot is typically less than the final system stellar mass. This work reinforces that there is no time-stable density contour that defines a star-forming core. The dendrogram itself can induce significant structure variation between timesteps due to small changes in the density field. Thus, one must use caution when comparing dendrograms of regions with different ages or environment properties because differences in dendrogram structure may not come solely from the physical evolution of dense cores., Comment: 20 pages, 17 figures. Submitted to MNRAS