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Star clusters are ubiquitous in galaxies of all types and at all stages of their evolution. We also observe them to be forming in a wide variety of environments, ranging from nearby giant molecular clouds to the supergiant molecular clouds found in starburst and merging galaxies. The typical star in our galaxy and probably in others formed as a member of a star cluster, so star formation is an intrinsically clustered and not an isolated phenomenon. The greatest challenge regarding clustered star formation is to understand why stars have a mass spectrum that appears to be universal. This review examines the observations and models that have been proposed to explain these fundamental issues in stellar formation.

Energetic, highly collimated, episodic jets are observed in active galactic nuclei, binary stellar systems harbouring a black hole or white dwarf, and in association with stars in the process of formation. The common feature of these systems is that gas is fed onto the central object through an accretion disk. Time-dependent magnetohydrodynamical simulations show that magnetic fields anchored in the accretion disk can accelerate and collimate outflows into jets. For certain magnetic field configurations, episodic knots within the jet are produced.

This article summarizes recent theoretical, numerical and observational progress on the nature of jets and outflows in regions of star formation. The emphasis is placed on the role of hydromagnetic phenonmena in understanding these new results. The confluence of sophisticated 3D numerical MHD simulations and the recent observations of rotating jets makes it possible, for the first time, to rigorously test jet models.

The fragmentation mode of high-mass molecular clumps and the accretion processes that form the most massive stars (\\(M\\gtrsim 8M_\\odot\\)) are still not well understood. To this end, we have undertaken a large observational program (CORE) making use of interferometric observations from the Northern Extended Millimetre Array (NOEMA) for a sample of 20 luminous (\\(L>10^4L_\\odot\\)) protostellar objects in the 1.37 mm wavelength regime in both continuum and line emission, reaching \\(\\sim\\)0.4\" resolution (800 au at 2 kpc). Using the dense gas tracer CH\\(_3\\)CN, we find velocity gradients across 13 cores perpendicular to the directions of bipolar molecular outflows, making them excellent disk candidates. Specific angular momentum (\\(j\\)) radial profiles are on average \\(\\sim10^{-3}\\) km /s pc and follow \\(j \\propto r^{1.7}\\), consistent with a poorly resolved rotating and infalling envelope/disk model. Fitting the velocity profiles with a Keplerian model, we find protostellar masses in the range of \\(\\sim 10-25\\) \\(M_\\odot\\). Modelling the level population of CH\\(_3\\)CN lines, we present temperature maps and find median gas temperatures in the range \\(70-210\\) K. We create Toomre \\(Q\\) maps to study the stability of the disks and find almost all (11 of 13) disk candidates to be prone to fragmentation due to gravitational instabilities at the scales probed by our observations. In particular, disks with masses greater than \\(\\sim10-20\\%\\) of the mass of their host (proto)stars are Toomre unstable, and more luminous protostellar objects tend to have disks that are more massive and hence more prone to fragmentation. Our finings show that most disks around high-mass protostars are prone to disk fragmentation early in their formation due to their high disk to stellar mass ratio. This impacts the accretion evolution of high-mass protostars which will have significant implications for the formation of the most massive stars.

We aim to characterize the physical and chemical properties of fragmented cores during the earliest evolutionary stages in the very young star-forming regions ISOSS J22478+6357 and ISOSS J23053+5953. NOEMA 1.3 mm data are used in combination with archival mid- and far-infrared observations to construct and fit the SEDs of individual fragmented cores. The radial density profiles are inferred from the 1.3 mm continuum visibility profiles and the radial temperature profiles are estimated from H2CO rotation temperature maps. Molecular column densities are derived with the line fitting tool XCLASS. The physical and chemical properties are combined by applying the physical-chemical model MUSCLE in order to constrain the chemical timescales of a few line-rich cores. The morphology and spatial correlations of the molecular emission are analyzed using the HOG method. The mid-infrared data show that both regions contain a cluster of young stellar objects. Bipolar molecular outflows are observed in the CO 2-1 transition toward the strong mm cores indicating protostellar activity. We find strong molecular emission of SO, SiO, H2CO, and CH3OH in locations which are not associated with the mm cores. These shocked knots can be either associated with the bipolar outflows or, in the case of ISOSS J23053+5953, with a colliding flow that creates a large shocked region between the mm cores. The mean chemical timescale of the cores is lower (20 000 yr) compared to that of the sources of the more evolved CORE sample (60 000 yr). With the HOG method, we find that the spatial emission of species tracing the extended emission and of shock-tracing molecules are well correlated within transitions of these groups.

Increasing evidence suggests that, similar to their low-mass counterparts, high-mass stars form through a disk-mediated accretion process. At the same time, formation of high-mass stars still necessitates high accretion rates, and hence, high gas densities, which in turn can cause disks to become unstable against gravitational fragmentation. We study the kinematics and fragmentation of the disk around the high-mass star forming region AFGL 2591-VLA 3 which was hypothesized to be fragmenting based on the observations that show multiple outflow directions. We use a new set of high-resolution (0.19 arcsec) IRAM/NOEMA observations at 843 micron towards VLA 3 which allow us to resolve its disk, characterize the fragmentation, and study its kinematics. In addition to the 843 micron continuum emission, our spectral setup targets warm dense gas and outflow tracers such as HCN, HC\\(_3\\)N and SO\\(_2\\), as well as vibrationally excited HCN lines. The high resolution continuum and line emission maps reveal multiple fragments with subsolar masses within the inner 1000 AU of VLA 3. Furthermore, the velocity field of the inner disk observed at 843 micron shows a similar behavior to that of the larger scale velocity field studied in the CORE project at 1.37 mm. We present the first observational evidence for disk fragmentation towards AFGL 2591-VLA 3, a source that was thought to be a single high-mass core. While the fragments themselves are low-mass, the rotation of the disk is dominated by the protostar with a mass of 10.3\\(\\pm 1.8~M_{\\odot}\\). These data also show that NOEMA Band 4 can obtain the highest currently achievable spatial resolution at (sub-)mm wavelengths in observations of strong northern sources.

In the massive star-forming region IRAS 21078+5211, a highly fragmented cluster (0.1~pc in size) of molecular cores is observed, located at the density peak of an elongated (1~pc in size) molecular cloud. A small (1~km/s per 0.1~pc) LSR velocity (Vlsr) gradient is detected across the axis of the molecular cloud. Assuming we are observing a mass flow from the harboring cloud to the cluster, we derive a mass infall rate of about 10^{-4}~M_{sun}~yr^{-1}. The most massive cores (labeled 1, 2, and 3) are found at the center of the cluster, and these are the only ones that present a signature of protostellar activity in terms of emission from high-excitation molecular lines or a molecular outflow. We reveal an extended (size about 0.1~pc), bipolar collimated molecular outflow emerging from core 1. We believe this is powered by a (previously discovered) compact (size <= 1000~au) radio jet, ejected by a YSO embedded in core 1 (named YSO-1), since the molecular outflow and the radio jet are almost parallel and have a comparable momentum rate. By means of high-excitation lines, we find a large (14~km/s over 500~au) Vlsr gradient at the position of YSO-1, oriented approximately perpendicular to the radio jet. Assuming this is an edge-on, rotating disk and fitting a Keplerian rotation pattern, we determine the YSO-1 mass to be 5.6+/-2.0~M_{sun}. The water masers (previously observed with VLBI) emerge within 100-300~au from YSO-1 and are unique tracers of the jet kinematics. Their three-dimensional (3D) velocity pattern reveals that the gas flows along, and rotates about, the jet axis. We show that the 3D maser velocities are fully consistent with the magneto-centrifugal disk-wind models predicting a cylindrical rotating jet. Under this hypothesis, we determine the jet radius to be about 16~au and the corresponding launching radius and terminal velocity to be about 2.2~au and 200~km/s, respectively.

We present the results of very high resolution CDM simulations of galaxy formation designed to follow the formation and evolution of self-gravitating, supergiant star-forming clouds. We find that the mass spectrum of these clouds is identical to that of globular clusters and GMCs; dN/dM M ^sup -1.7^ ± 0.1.[PUBLICATION ABSTRACT]

We analyse simulations of turbulent, magnetised molecular cloud cores focussing on the formation of Class 0 stage protostellar discs and the physical conditions in their surroundings. We show that for a wide range of initial conditions Keplerian discs are formed in the Class 0 stage already. In particular, we show that even subsonic turbulent motions reduce the magnetic braking efficiency sufficiently in order to allow rotationally supported discs to form. We therefore suggest that already during the Class 0 stage the fraction of Keplerian discs is significantly higher than 50%, consistent with recent observational trends but significantly higher than predictions based on simulations with misaligned magnetic fields, demonstrating the importance of turbulent motions for the formation of Keplerian discs. We show that the accretion of mass and angular momentum in the surroundings of protostellar discs occurs in a highly anisotropic manner, by means of a few narrow accretion channels. The magnetic field structure in the vicinity of the discs is highly disordered, revealing field reversals up to distances of 1000 AU. These findings demonstrate that as soon as even mild turbulent motions are included, the classical disc formation scenario of a coherently rotating environment and a well-ordered magnetic field breaks down. Hence, it is highly questionable to assess the magnetic braking efficiency based on non-turbulent collapse simulation. We strongly suggest that, in addition to the global magnetic field properties, the small-scale accretion flow and detailed magnetic field structure have to be considered in order to assess the likelihood of Keplerian discs to be present.

This study is part of the project ``CORE'', an IRAM/NOEMA large program consisting of observations of the millimeter continuum and molecular line emission towards 20 selected high-mass star forming regions. We focus on IRAS23385+6053, which is believed to be the least evolved source of the CORE sample. The observations were performed at ~1.4 mm and employed three configurations of NOEMA and additional single-dish maps, merged with the interferometric data to recover the extended emission. Our correlator setup covered a number of lines from well-known hot core tracers and a few outflow tracers. The angular (~0.45\"\\(-\\)0.9\") and spectral (0.5 km/s) resolutions were sufficient to resolve the clump in IRAS23385+6053 and investigate the existence of large-scale motions due to rotation, infall, or expansion. We find that the clump splits into six distinct cores when observed at sub-arcsecond resolution. These are identified through their 1.4 mm continuum and molecular line emission. We produce maps of the velocity, line width, and rotational temperature from the methanol and methyl cyanide lines, which allow us to investigate the cores and reveal a velocity and temperature gradient in the most massive core. We also find evidence of a bipolar outflow, possibly powered by a low-mass star. We present the tentative detection of a circumstellar self-gravitating disk lying in the most massive core and powering a large-scale outflow previously known in the literature. In our scenario, the star powering the flow is responsible for most of the luminosity of IRAS23385+6053 (~\\(3000~L_\\odot\\)). The other cores, albeit with masses below the corresponding virial masses, appear to be accreting material from their molecular surroundings and are possibly collapsing or on the verge of collapse. We conclude that we are observing a sample of star-forming cores that is bound to turn into a cluster of massive stars.