We derive an analytical theory of the prestellar core initial mass function ( IMF) based on an extension of the PressSchechter statistical formalism. Our approach relies on the general concept of the gravothermal and gravoturbulent collapse of a molecular cloud, with a selection criterion based on the thermal or turbulent Jeans mass, which yields the derivation of the mass spectrum of self-gravitating objects in a quiescent or a turbulent environment. The same formalism also yields the mass spectrum of non-self-gravitating clumps produced in supersonic flows. The mass spectrum of the self-gravitating cores reproduces well the observed IMF. The theory predicts that the shape of the IMF results from two competing contributions, namely, a power law at large scales and an exponential cutoff ( lognormal form) centered around the characteristic mass for gravitational collapse. The cutoff exists both in the case of thermal or turbulent collapse, provided that the underlying density field has a lognormal distribution. Whereas pure thermal collapse produces a power-law tail steeper than the Salpeter value, dN/d log M / M Àx with x ' 1:35, the latter is recovered exactly for the (three-dimensional) value of the spectral index of the velocity power spectrum, n ' 3:8, found in observations and in numerical simulations of isothermal supersonic turbulence. Indeed, the theory predicts that x ¼ (n þ 1)/(2n À 4) for self-gravitating structures and x ¼ 2 À n 0 /3 for non-self-gravitating structures, where n 0 is the power spectrum index of log . We show that, whereas supersonic turbulence promotes the formation of both massive stars and brown dwarfs, it has an overall negative impact on star formation, decreasing the star formation efficiency. This theory provides a novel theoretical foundation to understand the origin of the IMF and provides useful guidance to numerical simulations exploring star formation, while making testable predictions.

Context. Theoretical studies of collapsing clouds have found that even a relatively weak magnetic field may prevent the formation of disks and their fragmentation. However, most previous studies have been limited to cases where the magnetic field and the rotation axis of the cloud are aligned. Aims. We study the transport of angular momentum, and its effects on disk formation, for non-aligned initial configurations and a range of magnetic intensities. Methods. We perform three-dimensional, adaptive mesh, numerical simulations of magnetically supercritical collapsing dense cores using the magneto-hydrodynamic code Ramses. We compute the contributions of all the relevant processes transporting angular momentum, in both the envelope and the region of the disk. We clearly define centrifugally supported disks and thoroughly study their properties. Results. At variance with earlier analyses, we show that the transport of angular momentum acts less efficiently in collapsing cores with non-aligned rotation and magnetic field. Analytically, this result can be understood by taking into account the bending of field lines occurring during the gravitational collapse. For the transport of angular momentum, we conclude that magnetic braking in the mean direction of the magnetic field tends to dominate over both the gravitational and outflow transport of angular momentum. We find that massive disks, containing at least 10% of the initial core mass, can form during the earliest stages of star formation even for mass-to-flux ratios as small as three to five times the critical value. At higher field intensities, the early formation of massive disks is prevented. Conclusions. Given the ubiquity of Class I disks, and because the early formation of massive disks can take place at moderate magnetic intensities, we speculate that for stronger fields, disks will form later, when most of the envelope will have been accreted. In addition, we speculate that some observed early massive disks may actually be outflow cavities, mistaken for disks by projection effects.

The relative importance of primordial molecular cloud fragmentation versus large-scale accretion still remains to be assessed in the context of massive core/star formation. Studying the kinematics of the dense gas surrounding massive-star progenitors can tell us the extent to which large-scale flow of material impacts the growth in mass of star-forming cores. Here we present a comprehensive dataset of the 5500(±800) M infrared dark cloud SDC335.579-0.272 (hereafter SDC335), which exhibits a network of cold, dense, parsec-long filaments. Atacama Large Millimeter Array (ALMA) Cycle 0 observations reveal two massive star-forming cores, MM1 and MM2, sitting at the centre of SDC335 where the filaments intersect. With a gas mass of 545( +770 −385 ) M contained within a source diameter of 0.05 pc, MM1 is one of the most massive, compact protostellar cores ever observed in the Galaxy. As a whole, SDC335 could potentially form an OB cluster similar to the Trapezium cluster in Orion. ALMA and Mopra single-dish observations of the SDC335 dense gas furthermore reveal that the kinematics of this hub-filament system are consistent with a global collapse of the cloud. These molecular-line data point towards an infall velocity V inf = 0.7(±0.2) km s −1 , and a total mass infall rateṀ inf 2.5(±1.0) × 10 −3 M yr −1 towards the central pc-size region of SDC335. This infall rate brings 750(±300) M of gas to the centre of the cloud per free-fall time (t ff = 3 × 10 5 yr). This is enough to double the mass already present in the central pc-size region in 3.5 +2.2 −1.0 × t ff . These values suggest that the global collapse of SDC335 over the past million year resulted in the formation of an early O-type star progenitor at the centre of the cloud's gravitational potential well.

Context. The formation of massive stars is a highly complex process in which it is unclear whether the star-forming gas is in global gravitational collapse or an equilibrium state supported by turbulence and/or magnetic fields. In addition, magnetic fields may play a decisive role in the star-formation process since they influence the efficiency of gas infall onto the protostar. Aims. By studying one of the most massive and dense star-forming regions in the Galaxy at a distance of less than 3 kpc, i.e. the filament containing the well-known sources DR21 and DR21(OH), we attempt to obtain observational evidence to help us to discriminate between these two views. Methods. We use molecular line data from our 13 CO 1 → 0, CS 2 → 1, and N 2 H + 1 → 0 survey of the Cygnus X region obtained with the FCRAO and high-angular resolution observations in isotopomeric lines of CO, CS, HCO + , N 2 H + , and H 2 CO, obtained with the IRAM 30 m telescope, to investigate the distribution of the different phases of molecular gas. Gravitational infall is identified by the presence of inverse P Cygni profiles that are detected in optically thick lines, while the optically thinner isotopomers are found to reach a peak in the self-absorption gap. Results. We observe a complex velocity field and velocity dispersion in the DR21 filament in which regions of the highest columndensity, i.e., dense cores, have a lower velocity dispersion than the surrounding gas and velocity gradients that are not (only) due to rotation. Infall signatures in optically thick line profiles of HCO + and 12 CO are observed along and across the whole DR21 filament. By modelling the observed spectra, we obtain a typical infall speed of ∼0.6 km s −1 and mass accretion rates of the order of a few 10 −3 M yr −1 for the two main clumps constituting the filament. These massive clumps (4900 and 3300 M at densities of around 10 5 cm −3 within 1 pc diameter) are both gravitationally contracting (with free-fall times much shorter than sound crossing times and low virial parameter α). The more massive of the clumps, DR21(OH), is connected to a sub-filament, apparently "falling" onto the clump. This filament runs parallel to the magnetic field. Conclusions. All observed kinematic features in the DR21 filament (velocity field, velocity dispersion, and infall), its filamentary morphology, and the existence of (a) sub-filament(s) can be explained if the DR21 filament was formed by the convergence of flows on large scales and is now in a state of global gravitational collapse. Whether this convergence of flows originated from self-gravity on larger scales or from other processes cannot be determined by the present study. The observed velocity field and velocity dispersion are consistent with results from (magneto)-hydrodynamic simulations where the cores lie at the stagnation points of convergent turbulent flows.

Stars form within molecular clouds but our understanding of this fundamental process remains hampered by the complexity of the physics that drives their evolution. We review our observational and theoretical knowledge of molecular clouds trying to confront the two approaches wherever possible. After a broad presentation of the cold interstellar medium and molecular clouds, we emphasize the dynamical processes with special focus to turbulence and its impact on cloud evolution. We then review our knowledge of the velocity, density and magnetic fields. We end by openings towards new chemistry models and the links between molecular cloud structure and star--formation rates.Comment: To be published in AARv, 58 pages, 13 figures (higher resolution figures will be available on line

Abstract. We present a numerical and analytical study of the thermal fragmentation of a turbulent flow of interstellar hydrogen. We first present the different dynamical processes and the large range of spatial (and temporal) scales that need to be adequately represented in numerical simulations. Next, we present bidimensional simulations of turbulent converging flows which induce the dynamical condensation of the warm neutral phase into the cold phase. We then analyse the cold structures and the fraction of unstable gas in each simulation, paying particular attention to the influence of the degree of turbulence. When the flow is very turbulent a large fraction of the gas remains in the thermally unstable domain. This unstable gas forms a filamentary network. We show that the fraction of thermally unstable gas is strongly correlated with the level of turbulence of the flow. We then develop a semi-analytical model to explain the origin of this unstable gas. This simple model is able to quantitatively reproduce the fraction of unstable gas observed in the simulations and its correlation with turbulence. Finally, we stress the fact that even when the flow is very turbulent and in spite of the fact that a large fraction of the gas is maintained dynamically in the thermally unstable domain, the classical picture of a 2-phase medium with stiff thermal fronts and local pressure equilibrium turns out to be still relevant in the vicinity of the cold structures.

Aims. In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport. Methods. The algorithm is based on a previous work in which the MUSCL-Hancock scheme was used to evolve the induction equation. In this paper, we detail the extension of this scheme to the full MHD equations and discuss its properties. Results. Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax-Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to two completely different astrophysical situations well studied in the past years: the growth of the magnetorotational instability in the shearing box and the collapse of magnetized cloud cores. Conclusions. We have implemented a new Godunov scheme to solve the ideal MHD equations in the AMR code RAMSES. We have shown that it results in a powerful tool that can be applied to a great variety of astrophysical problems, ranging from galaxies formation in the early universe to high resolution studies of molecular cloud collapse in our galaxy.

We describe a morphological imprint of magnetization found when considering the relative orientation of the magnetic field direction with respect to the density structures in simulated turbulent molecular clouds. This imprint was found using the Histogram of Relative Orientations (HRO): a new technique that utilizes the gradient to characterize the directionality of density and column density structures on multiple scales. We present results of the HRO analysis in three models of molecular clouds in which the initial magnetic field strength is varied, but an identical initial turbulent velocity field is introduced, which subsequently decays. The HRO analysis was applied to the simulated data cubes and mock-observations of the simulations produced by integrating the data cube along particular lines of sight. In the 3D analysis we describe the relative orientation of the magnetic field B with respect to the density structures, showing that: 1.The magnetic field shows a preferential orientation parallel to most of the density structures in the three simulated cubes. 2.The relative orientation changes from parallel to perpendicular in regions with density over a critical density n T in the highest magnetization case. 3.The change of relative orientation is largest for the highest magnetization and decreases in lower magnetization cases. This change in the relative orientation is also present in the projected maps. In conjunction with simulations HROs can be used to establish a link between the observed morphology in polarization maps and the physics included in simulations of molecular clouds.