There has been considerable progress in our understanding of how massive stars form but still much confusion as to why they form. Recent work from several sources has shown that the formation of massive stars through disc accretion, possibly aided by gravitational and Rayleigh-Taylor instabilities is a viable mechanism. Stellar mergers, on the other hand, are unlikely to occur in any but the most massive clusters and hence should not be a primary avenue for massive star formation. In contrast to this success, we are still uncertain as to how the mass that forms a massive star is accumulated. there are two possible mechanisms including the collapse of massive prestellar cores and competitive accretion in clusters. At present, there are theoretical and observational question marks as to the existence of high-mass prestellar cores. theoretically, such objects should fragment before they can attain a relaxed, centrally condensed and high-mass state necessary to form massive stars. Numerical simulations including cluster formation, feedback and magnetic fields have not found such objects but instead point to the continued accretion in a cluster potential as the primary mechanism to form high-mass stars. Feedback and magnetic fields act to slow the star formation process and will reduce the efficiencies from a purely dynamical collapse but otherwise appear to not significantly alter the process.

High resolution, multi-wavelength maps of a sizeable set of nearby galaxies have made it possible to study how the surface densities of H i, H2 and star formation rate (ΣHI, ΣH2, ΣSFR) relate on scales of a few hundred parsecs. At these scales, individual galaxy disks are comfortably resolved, making it possible to assess gas-SFR relations with respect to environment within galaxies. ΣH2, traced by CO intensity, shows a strong correlation with ΣSFR and the ratio between these two quantities, the molecular gas depletion time, appears to be constant at about 2 Gyr in large spiral galaxies. Within the star-forming disks of galaxies, ΣSFR shows almost no correlation with ΣHI. In the outer parts of galaxies, however, ΣSFR does scale with ΣHI, though with large scatter. Combining data from these different environments yields a distribution with multiple regimes in Σgas – ΣSFR space. If the underlying assumptions to convert observables to physical quantities are matched, even combined datasets based on different SFR tracers, methodologies and spatial scales occupy a well define locus in Σgas – ΣSFR space.

Low-mass protostars are less luminous than expected. This luminosity problem is important because the observations appear to be inconsistent with some of the basic premises of star formation theory. Two possible solutions are that stars form slowly, which is supported by recent data, and/or that protostellar accretion is episodic; current data suggest that the latter accounts for less than half the missing luminosity. The solution to the luminosity problem bears directly on the fundamental problem of the time required to form a low-mass star. The protostellar mass and luminosity functions provide powerful tools both for addressing the luminosity problem and for testing theories of star formation. Results are presented for the collapse of singular isothermal spheres, for the collapse of turbulent cores, and for competitive accretion.

Star formation is regulated through a variety of feedback processes. In this study, we treat feedback by metal injection and a UV background as well as by X-ray irradiation. Our aim is to investigate whether star formation is significantly affected when the ISM of a proto-galaxxy enjoys different metallicities and when a star forming cloud resides in the vicinity of a strong X-ray source. We perform cosmological Enzo simulations with a detailed treatment of non-zero metallicity chemistry and thermal balance. We also perform FLASH simulations with embedded Lagrangian sink particles of a collapsing molecular cloud near a massive, 107 M⊙, black hole that produces X-ray radiation.

We find that a multi-phase ISM forms for metallicites as small as 10−4 Solar at z = 6, with higher (10−2Z⊙) metallicities supporting a cold (<100 K) and dense (>103 cm−3) phase at higher (z = 20) redshift. A star formation recipe based on the presence of a cold dense phase leads to a self-regulating mode in the presence of supernova and radiation feedback. We also find that when there is strong X-ray feedback a collapsing cloud fragments into larger clumps whereby fewer but more massive protostellar cores are formed. This is a consequence of the higher Jeans mass in the warm (50 K, due to ionization heating) molecular gas. Accretion processes dominate the mass function and a near-flat, non-Salpeter IMF results.

We review the various theories which have been proposed along the years to explain the origin of the stellar initial mass function. We pay particular attention to four models, namely the competitive accretion and the theories based respectively on stopped accretion, MHD shocks and turbulent dispersion. In each case, we derive the main assumptions and calculations that support each theory and stress their respective successes and failures or difficulties.

Star formation depends on the available gaseous “fuel” as well as galactic environment, with higher specific star formation rates where gas is predominantly molecular and where stellar (and dark matter) densities are higher. The partition of gas into different thermal components must itself depend on the star formation rate, since a steady state distribution requires a balance between heating (largely from stellar UV for the atomic component) and cooling. In this presentation, I discuss a simple thermal and dynamical equilibrium model for the star formation rate in disk galaxies, where the basic inputs are the total surface density of gas and the volume density of stars and dark matter, averaged over ~kpc scales. Galactic environment is important because the vertical gravity of the stars and dark matter compress gas toward the midplane, helping to establish the pressure, and hence the cooling rate. In equilibrium, the star formation rate must evolve until the gas heating rate is high enough to balance this cooling rate and maintain the pressure imposed by the local gravitational field. In addition to discussing the formulation of this equilibrium model, I review the current status of numerical simulations of multiphase disks, focusing on measurements of quantities that characterize the mean properties of the diffuse ISM. Based on simulations, turbulence levels in the diffuse ISM appear relatively insensitive to local disk conditions and energetic driving rates, consistent with observations. It remains to be determined, both from observations and simulations, how mass exchange processes control the ratio of cold-to-warm gas in the atomic ISM.

Protostellar outflows can inject sufficient mass, momentum, and kinetic energy into their parent star-forming clumps to dramatically alter their structure, generate turbulence, and even to disrupt them. Outflows represent the lowest rung on a ‘feedback ladder’ consisting of increasingly powerful mechanisms which kick-in if star formation escalates towards the production of more massive stars, higher efficiency, and larger clusters. Outflow feedback may dominate turbulence generation and cloud disruption on the scale of cluster-forming clumps having dimensions up to a few parsecs. Outflows inject energy and momentum on a wide-range of length-scales from less than 0.01 pc to over 30 pc. However, they fail by several orders of magnitude to inject sufficient momentum and kinetic energy to drive turbulent motions on the size and mass-scales of GMCs. Injection from higher rungs on the feedback ladder or momentum injected by Galactic-scale processes are needed to power the observed turbulence on the 10 to 100 pc scales of GMCs.

It is now well established that the majority of young stars are found in multiple systems, so that any theory of stellar formation must account for their existence and properties. Studying the properties of multiple star systems therefore represents a very powerful approach to place observational constraints on star formation theories. Additionally, multiple systems offer other advantages. They provide the most accurate and unambiguous way to measure masses, using orbital fitting and Kepler's laws, and even the stellar radius in the special case of eclipsing binaries. They also allow to compare the properties of 2 coeval objects with different masses, providing important tests for the evolutionary models.

Ambipolar diffusion (AD) is a key process in molecular clouds (MCs). Non-ideal MHD turbulence simulations are technically very challenging because of the large Alfvén speed of ions in weakly ionized clouds. Using the Heavy-Ion Approximation method (Li, McKee & Klein 2006), we have carried out two-fluid simulations of AD in isothermal, turbulent boxes at a resolution of 5123, to investigate the effect of AD on the weakly ionized turbulence in MCs. Our simulation results show that the neutral gas component of the two-fluid system gradually transforms from an ideal MHD turbulence system to near a pure hydrodynamic turbulence system within the standard AD regime, in which the neutrals and ions are coupled over a flow time. The change of the turbulent state has a profound effect on the weakly ionized MCs.

Submillimeter observations are a key for answering many of the big questions in modern-day astrophysics, such as how stars and planets form, how galaxies evolve, and how material cycles through stars and the interstellar medium. With the upcoming large submillimeter facilities ALMA and Herschel a new window will open to study these questions. ARTIST is a project funded in context of the European ASTRONET program with the aim of developing a next generation model suite for comprehensive multi-dimensional radiative transfer calculations of the dust and line emission, as well as their polarization, to help interpret observations with these groundbreaking facilities.

This work presents a new physical model of the star formation rate (SFR), tested with a large set of numerical simulations of driven, supersonic, self-gravitating, magneto-hydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, αvir, the rms sonic Mach number, S,0, and the ratio of mean gas pressure to mean magnetic pressure, β0. The SFR is predicted to decrease with increasing αvir (stronger turbulence relative to gravity), and to depend weakly on S,0 and β0, for values typical of star forming regions (S,0≈4-20 and β0≈1-20). The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. Both the value of the SFR and its dependence on the virial parameter found in the simulations agree very well with the theoretical predictions.

We review an approach to observation-theory comparisons we call “Taste-Testing.” In this approach, synthetic observations are made of numerical simulations, and then both real and synthetic observations are “tasted” (compared) using a variety of statistical tests. We first lay out arguments for bringing theory to observational space rather than observations to theory space. Next, we explain that generating synthetic observations is only a step along the way to the quantitative, statistical, taste tests that offer the most insight. We offer a set of examples focused on polarimetry, scattering and emission by dust, and spectral-line mapping in star-forming regions. We conclude with a discussion of the connection between statistical tests used to date and the physics we seek to understand. In particular, we suggest that the “lognormal” nature of molecular clouds can be created by the interaction of many random processes, as can the lognormal nature of the IMF, so that the fact that both the “Clump Mass Function” (CMF) and IMF appear lognormal does not necessarily imply a direct relationship between them.

Stars form from molecular clouds, mostly in clusters with tens to tens of thousands of members, and the mass distribution within these clusters, or the Initial Mass Function, seems to be invariable against many parameters and over a wide range of masses. However, masses are a very difficult quantity to assess, and the precision of our determinations of the IMF is systematically lower than usually quoted. I will discuss the process of determining masses from observations and the type of uncertainties associated with this process.

Feedback from photoionisation may dominate on parsec scales in massive star-forming regions. Such feedback may inhibit or enhance the star formation efficiency and sustain or even drive turbulence in the parent molecular cloud. Photoionisation feedback may also provide a mechanism for the rapid expulsion of gas from young clusters' potentials, often invoked as the main cause of ‘infant mortality’. There is currently no agreement, however, with regards to the efficiency of this process and how environment may affect the direction (positive or negative) in which it proceeds. The study of the photoionisation process as part of hydrodynamical simulations is key to understanding these issues, however, due to the computational demand of the problem, crude approximations for the radiation transfer are often employed.

We will briefly review some of the most commonly used approximations and discuss their major drawbacks. We will then present the results of detailed tests carried out using the detailed photoionisation code mocassin and the SPH+ionisation code iVINE code, aimed at understanding the error introduced by the simplified photoionisation algorithms. This is particularly relevant as a number of new codes have recently been developed along those lines.

We will finally propose a new approach that should allow to efficiently and self-consistently treat the photoionisation problem for complex radiation and density fields.

A systematic, high angular-resolution study of IR-quiet Massive Dense Cores (MDCs) of Cygnus-X in continuum and high-density molecular tracers is presented. The results are compared with the quasi-static and the dynamical evolutionary scenario. We find that the fragmentation properties are not compatible with the quasi-static, monolithic collapse scenario, nor are they entirely compatible with the formation of a cluster of mostly low-mass stars. The kinematics of MDCs shows individual velocity components appearing as coherent flows, which indicate important dynamical processes at the scale of the mass reservoir around high-mass protostars.

I review recent numerical and analytical work on the feedback from both low- and high-mass cluster stars into their gaseous environment. The main conclusions are that i) outflow driving appears capable of maintaing the turbulence in parsec-sized clumps and retarding their collapse from the free-fall rate, although there exist regions within molecular clouds, and even some examples of whole clouds, which are not actively forming stars, yet are just as turbulent, so that a more universal turbulence-driving mechanism is needed; ii) outflow-driven turbulence exhibits specific spectral features that can be tested observationally; iii) feedback plays an important role in reducing the SFR; iv) nevertheless, numerical simulations suggest feedback cannot completely prevent a net contracting motion of clouds and clumps. Therefore, an appealing source for driving the turbulence everywhere in GMCs is the accretion from the environment, at all scales. In this case, feedback's most important role may be to prevent a fraction of the gas nearest to newly formed stars from actually reaching them, thus reducing the SFE.

In this paper, we review the radiative hydrodynamics methods based upon Smoothed Particle Hydrodynamics(SPH). There are already various implementations so far, which can be categorized into three types: moment equation solvers, Monte Carlo methods, and ray-tracing schemes. These codes have been applied to various astrophysical problems including dynamics of dense proto-stellar cores, photoionization feedback of massive stars on molecular clouds, radiative feedback in the early universe, etc. Among these different methods, we focus on the ray-tracing schemes. We also describe one particular ray-tracing code RSPH in some details.

We provide a brief overview of recent advances and outstanding issues in simulations of interstellar turbulence, including isothermal models for interior structure of molecular clouds and larger-scale multiphase models designed to simulate the formation of molecular clouds. We show how self-organization in highly compressible magnetized turbulence in the multiphase ISM can be exploited in simple numerical models to generate realistic initial conditions for star formation.