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.

Cosmological Adaptive Mesh Refinement simulations are used to study the specific star formation rate (sSFR=SSF/Ms) history and the stellar mass fraction, fs=Ms/MT, of small galaxies, total masses MT between few × 1010 M⊙ to few ×1011 M⊙. Our results are compared with recent observational inferences that show the so-called “downsizing in sSFR” phenomenon: the less massive the galaxy, the higher on average is its sSFR, a trend seen at least since z ~ 1. The simulations are not able to reproduce this phenomenon, in particular the high inferred values of sSFR, as well as the low values of fs constrained from observations. The effects of resolution and sub-grid physics on the SFR and fs of galaxies are discussed.

The pre-stellar cores in which low mass stars form are generally well magnetized. Our simulations show that early protostellar discs are massive and experience strong magnetic torques in the form of magnetic braking and protostellar outflows. Simulations of protostellar disk formation suggest that these torques are strong enough to suppress a rotationally supported structure from forming for near critical values of mass-to-flux. We demonstrate through the use of a 3D adaptive mesh refinement code – including cooling, sink particles and magnetic fields – that one produces transient 1000 AU discs while simultaneously generating large outflows which leave the core region, carrying away mass and angular momentum. Early inflow/outflow rates suggest that only a small fraction of the mass is lost in the initial magnetic tower/jet event.

Star formation in galaxies has been suggested to depend on large-scale gravitational instability or on the pressure required to form molecular hydrogen. I present numerical models and analysis of observations in support of the gravitational instability hypothesis. I also consider whether the correlation between the surface densities of molecular hydrogen and star formation implies causation, and if so in which direction.

We present high resolution simulations on the impact of ionizing radiation on turbulent molecular clouds. The combination of hydrodynamics, gravitational forces and ionization in the tree-SPH code iVINE naturally leads to the formation of elongated filaments and clumps, which are in excellent agreement with the pillars observed around HII regions. Including gravity the formation of a second generation of low-mass stars with surrounding protostellar disks is triggered at the tips of the pillars, as also observed. A parameter study allows us to determine the physical conditions under which irregular structures form and whether they resemble large pillars or a system of small, isolated globules.

I review the progress of SPH calculations for modelling galaxies, and resolving gas dynamics on GMC scales. SPH calculations first investigated the response of isothermal gas to a spiral potential, in the absence of self gravity and magnetic fields. Surprisingly though, even these simple calculations displayed substructure along the spiral arms. Numerical tests indicate that this substructure is still present at high resolution (100 million particles, ~10 pc), and is independent of the initial particle distribution. One interpretation of the formation of substructure is that smaller clouds can agglomerate into more massive GMCs via dissipative collisions. More recent calculations have investigated how other processes, such as the thermodynamics of the ISM, and self gravity affect this simple picture. Further research has focused on developing models with a more realistic spiral structure, either by including stars, or incorporating a tidal interaction.

In this paper I relate progress in the simulation of star formation to a remarkable early (1962) paper by Fowler and Hoyle who analyzed star formation in terms of the relevant energies starting from the formation of a large (100 pc) cloud and ending with the final mass distribution of the stars. The way in which modern simulations have clarified and corrected the Fowler-Hoyle picture, and areas where we could improve our simulations, are discussed.

Most stars seem to form in clusters, but the vast majority of these clusters do not seem to survive much beyond their embedded phase. The most favoured mechanism for the early destruction of star clusters is the effect of the removal of residual gas by feedback which dramatically changes the cluster potential. The effects of feedback depend on the ratio of the masses of stars and gas, and the velocity dispersion of the stars at the onset of gas removal. As gas removal is delayed by a few Myr from star formation these crucial parameters can change significantly from their initial values. In particular, in dynamically cool and clumpy clusters, the stars will collapse to a far denser state and if they decouple from the gas then gas removal may be far less destructive than previously thought. This might well help explain the survival of very massive clusters, such as globular clusters, without the need for extremely high star formation efficiencies or initial masses far greater than their current masses.

We present simulations of stable isothermal clouds exposed to ionizing radiation from a discrete external source, and identify the conditions that lead to Radiatively Driven Implosion and Star Formation. We use the Smoothed Particle Hydrodynamics code SEREN (Hubber et al. 2010) and the HEALPix-based photoionization algorithm described in Bisbas et al. (2009). We find that the incident ionizing flux is the critical parameter determining the evolution; high fluxes disperse the cloud, whereas low fluxes trigger star formation. We find a clear connection between the intensity of the incident flux and the parameters of star formation.

I provide a pedagogic review of adaptive mesh refinement (AMR) radiation hydrodynamics (RHD) methods and codes used in simulations of star formation, at a level suitable for researchers who are not computational experts. I begin with a brief overview of the types of RHD processes that are most important to star formation, and then I formally introduce the equations of RHD and the approximations one uses to render them computationally tractable. I discuss strategies for solving these approximate equations on adaptive grids, with particular emphasis on identifying the main advantages and disadvantages of various approximations and numerical approaches. Finally, I conclude by discussing areas ripe for improvement.

Extinction maps at 8μm from the Spitzer Space Telescope show that many Class 0 protostars exhibit complex, irregular, and non-axisymmetric structure within the densest regions of their dusty envelopes. Many of the systems have highly irregular and non-axisymmetric morphologies on scales ~1000 AU, with a quarter of the sample exhibiting filamentary or flattened dense structures. Complex envelope structure is observed in regions spatially distinct from outflow cavities, and the densest structures often show no systematic alignment perpendicular to the cavities. We suggest that the observed envelope complexity is the result of collapse from protostellar cores with initially non-equilibrium structures. The striking non-axisymmetry in many envelopes could provide favorable conditions for the formation of binary systems. We then show that the kinematics around L1165 as probed with N2H+ are indicative of asymmetric infall; the velocity gradient is not perpendicular to the outflow.

We studied the formation process of star clusters using high-resolution N-body/smoothed particle hydrodynamics simulations of colliding galaxies. The total number of particles is 1.2×108 for our high resolution run. The gravitational softening is 5 pc and we allow gas to cool down to ~10 K. During the first encounter of the collision, a giant filament consists of cold and dense gas found between the progenitors by shock compression. A vigorous starburst took place in the filament, resulting in the formation of star clusters. The mass of these star clusters ranges from 105−8M⊙. These star clusters formed hierarchically: at first small star clusters formed, and then they merged via gravity, resulting in larger star clusters.

We use images derived from collapsing, turbulent molecular cloud simulations without sinks to explore the effects of finite image angular resolution and noise on the derived clump mass function. These effects randomly perturb the clump masses, producing a lognormal clump mass function with a Salpeter-like high mass end. We show that the characteristic break mass of the simulated clump mass functions changes with the angular resolution of the images in a way that is entirely consistent with the observations. We also present some cautionary tales regarding sink particles and highlight the need to ensure that sinks actually correspond to distinct collapsing objects. We test several popular numerical sink criteria in the literature and compare to converged, non-sink results.

We present the first results of a large suite of convergence tests between Adaptive Mesh Refinement (AMR) Finite Difference Hydrodynamics and Smoothed Particle Hydrodynamics (SPH) simulations of the non-linear thin shell instability and the Kelvin-Helmholtz instability. We find that the two methods converge in the limit of high resolution and accuracy. AMR and SPH simulations of the non-linear thin shell instability converge with each other with standard algorithms and parameters. The Kelvin-Helmholtz instability in SPH requires both an artificial conductivity term and a kernel with larger compact support and more neighbours (e.g. the quintic kernel) in order converge with AMR. For purely hydrodynamical problems, SPH simulations take an order of magnitude longer than the grid code when converged.

I review what has been learnt so far regarding the origin of stellar properties from numerical simulations of the formation of groups and clusters of stars. In agreement with observations, stellar properties are found to be relatively robust to variations of initial conditions in terms of molecular cloud structure and kinetics, as long as extreme initial conditions (e.g. strong central condensation, weak or no turbulence) and small-scale driving are avoided, but properties may differ between bound and unbound clouds. Radiative feedback appears crucial for setting stellar masses, even for low-mass stars, while magnetic fields can provide low star formation rates.