The feedback form pre-main sequence and young stars influences their vicinity. The stars are formed in clusters, which implies that the winds of individual stars collide with each other. Inside of a star cluster, winds thermalize a fraction of their kinetic energy, forming a very hot medium able to escape from the cluster in the form of a large-scale wind. Outside of the cluster, the cluster wind forms a shock front as it interacts with the ambient medium which is accreted onto the expanding shell. A variety of instabilities may develop in such shells, and in some cases they fragment, triggering second generation of star formation. However, if the cluster surpasses a certain mass (depending on the radius and other parameters) the hot medium starts to be thermally unstable even inside of the cluster, forming dense warm clumps. The formation of next generations of stars may start if the clumps are big enough to self-shield against stellar radiation creating cold dense cores.

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.

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.

Recent numerical studies have focused their interest on the impact outflows have on the cloud's turbulence. The contradictory results obtained by these studies indicate that it is essential for observers to provide the required data to constrain the models. Here we discuss the impact of outflows on the environment surrounding clusters of young stellar objects, from an observer's point of view. We have conducted several studies of outflows in different active star-forming regions. In all cases it is clear that outflows have the power to sustain the observed turbulence in the gas surrounding protostellar clusters. We investigate whether there is a correlation between outflow strength and star formation efficiency, as predicted by numerical simulations, for six different regions in the Perseus molecular cloud complex. We argue that results of other recent studies that use CO line maps to study the turbulence driving length should not be used to discard outflows as major drivers of turbulence in clusters.

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.

We use numerical simulations to investigate how the expansion of an HII region is affected by an ambient magnetic field. First we consider the test problem of expansion in a uniform medium with a unidirectional magnetic field. We then describe the expansion of an HII region in a turbulent medium, taking as our initial conditions the results of and MHD turbulence simulation. We find that although in the uniform medium case the magnetic field does produce interesting effects over long length and timescales, in the turbulent medium case the main effect of the magnetic field is to reduce the efficiency of fragmentation of the molecular gas.

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.

Supernovae are the most energetic stellar events and influence the interstellar medium by their gasdynamics and energetics. By this, both also affect the star formation positively and negatively. In this paper, we review the development of the complexity of investigations aiming at understanding the interchange between supernovae and their released hot gas with the star-forming molecular clouds. Commencing from analytical studies the paper advances to numerical models of supernova feedback from superbubble scales to galaxy structure. We also discuss parametrizations of star-formation and supernova-energy transfer efficiencies. Since evolutionary models from the interstellar medium to galaxies are numerous and apply multiple recipes of these parameters, only a representative selection of studies can be discussed here.

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.

We describe an algorithm for constructing fractal molecular clouds that obeys prescribed mass and velocity scaling relations.The algorithm involves a random seed, so that many different realisations corresponding to the same fractal dimension and the same scaling relations can be generated. It first generates all the details of the density field, and then position the SPH particles, so that the same simulation can be repeated with different numbers of particles to explore convergence. It can also be used to initialise finite-difference simulations. We then present preliminary numerical simulations of Hii regions expanding into such clouds, and explore the resulting patterns of star formation. If the cloud has low fractal dimension, it already contains many small self-gravitating condensations, and the principal mechanism of star formation is radiatively driven implosion. This results in star formation occurring quite early, throughout the cloud. The stars resulting from the collapse and fragmentation of a single condensation are often distributed in a filament pointing radially away from the source of ionising radiation; as the remainder of the condensation is dispersed, these stars tend to get left behind in the Hii region. If the cloud has high fractal dimension, the cloud does not initially contain dense condensations, and star formation is therefore delayed until the expanding Hii region has swept up a sufficiently massive shell. The shell then becomes gravitationally unstable and breaks up into protostars. In this collect-and-collapse mode, the protostars are distributed in tangential arcs, they tend to be somewhat more massive, and as the expansion of the shell stalls they move ahead of the ionisation front.

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.

Galaxies cover a wide range of masses and star formation histories. In this review, I summarize some of the evolutionary key features of common galaxy types. At the high-mass end, very rapid, efficient early star formation is observed, accompanied by strong enrichment and later quiescence, well-described by downsizing scenarios. In the intermediate-mass regime, early-type galaxies may still show activity in low-mass environments or when being rejuvenated by wet mergers. In late-type galaxies, we find continuous, though variable star formation over a Hubble time. In the dwarf regime, a wide range of properties from bursty activity to quiescence is observed. Generally, stochasticity dominates here, and star formation rates and efficiencies tend to be low. Morphological types and their star formation properties correlate with environment.

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 present simulations of supersonic collisions between molecular clouds of mass 500 M⊙ and radius 2.24 pc. The simulations are performed with the SEREN SPH code. The code treats the energy equation and the associated transport of heating and cooling radiation. The formation of protostars is captured by introducing sink particles. Low velocity collisions form a shock-compressed layer which fragments to form stars. For high-velocity collisions, υrel ⪆ 5 km s−1, the non-linear thin shell instability strongly disrupts the shock-compressed layer, and may inhibit the formation of stars.

Gas materials in the inner Galactic disk continuously migrate toward the Galactic center (GC) due to interactions with the bar potential, magnetic fields, stars, and other gaseous materials. Those in forms of molecules appear to accumulate around 200 pc from the center (the central molecular zone, CMZ) to form stars there and further inside. The bar potential in the GC is thought to be responsible for such accumulation of molecules and subsequent star formation, which is believed to have been continuous throughout the lifetime of the Galaxy. We present 3-D hydrodynamic simulations of the CMZ that consider self-gravity, radiative cooling, and supernova feedback, and discuss the efficiency and role of the star formation in that region. We find that the gas accumulated in the CMZ by a bar potential of the inner bulge effectively turns into stars, supporting the idea that the stellar cusp inside the central 200 pc is a result of the sustained star formation in the CMZ. The obtained star formation rate in the CMZ, 0.03–0.1 M⊙, is consistent with the recent estimate based on the mid-infrared observations by Yusef-Zadeh et al. (2009).

Spiral structures in the disk galaxies have been extensively studied by many theoretical papers, but conventional steady-state models are not consistent with what we observe in time-dependent, multi-dimensional numerical simulations and also in real galaxies. Here we review recent progress in numerical modeling of stellar and gas spirals in disk galaxies. The spiral arms excited in a stellar disk can last for 10 Gyrs without the ISM, but each spiral arm is short-lived and is recurrently formed. The stellar spirals are not waves propagating with a single pattern speed. The ISM is concentrated in local potential minima, which roughly follow the galactic rotation together with the stellar arms, therefore galactic dust lanes are not the classic ‘galactic shocks’.

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 simulated an isolated quiescent Milky Way-type galaxy with a maximum effective resolution of 7.8 pc. Clouds formed in the interstellar medium through gravitational fragmentation and became the sites for star formation. We tracked the evolution of the clouds through 300 Myr in the presence of star formation, photoelectric heating and feedback from Type II supernovae. The cloud mass distribution agreed well with observational results. Feedback suppressed star formation but did not destroy the surrounding cloud. Collisions between clouds were found to be sufficiently frequent to be a significant factor in determining the star formation rate.

Modern hydrodynamic simulations of galaxy formation are able to predict accurately the rates and locations of the assembly of giant molecular clouds in early galaxies. These clouds could host star clusters with the masses and sizes of real globular clusters. I describe current state-of-the-art simulations aimed at understanding the origin of the cluster mass function and metallicity distribution. Metallicity bimodality of globular cluster systems appears to be a natural outcome of hierarchical formation and gradually declining fraction of cold gas in galaxies. Globular cluster formation was most prominent at redshifts z > 3, when massive star clusters may have contributed as much as 20% of all galactic star formation.

Super-star clusters are probably the largest star-forming entities in our local Universe, containing hundreds of thousands to millions of young stars usually within less than a few parsecs. While no such systems are known in the Milky Way (MW), they are found especially in pairs of interacting galaxies but also in some dwarf galaxies like R 136 in the Large Magelanic Cloud (LMC). With the use of SPH calculations we show that a natural explanation for this phenomenon is the presence of shear in normal spiral galaxies which facilitates the formation of low-density loose OB associations from giant molecular clouds (GMC) instead of dense super-star clusters. In contrast, in interacting galaxies and in dwarf galaxies, regions can collapse without having a large-scale sense of rotation. This lack of rotational support allows the giant molecular clouds to concentrate into a single, dense and gravitationally bound system.