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.

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 developed a fast numerical scheme for solving ambipolar diffusion MHD equations with the strong coupling approximation, which can be written as the ideal MHD equations with an additional ambipolar diffusion term in the induction equation. The mass, momentum, magnetic fluxes due to the ideal MHD equations can be easily calculated by any Godunov-type schemes. Additional magnetic fluxes due to the ambipolar diffusion term are added in the magnetic fluxes, because of two same spatial gradients operated on the advection fluxes and the ambipolar diffusion term. In this way, we easily kept divergence-free magnetic fields using the constraint transport scheme. In order to overcome a small time step imposed by ambipolar diffusion, we used the super time stepping method. The resultant scheme is fast and robust enough to do the long term evolution of star formation simulations. We also proposed that the decay of alfen by ambipolar diffusion be a good test problem for our codes.

The formation of high-mass stars represents a challenge from both a theoretical and an observational point of view. Here, we present an overview of the current status of the observational research on this field, outlining the progress achieved in recent years on our knowledge of the initial phases of massive star formation. The fragmentation of cold, infrared-dark clouds, and the evidence for star formation activity on some of them will be discussed, together with the kinematics of the gas in hot molecular cores, which can give us insights on the mechanism leading to the birth of an OB star.

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).

In this contribution, I briefly review our empirical knowledge of disks around ≲2M⊙ pre-main sequence (T Tauri) stars, focusing first on the dichotomic question of their frequency before moving on to some more detailed disk properties (overall orientation, total mass, outer radius). Finally, I conclude with a brief discussion of disks around embedded protostars, which will play in the next few years a major role in testing star formation theory and simulations.

Advances in available computing facilities, judiciously employed by our colleagues, have undoubtedly enhanced our understanding of the processes by which stars (and planets) form, from very diffuse gas to something you could almost live around. Nevertheless we remain very far from being able to describe (let alone explain) what is going on in many cases. And this is likely to remain true even as Moore's Law growth begins to hit its head against energy and power considerations. A large fraction of long-standing questions appear to have honest answers of the general form, “yes and no”, “all of the above”, or “some of them are and some of them aren't”. This includes many of my favorites, like triggering, formation of binary populations, and the role of magnetic fields. Rather few questions have actually been retired from the universe of discourse in recent years.

Observations show that expanding H ii regions may trigger star formation. We discuss several aspects of this type of star formation, and try to estimate its prevalence. We show how LMC H ii regions may help us to understand what we see in our Galaxy.

A large fraction of brown dwarfs and low-mass stars may form by gravitational fragmentation of relatively massive (a few 0.1 M⊙) and extended (a few hundred AU) discs around Sun-like stars. We present an ensemble of radiative hydrodynamic simulations that examine the conditions for disc fragmentation. We demonstrate that this model can explain the low-mass IMF, the brown dwarf desert, and the binary properties of low-mass stars and brown dwarfs. Observing discs that are undergoing fragmentation is possible but very improbable, as the process of disc fragmentation is short lived (discs fragment within a few thousand years).

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.

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.

We present the first results from a project to model the prestellar cores in Ophiuchus, using initial conditions constrained as closely as possible by observation. The prestellar cores in Ophiuchus appear to be evolving in isolation — in the sense that the timescale on which an individual prestellar core collapses and fragments is estimated to be much shorter than the timescale on which it is likely to interact dynamically with another core. Therefore it is realistic to simulate individual cores separately, and this in turn makes it feasible (a) to perform multiple realisations of the evolution of each core (to allow for uncertainties in the initial conditions which persist, even for the most comprehensively observed cores), and (b) to do so at high resolution (so that even the smallest protostars are well resolved). The aims of this project are (i) to address how best to convert the observations into initial conditions; (ii) to explore, by means of numerical simulations, how the observed cores are likely to evolve in the future; (iii) to predict the properties of the protostars that they will form (mass function, multiplicity statistics, etc.); and (iv) to compare these properties with the properties of the observed pre-Main Sequence stars in Ophiuchus. We find that if the observed non-thermal velocities in the Ophiuchus prestellar cores are attributed to purely solenoidal turbulence, they do not fragment; they all collapse to form single protostars. If the non-thermal velocities are attributed to a mixture of solenoidal and compressive turbulence, multiple systems form readily. The turbulence first generates a network of filaments, and material then tends to flow along the filaments, at first into a primary protostar, and then onto a compact accretion disc around this protostar; secondary protostars condense out of the material flowing into the disc along the filaments. If the turbulence is purely solenoidal, but part of the non-thermal velocity dispersion is attributed to solid-body rotation, then again multiple systems form readily, but the pattern of fragmentation is quite different. A primary protostar forms near the centre of the core, and then an extended accretion disc forms around the primary protostar, and eventually becomes so massive that it fragments to produce low-mass secondaries; these frequently end up in hierarchical multiple systems.

There have been a number of theoretical and computational models which state that magnetic fields play an important role in the process of star formation. Competing theories instead postulate that it is turbulence which is dominant and magnetic fields are weak. The recent installation of a polarimetry system at the Submillimeter Array (SMA) has enabled us to conduct observations that could potentially distinguish between the two theories. Some of the nearby low mass star forming regions show hour-glass shaped magnetic field structures that are consistent with theoretical models in which the magnetic field plays a dominant role. However, there are other similar regions where no significant polarization is detected. Future polarimetry observations made by the Submillimeter Array should be able to increase the sample of observed regions. These measurements will allow us to address observationally the important question of the role of magnetic fields and/or turbulence in the process of star formation.

This brief review emphasizes the wide range of environments where interaction induced star formation occurs. In these environments we can study the numerous elaborations of a few basic physical processes, including: gravitational instability, accretion and large-scale shocks.

At present, hydrodynamical simulations in computational star formation are either carried out with Eulerian mesh-based approaches or with the Lagrangian smoothed particle hydrodynamics (SPH) technique. Both methods differ in their strengths and weaknesses, as well as in their error properties. It would be highly desirable to find an intermediate discretization scheme that combines the accuracy advantage of mesh-based methods with the automatic adaptivity and Galilean invariance of SPH. Here we briefly describe the novel AREPO code which achieves these goals based on a moving unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order unsplit Godunov scheme with an exact Riemann solver. A particularly powerful feature is that the mesh-generating points can in principle be moved arbitrarily. If they are given the velocity of the local flow, an accurate Lagrangian formulation of continuum hydrodynamics is obtained that features a very low numerical diffusivity and is free of mesh distortion problems. If the points are kept fixed, the scheme is equivalent to a Eulerian code on a structured mesh. The new AREPO code appears especially well suited for problems such as gravitational fragmentation or compressible turbulence.

The time evolution of protostellar disks in the embedded phase of star formation (EPSF) is reviewed based on numerical hydrodynamics simulations of the gravitational collapse of two cloud cores with distinct initial masses. Special emphasis is given to disk, stellar, and envelope masses and also mass accretion rates onto the star. It is shown that accretion is highly variable in the EPSF, in agreement with recent theoretical and observational expectations. Protostellar disks quickly accumulate mass upon formation and may reach a sizeable fraction of the envelope mass (~35%) by the end of the Class 0 phase. Systems with disk-to-star mass ratio ξ≈0.5 are common but systems with ξ≥1.0 are rare because the latter quickly evolve into binary or multiple systems. Embedded disks are characterized by radial pulsations, the amplitude of which increases with growing core mass.

The interstellar medium (ISM) in galaxies is multiphase and cloudy, with stars forming in the very dense, cold gas found in Giant Molecular Clouds (GMCs). Simulating the evolution of an entire galaxy, however, is a computational problem which covers many orders of magnitude, so many simulations cannot reach densities high enough or temperatures low enough to resolve this multiphase nature. Therefore, the formation of GMCs is not captured and the resulting gas distribution is smooth, contrary to observations. We investigate how star formation (SF) proceeds in simulated galaxies when we obtain parsec-scale resolution and more successfully capture the multiphase ISM. Both major mergers and the accretion of cold gas via filaments are dominant contributors to a galaxy's total stellar budget and we examine SF at high resolution in both of these contexts.

The idea that stars are formed by gravity goes back more than 300 years to Newton, and the idea that gravitational instability plays a role goes back more than 100 years to Jeans, but the idea that stars are forming at the present time in the interstellar medium is more recent and did not emerge until the energy source of stars had been identified and it was realized that the most luminous stars have short lifetimes and therefore must have formed recently. The first suggestion that stars may be forming now in the interstellar medium was credited by contemporary authors to a paper by Spitzer in 1941 in which he talks about the formation of interstellar condensations by radiation pressure, but then oddly says nothing about star formation. That may be because, as Spitzer later told me, when he first suggested very tentatively in a paper submitted to The Astrophysical Journal that stars might be forming now from interstellar matter, this was considered a radical idea and the referee said it was much too speculative and should be taken out of the paper. So Spitzer removed the speculation about star formation from the published version of his paper.

I'll overview the past, present, and future of the GRAPE project, which started as the effort to design and develop specialized hardware for gravitational N-body problem. The current hardware, GRAPE-DR, has an architecture quite different from previous GRAPEs, in the sense that it is a collection of small, but programmable processors, while previous GRAPEs had hardwired pipelines. I'll discuss pros and cons of these two approaches, comparisons with other accelerators and future directions.