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’.

We implemented sink particles in the Adaptive Mesh Refinement (AMR) code FLASH to model the gravitational collapse and accretion in turbulent molecular clouds and cores. Sink particles are frequently used to measure properties of star formation in numerical simulations, such as the star formation rate and efficiency, and the mass distribution of stars. We show that only using a density threshold for sink particle creation is insufficient in case of supersonic flows, because the density can exceed the threshold in strong shocks that do not necessarily lead to local collapse. Additional physical collapse indicators have to be considered. We apply our AMR sink particle module to the formation of a star cluster, and compare it to a Smoothed Particle Hydrodynamics (SPH) code with sink particles. Our comparison shows encouraging agreement of gas and sink particle properties between the AMR and SPH code.

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.

We present radiation hydrodynamics simulations of the collapse of massive pre-stellar cores. We treat frequency dependent radiative feedback from stellar evolution and accretion luminosity at a numerical resolution down to 1.27 AU. In the 2D approximation of axially symmetric simulations, it is possible for the first time to simulate the whole accretion phase of several 105 yr for the forming massive star and to perform a comprehensive scan of the parameter space. Our simulation series show evidently the necessity to incorporate the dust sublimation front to preserve the high shielding property of massive accretion disks. Our disk accretion models show a persistent high anisotropy of the corresponding thermal radiation field, yielding to the growth of the highest-mass stars ever formed in multi-dimensional radiation hydrodynamics simulations. Non-axially symmetric effects are not necessary to sustain accretion. The radiation pressure launches a stable bipolar outflow, which grows in angle with time as presumed from observations. For an initial mass of the pre-stellar host core of 60, 120, 240, and 480⊙ the masses of the final stars formed in our simulations add up to 28.2, 56.5, 92.6, and at least 137.2⊙ respectively.

GAMER is a GPU-accelerated Adaptive-MEsh-Refinement code for astrophysical simulations. In this work, two further extensions of the code are reported. First, we have implemented the MUSCL-Hancock method with the Roe's Riemann solver for the hydrodynamic evolution, by which the accuracy, overall performance and the GPU versus CPU speed-up factor are improved. Second, we have implemented the out-of-core computation, which utilizes the large storage space of multiple hard disks as the additional run-time virtual memory and permits an extremely large problem to be solved in a relatively small-size GPU cluster. The communication overhead associated with the data transfer between the parallel hard disks and the main memory is carefully reduced by overlapping it with the CPU/GPU computations.

Information of astronomical objects is obtained mainly through their radiation. Thus, the radiative transfer problem has a central role in all astrophysical research. Basic radiative transfer analysis or more complex modeling is needed both to interpret observations and to make predictions on the basis of numerical models. In this paper I will discuss radiative transfer in the context of interstellar molecular clouds where the main scientific questions involve the structure and evolution of the clouds and the star formation process. The studies rely on the analysis of spectral line and dust continuum observations. After a discussion of the corresponding radiative transfer methods, I will examine some of the current challenges in the field. Finally, I will present three studies where radiative transfer modeling pays a central role: the polarized dust emission, the Zeeman effect in emission lines, and the continuum emission from dense cloud cores.

It is possible to extract, from the observations, distribution functions of the birth dynamical properties of a stellar population, and to also infer that these are quite invariant to the physical conditions of star formation. The most famous example is the stellar IMF, and the initial binary population (IBP) seems to follow suit. A compact mathematical formulation of the IBP can be derived from the data. It has three broad parts: the IBP of the dominant stellar population (0.08–2M⊙), the IBP of the more-massive stars and the IBP of brown dwarfs. These three mass regimes correspond to different physical regimes of star formation but not to structure in the IMF. With this formulation of the IBP it becomes possible to synthesize the stellar-population of whole galaxies.

We briefly review ground-based (sub)millimeter dust continuum observations of the prestellar core mass function (CMF) and its connection to the stellar initial mass function (IMF). We also summarize the first results obtained on this topic from the Herschel Gould Belt survey, one of the largest key projects with the Herschel Space Observatory. Our early findings with Herschel confirm the existence of a close relationship between the CMF and the IMF. Furthermore, they suggest a scenario according to which the formation of prestellar cores occurs in two main steps: 1) complex networks of long, thin filaments form first, probably as a result of interstellar MHD turbulence; 2) the densest filaments then fragment and develop prestellar cores via gravitational instability.

Graphics Processing Units (GPUs) offer a new way to accelerate numerical calculations by means of on-board massive parallelisation. We discuss two examples of GPU implementation relevant for cosmological simulations, an N-Body Particle-mesh solver and a radiative transfer code. The latter has also been ported on multi-GPU clusters. The range of acceleration (x30-x80) achieved here offer bright perspective for large scale simulations driven by GPUs.

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.

Stars form in the densest regions of clouds of cold molecular hydrogen. Measuring structure in these clouds is far from trivial as 99% of the mass of a molecular cloud is inaccessible to direct observation. Over the last decade we have been developing an alternative, more robust density tracer technique based on dust extinction measurements towards background starlight. The new technique does not suffer from the complications plaguing the more conventional molecular line and dust emission techniques, and when used with these can provide unique views on cloud chemistry and dust grain properties in molecular clouds. In this brief communication we summarize the main results achieved so far using this technique.

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.

This contribution contains the introductory remarks that I presented at IAU Symposium 270 on “Computational Star Formation” held in Barcelona, Spain, May 31–June 4, 2010. I discuss the historical development of numerical MHD methods in astrophysics from a personal perspective. The recent advent of robust, higher-order accurate MHD algorithms and adaptive mesh refinement numerical simulations promises to greatly improve our understanding of the role of magnetic fields in star formation.

The study of the internal structure of star clusters provides important clues concerning their formation mechanism and dynamical evolution. There are both observational and numerical evidences indicating that open clusters evolve from an initial clumpy structure, presumably a direct consequence of the formation in a fractal medium, toward a centrally condensed state. This simple picture has, however, several drawbacks. There can be very young clusters exhibiting radial patterns maybe reflecting the early effect of gravity on primordial gas. There can be also very evolved clusters showing fractal patterns that either have survived through time or have been generated subsequently by some (unknown) mechanism. Additionally, the fractal structure of some open clusters is much clumpier than the average structure of the interstellar medium in the Milky Way, although in principle a very similar structure should be expected. Here we summarize and discuss observational and numerical results concerning this subject.

Radiative feedback and magnetic field are understood to have a strong impact on the protostellar collapse. We present high resolution numerical calculations of the collapse of a 1 M⊙ dense core in solid body rotation, including both radiative transfer and magnetic field. Using typical parameters for low-mass cores, we study thoroughly the effect of radiative transfer and magnetic field on the first core formation and fragmentation. We show that including the two aforementioned physical processes does not correspond to the simple picture of adding them separately. The interplay between the two is extremely strong, via the magnetic braking and the radiation from the accretion shock.

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.

Solving radiative transfer problems with ray casting methods is compared with the commonly used ‘Flux Limited Diffusion’ approximation. Whereas ray casting produces solutions that converge to the exact one as the number of rays is increased, flux-limited-diffusion is fundamentally a ‘look-alike’ method, which produces solutions that are reminiscent of the correct solution but which cannot be made to converge to it.

In star forming regions, we can observe different evolutionary stages of various objects and phenomena such as molecular clouds, protostellar jets and outflows, circumstellar disks, and protostars. However, it is difficult to directly observe the star formation process itself, because it is veiled by the dense infalling envelope. Numerical simulations can unveil the star formation process in the collapsing gas cloud. Recently, some studies showed protostar formation from the prestellar core stage, in which both molecular clouds and protostars are resolved with sufficient spatial resolution. These simulations showed fragmentation and binary formation, outflow and jet driving, and circumstellar disk formation in the collapsing gas clouds. In addition, the angular momentum transfer and dissipation process of the magnetic field in the star formation process were investigated. In this paper, I review recent developments in numerical simulations of low-mass star formation.

Using the AMR code ENZO we are simulating the formation of massive star clusters within turbulent Giant Molecular Clouds (GMCs). Here we discuss the simulations from the first stages of building realistic turbulent GMCs, to accurate star formation, and ultimately comprehensive feedback. These simulations aim to build a better understanding of how stars affect GMCs, helping to answer the questions of how long GMCs live and why only a small fraction of the GMC gas becomes stars.