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.

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.