Galaxy formation and evolution is one of the most challenging tasks in astrophysics. There is strongly increasing and substantial progress in this field not only due to the increase of telescope size and developments of new techniques providing observations allover the electromagnetic spectrum, but also the development of advanced computer architectures and of sophisticated numerical codes allow to tackle this problem from both sides and to link both research approaches to a fruitful progress in astrophysics. This review will not focus on the application of a single numerical method and the description of its result, but is instead aiming at providing an overview of different numerical tools on the basis of particle and grid schemes and to referring to important publications for the intersted reader.

In this brief review I sum up some recent progress in the area of stellar dynamics, focusing on the dynamics of self-bound stellar associations in isolation and in (approximate) equilibrium. The basics of stellar dynamics are first outlined and the importance of stellar evolution is stressed. Subsequently I argue that the evolution of multi-mass clusters in the point-mass approximation still holds clues to the dynamics of galaxy nuclei. I take a more personal standpoint when discussing the role of stellar evolution on the dynamics over relaxation time scales and draw from several recent models to underscore that a major step forward has been made in the coupling of stellar evolution and dynamics. I then briefly visit the issue of multiple stars and highlight some as yet unsolved problems.

Observing nearby interacting galaxies is a key to understanding galactic physics provided that we know the spatial and temporal perturbations acting on these galaxies. Thus, we have to know the orbits and the gross internal properties of the galaxies. In order to cope with the related extended parameter space, we developed the code MINGA which combines a genetic algorithm with a fast N-body method. As an example for this method, we present a re-analysis of the prototypical system NGC 4449 which is now based on both, the full HI data cube of the NGC 4449 system and on improved determinations of the galactic orbits within a restricted N-body calculation.

Motivated by the closest major merger, the Antennae Galaxies (NGC4038/4039), we want to improve our genetic algorithm based modeling code Minga (Theis 1999). The aim is to reveal the major interaction and galaxy parameters, e.g. orbital information and halo properties of such an equal mass merger system. Together with the sophisticated search strategy of Minga, one needs fast and reliable models in order to investigate the high dimensional parameter space of this problem. Therefore we use a restricted N-body code which is based on the approach by Toomre & Toomre (1972), however with some refinements like consistent orbits of extended dark matter halos. Recently also dynamical friction was included to this code (Petsch 2007). While a good description for dynamical friction was found for mass ratios up to q = 1/3 (Petsch & Theis 2008), major merger systems were only imperfectly remodeled. Here we show recent improvements for a major merger system by including mass-loss and using NFW halos.

We describe some results obtained with N-MODY, a code for N-body simulations of collisionless stellar systems in modified Newtonian dynamics (MOND). We found that a few fundamental dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter. In particular, violent relaxation, phase mixing and galaxy merging take significantly longer in MOND than in Newtonian gravity, while dynamical friction is more effective in a MOND system than in an equivalent Newtonian system with dark matter.

We aim to study of the formation and evolution of galaxies with high spatial and temporal resolution. We describe a new chemodynamical code to describe the physical interplay between the stars and the multiphase interstellar medium in galaxies, including a dust component. Preliminary results can be found in Champavert (2007).

We study the proximity effect around high redshift quasars in dependence on the quasar redshift and environment using 3D continuum radiative transfer simulations. Snapshots of dark matter only simulations at redshift 3, 4, and 4.9 are mapped to hydrogen densities and temperatures using an effective equation of state. The overionization zone around QSOs with luminosities LνHI = 1031and1032   ergHz-1s-1 is studied in a UV background field in radiation equilibrium. By analyzing synthetic spectra of lines of sight originating at the QSO, the proximity effect is studied. We find that the quasar spectral energy distribution, diffusion and shadowing due to Lyman Limit systems play a role in the signal. Density inhomogeneities around the QSO are responsible for a large scatter around the mean proximity effect seen in all simulated QSO spectra. This scatter is larger than the differences arising from varying quasar host environments.

We performed cosmological simulations based upon both a cold dark matter (CDM) and a warm dark matter (WDM) model. The focus of our investigations lies with selected spatial and kinematic properties of substructure halos (subhalos) orbiting within host halos, that form in both dark-matter cosmologies. We aim at using the dynamics of the subhalos as a probe of the respective cosmology.

Using a set of high-resolution dark matter only cosmological simulations we found a correlation between the dark matter halo mass M and its spin parameter λ for objects forming at redshifts z > 10: the spin parameter decreases with increasing mass. However, halos forming at later times do not exhibit such a strong correlation, in agreement with the findings of previous studies.

While we presented such a correlation in a previous study using the Bullock et al. (2001) spin parameter defintion we now defer to the classical definition showing that the results are independent of the definition.

We present a novel solver for an analogue to Poisson’s equation in the framework of modified Newtonian dynamics (MOND). This equation is highly non-linear and hence standard codes based upon tree structures and/or FFT’s in general are not applicable; one needs to defer to multi-grid relaxation techniques. We present results from the first cosmological simulations we made to compare cosmological structure formation of in the two paradigms. We found compatible results between the two simulations, at least at redshift z = 0.

Hot, underdense bubbles powered by active galactic nuclei (AGN) are likely to play a key role in halting catastrophic cooling in the centers of cool-core galaxy clusters. We present three-dimensional simulations that capture the evolution of such bubbles, using an adaptive-mesh hydrodynamic code, FLASH3, to which we have added a subgrid model of turbulence and mixing. Pure-hydro simulations indicate that AGN bubbles are disrupted into resolution-dependent pockets of underdense gas. However, proper modeling of subgrid turbulence shows that Rayleigh-Taylor instabilities act to mix the heated regions with their surroundings, while at the same time preserving them as coherent structures, consistent with observations. Thus bubbles are transformed into hot clouds of mixed material as they move outwards in the hydrostatic intracluster medium. Properly capturing the evolution of such clouds has important implications for many ICM properties.

Recently, the MID-infrared Interferometric instrument (MIDI) at the VLTI has shown that dust tori in the two nearby Seyfert galaxies NGC 1068 and the Circinus galaxy are geometrically thick and can be well described by a thin, warm central disk, surrounded by a colder and fluffy torus component. By carrying out hydrodynamical simulations with the help of the TRAMP code (Klahr et al. 1999), we follow the evolution of a young nuclear star cluster in terms of discrete mass-loss and energy injection from stellar processes. This naturally leads to a filamentary large scale torus component, where cold gas is able to flow radially inwards. The filaments join into a dense and very turbulent disk structure. In a post-processing step, we calculate spectral energy distributions and images with the 3D radiative transfer code MC3D Wolf (2003) and compare them to observations. Turbulence in the dense disk component is investigated in a separate project.

Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Analytical models based on the uncorrelated-ensemble approach predicted that any created field will be expelled from the disk before a significant amplification can occur. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for vertical stratification and galactic differential rotation, we find an exponential amplification of the mean field on timescales of 100 Myr. We highlight the importance of rotation in the generation of helicity by showing that a similar mechanism based on Cartesian shear does not lead to a sustained amplification of the mean magnetic field.

We present a numerical study on the behavior of the density power spectrum resulting from compressible hydrodynamic, thermally unstable simulations with different rms Mach numbers Mrms. We find that the spectrum becomes shallower as M increases and that spectral index values that are consistent with those reported from observations.

Stars can be seen as modern physics laboratory from which fundamental processes as diverse as atomic physics or turbulence can be studied and understood. Being able to model accurately their structure, dynamic and evolution is thus of fundamental importance and is the subject of intense research. In this short review we will present some of the numerical simulations in three dimensions performed in recent years to model such complex and nonlinear objects, focussing mostly our discussion on results obtained with the anelastic spherical harmonic (ASH) code. Using the Sun as a reference star, we wish to gain insight and to constrain magnetohydrodynamical processes (such as Reynolds and Maxwell stresses, meridional circulations, differential rotation (i.e. ω-effect), thermal wind, α-effect) at the origin of the solar small and large scale dynamics and magnetism. We will then extend our study to other stars, such as young Suns, massive stars or evolved RGB stars in order to identify which processes are at the origin of their significantly different dynamics.

The ANTARES code (A Numerical Tool for Astrophysical RESearch) is designed for doing 1D, 2D and 3D stellar (radiation-, magneto-) hydrodynamics with realistic microphysics, applying various high-resolution numerical schemes, optionally local grid refinement and works with rectilinear or spherical coordinates. – We present results on turbulent solar granulation flows which have been done in 2D and 3D and comment on our simulations of the pulsation-convection interaction in Cepheid variables, presently 2D.

Our paper intends to estimate the EUV dimming appearing in a prominence eruption into a coronal mass ejection from the observationally point of few and so well from a numerical model. We have performed a numerical MHD simulation on a solar radius and obtained a CME originating from a prominence. The mass dimming was revealed clearly and we compared the mass evolution of the CME to that of an event observed on 14 January 2001 by SOHO.

To explain important properties of extrasolar planetary systems (e.g. close-in hot Jupiters, resonant planets) an evolutionary scenario which allows for radial migration of planets in disks is required. During their formation protoplanets undergo a phase in which they are embedded in the disk and interact gravitationally with it. This planet-disk interaction results in torques (through gravitational forces) acting on the planet that will change its angular momentum and result in a radial migration of the planet through the disk. To determine the outcome of this very important process for planet formation, dedicated high resolution numerical modeling is required. This contribution focusses on some important aspects of the numerical approach that we found essential for obtaining successful results. We specifically mention the treatment of Coriolis forces, Cartesian grids, and the FARGO method.

We investigate the influence of radiative transport on the growth of the magnetorotational instability (MRI) in accretion discs. A general dispersion relation describing the growth of small disturbances on a homogeneous background shear flow is provided. It includes compressibility and radiative effects in the flux-limited diffusion approximation. All the effects of radiation transport can be subsumed into one single parameter, an effective speed of sound. Radiative diffusion does not affect the region where the MRI operates, but it alters the growth rates of the MRI either by increasing or decreasing them. We report about corresponding numerical simulations, which are also used for a first investigation of the non-linear stage of the MRI in gas-pressure dominated accretion discs with radiation transport included.