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The post-inflationary Universe can pass through a long epoch of effective matter-dominated expansion. This era may allow for both the parametric amplification of initial fluctuations and the gravitational collapse of inflaton perturbations. We perform first-of-their-kind high-resolution simulations that span the resonant phase and the subsequent gravitational collapse of the inflaton field by seguing from a full Klein-Gordon treatment of resonance to a computationally efficient Schrödinger-Poisson description that accurately captures the gravitational dynamics when most quanta are nonrelativistic. We consider a representative example in which resonance generates $\mathcal{O}(10^{-1})$ overdensities and gravitational collapse follows promptly as resonance ends. We observe the formation of solitonic cores inside inflaton halos and complex gravitational dynamics on scales of $10^{-27}\,\mathrm{m}$, greatly extending the possible scope of nonlinear post-inflationary gravitational dynamics.

Following inflation, the Universe may pass through an early matter-dominated phase supported by the oscillating inflaton condensate. Initially small fluctuations in the condensate grow gravitationally on subhorizon scales and can collapse to form nonlinear ``inflaton halos''. Their formation and subsequent tidal interactions will source gravitational waves, resulting in a stochastic background in the present Universe. We extend N-body simulations that model the growth and interaction of collapsed structures to compute the resulting gravitational wave emission. The spectrum of this radiation is well-matched by semi-analytical estimates based on the collapse of inflaton halos and their tidal evolution. We use this semi-analytic formalism to infer the spectrum for scenarios where the early matter-dominated phase gives way to a thermalized universe at temperatures as low as $100\,\mathrm{MeV}$ and we discuss the possible experimental opportunities created by this signal in inflationary models in which thermalization takes place long after inflation has completed.

Primordial magnetic fields (PMFs) are possible candidates for explaining the observed magnetic fields in galaxy clusters. Two competing scenarios of primordial magnetogenesis have been discussed in the literature: inflationary and phase-transitional. We study the amplification of both large- and small-scale correlated magnetic fields, corresponding to inflation- and phase transition-generated PMFs, in a massive galaxy cluster. We employ high-resolution magnetohydrodynamic cosmological zoom-in simulations to resolve the turbulent motions in the intracluster medium. We find that the turbulent amplification is more efficient for the large-scale inflationary models, while the phase transition-generated seed fields show moderate growth. The differences between the models are imprinted on the spectral characteristics of the field (such as the amplitude and the shape of the magnetic power spectrum) and therefore on the final correlation length. We find a one order of magnitude difference between the final strengths of the inflation- and phase transition-generated magnetic fields, and a factor of 1.5 difference between their final coherence scales. Thus, the final configuration of the magnetic field retains information about the PMF generation scenarios. Our findings have implications for future extragalactic Faraday rotation surveys with the possibility of distinguishing between different magnetogenesis scenarios.

The Peak-Patch algorithm is used to identify the densest minicluster seeds in the initial axion density field simulated from string decay. The fate of these dense seeds is found by tracking the subsequent gravitational collapse in cosmological $N$-body simulations. We find that miniclusters at late times are well described by NFW profiles, although for around 80\% of simulated miniclusters a single power-law density profile of $r^{-2.9}$ is an equally good fit due to the unresolved scale radius. Under the assumption that all miniclusters with an unresolved scale radius are described by a power-law plus axion star density profile, we identify a significant number of miniclusters that might be dense enough to give rise to gravitational microlensing if the axion mass is $0.2 \,\mathrm{meV}\lesssim m_a \lesssim 3\,\mathrm{meV}$. Higher resolution simulations resolving the inner structure and axion star formation are necessary to explore this possibility further.

The Universe may pass through an effectively matter-dominated epoch between inflation and Big Bang Nucleosynthesis during which gravitationally bound structures can form on subhorizon scales. In particular, the inflaton field can collapse into inflaton halos, forming "large scale" structure in the very early universe. We combine N-body simulations with high-resolution zoom-in regions in which the non-relativistic Schrödinger-Poisson equations are used to resolve the detailed, wave-like structure of inflaton halos. Solitonic cores form inside them, matching structure formation simulations with axion-like particles in the late-time universe. We denote these objects \textitinflaton stars, by analogy with boson stars. Based on a semi-analytic formalism we compute their overall mass distribution which shows that some regions will reach overdensities of $10^{15}$ if the early matter-dominated epoch lasts for 20 $e$-folds. The radii of the most massive inflaton stars can shrink below the Schwarzschild radius, suggesting that they could form primordial black holes prior to thermalization.

Fuzzy dark matter (FDM) made of ultra-light bosonic particles is a viable alternative to cold dark matter (CDM) with clearly distinguishable small-scale features in collapsed structures. On large scales, it behaves gravitationally like CDM deviating only by a cut-off in the initial power spectrum and can be studied using N-body methods. In contrast, wave interference effects near the de Broglie scale result in new phenomena unique to FDM. Interfering modes in filaments and halos yield a stochastically oscillating granular structure which condenses into solitonic cores during halo formation. Investigating these highly non-linear wave phenomena requires the spatially resolved numerical integration of the Schrödinger equation. In previous papers we introduced a hybrid zoom-in scheme that combines N-body methods to model the large-scale gravitational potential around and the mass accretion onto pre-selected halos with simulations of the Schrödinger-Poisson equation to capture wave-like effects inside these halos. In this work, we present a new, substantially improved reconstruction method for the wave function inside of previously collapsed structures. We demonstrate its capabilities with a deep zoom-in simulation of a well-studied sub-$L_\ast$-sized galactic halo from cosmological intitial conditions. With a particle mass of $m = 2.5\times 10^{-22}\,$eV and halo mass $M_{\text{vir}}=1.7\times 10^{11}\,M_{\odot}$ in a ($60$h${^{-1}}$ comoving Mpc)${}^{3}$ cosmological box, it reaches an effective resolution of 20 comoving pc. This pushes the values of $m$ and $M$ accessible to simulations significantly closer to those relevant for studying galaxy evolution in the allowed range of FDM masses.

The early Universe may have passed through an extended period of matter-dominated expansion following inflation and prior to the onset of radiation domination. Sub-horizon density perturbations grow gravitationally during such an epoch, collapsing into bound structures if it lasts long enough. The strong analogy between this phase and structure formation in the present-day universe allows the use of N-body simulations and approximate methods for halo formation to model the fragmentation of the inflaton condensate into inflaton halos. For a simple model we find these halos have masses of up to $20\,\mathrm{kg}$ and radii of the order of $10^{-20}\,\mathrm{m}$, roughly $10^{-24}$ seconds after the Big Bang. We find that the N-body halo mass function matches predictions of the mass-Peak Patch method and the Press-Schechter formalism within the expected range of scales. A long matter-dominated phase would imply that reheating and thermalization occurs in a universe with large variations in density, potentially modifying the dynamics of this process. In addition, large overdensities can source gravitational waves and may lead to the formation of primordial black holes.

This work studies the formation and growth of boson stars and their surrounding miniclusters by gravitational condensation using non-linear dynamical numerical methods. Fully dynamical attractive and repulsive self-interactions are also considered for the first time. In the case of pure gravity, we numerically prove that the growth of boson stars inside halos slows down and saturates as has been previously conjectured, and detail its conditions. Self-interactions are included using the Gross-Pitaevskii-Poisson equations. We find that in the case of strong attractive self-interactions the boson stars can become unstable and collapse, in agreement with previous stationary computations. At even stronger coupling, the condensate fragments. Repulsive self-interactions, as expected, promote boson star formation, and lead to solutions with larger radii.

The distinctive effects of fuzzy dark matter are most visible at non-linear galactic scales. We present the first simulations of mixed fuzzy and cold dark matter, obtained with an extended version of the Nyx code. Fuzzy (or ultralight, or axion-like) dark matter dynamics are governed by the comoving Schrödinger-Poisson equation. This is evolved with a pseudospectral algorithm on the root grid, and with finite differencing at up to six levels of adaptive refinement. Cold dark matter is evolved with the existing N-body implementation in Nyx. We present the first investigations of spherical collapse in mixed dark matter models, focusing on radial density profiles, velocity spectra and soliton formation in collapsed halos. We find that the effective granule masses decrease in proportion to the fraction of fuzzy dark matter which quadratically suppresses soliton growth, and that a central soliton only forms if the fuzzy dark matter fraction is greater than 10\%. The Nyx framework supports baryonic physics and key astrophysical processes such as star formation. Consequently, AxioNyx will enable increasingly realistic studies of fuzzy dark matter astrophysics.

Axion-like particle (ALP) dark matter shows distinctive behavior on scales where wavelike effects dominate over self-gravity. Ultralight axions are candidates for fuzzy dark matter (FDM) whose de Broglie wavelength in virialized halos reaches scales of kiloparsecs. Important features of FDM scenarios are the formation of solitonic halo cores, suppressed small-scale perturbations, and enhanced gravitational relaxation. More massive ALPs, including the QCD axion, behave like CDM on galactic scales but may be clumped into axion miniclusters if they were produced after inflation. Just as FDM halos, axion miniclusters may host the formation of coherent bound objects (axion stars) by Bose-Einstein condensation. This article presents a selection of topics in this field that are currently under active investigation.

We study the gravitational collapse of axion dark matter fluctuations in the post-inflationary scenario, so-called axion miniclusters, with N-body simulations. Largely confirming theoretical expectations, overdensities begin to collapse in the radiation-dominated epoch and form an early distribution of miniclusters with masses up to $10^{-12}\,M_\odot$. After matter-radiation equality, ongoing mergers give rise to a steep power-law distribution of minicluster halo masses. The density profiles of well-resolved halos are NFW-like to good approximation. The fraction of axion dark matter in these bound structures is $\sim 0.75$ at redshift $z=100$.

We present zoom-in simulations of fuzzy dark matter (FDM) halos including baryons and star-formation with sufficient resolution to follow the formation and evolution of central solitons. We find that their properties are determined by the local dark matter velocity dispersion in the combined dark matter-baryon gravitational potential. This motivates a simple prescription to estimate the radial density profiles of FDM cores in the presence of baryons. As cores become more massive and compact if baryons are included, galactic rotation curve measurements are likely harder to reconcile with FDM.

In a broad class of scenarios, inflation is followed by an extended era of matter-dominated expansion during which the inflaton condensate is nonrelativistic on subhorizon scales. During this phase density perturbations grow to the point of nonlinearity and collapse into bound structures. This epoch strongly resembles structure formation with ultra-light axion-like particles. This parallel permits us to adapt results from studies of cosmological structure formation to describe the nonlinear dynamics of this post-inflationary epoch. We show that the inflaton condensate fragments into "inflaton clusters", analogues of axion dark matter halos in present-day cosmology. Moreover, solitonic objects or "inflaton stars" can form inside these clusters, leading to density contrasts as large as $10^6$ in the post-inflationary universe.

We study the formation and the subsequent mass growth of axion stars inside axion miniclusters. Numerically solving the Schrödinger-Poisson equations with realistic initial conditions we find that the axion stars exhibit similar properties to solitonic cores in ultralight bosonic dark matter halos in terms of their radial density profiles and large-amplitude oscillations. A merger of two axion stars confirms a previously found empirical law for the mass of the merged axion star. Monitoring the axion star masses over time, we observe a mass growth consistent with the mass increase of Bose stars in the kinetic regime reported by Levkov et al., confirming that the mass evolution of axion stars can be understood in terms of wave condensation. Based on this result, we predict a saturation of mass growth in relation to the minicluster mass consistent with the core-halo mass relation previously found for ultra-light bosonic dark matter halos.

The fuzzy dark matter (FDM) model treats DM as a bosonic field with astrophysically large de Broglie wavelength. A striking feature of this model is $\mathcal{O}(1)$ fluctuations in the dark matter density on time scales which are shorter than the gravitational timescale. Including for the first time the effect of core oscillations, we demonstrate how such fluctuations lead to heating of star clusters, and thus an increase in their size over time. From the survival of the old star cluster in Eridanus II we infer $m_a\gtrsim 0.6\rightarrow 1\times 10^{-19}\text{ eV}$ within modelling uncertainty if FDM is to compose all of the DM, and derive constraints on the FDM fraction at lower masses. The subhalo mass function in the Milky Way implies $m_a\gtrsim 0.8\times 10^{-21}\text{ eV}$ to successfully form Eridanus II. The window between $10^{-21}\text{ eV}\lesssim m_a\lesssim 10^{-20}\text{ eV}$ is affected by narrow band resonances, and the limited applicability of the diffusion approximation. Some of this window may be consistent with observations of Eridanus II and more detailed investigations are required.

Axions are a potential dark matter candidate, which may condense and form self gravitating compact objects, called axion stars (ASs). In this work, we study for the first time head-on collisions of relativistic ASs with black holes (BHs) and neutron stars (NSs). In the case of BH-AS mergers we find that, in general, the largest scalar clouds are produced by mergers of low compactness ASs and spinning BHs. Although in most of the cases which we study the majority of the mass is absorbed by the BH within a short time after the merger, in favourable cases the remaining cloud surrounding the final BH remnant can be as large as 30% of the initial axion star mass, with a bosonic cloud mass of order ~ 0.1 M_BH and peak energy density comparable to that obtained in a superradiant build up. This provides a dynamical mechanism for the formation of long lived scalar hair, which could lead to observable signals in cases where the axion interacts with baryonic matter around the BH, or where it forms the seed of a future superradiant build up in highly spinning cases. Considering NS-AS collisions we find two possible final states (i) a BH surrounded by a (small) scalar cloud, or (ii) a stable NS enveloped in an axion cloud of roughly the same mass as the initial AS. Whilst for low mass ASs the NS is only mildly perturbed by the collision, a larger mass AS gives rise to a massive ejection of baryonic mass from the system, purely due to gravitational effects. Therefore, even in the absence of a direct axion coupling to baryonic matter, NS-AS collisions could give rise to electromagnetic observables in addition to their gravitational wave signatures.

Axions are increasingly favoured as a candidate particle for the dark matter in galaxies, since they satisfy the observational requirements for cold dark matter and are theoretically well motivated. Fluctuations in the axion field give rise to stable localised overdensities known as axion stars, which, for the most massive, compact cases, are potential neutron star mimickers. In principle, there are no fundamental arguments against the multi-messenger observations of GW170817/GRB170817A/AT2017gfo arising from the merger of a neutron star with a neutron star mimicker, rather than from a binary neutron star. To constrain this possibility and better understand the astrophysical signatures of a neutron star--axion star (NSAS) merger, we present in this work a detailed example case of a NSAS merger based on full 3D numerical relativity simulations, and give an overview of the many potential observables - ranging from gravitational waves, to optical and near-infrared electromagnetic signals, radio flares, fast radio bursts, gamma ray bursts, and neutrino emission. We discuss the individual channels and estimate to which distances current and future observatories might be able to detect such a NSAS merger. Such signals could constrain the unknown axion mass and its couplings to standard baryonic matter,thus enhancing our understanding of the dark matter sector of the Universe.

We simulate the formation and evolution of ultralight bosonic dark matter halos from cosmological initial conditions. Using zoom-in techniques we are able to resolve the detailed interior structure of the halos. We observe the formation of solitonic cores and confirm the core-halo mass relation previously found by Schive et al. The cores exhibit strong quasi-normal oscillations that remain largely undamped on evolutionary timescales. On the other hand, no conclusive growth of the core mass by condensation or relaxation can be detected. In the incoherent halo surrounding the cores, the scalar field density profiles and velocity distributions show no significant deviation from collisionless N-body simulations on scales larger than the coherence length. Our results are consistent with the core properties being determined mainly by the coherence length at the time of virialization, whereas the Schrödinger-Vlasov correspondence explains the halo properties when averaged on scales greater than the coherence length.

We study tidal stripping of fuzzy dark matter (FDM) subhalo cores using simulations of the Schrödinger-Poisson equations and analyze the dynamics of tidal disruption, highlighting the differences with standard cold dark matter. Mass loss outside of the tidal radius forces the core to relax into a less compact configuration, lowering the tidal radius. As the characteristic radius of a solitonic core scales inversely with its mass, tidal stripping results in a runaway effect and rapid tidal disruption of the core once its central density drops below $4.5$ times the average density of the host within the orbital radius. Additionally, we find that the core is deformed into a tidally locked ellipsoid with increasing eccentricities until it is completely disrupted. Using the core mass loss rate, we compute the minimum mass of cores that can survive several orbits for different FDM particle masses and compare it with observed masses of satellite galaxies in the Milky Way.

Lyman-$\alpha$ emitters (LAEs) are a promising probe of the large-scale structure at high redshift, $z\gtrsim 2$. In particular, the Hobby-Eberly Telescope Dark Energy Experiment aims at observing LAEs at 1.9 $<z<$ 3.5 to measure the Baryon Acoustic Oscillation (BAO) scale and the Redshift-Space Distortion (RSD). However, Zheng et al. (2011) pointed out that the complicated radiative transfer (RT) of the resonant Lyman-$\alpha$ emission line generates an anisotropic selection bias in the LAE clustering on large scales, $s\gtrsim 10$ Mpc. This effect could potentially induce a systematic error in the BAO and RSD measurements. Also, Croft et al. (2016) claims an observational evidence of the effect in the Lyman-$\alpha$ intensity map, albeit statistically insignificant. We aim at quantifying the impact of the Lyman-$\alpha$ RT on the large-scale galaxy clustering in detail. For this purpose, we study the correlations between the large-scale environment and the ratio of an apparent Lyman-$\alpha$ luminosity to an intrinsic one, which we call the `observed fraction', at $2<z<6$. We apply our Lyman-$\alpha$ RT code by post-processing the full Illustris simulations. We simply assume that the intrinsic luminosity of the Lyman-$\alpha$ emission is proportional to the star formation rate of galaxies in Illustris, yielding a sufficiently large sample of LAEs to measure the anisotropic selection bias. We find little correlations between large-scale environment and the observed fraction induced by the RT, and hence a smaller anisotropic selection bias than what was claimed by Zheng et al. (2011). We argue that the anisotropy was overestimated in the previous work due to the insufficient spatial resolution: it is important to keep the resolution such that it resolves the high density region down to the scale of the interstellar medium, $\sim1$ physical kpc. (abridged)

Major mergers are considered to be a significant source of turbulence in clusters. We performed a numerical simulation of a major merger event using nested-grid initial conditions, adaptive mesh refinement, radiative cooling of primordial gas, and a homogeneous ultraviolet background. By calculating the microscopic viscosity on the basis of various theoretical assumptions and estimating the Kolmogorov length from the turbulent dissipation rate computed with a subgrid-scale model, we are able to demonstrate that most of the warm-hot intergalactic medium can sustain a fully turbulent state only if the magnetic suppression of the viscosity is considerable. Accepting this as premise, it turns out that ratios of turbulent and thermal quantities change only little in the course of the merger. This confirms the tight correlations between the mean thermal and non-thermal energy content for large samples of clusters in earlier studies, which can be interpreted as second self-similarity on top of the self-similarity for different halo masses. Another long-standing question is how and to which extent turbulence contributes to the support of the gas against gravity. From a global perspective, the ratio of turbulent and thermal pressures is significant for the clusters in our simulation. On the other hand, a local measure is provided by the compression rate, i.e. the growth rate of the divergence of the flow. Particularly for the intracluster medium, we find that the dominant contribution against gravity comes from thermal pressure, while compressible turbulence effectively counteracts the support. For this reason it appears to be too simplistic to consider turbulence merely as an effective enhancement of thermal energy.

In the context of structure formation with ultralight axion dark matter, we offer an alternative explanation for the mass relation of solitonic cores and their host halos observed in numerical simulations. Our argument is based entirely on the mass gain that occurs during major mergers of binary cores and largely independent of the initial core-halo mass relation assigned to hosts that have just collapsed. We find a relation between the halo mass $M_h$ and corresponding core mass $M_c$, $M_c\propto M_h^{2\beta-1}$, where $(1-\beta)$ is the core mass loss fraction. Following the evolution of core masses in stochastic merger trees, we find empirical evidence for our model. Our results are useful for statistically modeling the effects of dark matter cores on the properties of galaxies and their substructures in axion dark matter cosmologies.

We derive the halo mass function (HMF) for fuzzy dark matter (FDM) by solving the excursion set problem explicitly with a mass-dependent barrier function, which has not been done before. We find that compared to the naive approach of the Sheth--Tormen HMF for FDM, our approach has a higher cut off mass and the cut off mass changes less strongly with redshifts. Using merger trees constructed with a modified version of the Lacey & Cole formalism that accounts for suppressed small scale power and the scale-dependent growth of FDM haloes and the semi-analytic GALACTICUS code, we study the statistics of halo substructure including the effects from dynamical friction and tidal stripping. We find that if the dark matter is a mixture of cold dark matter (CDM) and FDM, there will be a suppression on the halo substructure on small scales which may be able to solve the Missing Satellites Problem faced by the pure CDM model. The suppression becomes stronger with increasing FDM fraction or decreasing FDM mass. Thus, it may be used to constrain the FDM model.

We study cosmological structure formation with ultralight axion dark matter, or "fuzzy dark matter (FDM), using a particle-mesh scheme to account for the quantum pressure arising in the Madelung formulation of the Schrödinger-Poisson equations. Subpercent-level energy conservation and correct linear behavior are demonstrated. Whereas the code gives rise to the same core-halo profiles as direct simulations of the Schrödinger equation, it does not reproduce the detailed interference patterns. In cosmological simulations with FDM initial conditions, we find a maximum relative difference of O($10\%$) in the power spectrum near the quantum Jeans length compared to using a standard N-body code with identical initial conditions. This shows that the effect of quantum pressure during nonlinear structure formation cannot be neglected for precision constraints on a dark matter component consisting of ultralight axions.

Using three-dimensional simulations, we study the dynamics and final structure of merging solitonic cores predicted to form in ultra-light axion dark matter halos. The classical, Newtonian equations of motion of a self-gravitating scalar field are described by the Schrödinger-Poisson equations. We investigate mergers of ground state (boson star) configurations with varying mass ratios, relative phases, orbital angular momenta and initial separation with the primary goal to understand the mass loss of the emerging core by gravitational cooling. Previous results showing that the final density profiles have solitonic cores and NFW-like tails are confirmed. In binary mergers, the final core mass does not depend on initial phase difference or angular momentum and only depends on mass ratio, total initial mass, and total energy of the system. For non-zero angular momenta, the otherwise spherical cores become rotating ellipsoids. The results for mergers of multiple cores are qualitatively identical.

The gas in galaxy clusters is heated by shock compression through accretion (outer shocks) and mergers (inner shocks). These processes additionally produce turbulence. To analyse the relation between the thermal and turbulent energies of the gas under the influence of non-adiabatic processes, we performed numerical simulations of cosmic structure formation in a box of 152 Mpc comoving size with radiative cooling, UV background, and a subgrid scale model for numerically unresolved turbulence. By smoothing the gas velocities with an adaptive Kalman filter, we are able to estimate bulk flows toward cluster cores. This enables us to infer the velocity dispersion associated with the turbulent fluctuation relative to the bulk flow. For halos with masses above $10^{13}\,M_\odot$, we find that the turbulent velocity dispersions averaged over the warm-hot intergalactic medium (WHIM) and the intracluster medium (ICM) are approximately given by powers of the mean gas temperatures with exponents around 0.5, corresponding to a roughly linear relation between turbulent and thermal energies and transonic Mach numbers. However, turbulence is only weakly correlated with the halo mass. Since the power-law relation is stiffer for the WHIM, the turbulent Mach number tends to increase with the mean temperature of the WHIM. This can be attributed to enhanced turbulence production relative to dissipation in particularly hot and turbulent clusters.

We propose an anisotropic generalisation of the line correlation function (ALCF) to separate and quantify phase information in the large-scale structure of galaxies. The line correlation function probes the strictly non-linear regime of structure formation and since phase information drops out of the power spectrum, the line correlation function provides a complementary tool to commonly used techniques based on two-point statistics. Furthermore, it is independent of linear bias as well as the Gaussian variance on the modulus of the density field and thus may also prove to be advantageous compared to the bispectrum or similar higher-order statistics for certain cases. For future applications it is vital, though, to be able to account for observational effects that cause anisotropies in the distribution of galaxies. Based on a number of numerical studies, we find that our ALCF is well suited to accomplish this task and we demonstrate how the Alcock-Paczynski effect and kinematical redshift-space distortions can in principle be measured via the ALCF.

We present a subgrid-scale model for the Multi-phase Interstellar medium, Star formation, and Turbulence (MIST) and explore its behaviour in high-resolution large-eddy simulations of isolated disc galaxies. MIST follows the evolution of a clumpy cold and a diffuse warm component of the gas within a volume element which exchange mass and energy via various cooling, heating and mixing processes. The star formation rate is dynamically computed from the state of the gas in the cold phase. An important feature of MIST is the treatment of unresolved turbulence in the two phases and its interaction with star formation and feedback by supernovae. This makes MIST a particularly suitable model for the interstellar medium in galaxy simulations. We carried out a suite of simulations varying fundamental parameters of our feedback implementation. Several observational properties of galactic star formation are reproduced in our simulations, such as an average star formation efficiency ~1%, a typical velocity dispersion around ~10 km/s in star-forming regions, and an almost linear relationship between the column densities of star formation and dense molecular gas.

We investigate the radiative transfer of Lyman alpha photons through simplified anisotropic gas distributions, which represent physically motivated extensions of the popular 'shell-models'. Our study is motivated by the notion that (i) shell models do not always reproduce observed Lyman alpha spectral line profiles, (ii) (typical) shell models do not allow for the escape of ionizing photons, and (iii) the observation & expectation that winds are more complex, anisotropic phenomena. We examine the influence of inclination on the Lyman alpha spectra, relative fluxes and escape fractions. We find the flux to be enhanced/suppressed by factors up to a few depending on the parameter range of the models, corresponding to a boost in equivalent width of the same amplitude if we neglect dust. In general, lower mean optical depths tend to reduce the impact of anisotropies as is expected. We find a correlation between an observed peak in the -- occasionally triple-peaked -- spectrum at the systemic velocity and the existence of a low optical depth cavity along the line of sight. This can be of importance in the search for ionizing photons leaking from high- redshift galaxies since these photons will also be able to escape through the cavity.

Baryonic streaming motions produced prior to the epoch of recombination became supersonic during the cosmic dark ages. Various studies suggest that such streaming velocities change the halo statistics and also influence the formation of Population III stars. In this study, we aim to explore the impact of streaming velocities on the formation of supermassive black holes at $z>10$ via the direct collapse scenario. To accomplish this goal, we perform cosmological large eddy simulations for two halos of a few times $\rm 10^{7} M_{\odot}$ with initial streaming velocities of 3, 6 and 9 $\rm km/s$. These massive primordial halos illuminated by the strong Lyman Werner flux are the potential cradles for the formation of direct collapse seed black holes. To study the evolution for longer times, we employ sink particles and track the accretion for 10,000 years. Our findings show that higher streaming velocities increase the circular velocities from about 14 $\rm km/s$ to 16 $\rm km/s$. They also delay the collapse of halos for a few million years, but do not have any significant impact on the halo properties such as turbulent energy, radial velocity, density and accretion rates. Sink particles of about $\rm \sim 10^5 M_{\odot}$ are formed at the end of our simulations and no clear distribution of sink masses is observed in the presence of streaming motions. It is further found that the impact of streaming velocities is less severe in massive halos compared to the minihalos as reported in the previous studies.

We investigate turbulence generated by cosmological structure formation by means of large eddy simulations using adaptive mesh refinement. In contrast to the widely used implicit large eddy simulations, which resolve a limited range of length scales and treat the effect of turbulent velocity fluctuations below the grid scale solely by numerical dissipation, we apply a subgrid-scale model for the numerically unresolved fraction of the turbulence energy. For simulations with adaptive mesh refinement, we utilize a new methodology that allows us to adjust the scale-dependent energy variables in such a way that the sum of resolved and unresolved energies is globally conserved. We test our approach in simulations of randomly forced turbulence, a gravitationally bound cloud in a wind, and the Santa Barbara cluster. To treat inhomogeneous turbulence, we introduce an adaptive Kalman filtering technique that separates turbulent velocity fluctuations on resolved length scales from the non-turbulent bulk flow. From the magnitude of the fluctuating component and the subgrid-scale turbulence energy, a total turbulent velocity dispersion of several 100 km/s is obtained for the Santa Barbara cluster, while the low-density gas outside the accretion shocks is nearly devoid of turbulence. The energy flux through the turbulent cascade and the dissipation rate predicted by the subgrid-scale model correspond to dynamical time scales around 5 Gyr, independent of numerical resolution.

Black holes of a billion solar masses are observed in the infant universe a few hundred million years after the Big Bang. The direct collapse of protogalactic gas clouds in primordial halos with $\rm T_{vir} \geq 10^{4} K$ provides the most promising way to assemble massive black holes. In this study, we aim to determine the characteristic mass scale of seed black holes and the time evolution of the accretion rates resulting from the direct collapse model. We explore the formation of supermassive black holes via cosmological large eddy simulations (LES) by employing sink particles and following their evolution for twenty thousand years after the formation of the first sink. As the resulting protostars were shown to have cool atmospheres in the presence of strong accretion, we assume here that UV feedback is negligible during this calculation. We confirm this result in a comparison run without sinks. Our findings show that black hole seeds with characteristic mass of $\rm 10^{5} M_{\odot}$ are formed in the presence of strong Lyman Werner flux which leads to an isothermal collapse. The characteristic mass is a about two times higher in LES compared to the implicit large eddy simulations (ILES). The accretion rates increase with time and reach a maximum value of 10 $\rm M_{\odot}/yr$ after $\rm 10^{4}$ years. Our results show that the direct collapse model is clearly feasible as it provides the expected mass of the seed black holes.

Population III stars forming in the infant universe at z=30 heralded the end of the cosmic dark ages. They are presumed to be assembled in so-called minihaloes with virial temperatures of a few thousand K where collapse is triggered by molecular hydrogen cooling. A central question concerns their final masses, and whether fragmentation occurs during their formation. While studies employing Lagrangian codes suggest fragmentation via a self-gravitating disk, recent high resolution simulations indicated that disk formation is suppressed. Here we report the first high-resolution large-eddy simulations performed with the Eulerian grid-based code Enzo following the evolution beyond the formation of the first peak, to investigate the accretion of the central massive clump and potential fragmentation. For a total of 3 halos, we see that a disk forms around the first clump. The central clump reaches $\sim10$ solar masses after 40 years, while subsequent accretion is expected at a rate of $10^{-2}$ solar masses per year. In one of these halos, additional clumps form as a result of fragmentation which proceeds at larger scales. We note that subgrid-scale turbulence yields relevant contributions to the stability of the protostellar disks. We conclude that the first protostar may reach masses up to $\rm 40-100 M_{\odot}$, which are only limited by the effect of radiative feedback.

We investigate the correlations between the observed fraction of Lyman alpha emission from star-forming galaxies and the large scale structure by post-processing snapshots of a large, high resolution hydrodynamical simulation with a Lyman alpha radiative transfer code at redshifts z=4, 3, 2. We find correlations of the observed fraction with density, density gradient along the line of sight, velocity and velocity gradient along the line of sight, all within the same order of magnitude (tens of percent). Additionally, a correlation with the angular momentum of the dark matter halo is detected. In contrast to a previous study, we find no significant deformation of the 2-point correlation function due to selection effects from radiative transfer in the IGM within the limited statistics of the simulation volume.

Supermassive black holes with up to a $\rm 10^{9}~M_{\odot}$ dwell in the centers of present-day galaxies, and their presence has been confirmed at z $\geq$ 6. Their formation at such early epochs is still an enigma. Different pathways have been suggested to assemble supermassive black holes in the first billion years after the Big Bang. Direct collapse has emerged as a highly plausible scenario to form black holes as it provides seed masses of $\rm 10^{5}-10^{6}~M_{\odot}$. Gravitational collapse in atomic cooling haloes with virial temperatures T$_{vir} \geq 10^{4}$~K may lead to the formation of massive seed black holes in the presence of an intense background UV flux. Turbulence plays a central role in regulating accretion and transporting angular momentum. We present here the highest resolution cosmological large-eddy simulations to date which track the evolution of high-density regions on scales of $0.25$~AU beyond the formation of the first peak, and study the impact of subgrid-scale turbulence. The peak density reached in these simulations is $\rm 1.2 \times 10^{-8}~g~cm^{-3}$. Our findings show that while fragmentation occasionally occurs, it does not prevent the growth of a central massive object resulting from turbulent accretion and occasional mergers. The central object reaches $\rm \sim 1000~M_{\odot}$ within $4$ free-fall times, and we expect further growth up to $\rm 10^{6}~M_{\odot}$ through accretion in about 1 million years. The direct collapse model thus provides a viable pathway of forming high-mass black holes at early cosmic times.

We derive oscillatory signals in correlation functions in two-field open inflation by means of the in-in formalism; such signatures are caused by resonances between oscillations in the tunnelling field and fluctuations in the inflaton during the curvature dominated, intermediate and subsequent inflationary regime. While amplitudes are model-dependent, we find distinct oscillations in the power and bi-spectrum that can act as a direct probe of the curvature dominated phase and thus, indirectly, strengthen the claim of the string landscape if they were observed. We comment on the prospects of detecting these tell-tale signs in current experiments, which is challenging, but not impossible. At the technical level, we pay special attention to the applicability conditions for truncation fluctuations to the light (inflaton) field and derive upper limits on the oscillation amplitude of the heavy field. A violation of these bounds requires a multi-field analysis at the perturbed level.

The Square Kilometre Array (SKA) is the most ambitious radio telescope ever planned. With a collecting area of about a square kilometre, the SKA will be far superior in sensitivity and observing speed to all current radio facilities. The scientific capability promised by the SKA and its technological challenges provide an ideal base for interdisciplinary research, technology transfer, and collaboration between universities, research centres and industry. The SKA in the radio regime and the European Extreme Large Telescope (E-ELT) in the optical band are on the roadmap of the European Strategy Forum for Research Infrastructures (ESFRI) and have been recognised as the essential facilities for European research in astronomy. This "White Paper" outlines the German science and R&D interests in the SKA project and will provide the basis for future funding applications to secure German involvement in the Square Kilometre Array.

While present standard model of cosmology yields no clear prediction for the initial magnetic field strength, efficient dynamo action may compensate for initially weak seed fields via rapid amplification. In particular, the small-scale dynamo is expected to exponentially amplify any weak magnetic field in the presence of turbulence. We explore whether this scenario is viable using cosmological magneto-hydrodynamics simulations modeling the formation of the first galaxies, which are expected to form in so-called atomic cooling halos with virial temperatures $\rm T_{vir} \geq 10^{4}$ K. As previous calculations have shown that a high Jeans resolution is needed to resolve turbulent structures and dynamo effects, our calculations employ resolutions of up to 128 cells per Jeans length. The presence of the dynamo can be clearly confirmed for resolutions of at least 64 cells per Jeans length, while saturation occurs at approximate equipartition with turbulent energy. As a result of the large Reynolds numbers in primordial galaxies, we expect saturation to occur at early stages, implying magnetic field strengths of \sim0.1 $\mu$G at densities of 10^4 cm^-3.

We explore the amplification of magnetic fields in the high-redshift Universe. For this purpose, we perform high-resolution cosmological simulations following the formation of primordial halos with \sim10^7 M_solar, revealing the presence of turbulent structures and complex morphologies at resolutions of at least 32 cells per Jeans length. Employing a turbulence subgrid-scale model, we quantify the amount of unresolved turbulence and show that the resulting turbulent viscosity has a significant impact on the gas morphology, suppressing the formation of low-mass clumps. We further demonstrate that such turbulence implies the efficient amplification of magnetic fields via the small-scale dynamo. We discuss the properties of the dynamo in the kinematic and non-linear regime, and explore the resulting magnetic field amplification during primordial star formation. We show that field strengths of \sim10^-5 G can be expected at number densities of \sim5 cm^-3.

Atomic cooling haloes with virial temperatures $\rm T_{vir} \geq 10^{4}$ K are the most plausible sites for the formation of the first galaxies and the first intermediate mass black holes. It is therefore important to assess whether one can obtain robust results concerning their main properties from numerical simulations. A major uncertainty is the presence of turbulence, which is barely resolved in cosmological simulations. We explore the latter both by pursuing high-resolution simulations with up to 64 cells per Jeans length and by incorporating a subgrid-scale turbulence model to account for turbulent pressure and viscosity on unresolved scales. We find that the main physical quantities in the halo, in particular the density, temperature and energy density profile, are approximately converged. However, the morphologies in the central 500 AU change significantly with increasing resolution and appear considerably more turbulent. In a systematic comparison of three different haloes, we further found that the turbulence subgrid-scale model gives rise to more compact central structures, and decreases the amount of vorticity. Such compact morphologies may in particular favor the accretion onto the central object.

FEARLESS (Fluid mEchanics with Adaptively Refined Large Eddy SimulationS) is a numerical scheme for modelling subgrid-scale turbulence in cosmological adaptive mesh refinement simulations. In this contribution, the main features of this tool will be outlined. We discuss the application of this method to cosmological simulations of the large-scale structure. The simulations show that the production of turbulence has a different redshift dependence in the intra-cluster medium and the warm-hot intergalactic medium, caused by the distinct stirring mechanisms (mergers and shock interactions) acting in them. Some properties of the non-thermal pressure support in the two baryon phases are also described.

The injection and evolution of turbulence in the intergalactic medium is studied by means of mesh-based hydrodynamical simulations, including a subgrid scale (SGS) model for small-scale unresolved turbulence. The simulations show that the production of turbulence has a different redshift dependence in the intracluster medium (ICM) and the warm-hot intergalactic medium (WHIM). We show that turbulence in the ICM is produced chiefly by merger-induced shear flows, whereas the production in the WHIM is dominated by shock interactions. Secondly, the effect of dynamical pressure support on the gravitational contraction has been studied. This turbulent support is stronger in the WHIM gas at baryon overdensities 1 < delta < 100, and less relevant for the ICM. Although the relative mass fraction of the gas with large vorticity is considerable (52% in the ICM), we find that for only about 10% in mass this is dynamically relevant, namely not associated to an equally large thermal pressure support. According to this result, a significant non-thermal pressure support counteracting the gravitational contraction is a localised characteristic in the cosmic flow, rather than a widespread feature.

Context: The thermal instability is one of the dynamical agents for turbulence in the diffuse interstellar medium, where both, turbulence and thermal instability interact in a highly non-linear manner. Aims: We study basic properties of turbulence in thermally bistable gas for variable simulation parameters. The resulting cold gas fractions can be applied as parameterisation in simulations on galactic scales. Methods: Turbulent flow is induced on large scales by means of compressive stochastic forcing in a periodic box. The compressible Euler equations with constant UV heating and a parameterised cooling function are solved on uniform grids. We investigate several values of the mean density of the gas and different magnitudes of the forcing. For comparison with other numerical studies, solenoidal forcing is applied as well. Results: After a transient phase, we observe that a state of statistically stationary turbulence is approached. Compressive forcing generally produces a two-phase medium, with a decreasing fraction of cold gas for increasing forcing strength. This behaviour can be explained on the basis of turbulent mixing. We also find indications for power-law tails of probability density functions of the gas density. Solenoidal forcing, on the other hand, appears to prevent the evolution into a two-phase-medium for certain parameter regions. Conclusions: The dynamics of thermally bistable turbulence shows a substantial sensitivity on the initial state and the forcing properties.

In a landscape of compactifications with different numbers of macroscopic dimensions, it is possible that our universe has nucleated from a vacuum where some of our four large dimensions were compact while other, now compact, directions were macroscopic. From our perspective, this shapeshifting can be perceived as an anisotropic background spacetime. As an example, we present a model where our universe emerged from a tunneling event which involves the decompactification of two dimensions compactified on the two-sphere. In this case, our universe is of the Kantowski-Sachs type and therefore homogeneous and anisotropic. We study the deviations from statistical isotropy of the Cosmic Microwave Background induced by the anisotropic curvature, with particular attention to the anomalies. The model predicts a quadrupolar power asymmetry with the same sign and acoustic oscillations as found by WMAP. The amplitude of the effect is however too small given the current estimated bound on anisotropic curvature derived from the quadrupole.

The delayed detonation model describes the observational properties of the majority of type Ia supernovae very well. Using numerical data from a three-dimensional deflagration model for type Ia supernovae, the intermittency of the turbulent velocity field and its implications on the probability of a deflagration-to-detonation (DDT) transition are investigated. From structure functions of the turbulent velocity fluctuations, we determine intermittency parameters based on the log-normal and the log-Poisson models. On the other hand, the analysis of the turbulent velocity fluctuations in the vicinity of the flame front by Roepke suggests a much higher probability of large velocity fluctuations on the grid scale in comparison to the log-normal intermittency model. Following Pan et al., we computed probability density functions for a DDT for the different distributions. Assuming that a DDT can occur in the stirred flame regime, as proposed by Woosley et al., the log-normal model would imply a delayed detonation between 0.7 and 0.8 seconds after the beginning of the deflagration phase for the multi-spot ignition scenario used in the simulation. However, the probability drops to virtually zero if a DDT is further constrained by the requirement that the turbulent velocity fluctuations reach about 500 km/s. Under this condition, delayed detonations are only possible if the distribution of the velocity fluctuations is not log-normal. From our calculations follows that the distribution obtained by Roepke allow for multiple DDTs around 0.8 seconds after ignition at a transition density close to 1x10^7 g/cm^3.

Context: Turbulent deflagrations of Chandrasekhar mass White Dwarfs are commonly used to model Type Ia Supernova explosions. In this context, rapid rotation of the progenitor star is plausible but has so far been neglected. Aims: The aim of this work is to explore the influence of rapid rotation on the deflagration scenario. Methods: We use three dimensional hydrodynamical simulations to model turbulent deflagrations ignited within a variety of rapidly rotating CO WDs obeying rotation laws suggested by accretion studies. Results: We find that rotation has a significant impact on the explosion. The flame develops a strong anisotropy with a preferred direction towards the stellar poles, leaving great amounts of unburnt matter along the equatorial plane. Conclusions: The large amount of unburnt matter is contrary to observed spectral features of SNe Ia. Thus, rapid rotation of the progenitor star and the deflagration scenario are incompatible in order to explain SNe Ia.

Context: Superluminous type Ia supernovae (SNe Ia) may be explained by super-Chandrasekhar-mass explosions of rapidly rotating white dwarfs (WDs). In a preceding paper, we showed that the deflagration scenario applied to rapidly rotating WDs generates explosions that cannot explain the majority of SNe Ia. Aims: Rotation of the progenitor star allows super-Chandrasekhar-mass WDs to form that have a shallower density stratification. We use simple estimates of the production of intermediate and iron group elements in pure detonations of rapidly rotating WDs to assess their viability in explaining rare SNe Ia. Methods: We numerically construct WDs in hydrostatic equilibrium that rotate according to a variety of rotation laws. The explosion products are estimated by considering the density stratification and by evaluating the result of hydrodynamics simulations. Results: We show that a significant amount of intermediate mass elements is produced for theoretically motivated rotation laws, even for prompt detonations of WDs. Conclusions: Rapidly rotating WDs that detonate may provide an explanation of rare superluminous SNe Ia in terms of both burning species and explosion kinematics.

FEARLESS (Fluid mEchanics with Adaptively Refined Large Eddy SimulationS) is a new numerical scheme arising from the combined use of subgrid scale (SGS) model for turbulence at the unresolved length scales and adaptive mesh refinement (AMR) for resolving the large scales. This tool is especially suitable for the study of turbulent flows in strongly clumped media. In this contribution, the main features of FEARLESS are briefly outlined. We then summarize the main results of FEARLESS cosmological simulations of galaxy cluster evolution. In clusters, the production of turbulence is closely correlated with merger events; for minor mergers, we find that turbulent dissipation affects the cluster energy budget only locally. The level of entropy in the cluster core is enhanced in FEARLESS simulations, in accord with a better modeling of the unresolved flow, and with its feedback on the resolved mixing in the ICM.

We present a numerical scheme for modelling unresolved turbulence in cosmological adaptive mesh refinement codes. As a first application, we study the evolution of turbulence in the intra-cluster medium and in the core of a galaxy cluster. Simulations with and without subgrid scale model are compared in detail. Since the flow in the ICM is subsonic, the global turbulent energy contribution at the unresolved length scales is smaller than 1% of the internal energy. We find that the production of turbulence is closely correlated with merger events occurring in the cluster environment, and its dissipation locally affects the cluster energy budget. Because of this additional source of dissipation, the core temperature is larger and the density is smaller in the presence of subgrid scale turbulence than in the standard adiabatic run, resulting in a higher entropy core value.

In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In particular, we provide semi-analytic and numerical results for the modified nucleation rate in FLRW backgrounds, as well as a parameter study of bubble walls propagating into inhomogeneous (LTB) or FLRW spacetimes, both in the thin-wall approximation. We show that in our model, matter in the background often prevents bubbles from successful expansion and forces them to collapse. For cases where they do expand, we give arguments why the effects on the interior spacetime are small for a wide range of reasonable parameters and discuss the limitations of the employed approximations.

Colliding flows are a commonly used scenario for the formation of molecular clouds in numerical simulations. Due to the thermal instability of the warm neutral medium, turbulence is produced by cooling. We carry out a two-dimensional numerical study of such colliding flows in order to test whether statistical properties inferred from adaptive mesh refinement (AMR) simulations are robust with respect to the applied refinement criteria. We compare probability density functions of various quantities as well as the clump statistics and fractal dimension of the density fields in AMR simulations to a static-grid simulation. The static grid with 2048^2 cells matches the resolution of the most refined subgrids in the AMR simulations. The density statistics is reproduced fairly well by AMR. Refinement criteria based on the cooling time or the turbulence intensity appear to be superior to the standard technique of refinement by overdensity. Nevertheless, substantial differences in the flow structure become apparent. In general, it is difficult to separate numerical effects from genuine physical processes in AMR simulations.

We reconsider the dark matter problem in supersymmetric models with gauge mediated supersymmetry breaking, with and without R-parity breaking. In these classes of models, a light gravitino forms the dark matter.Consistency with the experimental data, in particular the dark matter abundance and the small-scale power spectrum, requires additional entropy production after the decoupling of the gravitino from the thermal bath. We demonstrate that the usual mechanism via messenger number violating interactions does not work in models where the messenger belongs to SU (5) representations. This is mainly a consequence of two facts: (i) there are at least two different types of lightest messenger particles and (ii) the lightest messenger particle with SU (2) quantum numbers decays dominantly into vector bosons once messenger number is broken, a feature which has been overlooked so far. In case of SO(10) messenger multiplets we find scenarios which work if the SM gauge singlet component is rather light.

We analyze the statistical properties of the turbulent velocity field in the deflagration model for Type Ia supernovae. In particular, we consider the question of whether turbulence is isotropic and consistent with the Kolmogorov theory at small length scales. Using numerical data from a high-resolution simulation of a thermonuclear supernova explosion, spectra of the turbulence energy and velocity structure functions are computed. We show that the turbulent velocity field is isotropic at small length scales and follows a scaling law that is consistent with the Kolmogorov theory until most of the nuclear fuel is burned. At length scales greater than a certain characteristic scale, turbulence becomes anisotropic. Here, the radial velocity fluctuations follow the scaling law of the Rayleigh-Taylor instability, whereas the angular component still obeys Kolmogorov scaling. In the late phase of the explosion, this characteristic scale drops below the numerical resolution of the simulation. The analysis confirms that a subgrid-scale model for the unresolved turbulence energy is required for the consistent calculation of the flame speed in deflagration models of Type Ia supernovae, and that the assumption of isotropy on these scales is appropriate.

We performed numerical simulations of supersonic isothermal turbulence driven by mostly compressive large-scale forcing, using both a static grid and adaptive mesh refinement with an effective resolution N=768^3. After a transient phase dominated by shocks, turbulence evolves into a steady state with an RMS Mach number about 2.5, in which cloud-like structures of over-dense gas are surrounded by highly rarefied gas. The index of the turbulence energy spectrum function beta = 2.0 in the shock-dominated phase. As the flow approaches statistical equilibrium, the spectrum flattens, with beta = 1.9. For the scaling exponent of the root mean square velocity fluctuation, we obtain gamma = 0.43 from the velocity structure functions of second order. These results are well within the range of observed scaling properties for the velocity dispersion in molecular clouds. Calculating structure functions of order p=1,...,5, we find for all scaling exponents significant deviations from the Kolmogorov-Burgers model proposed by Boldyrev. Our results are very well described by a general log-Poisson model with a higher degree of intermittency, which implies an influence of the forcing on the scaling properties. Contrary to previous numerical results for isothermal turbulence, we obtain a skewed probability density function of the mass density fluctuations that is not consistent with log-normal statistics and entails a substantially higher fraction of mass in the density peaks than implied by the Padoan-Nordlund relation between the variance of the density fluctuations and the Mach number. In conclusion, it seems necessary to account for the production mechanism of turbulence in the ISM.

The problem of the resolution of turbulent flows in adaptive mesh refinement (AMR) simulations is investigated by means of 3D hydrodynamical simulations in an idealised setup, representing a moving subcluster during a merger event. AMR simulations performed with the usual refinement criteria based on local gradients of selected variables do not properly resolve the production of turbulence downstream of the cluster. Therefore we apply novel AMR criteria which are optimised to follow the evolution of a turbulent flow. We demonstrate that these criteria provide a better resolution of the flow past the subcluster, allowing us to follow the onset of the shear instability, the evolution of the turbulent wake and the subsequent back-reaction on the subcluster core morphology. We discuss some implications for the modelling of cluster cold fronts.

The development of turbulent gas flows in the intra-cluster medium and in the core of a galaxy cluster is studied by means of adaptive mesh refinement (AMR) cosmological simulations. A series of six runs was performed, employing identical simulation parameters but different criteria for triggering the mesh refinement. In particular, two different AMR strategies were followed, based on the regional variability of control variables of the flow and on the overdensity of subclumps, respectively. We show that both approaches, albeit with different results, are useful to get an improved resolution of the turbulent flow in the ICM. The vorticity is used as a diagnostic for turbulence, showing that the turbulent flow is not highly volume-filling but has a large area-covering factor, in agreement with previous theoretical expectations. The measured turbulent velocity in the cluster core is larger than 200 km/s, and the level of turbulent pressure contribution to the cluster hydrostatic equilibrium is increased by using the improved AMR criteria.

The onset of the thermonuclear runaway in a Chandrasekhar-mass white dwarf, leading to the explosion as a type Ia supernova, is studied with hydrodynamical simulations. We investigate the evolution of temperature fluctuations (``bubbles'') in the WD's convective core by means of 2D numerical simulations. We show how the occurrence of the thermonuclear runaway depends on various bubble parameters. The relevance of the progenitor's composition for the ignition process is also discussed.

A simulation of the thermonuclear explosion of a Chandrasekhar-mass C+O white dwarf, the most popular scenario of a type Ia supernova (SN Ia), is presented. The underlying modeling is pursued in a self-consistent way, treating the combustion wave as a turbulent deflagration using well tested methods developed for laboratory combustion and based on the concept of `large eddy simulations' (LES). Such consistency requires to capture the onset of the turbulent cascade on resolved scales. This is achieved by computing the dynamical evolution on a 1024$^3$ moving grid, which resulted in the best-resolved three-dimensional SN Ia simulation carried out thus far, reaching the limits of what can be done on present supercomputers. Consequently, the model has no free parameters other than the initial conditions at the onset of the explosion, and therefore it has considerable predictive power. Our main objective is to determine to which extent such a simulation can account for the observations of normal SNe Ia. Guided by previous simulations with less resolution and a less sophisticated flame model, initial conditions were chosen that yield a reasonably strong explosion and a sufficient amount of radioactive nickel for a bright display. We show that observables are indeed matched to a reasonable degree. In particular, good agreement is found with the light curves of normal SNe Ia. Moreover, the model reproduces the general features of the abundance stratification as inferred from the analysis of spectra. This indicates that it captures the main features of the explosion mechanism of SNe Ia. However, we also show that even a seemingly best-choice pure deflagration model has shortcomings that indicate the need for a different mode of nuclear burning at late times, perhaps the transition to a detonation at low density.

Aims: We present the first full-star three-dimensional explosion simulations of thermonuclear supernovae including parameterized deflagration-to-detonation transitions that occur once the flame enters the distributed burning regime. Methods: Treating the propagation of both the deflagration and the detonation waves in a common front-tracking approach, the detonation is prevented from crossing ash regions. Results: Our criterion triggers the detonation wave at the outer edge of the deflagration flame and consequently it has to sweep around the complex structure and to compete with expansion. Despite the impeded detonation propagation, the obtained explosions show reasonable agreement with global quantities of observed type Ia supernovae. By igniting the flame in different numbers of kernels around the center of the exploding white dwarf, we set up three different models shifting the emphasis from the deflagration phase to the detonation phase. The resulting explosion energies and iron group element productions cover a large part of the diversity of type Ia supernovae. Conclusions: Flame-driven deflagration-to-detonation transitions, if hypothetical, remain a possibility deserving further investigation.

In the context of explosion models for Type Ia Supernovae, we present one- and two-dimensional simulations of fully resolved detonation fronts in degenerate C+O White Dwarf matter including clumps of previously burned material. The ability of detonations to survive the passage through sheets of nuclear ashes is tested as a function of the width and composition of the ash region. We show that detonation fronts are quenched by microscopically thin obstacles with little sensitivity to the exact ash composition. Front-tracking models for detonations in macroscopic explosion simulations need to include this effect in order to predict the amount of unburned material in delayed detonation scenarios.

We present a one-equation subgrid scale model that evolves the turbulence energy corresponding to unresolved velocity fluctuations in large eddy simulations. The model is derived in the context of the Germano consistent decomposition of the hydrodynamical equations. The eddy-viscosity closure for the rate of energy transfer from resolved toward subgrid scales is localised by means of a dynamical procedure for the computation of the closure parameter. Therefore, the subgrid scale model applies to arbitrary flow geometry and evolution. For the treatment of microscopic viscous dissipation a semi-statistical approach is used, and the gradient-diffusion hypothesis is adopted for turbulent transport. A priori tests of the localised eddy-viscosity closure and the gradient-diffusion closure are made by analysing data from direct numerical simulations. As an a posteriori testing case, the large eddy simulation of thermonuclear combustion in forced isotropic turbulence is discussed. We intend the formulation of the subgrid scale model in this paper as a basis for more advanced applications in numerical simulations of complex astrophysical phenomena involving turbulence.

The dynamics of the explosive burning process is highly sensitive to the flame speed model in numerical simulations of type Ia supernovae. Based upon the hypothesis that the effective flame speed is determined by the unresolved turbulent velocity fluctuations, we employ a new subgrid scale model which includes a localised treatment of the energy transfer through the turbulence cascade in combination with semi-statistical closures for the dissipation and non-local transport of turbulence energy. In addition, subgrid scale buoyancy effects are included. In the limit of negligible energy transfer and transport, the dynamical model reduces to the Sharp-Wheeler relation. According to our findings, the Sharp-Wheeler relation is insuffcient to account for the complicated turbulent dynamics of flames in thermonuclear supernovae. The application of a co-moving grid technique enables us to achieve very high spatial resolution in the burning region. Turbulence is produced mostly at the flame surface and in the interior ash regions. Consequently, there is a pronounced anisotropy in the vicinity of the flame fronts. The localised subgrid scale model predicts significantly enhanced energy generation and less unburnt carbon and oxygen at low velocities compared to earlier simulations.

In the framework of the Chandrasekhar-mass deflagration model for Type Ia supernovae (SNe Ia), a persisting free parameter is the initial morphology of the flame front, which is linked to the ignition process in the progenitor white dwarf. Previous analytical models indicate that the thermal runaway is driven by temperature perturbations (''bubbles'') that develop in the white dwarf's convective core. In order to probe the conditions at ignition (diameters, temperatures and evolutionary timescales), we have performed hydrodynamical 2D simulations of buoyant bubbles in white dwarf interiors. Our results show that fragmentation occurring during the bubble rise affects the outcome of the bubble evolution. Possible implications for the ignition process of SNe Ia are discussed.

We present a systematic survey of the capabilities of type Ia supernova explosion models starting from a number of flame seeds distributed around the center of the white dwarf star. To this end we greatly improved the resolution of the numerical simulations in the initial stages. This novel numerical approach facilitates a detailed study of multi-spot ignition scenarios with up to hundreds of ignition sparks. Two-dimensional simulations are shown to be inappropriate to study the effects of initial flame configurations. Based on a set of three-dimensional models, we conclude that multi-spot ignition scenarios may improve type Ia supernova models towards better agreement with observations. The achievable effect reaches a maximum at a limited number of flame ignition kernels as shown by the numerical models and corroborated by a simple dimensional analysis.

We apply an ad hoc model for dynamical ignition in three-dimensional numerical simulations of thermonuclear supernovae assuming pure deflagrations. The model makes use of the statistical description of temperature fluctuations in the pre-supernova core proposed by Wunsch & Woosley (2004). Randomness in time is implemented by means of a Poisson process. We are able to vary the explosion energy and nucleosynthesis depending on the free parameter of the model which controls the rapidity of the ignition process. However, beyond a certain threshold, the strength of the explosion saturates and the outcome appears to be robust with respect to number of ignitions. In the most energetic explosions, we find about 0.75 solar masses of iron group elements. Other than in simulations with simultaneous multi-spot ignition, the amount of unburned carbon and oxygen at radial velocities of a few 1000 km/s tends to be reduced for an ever increasing number of ignition events and, accordingly, more pronounced layering results.

We study the dynamics of thermonuclear flames propagating in fuel stirred by stochastic forcing. The fuel consists of carbon and oxygen in a state which is encountered in white dwarfs close to the Chandrasekhar limit. The level set method is applied to represent the flame fronts numerically. The computational domain for the numerical simulations is cubic, and periodic boundary conditions are imposed. The goal is the development of a suitable flame speed model for the small-scale dynamics of turbulent deflagration in thermonuclear supernovae. Because the burning process in a supernova explosion is transient and spatially inhomogeneous, the localised determination of subgrid scale closure parameters is essential. We formulate a semi-localised model based on the dynamical equation for the subgrid scale turbulence energy $k_{\mathrm{sgs}}$. The turbulent flame speed $s_{\mathrm{t}}$ is of the order $\sqrt{2k_{\mathrm{sgs}}}$. In particular, the subgrid scale model features a dynamic procedure for the calculation of the turbulent energy transfer from resolved toward subgrid scales, which has been successfully applied to combustion problems in engineering. The options of either including or suppressing inverse energy transfer in the turbulence production term are compared. In combination with the piece-wise parabolic method for the hydrodynamics, our results favour the latter option. Moreover, different choices for the constant of proportionality in the asymptotic flame speed relation, $s_{\mathrm{t}}\propto\sqrt{2k_{\mathrm{sgs}}}$, are investigated.

We show that a flame tracking/capturing scheme originally developed for deflagration fronts can be used to model thermonuclear detonations in multidimensional explosion simulations of type Ia supernovae. After testing the accuracy of the front model, we present a set of two-dimensional simulations of delayed detonations with a physically motivated off-center deflagration-detonation-transition point. Furthermore, we demonstrate the ability of the front model to reproduce the full range of possible interactions of the detonation with clumps of burned material. This feature is crucial for assessing the viability of the delayed detonation scenario.

The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers $\sim 0.1... 1$. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in these simulations is of purely numerical origin. For the dimensionless mean rate of dissipation, we find values in agreement with known results from mostly incompressible turbulence simulations. The calculation of a Smagorinsky length corresponding to the rate of numerical dissipation supports the notion of the PPM supplying an implicit subgrid scale model. In the turbulence energy spectra of various flow realisations, we find the so-called bottleneck phenomenon, i.e., a flattening of the spectrum function near the wavenumber of maximal dissipation. The shape of the bottleneck peak in the compensated spectrum functions is comparable to what is found in turbulence simulations with hyperviscosity. Although the bottleneck effect reduces the range of nearly inertial length scales considerably, we are able to estimate the value of the Kolmogorov constant. For steady turbulence with a balance between energy injection and dissipation, it appears that $C\approx 1.7$. However, a smaller value is found in the case of transonic turbulence with a large fraction of compressive components in the driving force. Moreover, we discuss length scales related to the dissipation, in particular, an effective numerical length scale $\Delta_{\mathrm{eff}}$, which can be regarded as the characteristic smoothing length of the implicit filter associated with the PPM.

We present numerical calculations of the parameters $C_{\nu}$, $C_{\epsilon}$ and $C_{\kappa}$ associated with the common closures for turbulence production, dissipation and diffusion. In the case of homogeneous and isotropic turbulence, these parameters are expected to be statistically scale-invariant within the inertial subrange. In order to scrutinise this conjecture, we utilised a generalisation of the Germano filtering formalism, which is applicable to compressible flows as well. The filtering of data obtained from three-dimensional direct numerical simulations of forced isotropic turbulence with Mach numbers in the range $\sim 0.1...1$ then yielded values of the closure parameters associated with different length scales. The results indicate that the closure parameters are nearly universal for subsonic or moderately transonic flows, although the resolution of $432^{3}$ grid cells in our simulations is not quite sufficient to clearly establish scale invariance. In addition, it was found that the customary assumption of a kinetic Prandtl number of about unity for the gradient-diffusion closure is flawed due to the misalignment between turbulent flux and the gradient of the turbulence energy. Nevertheless, sound correlation can be achieved if the flux magnitude rather than the flux vector is locally matched. This conclusion is particularly useful for the family of subgrid scale models based on the turbulence energy equation. Furthermore, the parameter of production $C_{\nu}$ was computed in the fashion of dynamical procedures. Thereby, superior agreement between modelled and explicitly evaluated turbulence stresses in comparison to the eddy-viscosity closure with constant $C_{\nu}$ was verified.

Type Ia supernovae have recently received considerable attention because it appears that they can be used as "standard candles" to measure cosmic distances out to billions of light years away from us. Observations of type Ia supernovae seem to indicate that we are living in a universe that started to accelerate its expansion when it was about half its present age. These conclusions rest primarily on phenomenological models which, however, lack proper theoretical understanding, mainly because the explosion process, initiated by thermonuclear fusion of carbon and oxygen into heavier elements, is difficult to simulate even on supercomputers. Here, we investigate a new way of modeling turbulent thermonuclear deflagration fronts in white dwarfs undergoing a type Ia supernova explosion. Our approach is based on a level set method which treats the front as a mathematical discontinuity and allows for full coupling between the front geometry and the flow field. New results of the method applied to the problem of type Ia supernovae are obtained. It is shown that in 2-D with high spatial resolution and a physically motivated subgrid scale model for the nuclear flames numerically "converged" results can be obtained, but for most initial conditions the stars do not explode. In contrast, simulations in 3-D, do give the desired explosions and many of their properties, such as the explosion energies, lightcurves and nucleosynthesis products, are in very good agreement with observed type Ia supernovae.