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In measuring the power spectrum of the distribution of large numbers of dark matter particles in simulations, or galaxies in observations, one has to use Fast Fourier Transforms (FFT) for calculational efficiency. However, because of the required mass assignment onto grid points in this method, the measured power spectrum $\la |\delta^f(k)|^2\ra$ obtained with an FFT is not the true power spectrum $P(k)$ but instead one that is convolved with a window function $|W(\vec k)|^2$ in Fourier space. In a recent paper, Jing (2005) proposed an elegant algorithm to deconvolve the sampling effects of the window function and to extract the true power spectrum, and tests using N-body simulations show that this algorithm works very well for the three most commonly used mass assignment functions, i.e., the Nearest Grid Point (NGP), the Cloud In Cell (CIC) and the Triangular Shaped Cloud (TSC) methods. In this paper, rather than trying to deconvolve the sampling effects of the window function, we propose to select a particular function in performing the mass assignment that can minimize these effects. An ideal window function should fulfill the following criteria: (i) compact top-hat like support in Fourier space to minimize the sampling effects; (ii) compact support in real space to allow a fast and computationally feasible mass assignment onto grids. We find that the scale functions of Daubechies wavelet transformations are good candidates for such a purpose. Our tests using data from the Millennium Simulation show that the true power spectrum of dark matter can be accurately measured at a level better than 2% up to $k=0.7k_N$, without applying any deconvolution processes. The new scheme is especially valuable for measurements of higher order statistics, e.g. the bi-spectrum,........

We investigate a numerical model for AGN feedback where for the first time a relativistic particle population in AGN-inflated bubbles is followed within a full cosmological context. In our high-resolution simulations of galaxy cluster formation, we assume that BH accretion is accompanied by energy feedback that occurs in two different modes, depending on the accretion rate itself. Unlike in previous work, we inject a non-thermal particle population of relativistic protons into the AGN bubbles, instead of adopting a purely thermal heating. We then follow the subsequent evolution of the cosmic ray (CR) plasma inside the bubbles, considering both its hydrodynamical interactions and dissipation processes relevant for the CR population. Due to the different buoyancy of relativistic plasma and the comparatively long CR dissipation timescale we find substantial changes in the evolution of clusters as a result of CR feedback. In particular, the non-thermal population can provide significant pressure support in central cluster regions at low thermal temperatures, providing a natural explanation for the decreasing temperature profiles found in cool core clusters. At the same time, the morphologies of the bubbles and of the induced X-ray cavities show a striking similarity to observational findings. AGN feedback with CRs also proves efficient in regulating cluster cooling flows so that the total baryon fraction in stars becomes limited to realistic values of the order of 10%. We find that the partial CR support of the intracluster gas also affects the expected signal of the thermal Sunyaev-Zel'dovich effect, with typical modifications of the integrated Compton-y parameter within the virial radius of the order of 10%. [Abridged]

We model the cosmological co-evolution of galaxies and their central supermassive black holes (BHs) within a semi-analytical framework developed on the outputs of the Millennium Simulation. This model, described in detail in Croton et al. (2006) and De Lucia & Blaizot (2007), introduces a `radio mode' feedback from Active Galactic Nuclei (AGN) at the centre of X-ray emitting atmospheres in galaxy groups and clusters. Thanks to this mechanism, the model can simultaneously explain: (i) the low observed mass drop-out rate in cooling flows; (ii) the exponential cut-off in the bright end of the galaxy luminosity function; and (iii) the bulge-dominated morphologies and old stellar ages of the most massive galaxies in clusters. This paper is the first of a series in which we investigate how well this model can also reproduce the physical properties of BHs and AGN. Here we analyze the scaling relations, the fundamental plane and the mass function of BHs, and compare them with the most recent observational data. Moreover, we extend the semi-analytic model to follow the evolution of the BH mass accretion and its conversion into radiation, and compare the derived AGN bolometric luminosity function with the observed one. While we find for the most part a very good agreement between predicted and observed BH properties, the semi-analytic model underestimates the number density of luminous AGN at high redshifts, independently of the adopted Eddington factor and accretion efficiency. However, an agreement with the observations is possible within the framework of our model, provided it is assumed that the cold gas fraction accreted by BHs at high redshifts is larger than at low redshifts., 15 pages, 7 figures, MNRAS submitted

We present a new and completely general technique for calculating the fine-grained phase-space structure of dark matter throughout the Galactic halo. Our goal is to understand this structure on the scales relevant for direct and indirect detection experiments. Our method is based on evaluating the geodesic deviation equation along the trajectories of individual DM particles. It requires no assumptions about the symmetry or stationarity of the halo formation process. In this paper we study general static potentials which exhibit more complex behaviour than the separable potentials studied previously. For ellipsoidal logarithmic potentials with a core, phase mixing is sensitive to the resonance structure, as indicated by the number of independent orbital frequencies. Regions of chaotic mixing can be identified by the very rapid decrease in the real space density of the associated dark matter streams. We also study the evolution of stream density in ellipsoidal NFW halos with radially varying isopotential shape, showing that if such a model is applied to the Galactic halo, at least $10^5$ streams are expected near the Sun. The most novel aspect of our approach is that general non-static systems can be studied through implementation in a cosmological N-body code. Such an implementation allows a robust and accurate evaluation of the enhancements in annihilation radiation due to fine-scale structure such as caustics. We embed the scheme in the current state-of-the-art code GADGET-3 and present tests which demonstrate that N-body discreteness effects can be kept under control in realistic configurations.

It is well known that cosmic rays (CRs) contribute significantly to the pressure of the interstellar medium in our own Galaxy, suggesting that they may play an important role in regulating star formation during the formation and evolution of galaxies. We here discuss a novel numerical treatment of the physics of CRs and its implementation in the parallel smoothed particle hydrodynamics code GADGET-2. In our methodology, the non-thermal CR population of each gaseous fluid element is approximated by a simple power law spectrum in particle momentum, characterized by an amplitude, a cut-off, and a fixed slope. Adiabatic compression, and a number of physical source and sink terms are modelled which modify the CR pressure of each particle. The most important sources considered are injection by supernovae and diffusive shock acceleration, while the primary sinks are thermalization by Coulomb interactions, and catastrophic losses by hadronic interactions. We also include diffusion of CRs. Our scheme allows us to carry out the first cosmological structure formation simulations that self-consistently account for CR physics. In simulations of isolated galaxies, we find that CRs can significantly reduce the star formation efficiencies of small galaxies, with virial velocities below \~80 km/s, an effect that becomes progressively stronger towards low mass scales. In cosmological simulations at high redshift, the total mass-to-light ratio of small halos and the faint-end of the luminosity function are strongly affected. When CR acceleration in shocks is followed as well, up to ~40% of the energy dissipated at structure formation shocks can appear as CR pressure at z~3-6, but this fraction drops to ~10% at low redshifts when the shock distribution becomes increasingly dominated by lower Mach numbers. (abridged), Comment: submitted to A&A, 36 pages, 27 figures (partially in reduced resolution)

Observations of the Cosmic Microwave Background (CMB) have revealed an unexpected quadrupole-octopole alignment along a preferred axis pointing toward the Virgo cluster. We here investigate whether this feature can be explained in the framework of the concordance model by secondary anisotropies produced by the non-linear evolution of the gravitational potential, the so-called Rees-Sciama (RS) effect. We focus on the effect caused by the local superclusters, which we calculate using a constrained high-resolution hydrodynamical simulation, based on the IRAS 1.2-Jy all-sky galaxy redshift survey, which reproduces the main structures of our Universe out to a distance of 110 Mpc from our Galaxy. The resulting RS effect peaks at low multipoles and has a minimum/maximum amplitude of -6.6\mu K 1.9\mu K. Even though its quadrupole is well aligned with the one measured for the CMB, its amplitude is not sufficient to explain the observed magnitude of the quadrupole/octopole alignment. In addition, we analyze the WMAP-3 data with a linear matched filter in an attempt to determine an upper limit for the RS signal amplitude on large scales. We found that it is possible to infer a weak upper limit of 30\mu K for its maximum amplitude., Comment: 7 pages, 4 figures, submitted to A&A

We have carried out a hydrodynamical code comparison study of interacting multiphase fluids. The two commonly used techniques of grid and smoothed particle hydrodynamics (SPH) show striking differences in their ability to model processes that are fundamentally important across many areas of astrophysics. Whilst Eulerian grid based methods are able to resolve and treat important dynamical instabilities, such as Kelvin-Helmholtz or Rayleigh-Taylor, these processes are poorly or not at all resolved by existing SPH techniques. We show that the reason for this is that SPH, at least in its standard implementation, introduces spurious pressure forces on particles in regions where there are steep density gradients. This results in a boundary gap of the size of the SPH smoothing kernel over which information is not transferred.

Deep Chandra exposures of the hot galaxy cluster 1E0657-56 have revealed that the cluster is observed shortly after the first core-passage of a massive infalling subcluster, which is preceded by a prominent bow shock with Mach number M~3. The inferred shock velocity of ~4700 km/s has been commonly interpreted as the velocity of the `bullet' subcluster itself. This velocity is unexpectedly high in the LCDM cosmology, which may require non-trivial modifications in the dark sector to be accommodated if taken at face value. Here we present explicit hydrodynamical toy models of galaxy cluster mergers which very well reproduce the observed dynamical state of 1E0657-56 and the mass models inferred from gravitational lensing observations. However, despite a shock speed of 4500 km/s, the subcluster's mass centroid is moving only with 2600 km/s in the rest frame of the system. The difference arises in part due to a gravitationally induced inflow velocity of the gas ahead of the shock, which amounts to ~1100 km/s for our assumed 10:1 mass ratio of the merger. A second effect is that the shock front moves faster than the subcluster itself. A generic LCDM collision model, where a bullet subcluster with concentration c=7.2 merges with a parent cluster with concentration c=3 on a zero-energy orbit, reproduces all the main observational features seen in 1E0657-56 with good accuracy, suggesting that 1E0657-56 is well in line with expectations from standard cosmological models. In theories with an additional 5th-force in the dark sector, the subcluster can be accelerated beyond the velocity reached in LCDM, and the spatial offset between the X-ray peak and the mass centroid of the subcluster can be significantly enlarged. (abridged)

We discuss a numerical model for black hole growth and its associated feedback processes that for the first time allows cosmological simulations of structure formation to self-consistently follow the build up of the cosmic population of galaxies and active galactic nuclei. Our model assumes that seed black holes are present at early cosmic epochs at the centres of forming halos. We then track their growth from gas accretion and mergers with other black holes in the course of cosmic time. For black holes that are active, we distinguish between two distinct modes of feedback, depending on the black hole accretion rate itself. Black holes that accrete at high rates are assumed to be in a `quasar regime', where we model their feedback by thermally coupling a small fraction of their bolometric luminosity to the surrounding gas. For black holes with low accretion rates, we conjecture that most of their feedback occurs in mechanical form, where AGN-driven bubbles are injected into a gaseous environment. Using our new model, we carry out TreeSPH cosmological simulations on the scales of individual galaxies to those of massive galaxy clusters, both for isolated systems and for cosmological boxes. We demonstrate that our model produces results for the black hole and stellar mass densities in broad agreement with observational constraints. We find that the black holes significantly influence the evolution of their host galaxies, changing their star formation history, their amount of cold gas, and their colours. Also, the properties of intracluster gas are affected strongly by the presence of massive black holes in the cores of galaxy clusters, leading to shallower metallicity and entropy profiles, and to a suppression of strong cooling flows. [Abridged]

We numerically model fragmentation of a gravitationally unstable gaseous disc under conditions that may be appropriate for the formation of the young massive stars observed in the central parsec of our Galaxy. In this study, we adopt a simple prescription with a locally constant cooling time. We find that, for cooling times just short enough to induce disc fragmentation, stars form with a top-heavy Initial Mass Function (IMF), as observed in the Galactic Centre (GC). For shorter cooling times, the disc fragments much more vigorously, leading to lower average stellar masses. Thermal feedback associated with gas accretion onto protostars slows down disc fragmentation, as predicted by some analytical models. We also simulate the fragmentation of a gas stream on an eccentric orbit in a combined Sgr A* plus stellar cusp gravitational potential. The stream precesses, self-collides and forms stars with a top-heavy IMF. None of our models produces large enough co-moving groups of stars that could account for the observed ``mini star cluster'' IRS13E in the GC. In all of the gravitationally unstable disc models that we explored, star formation takes place too fast to allow any gas accretion onto the central super-massive black hole. While this can help to explain the quiescence of `failed AGN' such as Sgr A*, it poses a challenge for understanding the high gas accretion rates infered for many quasars.

We have performed a large set of high-resolution cosmological simulations using smoothed particle hydrodynamics (SPH) to study the formation of the first luminous objects in theCDM cosmology. We follow the collapse of primordial gas clouds in eight early structures and document the scatter in the properties of the first star- forming clouds. Our first objects span formation redshifts from z � 10 to z � 50 and cover an order of magnitude in halo mass. We find that the physical properties of the central star-forming clouds are very similar in all of the simulated objects despite significant differences in formation redshift and environment. This suggests that the formation path of the first stars is largely independent of the collapse redshift; the physical properties of the clouds have little correlation with spin, mass, or assembly history of the host halo. The collapse of proto-stellar objects at higher redshifts pro- gresses much more rapidly due to the higher densities, which accelerates the formation of molecular hydrogen, enhances initial cooling and shortens the dynamical timescales. The mass of the star-forming clouds cover a broad range, from a few hundred to a few thousand solar masses, and exhibit various morphologies: some have disk-like structures which are nearly rotational supported; others form flattened spheroids; still others form bars. All of them develop a single protostellar 'seed' which does not frag- ment into multiple objects up to the moment that the central gas becomes optically thick to H2 cooling lines. At this time, the instantaneous mass accretion rate onto the centre varies significantly from object to object, with disk-like structures having the smallest mass accretion rates. The formation epoch and properties of the star-forming clouds are sensitive to the values of cosmological parameters.

We study the vertical structure of a stellar disk obtained from a fully cosmological high-resolution hydrodynamical simulation of the formation of a Milky Way-like galaxy. At the present day, the disk's mean vertical height shows a well-defined and strong pattern, with amplitudes as large as 3 kpc in its outer regions. This pattern is the result of a satellite - host halo - disk interaction and reproduces, qualitatively, many of the observable properties of the Monoceros Ring. In particular we find disk material at the distance of Monoceros ($R \sim$ 12-16 kpc, galactocentric) extending far above the mid plane ( 30$^{\circ}$, $\langle Z \rangle \sim$ 1-2 kpc) in both hemispheres, as well as well-defined arcs of disk material at heliocentric distances $\gtrsim 5$ kpc. The pattern was first excited $\approx 3$ Gyr ago as an $m=1$ mode that later winds up into a leading spiral pattern. Interestingly, the main driver behind this perturbation is a low-mass low-velocity fly-by encounter. The satellite has total mass, pericentre distance and pericentric velocity of $\sim 5\%$ of the host, $\sim 80$ kpc, and 215 km/s, respectively. The satellite is not massive enough to directly perturb the galactic disk but we show that the density field of the host dark matter halo responds to this interaction resulting in a strong amplification of the perturbative effects. This subsequently causes the onset and development of the Monoceros-like feature., 16 pages, 14 figures. Accepted to MNRAS after minor corrections

Numerical methods play an ever more important role in astrophysics. This is especially true in theoretical works, but of course, even in purely observational projects, data analysis without massive use of computational methods has become unthinkable. The key utility of computer simulations comes from their ability to solve complex systems of equations that are either intractable with analytic techniques or only amenable to highly approximative treatments. Simulations are best viewed as a powerful complement to analytic reasoning, and as the method of choice to model systems that feature enormous physical complexity such as star formation in evolving galaxies, the topic of this 43rd Saas Fee Advanced Course. The organizers asked me to lecture about high performance computing and numerical modelling in this winter school, and to specifically cover the basics of numerically treating gravity and hydrodynamics in the context of galaxy evolution. This is still a vast field, and I necessarily had to select a subset of the relevant material. The written notes presented here quite closely follow the lectures as held in Villars-sur-Ollon, which were meant to provide a general overview about some of the most pertinent techniques that may be relevant for students working on numerical models of galaxy evolution and star formation. The discussion is hence often at an introductory level, giving precedence to a presentation of the main numerical concepts rather than to a mathematically detailed exposition of the techniques.

We present an analysis of the evolving comoving cumulative number density of galaxy populations found in the Illustris simulation. Cumulative number density is commonly used to link galaxy populations across different epochs by assuming that galaxies preserve their number density in time. Our analysis allows us to examine the extent to which this assumption holds in the presence of galaxy mergers or when rank ordering is broken owing to variable stellar growth rates. Our primary results are as follows: (1) the inferred average stellar mass evolution obtained via a constant comoving number density assumption is systematically biased compared to the merger tree results at the factor of ∼2(4) level when tracking galaxies from redshift z = 0 to 2(3); (2) the median number density evolution for galaxy populations tracked forward in time is shallower than for galaxy populations tracked backward; (3) a similar evolution in the median number density of tracked galaxy populations is found regardless of whether number density is assigned via stellar mass, stellar velocity dispersion, or halo mass; (4) explicit tracking reveals a large diversity in the stellar and dark matter assembly histories that cannot be captured by constant number density analyses; (5) the significant scatter in galaxy linking methods is only marginally reduced (∼20 per cent) by considering additional physical galaxy properties. We provide fits for the median evolution in number density for use with observational data and discuss the implications of our analysis for interpreting multi-epoch galaxy property observations., National Science Foundation (U.S.) (DGE1144152), United States. Department of Energy (DE-FG02-97ER25308), United States. National Aeronautics and Space Administration (NNX12AC67G), National Science Foundation (U.S.) (AST-1312095)

Solving the Euler equations of ideal hydrodynamics as accurately and efficiently as possible is a key requirement in many astrophysical simulations. It is therefore important to continuously advance the numerical methods implemented in current astrophysical codes, especially also in light of evolving computer technology, which favours certain computational approaches over others. Here we introduce the new adaptive mesh refinement (AMR) code TENET, which employs a high order discontinuous Galerkin (DG) scheme for hydrodynamics. The Euler equations in this method are solved in a weak formulation with a polynomial basis by means of explicit Runge-Kutta time integration and Gauss-Legendre quadrature. This approach offers significant advantages over commonly employed second order finite volume (FV) solvers. In particular, the higher order capability renders it computationally more efficient, in the sense that the same precision can be obtained at significantly less computational cost. Also, the DG scheme inherently conserves angular momentum in regions where no limiting takes place, and it typically produces much smaller numerical diffusion and advection errors than a FV approach. A further advantage lies in a more natural handling of AMR refinement boundaries, where a fall-back to first order can be avoided. Finally, DG requires no wide stencils at high order, and offers an improved data locality and a focus on local computations, which is favourable for current and upcoming highly parallel supercomputers. We describe the formulation and implementation details of our new code, and demonstrate its performance and accuracy with a set of two- and three-dimensional test problems. The results confirm that DG schemes have a high potential for astrophysical applications., 23 pages, 12 figures, published in MNRAS November 2015, a movie may be accessed online: https://youtu.be/cTRQP6DSaqA

We performed a hydrodynamical cosmological simulation of the formation of a Milky Way-like galaxy in a warm dark matter (WDM) cosmology. Smooth and dense filaments, several co-moving mega parsec long, form generically above z 2 in this model. Atomic line cooling allows gas in the centres of these filaments to cool to the base of the cooling function, resulting in a very striking pattern of extended Lyman-limit systems (LLSs). Observations of the correlation function of LLSs might hence provide useful limits on the nature of the dark matter. We argue that the self-shielding of filaments may lead to a thermal instability resulting in star formation. We implement a sub-grid model for this, and find that filaments rather than haloes dominate star formation until z 6. Reionisation decreases the gas density in filaments, and the more usual star formation in haloes dominates below z 6, although star formation in filaments continues until z=2. Fifteen per cent of the stars of the z=0 galaxy formed in filaments. At higher redshift, these stars give galaxies a stringy appearance, which, if observed, might be a strong indication that the dark matter is warm., 8 pages, 7 figures. Accepted to MNRAS. Minor revision apart from adding more comparisons with CDM

Massive, quiescent galaxies at high redshift have been found to be considerably more compact than galaxies of similar mass in the local universe. How these compact galaxies formed has yet to be determined, though several progenitor populations have been proposed. Here we investigate the formation processes and quantify the assembly histories of such galaxies in Illustris, a suite of hydrodynamical cosmological simulations encompassing a sufficiently large volume to include rare objects, while simultaneously resolving the internal structure of galaxies. We select massive (~10^11 solar masses) and compact (stellar half-mass radius < 2 kpc) galaxies from the simulation at z=2. Within the Illustris suite, we find that these quantities are not perfectly converged, but are reasonably reliable for our purposes. The resulting population is composed primarily of quiescent galaxies, but we also find several star-forming compact galaxies. The simulated compact galaxies are similar to observed galaxies in star formation activity and appearance. We follow their evolution at high redshift in the simulation and find that there are multiple pathways to form these compact galaxies, dominated by two mechanisms: (i) intense, centrally concentrated starbursts generally triggered by gas-rich major mergers between z~2-4, reducing the galaxies' half-mass radii by a factor of a few to below 2 kpc, and (ii) assembly at very early times when the universe was much denser; the galaxies formed compact and remained so until z~2., 13 pages, 10 figures, MNRAS accepted version

Understanding the physical processes that drive star formation is a key challenge for galaxy formation models. In this article we study the tight correlation between the star formation rate (SFR) and stellar mass of galaxies at a given redshift, how halo growth influences star formation, and star formation histories of individual galaxies. We study these topics using Illustris, a state-of-the-art cosmological hydrodynamical simulation of galaxy formation. Illustris reproduces the observed relation (the star formation main sequence; SFMS) between SFR and stellar mass at redshifts z=0 and z=4, but at intermediate redshifts of z~2, the simulated SFMS has a significantly lower normalisation than reported by observations. The scatter in the relation is consistent with the observed scatter. However, the fraction of outliers above the SFR-stellar mass relation in Illustris is less than that observed. Galaxies with halo masses of ~10^{12} solar masses dominate the SFR density of the Universe, in agreement with the results of abundance matching. Furthermore, more-massive galaxies tend to form the bulk of their stars at high redshift, which indicates that `downsizing' occurs in Illustris. We also studied the star formation histories of individual galaxies, including the use of a principal component analysis decomposition. We find that for fixed stellar mass, galaxies that form earlier have more-massive black holes at z=0, indicating that star formation and black hole growth are tightly linked processes in Illustris. While many of the properties of normal star-forming galaxies are well-reproduced in the Illustris simulation, forming a realistic population of starbursts will likely require higher resolution and probably a more sophisticated treatment of star formation and feedback from stars and black holes., Comment: 16 pages, 16 figures, Accepted for MNRAS, Section 6 and Figure 16 are new. Data is available at http://martinsparre.com/dataproducts

Discrepancies between the observed and model-predicted radio flux ratios are seen in a number of quadruply-lensed quasars. The most favored interpretation of these anomalies is that CDM substructures present in lensing galaxies perturb the lens potentials and alter image magnifications and thus flux ratios. So far no consensus has emerged regarding whether or not the predicted CDM substructure abundance fully accounts for the lensing flux anomaly observations. Accurate modeling relies on a realistic lens sample in terms of both the lens environment and internal structures and substructures. In this paper we construct samples of generalised and specific lens potentials, to which we add (rescaled) subhalo populations from the galaxy-scale Aquarius and the cluster-scale Phoenix simulation suites. We further investigate the lensing effects from subhalos of masses several orders of magnitude below the simulation resolution limit. The resulting flux ratio distributions are compared to the currently best available sample of radio lenses. The observed anomalies in B0128+437, B0712+472 and B1555+375 are more likely to be caused by propagation effects or oversimplified lens modeling, signs of which are already seen in the data. Among the quadruple systems that have closely located image triplets/pairs, the anomalous flux ratios of MG0414+0534 can be reproduced by adding CDM subhalos to its macroscopic lens potential, with a probability of 5%-20%; for B0712+472, B1422+231, B1555+375 and B2045+265, these probabilities are only of a few percent. We hence find that CDM substructures are unlikely to be the whole reason for radio flux anomalies. We discuss other possible effects that might also be at work., Comment: 21 pages, 3 tables, 9 figures, accepted for publication in MNRAS. This paper supersedes our previous preprint arXiv:1307.4220. The methodology has been significantly improved and this has reached quantitatively different results

We study the properties of gas in and around 10^12 solar mass halos at z=2 using a suite of high-resolution cosmological hydrodynamic 'zoom' simulations. We quantify the thermal and dynamical structure of these gaseous reservoirs in terms of their mean radial distributions and angular variability along different sightlines. With each halo simulated at three levels of increasing resolution, the highest reaching a baryon mass resolution of ~10,000 solar masses, we study the interaction of filamentary inflow and the quasi-static hot halo atmosphere. We highlight the discrepancy between the spatial resolution available in the halo gas as opposed to within the galaxy itself, and find that stream morphologies become increasingly complex at higher resolution, with large coherent flows revealing density and temperature structure at progressively smaller scales. Moreover, multiple gas components co-exist at the same radius within the halo, making radially averaged analyses misleading. This is particularly true where the hot, quasi-static, high entropy halo atmosphere interacts with cold, rapidly inflowing, low entropy accretion. We investigate the process of gas virialization and identify different regimes for the heating of gas as it accretes from the intergalactic medium. Haloes at this mass have a well-defined virial shock, associated with a sharp jump in temperature and entropy at ~1.25 r_vir. The presence, radius, and radial width of this boundary feature, however, vary not only from halo to halo, but also as a function of angular direction, covering roughly ~85% of the 4pi sphere. Our findings are relevant for the proper interpretation of observations pertaining to the circumgalactic medium, including evidence for large amounts of cold gas surrounding massive haloes at intermediate redshifts., High-res PDF and simulation movies available at http://www.cfa.harvard.edu/~dnelson/#research (MNRAS submitted, comments welcome)

Accurate numerical solutions of the equations of hydrodynamics play an ever more important role in many fields of astrophysics. In this work, we reinvestigate the accuracy of the moving-mesh code \textsc{Arepo} and show how its convergence order can be improved for general problems. In particular, we clarify that for certain problems \textsc{Arepo} only reaches first-order convergence for its original formulation. This can be rectified by simple modifications we propose to the time integration scheme and the spatial gradient estimates of the code, both improving the accuracy of the code. We demonstrate that the new implementation is indeed second-order accurate under the $L^1$ norm, and in particular substantially improves conservation of angular momentum. Interestingly, whereas these improvements can significantly change the results of smooth test problems, we also find that cosmological simulations of galaxy formation are unaffected, demonstrating that the numerical errors eliminated by the new formulation do not impact these simulations. In contrast, simulations of binary stars followed over a large number of orbital times are strongly affected, as here it is particularly crucial to avoid a long-term build up of errors in angular momentum conservation., 11 pages, 9 figures, accepted for publication

We present our methods for generating a catalog of 7,000 synthetic images and 40,000 integrated spectra of redshift z = 0 galaxies from the Illustris Simulation. The mock data products are produced by using stellar population synthesis models to assign spectral energy distributions (SED) to each star particle in the galaxies. The resulting synthetic images and integrated SEDs therefore properly reflect the spatial distribution, stellar metallicity distribution, and star formation history of the galaxies. From the synthetic data products it is possible to produce monochromatic or color-composite images, perform SED fitting, classify morphology, determine galaxy structural properties, and evaluate the impacts of galaxy viewing angle. The main contribution of this paper is to describe the production, format, and composition of the image catalog that makes up the Illustris Simulation Obsevatory. As a demonstration of this resource, we derive galactic stellar mass estimates by applying the SED fitting code FAST to the synthetic galaxy products, and compare the derived stellar masses against the true stellar masses from the simulation. We find from this idealized experiment that systematic biases exist in the photometrically derived stellar mass values that can be reduced by using a fixed metallicity in conjunction with a minimum galaxy age restriction., Comment: 21 pages, 17 figures, submitted to MNRAS. Comments welcome

We have constructed merger trees for galaxies in the Illustris Simulation by directly tracking the baryonic content of subhalos. These merger trees are used to calculate the galaxy-galaxy merger rate as a function of descendant stellar mass, progenitor stellar mass ratio, and redshift. We demonstrate that the most appropriate definition for the mass ratio of a galaxy-galaxy merger consists in taking both progenitor masses at the time when the secondary progenitor reaches its maximum stellar mass. Additionally, we avoid effects from `orphaned' galaxies by allowing some objects to `skip' a snapshot when finding a descendant, and by only considering mergers which show a well-defined `infall' moment. Adopting these definitions, we obtain well-converged predictions for the galaxy-galaxy merger rate with the following main features, which are qualitatively similar to the halo-halo merger rate except for the last one: a strong correlation with redshift that evolves as $\sim (1+z)^{2.4-2.8}$, a power law with respect to mass ratio, and an increasing dependence on descendant stellar mass, which steepens significantly for descendant stellar masses greater than $\sim 2 \times 10^{11} \, {\rm M_{\odot}}$. These trends are consistent with observational constraints for medium-sized galaxies ($M_{\ast} \gtrsim 10^{10} \, {\rm M_{\odot}}$), but in tension with some recent observations of the close pair fraction for massive galaxies ($M_{\ast} \gtrsim 10^{11} \, {\rm M_{\odot}}$), which report a nearly constant or decreasing evolution with redshift. Finally, we provide a fitting function for the galaxy-galaxy merger rate which is accurate over a wide range of stellar masses, progenitor mass ratios, and redshifts., 17 pages, 10 figures, MNRAS published. The official Illustris website can be found at http://www.illustris-project.org/

The common envelope (CE) phase is an important stage in binary stellar evolution. It is needed to explain many close binary stellar systems, such as cataclysmic variables, Type Ia supernova progenitors, or X-ray binaries. To form the resulting close binary, the initial orbit has to shrink, thereby transferring energy to the primary giant's envelope that is hence ejected. The details of this interaction, however, are still not understood. Here, we present new hydrodynamic simulations of the dynamical spiral-in forming a CE system. We apply the moving-mesh code AREPO to follow the interaction of a $1M_\odot$ compact star with a $2M_\odot$ red giant possessing a $0.4M_\odot$ core. The nearly Lagrangian scheme combines advantages of smoothed particle hydrodynamics and traditional grid-based hydrodynamic codes and allows us to capture also small flow features at high spatial resolution. Our simulations reproduce the initial transfer of energy and angular momentum from the binary core to the envelope by spiral shocks seen in previous studies, but after about 20 orbits a new phenomenon is observed. Large-scale flow instabilities are triggered by shear flows between adjacent shock layers. These indicate the onset of turbulent convection in the common envelope, thus altering the transport of energy on longer time scales. At the end of our simulation, only 8% of the envelope mass is ejected. The failure to unbind the envelope completely may be caused by processes on thermal time scales or unresolved microphysics., Comment: 6 pages, 4 figures. This is an author-created, un-copyedited version of an article accepted for publication in The Astrophysical Journal Letters. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The thermal state of the intergalactic medium (IGM) at z < 6 constrains the nature and timing of cosmic reionization events, but its inference from the Ly-alpha forest is degenerate with the 3-D structure of the IGM on ~100 kpc scales, where, analogous to the classical Jeans argument, the pressure of the T~$10^4$ K gas supports it against gravity. We simulate the IGM using smoothed particle hydrodynamics, and find that, at z < 6, the gas density power spectrum does not exhibit the expected Jeans filtering cutoff, because dense gas in collapsed halos dominates the small-scale power masking pressure smoothing effects. We introduce a new statistic, the real-space Ly-alpha flux, $F_\mathrm{real}$, which naturally suppresses dense gas, and is thus robust against the poorly understood physics of galaxy formation, revealing pressure smoothing in the diffuse IGM. The $F_\mathrm{real}$ power spectrum is accurately described by a simple fitting function with cutoff at $\lambda_F$, allowing us to rigorously quantify the filtering scale for the first time: we find $\lambda_F$ = 79 kpc (comoving) at z=3 for our fiducial thermal model. This statistic has the added advantage that it directly relates to observations of correlated Ly-alpha forest absorption in close quasar pairs, recently proposed as a method to measure the filtering scale. Our results enable one to quantify the filtering scale in simulations, and ask meaningful questions about its dependence on reionization and thermal history. Accordingly, the standard description of the IGM in terms of the amplitude $T_0$ and slope $\gamma$ of the temperature-density relation $T = T_0\Delta^{\gamma-1}$ should be augmented with a third filtering scale parameter $\lambda_F$., Comment: Now published. New from previous version: Figure 14 and some nomenclature

A recent observational study of haloes of nearby Milky Way-like galaxies shows that only half (four out of eight) of the current sample exhibits strong negative metallicity ([Fe/H]) gradients. This is at odds with predictions from hydrodynamical simulations where such gradients are ubiquitous. In this Letter, we use high resolution cosmological hydrodynamical simulations to study the [Fe/H] distribution of galactic haloes. We find that kinematically selected stellar haloes, including both in-situ and accreted particles, have an oblate [Fe/H] distribution. Spherical [Fe/H] radial profiles show strong negative gradients within 100 kpc, in agreement with previous numerical results. However, the projected median [Fe/H] profiles along the galactic disc minor axis, typically obtained in observations, are significantly flatter. The median [Fe/H] values at a given radius are larger for the spherical profiles than for the minor axis profiles by as much as 0.4 dex within the inner 50 kpc. Similar results are obtained if only the accreted stellar component is considered indicating that the differences between spherical and minor axis profiles are not purely driven by heated disc star particles formed in situ. Our study highlights the importance of performing careful comparisons between models and observations of halo [Fe/H] distributions., Comment: 6 pages, 4 figures. Accepted for publication in MNRAS Letters; very minor edits to match the accepted version

Observations at low redshifts thus far fail to account for all of the baryons expected in the Universe according to cosmological constraints. A large fraction of the baryons presumably resides in a thin and warm-hot medium between the galaxies, where they are difficult to observe due to their low densities and high temperatures. Cosmological simulations of structure formation can be used to verify this picture and provide quantitative predictions for the distribution of mass in different large-scale structure components. Here we study the distribution of baryons and dark matter at different epochs using data from the Illustris simulation. We identify regions of different dark matter density with the primary constituents of large-scale structure, allowing us to measure mass and volume of haloes, filaments and voids. At redshift zero, we find that 49 % of the dark matter and 23 % of the baryons are within haloes more massive than the resolution limit of $2\times 10^8$ M$_\odot$. The filaments of the cosmic web host a further 45 % of the dark matter and 46 % of the baryons. The remaining 31 % of the baryons reside in voids. The majority of these baryons have been transported there through active galactic nuclei feedback. We note that the feedback model of Illustris is too strong for heavy haloes, therefore it is likely that we are overestimating this amount. Categorizing the baryons according to their density and temperature, we find that 17.8 % of them are in a condensed state, 21.6 % are present as cold, diffuse gas, and 53.9 % are found in the state of a warm-hot intergalactic medium., Comment: 12 pages, 15 figures

We study the impact of baryons on the distribution of dark matter in a Milky Way-size halo by comparing a high-resolution, moving-mesh cosmological simulation with its dark matter-only counterpart. We identify three main processes related to baryons -- adiabatic contraction, tidal disruption and reionization -- which jointly shape the dark matter distribution in both the main halo and its subhalos. The relative effect of each baryonic process depends strongly on the subhalo mass. For massive subhalos with maximum circular velocity $v_{\rm max} > 35 km/s$, adiabatic contraction increases the dark matter concentration, making these halos less susceptible to tidal disruption. For low-mass subhalos with $v_{\rm max} < 20 km/s$, reionization effectively reduces their mass on average by $\approx$ 30% and $v_{\rm max}$ by $\approx$ 20%. For intermediate subhalos with $20 km/s < v_{\rm max} < 35 km/s$, which share a similar mass range as the classical dwarf spheroidals, strong tidal truncation induced by the main galaxy reduces their $v_{\rm max}$. Moreover, the stellar disk of the main galaxy effectively depletes subhalos near the central region. As a combined result of reionization and increased tidal disruption, the total number of low-mass subhalos in the hydrodynamic simulation is nearly halved compared to that of the $\textit{N-}$body simulation. We do not find dark matter cores in dwarf galaxies, unlike previous studies that employed bursty feedback-driven outflows. The substantial impact of baryons on the abundance and internal structure of subhalos suggests that galaxy formation and evolution models based on $\textit{N}$-body simulations should include these physical processes as major components., 22 pages, accepted for publication in MNRAS

Supermassive black hole (BH) mergers produce powerful gravitational wave (GW) emission. Asymmetry in this emission imparts a recoil kick to the merged BH, which can eject the BH from its host galaxy altogether. Recoiling BHs could be observed as offset active galactic nuclei (AGN). Several candidates have been identified, but systematic searches have been hampered by large uncertainties regarding their observability. By extracting merging BHs and host galaxy properties from the Illustris cosmological simulations, we have developed a comprehensive model for recoiling AGN. Here, for the first time, we model the effects of BH spin alignment and recoil dynamics based on the gas-richness of host galaxies. We predict that if BH spins are not highly aligned, seeing-limited observations could resolve offset AGN, making them promising targets for all-sky surveys. For randomly-oriented spins, less than about 10 spatially-offset AGN may be detectable in HST-COSMOS, and > 10^3 could be found with Pan-STARRS, LSST, Euclid, and WFIRST. Nearly a thousand velocity-offset AGN are predicted within the SDSS footprint; the rarity of large broad-line offsets among SDSS quasars is likely due in part to selection effects but suggests that spin alignment plays a role in suppressing recoils. Nonetheless, in our most physically motivated model where alignment occurs only in gas-rich mergers, hundreds of offset AGN should be found in all-sky surveys. Our findings strongly motivate a dedicated search for recoiling AGN., 30 pages, 19 figures. Accepted to MNRAS after minor revisions

Hydrodynamical simulations of galaxy formation such as the Illustris simulations have progressed to a state where they approximately reproduce the observed stellar mass function from high to low redshift. This in principle allows self-consistent models of reionization that exploit the accurate representation of the diffuse gas distribution together with the realistic growth of galaxies provided by these simulations, within a representative cosmological volume. In this work, we apply and compare two radiative transfer algorithms implemented in a GPU-accelerated code to the $106.5\,{\rm Mpc}$ wide volume of Illustris in postprocessing in order to investigate the reionization transition predicted by this model. We find that the first generation of galaxies formed by Illustris is just about able to reionize the universe by redshift $z\sim 7$, provided quite optimistic assumptions about the escape fraction and the resolution limitations are made. Our most optimistic model finds an optical depth of $\tau\simeq 0.065$, which is in very good agreement with recent Planck 2015 determinations. Furthermore, we show that moment-based approaches for radiative transfer with the M1 closure give broadly consistent results with our angular-resolved radiative transfer scheme. In our favoured fiducial model, 20\% of the hydrogen is reionized by redshift $z=9.20$, and this rapidly climbs to 80\% by redshift $z=6.92$. It then takes until $z=6.24$ before 99\% of the hydrogen is ionized. On average, reionization proceeds `inside-out' in our models, with a size distribution of reionized bubbles that progressively features regions of ever larger size while the abundance of small bubbles stays fairly constant., Comment: 18 pages, 16 figures, revised version accepted for publication in MNRAS

We have developed a new scheme to treat a multiphase interstellar medium in smoothed particle hydrodynamics simulations of galaxy formation. This scheme can represent a co-spatial mixture of cold and hot ISM components, and is formulated without scale-dependent parameters. It is thus particularly suited to studies of cosmological structure formation where galaxies with a wide range of masses form simultaneously. We also present new algorithms for energy and heavy element injection by supernovae, and show that together these schemes can reproduce several important observed effects in galaxy evolution. Both in collapsing systems and in quiescent galaxies our codes can reproduce the Kennicutt relation between the surface densities of gas and of star formation. Strongly metal-enhanced winds are generated in both cases with ratios of mass-loss to star formation which are similar to those observed. This leads to a self-regulated cycle for star formation activity. The overall impact of feedback depends on galaxy mass. Star formation is suppressed at most by a factor of a few in massive galaxies, but in low-mass systems the effects can be much larger, giving star formation an episodic, bursty character. The larger the energy fraction assumed available in feedback, the more massive the outflows and the lower the final stellar masses. Winds from forming disks are collimated perpendicular to the disk plane, reach velocities up to 1000 km/s, and efficiently transport metals out of the galaxies. The asymptotically unbound baryon fraction drops from >95 per cent to ~30 per cent from the least to the most massive of our idealised galaxies, but the fraction of all metals ejected with this component exceeds 60 per cent regardless of mass. Such winds could plausibly enrich the intergalactic medium to observed levels., 18 pages, 13 figures, accepted for publication in MNRAS

We study structure formation in cosmological void regions using high-resolution hydrodynamical simulations. Despite being significantly underdense, voids are populated abundantly with small dark matter halos which should appear as dwarf galaxies if their star formation is not suppressed significantly. We here investigate to which extent the cosmological UV-background photo-evaporates baryons out of halos of dwarf galaxies, and thereby limits their cooling and star formation rates. Assuming a Haardt & Madau UV-background with reionisation at redshift z=6, our samples of simulated galaxies show that halos with masses below a characteristic mass of M_c(z=0) = 6.5 x 10^9 h^{-1} M_sun are baryon-poor, but in general not completely empty, because baryons that are in the condensed cold phase or are already locked up in stars resist evaporation. In halos with mass M < M_c, we find that photo-heating suppresses further cooling of gas. The redshift and UV-background dependent characteristic mass M_c(z) can be understood from the equilibrium temperature between heating and cooling at a characteristic overdensity of \delta ~ 1000. If a halo is massive enough to compress gas to this density despite the presence of the UV background, gas is free to `enter' the condensed phase and cooling continues in the halo, otherwise it stalls. By analysing the mass accretion histories of dwarf galaxies in voids, we show that they can build up a significant amount of condensed mass at early times before the epoch of reionisation. Later on, the amount of mass in this phase remains roughly constant, but the masses of the dark matter halos continue to increase. (abridged)

(Abridged) The violent hierarchical nature of the LCDM cosmology poses serious difficulties for the formation of disk galaxies. To help resolve these issues, we describe a new, merger-driven scenario for the cosmological formation of disk galaxies at high redshifts that supplements the standard model based on dissipational collapse.In this picture, large gaseous disks may be produced from high-angular momentum mergers of systems that are gas-dominated, i.e. M_gas/(M_gas +M_star > 0.5 at the height of the merger. Pressurization from the multiphase structure of the interstellar medium prevents the complete conversion of gas into stars during the merger, and if enough gas remains to form a disk, the remnant eventually resembles a disk galaxy. We perform numerical simulations of galaxy mergers to study how supernovae feedback strength, supermassive black hole growth and feedback, progenitor gas fraction, merger mass-ratio, and orbital geometry impact the formation of remnant disks. We find that disks can build angular momentum through mergers and the degree of rotational support of the baryons in the merger remnant is primarily related to feedback processes associated with star formation. Disk-dominated remnants are restricted to form in mergers that are gas-dominated at the time of final coalescence and gas-dominated mergers typically require extreme progenitor gas fractions (>80%). We also show that the formation of rotationally-supported stellar systems in mergers is not restricted to idealized orbits, or major or minor mergers. We suggest that the hierarchical nature of the LCDM cosmology and the physics of the interstellar gas may act together to form spiral galaxies by building the angular momentum of disks through early, gas-dominated mergers., Extended version accepted by ApJ, 10 figures (low-resolution)

All-sky thermal and kinetic Sunyaev-Zel'dovich (SZ) maps are presented for assessing how well the PLANCK-mission can find and characterise clusters of galaxies, especially in the presence of primary anisotropies of the cosmic microwave background (CMB) and various galactic and ecliptic foregrounds. The maps have been constructed from numerical simulations of structure formation in a standard LCDM cosmology and contain all clusters out to redshifts of z = 1.46 with masses exceeding 5e13 M_solar/h. By construction, the maps properly account for the evolution of cosmic structure, the halo-halo correlation function, the evolving mass function, halo substructure and adiabatic gas physics. The velocities in the kinetic map correspond to the actual density environment at the cluster positions. We characterise the SZ-cluster sample by measuring the distribution of angular sizes, the integrated thermal and kinetic Comptonisations, the source counts in the three relevant PLANCK-channels, and give the angular power-spectra of the SZ-sky. While our results are broadly consistent with simple estimates based on scaling relations and spherically symmetric cluster models, some significant differences are seen which may affect the number of cluster detectable by PLANCK.

We implement the hydro-PM (HPM) technique (Gnedin & Hui 1998) in the hydrodynamical simulation code GADGET-II and quantify the differences between this approximate method and full hydrodynamical simulations of the Lyman-alpha forest in a concordance LCDM model. At redshifts z=3 and z=4, the differences between the gas and dark matter (DM) distributions, as measured by the one-point distribution of density fluctuations, the density power spectrum and the flux power spectrum, systematically decrease with increasing resolution of the HPM simulqation. However, reducing these differences to less than a few percent requires a significantly larger number of grid-cells than particles, with a correspondingly larger demand for memory. Significant differences in the flux decrement distribution remain even for very high resolution hydro-PM simulations, particularly at low redshift. At z=2, the differences between the flux power spectra obtained from HPM simulations and full hydrodynamical simulations are generally large and of the order of 20-30 %, and do not decrease with increasing resolution of the HPM simulation. This is due to the presence of large amounts of shock-heated gas, a situation which is not adequately modelled by the HPM approximation. We confirm the results of Gnedin & Hui (1998) that the statistical properties of the flux distribution are discrepant by > 5-20 % when compared to full hydrodynamical simulations. The discrepancies in the flux power spectrum are strongly scale- and redshift-dependent and extend to large scales. Considerable caution is needed in attempts to use calibrated HPM simulations for quantitative predictions of the flux power spectrum and other statistical properties of the Lyman-alpha forest.

(Abridged) We examine the evolution of the black hole mass - stellar velocity dispersion (M-sigma) relation over cosmic time using simulations of galaxy mergers that include feedback from supermassive black hole growth. We consider mergers of galaxies varying the properties of the progenitors to match those expected at redshifts z=0-6. We find that the slope of the resulting M-sigma relation is the same at all redshifts considered. For the same feedback efficiency that reproduces the observed amplitude of the M-sigma relation at z=0, there is a weak redshift-dependence to the normalization that results from an increasing velocity dispersion for a given galactic stellar mass. We develop a formalism to connect redshift evolution in the M-sigma relation to the scatter in the local relation at z=0. We show that the scatter in the local relation places severe constraints on the redshift evolution of both the normalization and slope of the M-sigma relation. Furthermore, we demonstrate that cosmic downsizing introduces a black hole mass-dependent dispersion in the M-sigma relation and that the skewness of the distribution about the locally observed M-sigma relation is sensitive to redshift evolution in the normalization and slope. In principle, these various diagnostics provide a method for differentiating between theories for producing the M-sigma relation. In agreement with existing constraints, our simulations imply that hierarchical structure formation should produce the relation with small intrinsic scatter.

(Abridged) Based on numerical simulations of galaxy mergers that incorporate black hole (BH) growth, we predict the faint end slope of the quasar luminosity function (QLF) and its evolution with redshift. Our simulations have yielded a new model for quasar lifetimes where the lifetime depends on both the instantaneous and peak quasar luminosities. This motivates a new interpretation of the QLF in which the bright end consists of quasars radiating at nearly their peak luminosities, but the faint end is mostly made up of quasars in less luminous phases of evolution. The faint-end QLF slope is then determined by the faint-end slope of the quasar lifetime for quasars with peak luminosities near the observed break. We determine this slope from the quasar lifetime as a function of peak luminosity, based on a large set of simulations spanning a wide variety of host galaxy, merger, BH, and ISM gas properties. Brighter peak luminosity (higher BH mass) systems undergo more violent evolution, and expel and heat gas more rapidly in the final stages of quasar evolution, resulting in a flatter faint-end slope (as these objects fall below the observed break in the QLF more rapidly). Therefore, as the QLF break luminosity moves to higher luminosities with increasing redshift, implying a larger typical quasar peak luminosity, the faint-end QLF slope flattens. From the quasar lifetime as a function of peak luminosity and this interpretation of the QLF, we predict the faint-end QLF slope and its evolution with redshift in good agreement with observations. Although BHs grow anti-hierarchically (with lower-mass BHs formed primarily at lower redshifts), the observed change in slope and differential or luminosity dependent density evolution in the QLF is completely determined by the luminosity-dependent quasar lifetime and physics of quasar feedback., Comment: 13 pages, 4 figures, submitted to ApJ (Replacement with minor revisions and changed sign convention)

We perform a spectrophotometric analysis of galaxies at redshifts z = 4 - 6 in cosmological SPH simulations of a Lambda CDM universe. Our models include radiative cooling and heating by a uniform UV background, star formation, supernova feedback, and a phenomenological model for galactic winds. Analysing a series of simulations of varying boxsize and particle number allows us to isolate the impact of numerical resolution on our results. Specifically, we determine the luminosity functions in B, V, R, i', and z' filters, and compare the results with observed galaxy surveys done with the Subaru telescope and the Hubble Space Telescope. We find that the simulated galaxies have UV colours consistent with observations and fall in the expected region of the colour-colour diagrams used by the Subaru group. Assuming a uniform extinction of E(B-V) = 0.15, we also find reasonable agreement between simulations and observations in the space density of UV bright galaxies at z = 3 - 6, down to the magnitude limit of each survey. For the same moderate extinction level of E(B-V) ~ 0.15, the simulated luminosity functions match observational data, but have a steep faint-end slope with alpha ~ -2.0. We discuss the implications of the steep faint-end slope found in the simulations.

(ABRIDGED) We present in detail our new 3D numerical models for the accretion of stellar winds on to Sgr A*. In our most sophisticated models, we put stars on realistic orbits around Sgr A*, include `slow' winds (300 km/s), and account for radiative cooling. We first model only one phase `fast' stellar winds (1000 km/s). For wind sources fixed in space, the accretion rate is Mdot ~ 1e-5 Msun/yr, fluctuates by < 10%, and is in a good agreement with previous models. In contrast, Mdot decreases by an order of magnitude for stars following circular orbits, and fluctuates by ~ 50%. Then we allow a fraction of stars to produce slow winds. Much of these winds cool radiatively, forming cold clumps immersed into the X-ray emitting gas. We test two orbital configurations for the stars in this scenario, an isotropic distribution and two rotating discs with perpendicular orientation. The morphology of cold gas is quite sensitive to the orbits. In both cases, however, most of the accreted gas is hot, with an almost constant Mdot ~ 3e-6 Msun/yr, consistent with Chandra observations. The cold gas accretes in intermittent, short but powerful episodes which may give rise to large amplitude variability in the luminosity of Sgr A* on time scales of 10s to 100s of years. The circularisation radii for the flows are ~ 1e3 and 1e4 Rsch, for the one and two-phase wind simulations, respectively, never forming the quasi-spherical accretion flows suggested in some previous work. Our work suggests that, averaged over time scales of 100s to 1000s of years, the radiative and mechanical luminosity of Sgr A* may be substantially higher than it is in its current state. Further improvements of the wind accretion modelling of Sgr A* will rely on improved observational constraints for the wind properties and stellar orbits., 16 pages, 18 colour figures. Accepted by MNRAS. Full resolution paper and movies available at http://www.mpa-garching.mpg.de/~jcuadra/Winds/ . (v2: minor changes)

We take advantage of the largest high-resolution simulation of cosmic structure growth ever carried out -- the Millennium Simulation of the concordance LambdaCDM cosmogony -- to study how the star formation histories, ages and metallicities of elliptical galaxies depend on environment and on stellar mass. We concentrate on a galaxy formation model which is tuned to fit the joint luminosity/colour/morphology distribution of low redshift galaxies. Massive ellipticals in this model have higher metal abundances, older luminosity-weighted ages, shorter star formation timescales, but lower assembly redshifts than less massive systems. Within clusters the typical masses, ages and metal abundances of ellipticals are predicted to decrease, on average, with increasing distance from the cluster centre. We also quantify the effective number of progenitors of ellipticals as a function of present stellar mass, finding typical numbers below 2 for M* < 10^{11} Msun, rising to about 5 for the most massive systems. These findings are consistent with recent observational results that suggest ``down-sizing'' or ``anti-hierarchical'' behaviour for the star formation history of the elliptical galaxy population, despite the fact that our model includes all the standard elements of hierarchical galaxy formation and is implemented on the standard, LambdaCDM cosmogony., 12 pages, 11 figures, minor revisions, MNRAS accepted

We analyse a hydrodynamical simulation model for the recurrent heating of the central intracluster medium (ICM) by active galactic nuclei (AGN). Besides the self-gravity of the dark matter and gas components, our approach includes the radiative cooling and photoheating of the gas, as well as a subresolution multiphase model for star formation and supernova feedback. Additionally, we incorporate a periodic heating mechanism in the form of hot, buoyant bubbles, injected into the intragalactic medium (IGM) during the active phases of the accreting central AGN. We use simulations of isolated cluster halos of different masses to study the bubble dynamics and the heat transport into the IGM. We also apply our model to self-consistent cosmological simulations of the formation of galaxy clusters with a range of masses. Our numerical schemes explore a variety of different assumptions for the spatial configuration of AGN-driven bubbles, for their duty cycles and for the energy injection mechanism, in order to obtain better constraints on the underlying physical picture. We argue that AGN heating can substantially affect the properties of both the stellar and gaseous components of clusters of galaxies. Most importantly, it alters the properties of the central dominant (cD) galaxy by reducing the mass deposition rate of freshly cooled gas out of the ICM, thereby offering an energetically plausible solution to the cooling flow problem. At the same time, this leads to reduced or eliminated star formation in the central cD galaxy, giving it red stellar colours as observed., 22 pages, 15 figures, minor revisions, MNRAS accepted

We simulate the growth of galaxies and their central supermassive black holes by implementing a suite of semi-analytic models on the output of the Millennium Run, a very large simulation of the concordance LCDM cosmogony. Our procedures follow the detailed assembly history of each object and are able to track the evolution of all galaxies more massive than the Small Magellanic Cloud throughout a volume comparable to that of large modern redshift surveys. In this first paper we supplement previous treatments of the growth and activity of central black holes with a new model for `radio' feedback from those AGN that lie at the centre of a quasistatic X-ray emitting atmosphere in a galaxy group or cluster. We show that for energetically and observationally plausible parameters such a model can simultaneously explain: (i) the low observed mass drop-out rate in cooling flows; (ii) the exponential cut-off at the bright end of the galaxy luminosity function; and (iii) the fact that the most massive galaxies tend to be bulge-dominated systems in clusters and to contain systematically older stars than lower mass galaxies. This success occurs because static hot atmospheres form only in the most massive structures, and radio feedback (in contrast, for example, to supernova or starburst feedback) can suppress further cooling and star formation without itself requiring star formation. We discuss possible physical models which might explain the accretion rate scalings required for our phenomenological `radio mode' model to be successful., 21 pages, 12 figures, accepted MNRAS, Millennium Run semi-analytic galaxy catalogues are available for download at http://www.mpa-garching.mpg.de/galform/agnpaper (~9 million galaxies brighter than -17.4 in r), mini Millennium Run catalogues also available for testing purposes

We investigate how the way galaxies acquire their gas across cosmic time in cosmological hydrodynamic simulations is modified by a comprehensive physical model for baryonic feedback processes. To do so, we compare two simulations -- with and without feedback -- both evolved with the moving mesh code AREPO. The feedback runs implement the full physics model of the Illustris simulation project, including star formation driven galactic winds and energetic feedback from supermassive blackholes. We explore: (a) the accretion rate of material contributing to the net growth of galaxies and originating directly from the intergalactic medium, finding that feedback strongly suppresses the raw, as well as the net, inflow of this "smooth mode" gas at all redshifts, regardless of the temperature history of newly acquired gas. (b) At the virial radius the temperature and radial flux of inflowing gas is largely unaffected at z=2. However, the spherical covering fraction of inflowing gas at 0.25 rvir decreases substantially, from more than 80% to less than 50%, while the rates of both inflow and outflow increase, indicative of recycling across this boundary. (c) The fractional contribution of smooth accretion to the total accretion rate is lower in the simulation with feedback, by roughly a factor of two across all redshifts. Moreover, the smooth component of gas with a cold temperature history, is entirely suppressed in the feedback run at z, MNRAS published, comments welcome. The official Illustris website can be found at http://www.illustris-project.org

The formation and early evolution of circumstellar discs often occurs within dense, newborn stellar clusters. For the first time, we apply the moving-mesh code AREPO, to circumstellar discs in 3-D, focusing on disc-disc interactions that result from stellar fly-bys. Although a small fraction of stars are expected to undergo close approaches, the outcomes of the most violent encounters might leave an imprint on the discs and host stars that will influence both their orbits and their ability to form planets. We first construct well-behaved 3-D models of self-gravitating discs, and then create a suite of numerical experiments of parabolic encounters, exploring the effects of pericenter separation r_p, disc orientation and disc-star mass ratio (M_d/M_*) on the orbital evolution of the host stars. Close encounters (2r_p, Comment: 20 pages, 14 figures, 1 table. Published by MNRAS

(Abridged) We describe a new iterative approach for the realization of equilibrium N-body systems for given density distributions. Our method uses elements of Schwarzschild's technique and of the made-to-measure method, but is based on a different principle. Starting with some initial assignment of particle velocities, we calculate their orbits using a flexible tree-based force algorithm in the stationary potential of the target density distribution. The difference of the time-averaged density response produced by these orbits with respect to the initial density configuration is characterized through a merit function, and a stationary solution of the collisionless Boltzmann equation is found by minimizing this merit function directly by iteratively adjusting the initial velocities. Because the distribution function is in general not unique for a given density structure, we augment the merit function with additional constraints that single out a desired target solution. We do this for broad classes of axisymmetric density distributions by numerically solving the Jeans equations to obtain the second velocity moments, which are then imposed as further constraints in the optimization process. The velocity adjustment is carried out with a stochastic process in which new velocities are randomly drawn from an approximate solution of the distribution function, but are kept only when they improve the fit. Our method converges rapidly and is flexible enough to allow the construction of solutions with third integrals of motion, including disk galaxies with realistic velocity distributions. We demonstrate that the new method reproduces analytic distribution functions where they are known (such as the Hernquist sphere), and that it yields very stable N-body realizations for a variety of examples of compound galaxy models, considerably improving on widely used moment-based approaches., Comment: 18 pages, 15 figures, 1 table. Accepted by MNRAS. Minor changes from submitted version. The source code of GALIC is publicly available now and can be downloaded here: http://www.h-its.org/tap/galic/

We have updated the Munich galaxy formation model to the Planck first-year cosmology, while modifying the treatment of baryonic processes to reproduce recent data on the abundance and passive fractions of galaxies from z= 3 down to z=0. Matching these more extensive and more precise observational results requires us to delay the reincorporation of wind ejecta, to lower the surface density threshold for turning cold gas into stars, to eliminate ram-pressure stripping in haloes less massive than ~10^14 Msun, and to modify our model for radio mode feedback. These changes cure the most obvious failings of our previous models, namely the overly early formation of low-mass galaxies and the overly large fraction of them that are passive at late times. The new model is calibrated to reproduce the observed evolution both of the stellar mass function and of the distribution of star formation rate at each stellar mass. Massive galaxies (M>10^11 [Msun]) assemble most of their mass before z=1 and are predominantly old and passive at z=0, while lower mass galaxies assemble later and, for M, Revised to match published MNRAS version. New databases containing the full galaxy data at all redshifts and for both the Millennium and Millennium-II simulations are publicly released at http://www.mpa-garching.mpg.de/millennium/. Submission includes 15 pages of Supplementary Material with a full description of the treatment of astrophysical processes

We describe techniques for incorporating feedback from star formation and black hole accretion into simulations of isolated and merging galaxies. At present, the details of these processes cannot be resolved in simulations on galactic scales. Our basic approach therefore involves forming coarse-grained representations of the properties of the interstellar medium and black hole accretion starting from basic physical assumptions, so that the impact of these effects can be included on resolved scales. We illustrate our method using a multiphase description of star-forming gas. Feedback from star formation pressurises highly overdense gas, altering its effective equation of state. We show that this allows the construction of stable galaxy models with much larger gas fractions than possible in earlier numerical work. We extend the model by including a treatment of gas accretion onto central supermassive black holes in galaxies. Assuming thermal coupling of a small fraction of the bolometric luminosity of accreting black holes to the surrounding gas, we show how this feedback regulates the growth of black holes. In gas-rich mergers of galaxies, we observe a complex interplay between starbursts and central AGN activity when the tidal interaction triggers intense nuclear inflows of gas. Once an accreting supermassive black hole has grown to a critical size, feedback terminates its further growth, and expels gas from the central region in a powerful quasar-driven wind. Our simulation methodology is therefore able to address the coupled processes of gas dynamics, star formation, and black hole accretion during the formation of galaxies., Comment: submitted to MNRAS, 20 pages, 16 figures (partly reduced in resolution)

Recent observations have revealed a population of red massive galaxies at high redshift which are challenging to explain in hierarchical galaxy formation models. We analyze this ``massive galaxy problem'' with two different types of hydrodynamic simulations -- Eulerian TVD and SPH -- of a concordance Lambda CDM universe. We consider two separate but connected aspects of the problem posed by these extremely red objects (EROs): (1) the mass-scale, and (2) red colors. We perform spectrophotometric analyses of simulated galaxies in B, z, R, I, Js, Ks, K filters, and compare their near-IR properties with observations at redshift z=1-3. We find that the simulated galaxies brighter than the magnitude limit of K_vega=20 mag have stellar masses Mstar >= 10^{11} Msun/h and a number density of a few \times 10^{-4} h^3 Mpc^{-3} at z~2, in good agreement with the observed number density in the K20 survey. Therefore, our hydrodynamic simulations do not exhibit the ``mass-scale problem''. The answer to the ``redness problem'' is less clear because of our poor knowledge of the amount of dust extinction in EROs and the uncertain fraction of star-forming EROs. However, our simulations can account for the observed comoving number density of ~ 1e-4 Mpc^{-3} at z=1-2 if we assume a uniform extinction of E(B-V)=0.4 for the entire population of simulated galaxies. The critical question of the existence of a significant population of old, passively evolving massive EROs should continue to be tested with future hydrodynamic simulations. Upcoming observations of the thermal emission of dust in 24 micron by the Spitzer Space Telescope will help to better estimate the dust content of EROs at z=1-3, and thus to further constrain the star formation history of the Universe, and theoretical models of galaxy formation. (abridged)

Sgr A* is currently being fed by winds from a cluster of gravitationally bound young mass-loosing stars. Using observational constraints on the orbits, mass loss rates and wind velocities of these stars, we numerically model the distribution of gas in the ~ 0.1--10'' region around Sgr A*. We find that radiative cooling of recently discovered slow winds leads to the formation of many cool filaments and blobs, and to a thin and rather light accretion disc of about an arcsecond scale. The disc however does not extend all the way to our inner boundary. Instead, hot X-ray emitting gas dominates the inner arcsecond. In our simulations, cool streams of gas frequently enter this region on low angular momentum orbits, and are then disrupted and heated up to the ambient hot gas temperature. The accreting gas around Sgr A* is thus two-phase, with a hot component, observable at X-ray wavelengths, and a cool component, which may be responsible for the majority of time variability of Sgr A* emission on hundred and thousand years time-scales. We obtain an accretion rate of a few times 10^-6 msun/year, consistent with Chandra estimates, but variable on time-scales even shorter than hundred years. These results strongly depend on the chosen stellar orbits and wind parameters. Further observational input is thus key to a better modelling of Sgr A* wind accretion., 5 pages, 2 figures. MNRAS Letter, accepted. For associated movies, see http://www.mpa-garching.mpg.de/~jcuadra/Winds . (v2: extended discussion and description of the numerical method.)

The cold dark matter model has become the leading theoretical picture for the formation of structure in the Universe. This model, together with the theory of cosmic inflation, makes a clear prediction for the initial conditions for structure formation and predicts that structures grow hierarchically through gravitational instability. Testing this model requires that the precise measurements delivered by galaxy surveys can be compared to robust and equally precise theoretical calculations. Here we present a simulation of the growth of dark matter structure using 2,160(3) particles, following them from redshift z = 127 to the present in a cube-shaped region 2.230 billion lightyears on a side. In postprocessing, we also follow the formation and evolution of the galaxies and quasars. We show that baryon-induced features in the initial conditions of the Universe are reflected in distorted form in the low-redshift galaxy distribution, an effect that can be used to constrain the nature of dark energy with future generations of observational surveys of galaxies.