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.

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 Λ cold dark matter 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 active galactic nuclei that lie at the centre of a quasi‐static 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 that might explain the accretion rate scalings required for our phenomenological ‘radio mode’ model to be successful.

We describe the newly written code GADGET which is suitable both for cosmological simulations of structure formation and for the simulation of interacting galaxies. GADGET evolves self-gravitating collisionless fluids with the traditional N-body approach, and a collisional gas by smoothed particle hydrodynamics. Along with the serial version of the code, we discuss a parallel version that has been designed to run on massively parallel supercomputers with distributed memory. While both versions use a tree algorithm to compute gravitational forces, the serial version of GADGET can optionally employ the special-purpose hardware GRAPE instead of the tree. Periodic boundary conditions are supported by means of an Ewald summation technique. The code uses individual and adaptive timesteps for all particles, and it combines this with a scheme for dynamic tree updates. Due to its Lagrangian nature, GADGET thus allows a very large dynamic range to be bridged, both in space and time. So far, GADGET has been successfully used to run simulations with up to 7.5×10 7 particles, including cosmological studies of large-scale structure formation, high-resolution simulations of the formation of clusters of galaxies, as well as workstation-sized problems of interacting galaxies. In this study, we detail the numerical algorithms employed, and show various tests of the code. We publically release both the serial and the massively parallel version of the code.

We combine data from a number of N‐body simulations to predict the abundance of dark haloes in cold dark matter (CDM) universes over more than four orders of magnitude in mass. A comparison of different simulations suggests that the dominant uncertainty in our results is systematic and is smaller than 10–30 per cent at all masses, depending on the halo definition used. In particular, our ‘Hubble volume’ simulations of τCDM and ΛCDM cosmologies allow the abundance of massive clusters to be predicted with uncertainties well below those expected in all currently planned observational surveys. We show that for a range of CDM cosmologies and for a suitable halo definition, the simulated mass function is almost independent of epoch, of cosmological parameters and of the initial power spectrum when expressed in appropriate variables. This universality is of exactly the kind predicted by the familiar Press–Schechter model, although this model predicts a mass function shape that differs from our numerical results, overestimating the abundance of ‘typical’ haloes and underestimating that of massive systems.

Primordial stars are formed from a chemically pristine gas consisting of hydrogen and helium. They are believed to have been born at some early epoch in the history of the Universe and to have enriched the interstellar medium with synthesized heavy elements before the emergence of ordinary stellar populations. We study the formation of the first generation of stars in the standard cold dark matter model. We follow the gravitational collapse and thermal evolution of primordial gas clouds within early cosmic structures using very high-resolution, cosmological hydrodynamic simulations. Our simulation achieves a dynamic range of ∼ 10 10 in length scale. With accurate treatment of atomic and molecular physics, it allows us to study the chemo-thermal evolution of primordial gas clouds to densities up to ρ ∼ 2 × 10 −8 g cm −3 (n H ∼ 10 16 cm −3 ) without assuming any a priori equation of state; a six orders of magnitudes improvement over previous three-dimensional calculations. We implement an extensive chemistry network for hydrogen, helium and deuterium. All the relevant atomic and molecular cooling and heating processes, including cooling by collision-induced continuum emission, are implemented. For calculating optically thick H 2 cooling at high densities, we use the Sobolev method (Sobolev 1960) and evaluate the molecular line opacities for a few hundred lines. We validate the accuracy of the method by performing a spherical collapse test and comparing the results with those of accurate one-dimensional calculations that treat the line radiative transfer problem in a fully self-consistent manner.We then perform a cosmological simulation adopting the standard ΛCDM model. Dense gas clumps are formed at the centers of low mass (∼ 10 5−6 M ⊙ ) dark matter halos at redshifts z ∼ 20, and they collapse gravitationally when the cloud mass exceeds a few hundred solar masses. To examine possible gas fragmentation owing to thermal instability, we compute explicitly the growth rate of isobaric perturbations. We show that the cloud core does not fragment in either the low-density (n H ∼ 10 10 cm −3 ) or high-density (∼ 10 15 cm −3 ) regimes, where gas cooling rate is increased owing to three-body molecule formation and collision-induced emission, respectively. The cloud core becomes marginally unstable against chemo-thermal instability in the low-density regime. However, since the core is already compact at that point and correspondingly the sound-crossing time as well as the free-fall time are short, or comparable to the perturbation growth timescale, it does not fragment. Run-away cooling simply leads to fast condensation of the core to form a single proto-stellar seed. We also show that the core remains stable against gravitational deformation and fragmentation throughout the evolution. We trace in Lagrangian space the gas elements that end up at the center of the cloud, and study the evolution of the specific angular momentum. We show that, during the final dynamical collapse, small angular momentum material collapses faster...