We discuss the cosmological simulation code gadget‐2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N‐body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short‐range forces are computed with the ‘tree’ method while long‐range forces are determined with Fourier techniques. Time integration is based on a quasi‐symplectic scheme where long‐range and short‐range forces can be integrated with different time‐steps. Individual and adaptive short‐range time‐steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space‐filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N‐body simulation with more than 1010 dark matter particles, reaching a homogeneous spatial dynamic range of 105 per dimension in a three‐dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. gadget‐2 is publicly released to the research community.

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.

In the early Universe, while galaxies were still forming, black holes as massive as a billion solar masses powered quasars. Supermassive black holes are found at the centers of most galaxies today 1,2,3 , where their masses are related to the velocity dispersions of stars in their host galaxies and hence to the mass of the central bulge of the galaxy 4,5 . This suggests a link between the growth of the black holes and the host galaxies 6,7,8,9 , which has indeed been assumed for a number of years. But the origin of the observed relation between black hole mass and stellar velocity dispersion, and its connection with the evolution of galaxies have remained unclear. Here we report hydrodynamical simulations that simultaneously follow star formation and the growth of black holes during galaxy-galaxy collisions. We find that in addition to generating a burst of star formation 10 , a merger leads to strong inflows that feed gas to the supermassive black hole and thereby power the quasar. The energy released by the quasar expels enough gas to quench both star formation and further black hole growth. This determines the lifetime of the quasar phase (approaching 100 million years) and explains the relationship between the black hole mass and the stellar velocity

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 have performed the largest ever particle simulation of a Milky Way sized dark matter halo, and present the most comprehensive convergence study for an individual dark matter halo carried out thus far. We have also simulated a sample of six ultrahighly resolved Milky Way sized haloes, allowing us to estimate the halo-to-halo scatter in substructure statistics. In our largest simulation, we resolve nearly 300 000 gravitationally bound subhaloes within the virialized region of the halo. Simulations of the same object differing in mass resolution by factors of up to 1800 accurately reproduce the largest subhaloes with the same mass, maximum circular velocity and position, and yield good convergence for the abundance and internal properties of dark matter substructures. We detect up to four generations of subhaloes within subhaloes, but contrary to recent claims, we find less substructure in subhaloes than in the main halo when regions of equal mean overdensity are compared. The overall substructure mass fraction is much lower in subhaloes than in the main halo. Extrapolating the main halo's subhalo mass spectrum down to an Earth mass, we predict the mass fraction in substructure to be well below 3 per cent within 100 kpc, and to be below 0.1 per cent within the solar circle. The inner density profiles of subhaloes show no sign of converging to a fixed asymptotic slope and are well fitted by gently curving profiles of Einasto form. The mean concentrations of isolated haloes are accurately described by the fitting formula of Neto et al. down to maximum circular velocities of 1.5 km s −1 , an extrapolation over some five orders of magnitude in mass. However, at equal maximum circular velocity, subhaloes are more concentrated than field haloes, with a characteristic density that is typically ∼2.6 times larger and increases with decreasing distance from halo centre.

We present a model for star formation and supernova feedback that describes the multiphase structure of star‐forming gas on scales that are typically not resolved in cosmological simulations. Our approach includes radiative heating and cooling, the growth of cold clouds embedded in an ambient hot medium, star formation in these clouds, feedback from supernovae in the form of thermal heating and cloud evaporation, galactic winds and outflows, and metal enrichment. Implemented using smoothed particle hydrodynamics, our scheme is a significantly modified and extended version of the grid‐based method of Yepes et al., and enables us to achieve a high dynamic range in simulations of structure formation. We discuss properties of the feedback model in detail and show that it predicts a self‐regulated, quiescent mode of star formation, which, in particular, stabilizes the star‐forming gaseous layers of disc galaxies. The parametrization of this mode can be reduced to a single free quantity that determines the overall time‐scale for star formation. We fix this parameter numerically to match the observed rates of star formation in local disc galaxies. When normalized in this manner, cosmological simulations employing our model nevertheless overproduce the observed cosmic abundance of stellar material. We are thus motivated to extend our feedback model to include galactic winds associated with star formation. Using small‐scale simulations of individual star‐forming disc galaxies, we show that these winds produce either galactic fountains or outflows, depending on the depth of the gravitational potential. In low‐mass haloes, winds can greatly suppress the overall efficiency of star formation. When incorporated into cosmological simulations, our combined model for star formation and winds predicts a cosmic star formation density that is consistent with observations, provided that the winds are sufficiently energetic. Moreover, outflows from galaxies in these simulations drive chemical enrichment of the intergalactic medium – in principle, accounting for the presence of metals in the Lyman α forest.

A B S T R A C TWe simulate the assembly of a massive rich cluster and the formation of its constituent galaxies in a flat, low-density universe. Our most accurate model follows the collapse, the star formation history and the orbital motion of all galaxies more luminous than the Fornax dwarf spheroidal, while dark halo structure is tracked consistently throughout the cluster for all galaxies more luminous than the SMC. Within its virial radius this model contains about 2 Â 10 7 dark matter particles and almost 5000 distinct dynamically resolved galaxies. Simulations of this same cluster at a variety of resolutions allow us to check explicitly for numerical convergence both of the dark matter structures produced by our new parallel N-body and substructure identification codes, and of the galaxy populations produced by the phenomenological models we use to follow cooling, star formation, feedback and stellar aging. This baryonic modelling is tuned so that our simulations reproduce the observed properties of isolated spirals outside clusters. Without further parameter adjustment our simulations then produce a luminosity function, a mass-to-light ratio, luminosity, number and velocity dispersion profiles, and a morphology -radius relation which are similar to those observed in real clusters. In particular, since our simulations follow galaxy merging explicitly, we can demonstrate that it accounts quantitatively for the observed cluster population of bulges and elliptical galaxies.

We describe techniques for incorporating feedback from star formation and black hole (BH) 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 (ISM) and BH 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 pressurizes highly overdense gas, altering its effective equation of state (EOS). 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 BHs in galaxies. Assuming thermal coupling of a small fraction of the bolometric luminosity of accreting BHs to the surrounding gas, we show how this feedback regulates the growth of BHs. In gas‐rich mergers of galaxies, we observe a complex interplay between starbursts and central active galactic nuclei (AGN) activity when the tidal interaction triggers intense nuclear inflows of gas. Once an accreting supermassive BH 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 BH accretion during the formation of galaxies.