Volker Springel

The cosmological simulation code gadget-2

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 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 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. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

Simulations of the formation, evolution and clustering of galaxies and quasars

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 2,1603 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.Numerical simulations are a primary theoretical tool to study the nonlinear gravitational growth of structure in the Universe, and to link the initial conditions of cold dark matter (CDM) cosmogonies to observations of galaxies at the present day. Without direct numerical simulation, the hierarchical build-up of structure with its threedimensional dynamics would be largely inaccessible. Since the dominant mass component, the dark matter, is assumed to consist of weakly interacting elementary particles that interact only gravitationally, such simulations use a set of discrete point particles to represent the collisionless dark matter fluid. This representation as an N-body system is obviously only a coarse approximation, and im-

Energy input from quasars regulates the growth and activity of black holes and their host 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 centres of most galaxies today, 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. This suggests a link between the growth of the black holes and their host galaxies, 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 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, 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 dispersion.

Modelling feedback from stars and black holes in galaxy mergers

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.

Cosmological smoothed particle hydrodynamics simulations: a hybrid multiphase model for star formation

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.

Populating a cluster of galaxies – I. Results at z = 0

ABSTRA C T We 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 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.

GADGET: A Code for collisionless and gasdynamical cosmological simulations

Abstract 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 7.5×107 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 publicly release both the serial and the massively parallel version of the code.

The Aquarius project: the subhaloes of galactic haloes

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 halos 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 similar to 2.6 times larger and increases with decreasing distance from halo centre.

A Unified, Merger-driven Model of the Origin of Starbursts, Quasars, the Cosmic X-Ray Background, Supermassive Black Holes, and Galaxy Spheroids

We present an evolutionary model for starbursts, quasars, and spheroidal galaxies in which mergers between gas-rich galaxies drive nuclear inflows of gas, producing starbursts and feeding the buried growth of supermassive black holes (BHs) until feedback expels gas and renders a briefly visible optical quasar. The quasar lifetime and obscuring column density depend on both the instantaneous and peak quasar luminosity, and we determine this dependence using a large set of galaxy merger simulations varying galaxy properties, orbital geometry, and gas physics. We use these fits to deconvolve observed quasar luminosity functions and obtain the evolution of the formation rate of quasars with peak luminosity, (Lpeak, z). Quasars spend extended periods at luminosities well below peak, so (Lpeak) has a maximum corresponding to the break in the observed luminosity function. From (Lpeak) and our simulations, we obtain self-consistent hard and soft X-ray and optical luminosity functions and predict many observables at multiple redshifts, including column density distributions of optical and X-ray samples, the luminosity function of broad-line quasars in X-ray samples and broad-line fraction versus luminosity, active BH mass functions, the distribution of Eddington ratios, the mass function of relic BHs and total BH mass density, and the cosmic X-ray background. In every case, our predictions agree well with observed estimates, without invoking ad hoc assumptions about source properties or distributions. We provide a library of Monte Carlo realizations of our models for comparison with observations.

Cosmological smoothed particle hydrodynamics simulations: the entropy equation

We discuss differences in simulation results that arise between the use of either the thermal energy or the entropy as an independent variable in smoothed particle hydrodynamics (SPH). In this context, we derive a new version of SPH that manifestly conserves both energy and entropy if smoothing lengths are allowed to adapt freely to the local mass resolution. To test various formu- lations of SPH, we consider point-like energy injection and find that powerful explosions are well represented by SPH even when the energy is deposited into a single particle, provided that the entropy equation is integrated. If the thermal energy is instead used as an independent variable, unphysical solutions can be obtained for this problem. We also examine the radiative cooling of gas spheres that collapse and virialize in isolation and of halos that form in cosmological simulations of structure formation. When applied to these problems, the thermal energy version of SPH leads to substantial overcooling in halos that are resolved with up to a few thousand particles, while the entropy formulation is biased only moderately low for these halos. For objects resolved with much larger particle numbers, the two approaches yield consistent results. We trace the origin of the differences to systematic resolution effects in the outer parts of cooling flows. The cumulative effect of this overcooling can be significant. In cosmological simulations of moderate size, we find that the fraction of baryons which cool and condense can be reduced by up to a factor ~2 if the entropy equation is employed rather than the thermal energy equation. We also demonstrate that the entropy method leads to a greatly reduced scatter in the density-temperature relation of the low-density Ly-alpha forest relative to the thermal energy approach, in accord with theoretical expectations.(abridged)