H. M. P. Couchman

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-

Stable clustering, the halo model and non-linear cosmological power spectra

We present the results of a large library of cosmological N-body simulations, using power-law initial spectra.

The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions

We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including smoothed particle hydrodynamics (SPH) and grid methods with fixed, deformable, or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gasdynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be nonradiative. We compare images of the cluster at different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying, although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of 2. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to within about 10%, and the ratio of specific dark matter kinetic to gas thermal energies agree to within about 5%. Various factors, including differences in the internal timing of the simulations, contribute to the spread in calculated cluster properties. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modeled.

The Aquila comparison project: the effects of feedback and numerical methods on simulations of galaxy formation

We compare the results of various cosmological gas-dynamical codes used to simulate the formation of a galaxy in the Λ cold dark matter structure formation paradigm. The various runs (13 in total) differ in their numerical hydrodynamical treatment [smoothed particle hydrodynamics (SPH), moving mesh and adaptive mesh refinement] but share the same initial conditions and adopt in each case their latest published model of gas cooling, star formation and feedback. Despite the common halo assembly history, we find large code-to-code variations in the stellar mass, size, morphology and gas content of the galaxy at z= 0, due mainly to the different implementations of star formation and feedback. Compared with observation, most codes tend to produce an overly massive galaxy, smaller and less gas rich than typical spirals, with a massive bulge and a declining rotation curve. A stellar disc is discernible in most simulations, although its prominence varies widely from code to code. There is a well-defined trend between the effects of feedback and the severity of the disagreement with observed spirals. In general, models that are more effective at limiting the baryonic mass of the galaxy come closer to matching observed galaxy scaling laws, but often to the detriment of the disc component. Although numerical convergence is not particularly good for any of the codes, our conclusions hold at two different numerical resolutions. Some differences can also be traced to the different numerical techniques; for example, more gas seems able to cool and become available for star formation in grid-based codes than in SPH. However, this effect is small compared to the variations induced by different feedback prescriptions. We conclude that state-of-the-art simulations cannot yet uniquely predict the properties of the baryonic component of a galaxy, even when the assembly history of its host halo is fully specified. Developing feedback algorithms that can effectively regulate the mass of a galaxy without hindering the formation of high angular momentum stellar discs remains a challenge.

Making Galaxies In a Cosmological Context: the need for early stellar feedback

We introduce the Making Galaxies in a Cosmological Context (MaGICC) program of smoothed particle hydrodynamics (SPH) simulations. We describe a parameter study of galaxy formation simulations of an L* galaxy that uses early stellar feedback combined with supernova feedback to match the stellar mass--halo mass relationship. While supernova feedback alone can reduce star formation enough to match the stellar mass--halo mass relationship, the galaxy forms too many stars before z=2 to match the evolution seen using abundance matching. Our early stellar feedback is purely thermal and thus operates like a UV ionization source as well as providing some additional pressure from the radiation of massive, young stars. The early feedback heats gas to >10^6 K before cooling to 10^4 K. The pressure from this hot gas creates a more extended disk and prevents more star formation prior to z=1 than supernovae feedback alone. The resulting disk galaxy has a flat rotation curve, an exponential surface brightness profile, and matches a wide range of disk scaling relationships. The disk forms from the inside-out with an increasing exponential scale length as the galaxy evolves. Overall, early stellar feedback helps to simulate galaxies that match observational results at low and high redshifts.

Hydra: an Adaptive-Mesh Implementation of P 3M-SPH

We present an implementation of Smoothed Particle Hydrodynamics (SPH) in an adaptive-mesh PPPM algorithm. The code evolves a mixture of purely gravitational particles and gas particles. The code retains the desirable properties of previous PPPM--SPH implementations; speed under light clustering, naturally periodic boundary conditions and accurate pairwise forces. Under heavy clustering the cycle time of the new code is only 2--3 times slower than for a uniform particle distribution, overcoming the principal disadvantage of previous implementations\dash a dramatic loss of efficiency as clustering develops. A 1000 step simulation with 65,536 particles (half dark, half gas) runs in one day on a Sun Sparc10 workstation. The choice of time integration scheme is investigated in detail. A simple single-step Predictor--Corrector type integrator is most efficient. A method for generating an initial distribution of particles by allowing a a uniform temperature gas of SPH particles to relax within a periodic box is presented. The average SPH density that results varies by

Stellar feedback in dwarf galaxy formation.

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The removal of cusps from galaxy centres by stellar feedback in the early Universe

\%. We present a modified form of the Layzer--Irvine equation which includes the thermal contribution of the gas together with radiative cooling. Tests of sound waves, shocks, spherical infall and collapse are presented. Appropriate timestep constraints sufficient to ensure both energy and entropy conservation are discussed. A cluster simulation, repeating Thomas and

Implementing Feedback in Simulations of Galaxy Formation: A Survey of Methods

Dwarf galaxies pose substantial challenges for cosmological models. In particular, current models predict a dark-matter density that is divergent at the center, which is in sharp contrast with observations that indicate a core of roughly constant density. Energy feedback, from supernova explosions and stellar winds, has been proposed as a major factor shaping the evolution of dwarf galaxies. We present detailed cosmological simulations with sufficient resolution both to model the relevant physical processes and to directly assess the impact of stellar feedback on observable properties of dwarf galaxies. We show that feedback drives large-scale, bulk motions of the interstellar gas, resulting in substantial gravitational potential fluctuations and a consequent reduction in the central matter density, bringing the theoretical predictions in agreement with observations.

Halo Expansion in Cosmological Hydro Simulations: Toward a Baryonic Solution of the Cusp/Core Problem in Massive Spirals

The standard cosmological model, now strongly constrained by direct observations of the Universe at early epochs, is very successful in describing the evolution of structure on large and intermediate scales. Unfortunately, serious contradictions remain on smaller, galactic scales. Among the main small-scale problems is a significant and persistent discrepancy between observations of nearby galaxies, which imply that galactic dark matter haloes have a density profile with a flat core, and the cosmological model, which predicts that the haloes should have divergent density (a cusp) at the centre. Here we report numerical simulations that show that random bulk motions of gas in small primordial galaxies, of the magnitude expected in these systems, will result in a flattening of the central dark matter cusp on relatively short timescales (∼108 years). Gas bulk motions in early galaxies are driven by supernova explosions that result from ongoing star formation. Our mechanism is general, and would have operated in all star-forming galaxies at redshifts z ≥ 10. Once removed, the cusp cannot be reintroduced during the subsequent mergers involved in the build-up of larger galaxies. As a consequence, in the present Universe both small and large galaxies would have flat dark matter core density profiles, in agreement with observations.The standard cosmological model, now strongly constrained by direct observation at early epochs, is very successful in describing the structure of the evolved universe on large and intermediate scales. Unfortunately, serious contradictions remain on smaller, galactic scales. Among the major small-scale problems is a significant and persistent discrepancy between observations of nearby galaxies, which imply that galactic dark matter (DM) haloes have a density profile with a flat core, and the cosmological model, which predicts that the haloes should have divergent density (a cusp) at the centre. Here we use numerical N-body simulations to show that random bulk motions of gas in small primordial galaxies, of the magnitude expected in these systems, result in a flattening of the central DM cusp on short timescales (of order 10^8 years). Gas bulk motions in early galaxies are driven by supernova explosions which result from ongoing star formation. Our mechanism is general and would have operated in all star-forming galaxies at redshifts z>~ 10. Once removed, the cusp cannot be reintroduced during the subsequent mergers involved in the build-up of larger galaxies. As a consequence, in the present universe both small and large galaxies would have flat DM core density profiles, in agreement with observations.