Katrin Heitmann

THE COYOTE UNIVERSE. I. PRECISION DETERMINATION OF THE NONLINEAR MATTER POWER SPECTRUM

Near-future cosmological observations targeted at investigations of dark energy pose stringent requirements on the accuracy of theoretical predictions for the nonlinear clustering of matter. Currently, N-body simulations comprise the only viable approach to this problem. In this paper, we study various sources of computational error and methods to control them. By applying our methodology to a large suite of cosmological simulations we show that results for the (gravity-only) nonlinear matter power spectrum can be obtained at 1% accuracy out to k {approx} 1 h Mpc{sup -1}. The key components of these high accuracy simulations are precise initial conditions, very large simulation volumes, sufficient mass resolution, and accurate time stepping. This paper is the first in a series of three; the final aim is a high-accuracy prediction scheme for the nonlinear matter power spectrum that improves current fitting formulae by an order of magnitude.

The Halo Mass Function: High-Redshift Evolution and Universality

We study the formation of dark matter halos in the concordance ΛCDM model over a wide range of redshifts, from -->z = 20 to the present. Our primary focus is the halo mass function, a key probe of cosmology. By performing a large suite of nested-box N-body simulations with careful convergence and error controls (60 simulations with box sizes from 4 to 256 h−1 Mpc), we determine the mass function and its evolution with excellent statistical and systematic errors, reaching a few percent over most of the considered redshift and mass range. Across the studied redshifts, the halo mass is probed over 6 orders of magnitude (107-1013.5 h−1 M☉). Historically, there has been considerable variation in the high-redshift mass function as obtained by different groups. We have made a concerted effort to identify and correct possible systematic errors in computing the mass function at high redshift and to explain the discrepancies between some of the previous results. We discuss convergence criteria for the required force resolution, simulation box size, halo mass range, initial and final redshifts, and time stepping. Because of conservative cuts on the mass range probed by individual boxes, our results are relatively insensitive to simulation volume, the remaining sensitivity being consistent with extended Press-Schechter theory. Previously obtained mass function fits near -->z = 0, when scaled by linear theory, are in good agreement with our results at all redshifts, although a mild redshift dependence consistent with that found by Reed et al. may exist at low redshifts. Overall, our results are consistent with a universal form for the mass function at high redshifts.

THE COYOTE UNIVERSE. III. SIMULATION SUITE AND PRECISION EMULATOR FOR THE NONLINEAR MATTER POWER SPECTRUM

Many of the most exciting questions in astrophysics and cosmology, including the majority of observational probes of dark energy, rely on an understanding of the nonlinear regime of structure formation. In order to fully exploit the information available from this regime and to extract cosmological constraints, accurate theoretical predictions are needed. Currently, such predictions can only be obtained from costly, precision numerical simulations. This paper is the third in a series aimed at constructing an accurate calibration of the nonlinear mass power spectrum on Mpc scales for a wide range of currently viable cosmological models, including dark energy models with w ≠ –1. The first two papers addressed the numerical challenges and the scheme by which an interpolator was built from a carefully chosen set of cosmological models. In this paper, we introduce the Coyote Universe simulation suite which comprises nearly 1000 N-body simulations at different force and mass resolutions, spanning 38 w CDM cosmologies. This large simulation suite enables us to construct a prediction scheme, or emulator, for the nonlinear matter power spectrum accurate at the percent level out to k 1 h Mpc–1. We describe the construction of the emulator, explain the tests performed to ensure its accuracy, and discuss how the central ideas may be extended to a wider range of cosmological models and applications. A power spectrum emulator code is released publicly as part of this paper.

THE COYOTE UNIVERSE. II. COSMOLOGICAL MODELS AND PRECISION EMULATION OF THE NONLINEAR MATTER POWER SPECTRUM

The power spectrum of density fluctuations is a foundational source of cosmological information. Precision cosmological probes targeted primarily at investigations of dark energy require accurate theoretical determinations of the power spectrum in the nonlinear regime. To exploit the observational power of future cosmological surveys, accuracy demands on the theory are at the 1% level or better. Numerical simulations are currently the only way to produce sufficiently error-controlled predictions for the power spectrum. The very high computational cost of (precision) N-body simulations is a major obstacle to obtaining predictions in the nonlinear regime, while scanning over cosmological parameters. Near-future observations, however, are likely to provide a meaningful constraint only on constant dark energy equation of state, wCDM, cosmologies. In this paper, we demonstrate that a limited set of only 37 cosmological models—the Coyote Universe suite—can be used to predict the nonlinear matter power spectrum to 1% over a prior parameter range set by current cosmic microwave background observations. This paper is the second in a series of three, with the final aim to provide a high-accuracy prediction scheme for the nonlinear matter power spectrum for wCDM cosmologies.

MASS FUNCTION PREDICTIONS BEYOND ΛCDM

The statistics of dark matter halos is an essential component of precision cosmology. The mass distribution of halos, as specified by the halo mass function, is a key input for several cosmological probes. The sizes of N-body simulations are now such that, for the most part, results need no longer be statistics-limited, but are still subject to various systematic uncertainties. Discrepancies in the results of simulation campaigns for the halo mass function remain in excess of statistical uncertainties and of roughly the same size as the error limits set by near-future observations; we investigate and discuss some of the reasons for these differences. Quantifying error sources and compensating for them as appropriate, we carry out a high-statistics study of dark matter halos from 67 N-body simulations to investigate the mass function and its evolution for a reference ?CDM cosmology and for a set of wCDM cosmologies. For the reference ?CDM cosmology (close to WMAP5), we quantify the breaking of universality in the form of the mass function as a function of redshift, finding an evolution of as much as 10% away from the universal form between redshifts z = 0 and z = 2. For cosmologies very close to this reference we provide a fitting formula to our results for the (evolving) ?CDM mass function over a mass range of 6 ? 1011-3 ? 1015 M ? to an estimated accuracy of about 2%. The set of wCDM cosmologies is taken from the Coyote Universe simulation suite. The mass functions from this suite (which includes a ?CDM cosmology and others with w ?1) are described by the fitting formula for the reference ?CDM case at an accuracy level of 10%, but with clear systematic deviations. We argue that, as a consequence, fitting formulae based on a universal form for the mass function may have limited utility in high-precision cosmological applications.

ROBUSTNESS OF COSMOLOGICAL SIMULATIONS. I. LARGE-SCALE STRUCTURE

The gravitationally driven evolution of cold dark matter dominates the formation of structure in the universe over a wide range of length scales. While the longest scales can be treated by perturbation theory, a fully quantitative understanding of nonlinear effects requires the application of large-scale particle simulation methods. Additionally, precision predictions for next-generation observatio-ns, such as weak gravitational lensing, can only be obtained from numerical simulations. In this paper, we compare results from several N-body codes using test problems and a diverse set of diagnostics, focusing on a medium-resolution regime appropriate for studying many observationally relevant aspects of structure formation. Our conclusions are that—despite the use of different algorithms and error-control methodologies—overall, the codes yield consistent results. The agreement over a wide range of scales for the cosmological tests is test-dependent. In the best cases, it is at the 5% level or better, however, for other cases it can be significantly larger than 10%. These include the halo mass function at low masses and the mass power spectrum at small scales. While there exist explanations for most of the discrepancies, our results point to the need for significant improvement in N-body errors and their understanding to match the precision of near-future observations. The simulation results, including halo catalogs, and initial conditions used, are publicly available.

The cosmic code comparison project

Current and upcoming cosmological observations allow us to probe structures on smaller and smaller scales, entering highly nonlinear regimes. In order to obtain theoretical predictions in these regimes, large cosmological simulations have to be carried out. The promised high accuracy from observations makes the simulation task very demanding: the simulations have to be at least as accurate as the observations. This requirement can only be fulfilled by carrying out an extensive code verification program. The first step of such a program is the comparison of different cosmology codes including gravitational interactions only. In this paper, we extend a recently carried out code comparison project to include five more simulation codes. We restrict our analysis to a small cosmological volume which allows us to investigate properties of halos. For the matter power spectrum and the mass function, the previous results hold, with the codes agreeing at the 10% level over wide dynamic ranges. We extend our analysis to the comparison of halo profiles and investigate the halo count as a function of local density. We introduce and discuss ParaView as a flexible analysis tool for cosmological simulations, the use of which immensely simplifies the code comparison task.

The Structure of Halos: Implications for Group and Cluster Cosmology

The dark matter halo mass function is a key repository of cosmological information over a wide range of mass scales, from individual galaxies to galaxy clusters. N-body simulations have established that the friends-of-friends (FOF) mass function has a universal form to a surprising level of accuracy (10%). The high-mass tail of the mass function is exponentially sensitive to the amplitude of the initial density perturbations, the mean matter density parameter, Ω m , and to the dark energy controlled late-time evolution of the density field. Observed group and cluster masses, however, are usually stated in terms of a spherical overdensity (SO) mass which does not map simply to the FOF mass. Additionally, the widely used halo models of structure formation—and halo occupancy distribution descriptions of galaxies within halos—are often constructed exploiting the universal form of the FOF mass function. This again raises the question of whether FOF halos can be simply related to the notion of a spherical overdensity mass. By employing results from Monte Carlo realizations of ideal Navarro-Frenk-White (NFW) halos and N-body simulations, we study the relationship between the two definitions of halo mass. We find that the vast majority of halos (80%-85%) in the mass-range 1012.5-1015.5 h –1 M ☉ indeed allow for an accurate mapping between the two definitions (~5%), but only if the halo concentrations are known. Nonisolated halos fall into two broad classes: those with complex substructure that are poor fits to NFW profiles and those bridged by the (isodensity-based) FOF algorithm. A closer investigation of the bridged halos reveals that the fraction of these halos and their satellite mass distribution is cosmology dependent. We provide a preliminary discussion of the theoretical and observational ramifications of these results.

Nonequilibrium and nonlinear dynamics in Berea and Fontainebleau sandstones: Low‐strain regime

[1]xa0Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10−7. In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations, we are able to systematically and reproducibly study dynamical behavior at strains as low as 10−9. Our study establishes the existence of two strain regimes separated by eM. At strains below eM the material is nonlinear and quasi-equilibrium thermodynamics applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above eM the behavior becomes truly nonequilibrium, as demonstrated by the existence of material conditioning, and Landau theory no longer applies. The main focus of this paper is the study of the first region, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.

Shapes and sizes of voids in the Lambda cold dark matter universe: excursion set approach

We study the global distribution and morphology of dark matter voids in a Lambda cold dark matter (� CDM) universe using density fields generated by N-body simulations. Voids are defined as isolated regions of the low-density excursion set specified via density thresholds, the density thresholds being quantified by the corresponding filling factors, i.e. the fraction of the total volume in the excursion set. Our work encompasses a systematic investigation of the void volume function, the volume fraction in voids and the fitting of voids to corresponding ellipsoids and spheres. We emphasize the relevance of the percolation threshold to the void volume statistics of the density field in the high redshift, Gaussian random field regime as well as in the present epoch. By using measures such as the Inverse Porosity, we characterize the quality of ellipsoidal fits to voids, finding that such fits are a poor representation of the larger voids that dominate the volume of the void excursion set.