The rockstar phase-space temporal halo finder and the velocity offsets of cluster cores
TL;DR: In this paper, the authors present a new algorithm for detecting dark matter halos, substructure, and tidal features based on adaptive hierarchical refinement of friends-of-friends groups in six phase-space dimensions and one time dimension.
Abstract: We present a new algorithm for identifying dark matter halos, substructure, and tidal features. The approach is based on adaptive hierarchical refinement of friends-of-friends groups in six phase-space dimensions and one time dimension, which allows for robust (grid-independent, shape-independent, and noise-resilient) tracking of substructure; as such, it is named Rockstar (Robust Overdensity Calculation using K-Space Topologically Adaptive Refinement). Our method is massively parallel (up to 10 5 CPUs) and runs on the very largest simulations (>10 10 particles) with high efficiency (10 CPU hours and 60 gigabytes of memory required per billion particles analyzed). A previous paper (Knebe et al. 2011) has shown Rockstar to have class-leading recovery of halo properties; we expand on these comparisons with more tests and higher-resolution simulations. We show a significant improvement in substructure recovery as compared to other halo finders and discuss the theoretical and practical limits of simulations in this regard. Finally, we present results which demonstrate conclusively that dark matter halo cores are not at rest relative to the halo bulk or satellite average velocities and have coherent velocity offsets across a wide range of halo masses and redshifts. For massive clusters, these offsets can be up to 400 km s -1 at z = 0 and even higher at high redshifts. Our implementation is publicly available at http://code.google.com/p/rockstar. Subject headings: dark matter — galaxies: abundances — galaxies: evolution — methods: N-body simulations
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TL;DR: In this article, a robust method to constrain average galaxy star formation rates, star formation histories (SFHs), and the intracluster light (ICL) as a function of halo mass is presented.
Abstract: We present a robust method to constrain average galaxy star formation rates (SFRs), star formation histories (SFHs), and the intracluster light (ICL) as a function of halo mass. Our results are consistent with observed galaxy stellar mass functions, specific star formation rates (SSFRs), and cosmic star formation rates (CSFRs) from z = 0 to z = 8. We consider the effects of a wide range of uncertainties on our results, including those affecting stellar masses, SFRs, and the halo mass function at the heart of our analysis. As they are relevant to our method, we also present new calibrations of the dark matter halo mass function, halo mass accretion histories, and halo-subhalo merger rates out to z = 8. We also provide new compilations of CSFRs and SSFRs; more recent measurements are now consistent with the buildup of the cosmic stellar mass density at all redshifts. Implications of our work include: halos near 1012 M ☉ are the most efficient at forming stars at all redshifts, the baryon conversion efficiency of massive halos drops markedly after z ~ 2.5 (consistent with theories of cold-mode accretion), the ICL for massive galaxies is expected to be significant out to at least z ~ 1-1.5, and dwarf galaxies at low redshifts have higher stellar mass to halo mass ratios than previous expectations and form later than in most theoretical models. Finally, we provide new fitting formulae for SFHs that are more accurate than the standard declining tau model. Our approach places a wide variety of observations relating to the SFH of galaxies into a self-consistent framework based on the modern understanding of structure formation in ΛCDM. Constraints on the stellar mass-halo mass relationship and SFRs are available for download online.
2,085 citations
TL;DR: The Illustris Project as mentioned in this paper is a series of large-scale hydrodynamical simulations of galaxy formation, which includes primordial and metal-line cooling with self-shielding corrections, stellar evolution, stellar feedback, gas recycling, chemical enrichment, supermassive black hole growth, and feedback from active galactic nuclei.
Abstract: We introduce the Illustris Project, a series of large-scale hydrodynamical simulations of galaxy formation. The highest resolution simulation, Illustris-1, covers a volume of (106.5 Mpc)^3, has a dark mass resolution of 6.26 × 10^6 M_⊙, and an initial baryonic matter mass resolution of 1.26 × 10^6 M_⊙. At z = 0 gravitational forces are softened on scales of 710 pc, and the smallest hydrodynamical gas cells have an extent of 48 pc. We follow the dynamical evolution of 2 × 1820^3 resolution elements and in addition passively evolve 1820^3 Monte Carlo tracer particles reaching a total particle count of more than 18 billion. The galaxy formation model includes: primordial and metal-line cooling with self-shielding corrections, stellar evolution, stellar feedback, gas recycling, chemical enrichment, supermassive black hole growth, and feedback from active galactic nuclei. Here we describe the simulation suite, and contrast basic predictions of our model for the present-day galaxy population with observations of the local universe. At z = 0 our simulation volume contains about 40 000 well-resolved galaxies covering a diverse range of morphologies and colours including early-type, late-type and irregular galaxies. The simulation reproduces reasonably well the cosmic star formation rate density, the galaxy luminosity function, and baryon conversion efficiency at z = 0. It also qualitatively captures the impact of galaxy environment on the red fractions of galaxies. The internal velocity structure of selected well-resolved disc galaxies obeys the stellar and baryonic Tully–Fisher relation together with flat circular velocity curves. In the well-resolved regime, the simulation reproduces the observed mix of early-type and late-type galaxies. Our model predicts a halo mass dependent impact of baryonic effects on the halo mass function and the masses of haloes caused by feedback from supernova and active galactic nuclei.
2,012 citations
TL;DR: In this paper, the authors used the suite of MultiDark cosmological simulations to study the evolution of dark matter halo density profiles, concentrations, and velocity anisotropies.
Abstract: Predicting structural properties of dark matter haloes is one of the fundamental goals of modern cosmology. We use the suite of MultiDark cosmological simulations to study the evolution of dark matter halo density profiles, concentrations, and velocity anisotropies. We find that in order to understand the structure of dark matter haloes and to make 1–2 per cent accurate predictions for density profiles, one needs to realize that halo concentration is more complex than the ratio of the virial radius to the core radius in the Navarro–Frenk–White (NFW) profile. For massive haloes, the average density profile is far from the NFW shape and the concentration is defined by both the core radius and the shape parameter α in the Einasto approximation. We show that haloes progress through three stages of evolution. They start as rare density peaks and experience fast and nearly radial infall that brings mass closer to the centre, producing a highly concentrated halo. Here, the halo concentration increases with increasing halo mass and the concentration is defined by the α parameter with a nearly constant core radius. Later haloes slide into the plateau regime where the accretion becomes less radial, but frequent mergers still affect even the central region. At this stage, the concentration does not depend on halo mass. Once the rate of accretion and merging slows down, haloes move into the domain of declining concentration–mass relation because new accretion piles up mass close to the virial radius while the core radius is staying constant. Accurate analytical fits are provided.
808 citations
Columbia University1, University of California, San Diego2, Michigan State University3, Stanford University4, Georgia Institute of Technology5, Southern Methodist University6, Florida State University7, Nvidia8, University of Colorado Boulder9, University of Edinburgh10, Oak Ridge National Laboratory11, University of California, Santa Cruz12, University of California, Berkeley13, University of Arizona14, Hokkaido University15, ETH Zurich16, American Museum of Natural History17, Princeton University18
TL;DR: Enzo as discussed by the authors uses block-structured adaptive mesh refinement to provide high spatial and temporal resolution for modeling astrophysical fluid flows, which can be run in one, two, and three dimensions, and supports a wide variety of physics, including hydrodynamics, ideal and non-ideal magnetohydrodynamic, N-body dynamics, primordial gas chemistry, optically thin radiative cooling of primordial and metal-enriched plasmas, and models for star formation and feedback in a cosmological context.
Abstract: This paper describes the open-source code Enzo, which uses block-structured adaptive mesh refinement to provide high spatial and temporal resolution for modeling astrophysical fluid flows. The code is Cartesian, can be run in one, two, and three dimensions, and supports a wide variety of physics including hydrodynamics, ideal and non-ideal magnetohydrodynamics, N-body dynamics (and, more broadly, self-gravity of fluids and particles), primordial gas chemistry, optically thin radiative cooling of primordial and metal-enriched plasmas (as well as some optically-thick cooling models), radiation transport, cosmological expansion, and models for star formation and feedback in a cosmological context. In addition to explaining the algorithms implemented, we present solutions for a wide range of test problems, demonstrate the code's parallel performance, and discuss the Enzo collaboration's code development methodology.
740 citations
TL;DR: Giacconi Fellowship from the Space Telescope Science Institute; NASA through a Hubble Fellowship grant from NASA's HST-HF2-51353.001-A; NASANational Aeronautics & Space Administration (NAS5-26555); NSFNational Science Foundation (NSF) [1066293]; National Science Foundation(NSF)'s National Research Foundation (NRF) [PHY11-25915]; Munich Institute for Astro-and Particle Physics (MIAPP) of the DFG cluster of excellence 'Origin and Structure of the Universe'
Abstract: Giacconi Fellowship from the Space Telescope Science Institute; NASA through a Hubble Fellowship grant from the Space Telescope Science Institute [HST-HF2-51353.001-A]; NASANational Aeronautics & Space Administration (NASA) [NAS5-26555]; NSFNational Science Foundation (NSF) [1066293]; National Science Foundation (NSF)National Science Foundation (NSF) [PHY11-25915]; Munich Institute for Astro-and Particle Physics (MIAPP) of the DFG cluster of excellence 'Origin and Structure of the Universe; Office of Science of the U.S. Department of EnergyUnited States Department of Energy (DOE) [DE-AC02-05CH11231]; DOEUnited States Department of Energy (DOE) [DE-AC02-76SF00515]; NASA High-EndComputing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center; PRACE [012060963]; Alfred P. Sloan FoundationAlfred P. Sloan Foundation; U.S. Department of Energy Office of ScienceUnited States Department of Energy (DOE); University of Arizona; Brazilian Participation Group; Brookhaven National LaboratoryUnited States Department of Energy (DOE); Carnegie Mellon University; French Participation Group; German Participation Group; Harvard University; Instituto de Astrofisica de Canarias; Michigan State/Notre Dame/JINA Participation Group; Johns Hopkins UniversityJohns Hopkins University; Lawrence Berkeley National LaboratoryUnited States Department of Energy (DOE); Max Planck Institute for Astrophysics; Max Planck Institute for Extraterrestrial Physics; Pennsylvania State University; Princeton UniversityPrinceton University; Spanish Participation Group; Yale University; University of FloridaUniversity of Florida; NewMexico State University; New York University; Ohio State UniversityOhio State University; University of Portsmouth; University of Tokyo; University of Utah; Vanderbilt University; University of Virginia; University of WashingtonUniversity of Washington
612 citations
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TL;DR: In this article, a combination of seven-year data from WMAP and improved astrophysical data rigorously tests the standard cosmological model and places new constraints on its basic parameters and extensions.
Abstract: The combination of seven-year data from WMAP and improved astrophysical data rigorously tests the standard cosmological model and places new constraints on its basic parameters and extensions. By combining the WMAP data with the latest distance measurements from the baryon acoustic oscillations (BAO) in the distribution of galaxies and the Hubble constant (H0) measurement, we determine the parameters of the simplest six-parameter ΛCDM model. The power-law index of the primordial power spectrum is ns = 0.968 ± 0.012 (68% CL) for this data combination, a measurement that excludes the Harrison–Zel’dovich–Peebles spectrum by 99.5% CL. The other parameters, including those beyond the minimal set, are also consistent with, and improved from, the five-year results. We find no convincing deviations from the minimal model. The seven-year temperature power spectrum gives a better determination of the third acoustic peak, which results in a better determination of the redshift of the matter-radiation equality epoch. Notable examples of improved parameters are the total mass of neutrinos, � mν < 0.58 eV (95% CL), and the effective number of neutrino species, Neff = 4.34 +0.86 −0.88 (68% CL), which benefit from better determinations of the third peak and H0. The limit on a constant dark energy equation of state parameter from WMAP+BAO+H0, without high-redshift Type Ia supernovae, is w =− 1.10 ± 0.14 (68% CL). We detect the effect of primordial helium on the temperature power spectrum and provide a new test of big bang nucleosynthesis by measuring Yp = 0.326 ± 0.075 (68% CL). We detect, and show on the map for the first time, the tangential and radial polarization patterns around hot and cold spots of temperature fluctuations, an important test of physical processes at z = 1090 and the dominance of adiabatic scalar fluctuations. The seven-year polarization data have significantly improved: we now detect the temperature–E-mode polarization cross power spectrum at 21σ , compared with 13σ from the five-year data. With the seven-year temperature–B-mode cross power spectrum, the limit on a rotation of the polarization plane due to potential parity-violating effects has improved by 38% to Δα =− 1. 1 ± 1. 4(statistical) ± 1. 5(systematic) (68% CL). We report significant detections of the Sunyaev–Zel’dovich (SZ) effect at the locations of known clusters of galaxies. The measured SZ signal agrees well with the expected signal from the X-ray data on a cluster-by-cluster basis. However, it is a factor of 0.5–0.7 times the predictions from “universal profile” of Arnaud et al., analytical models, and hydrodynamical simulations. We find, for the first time in the SZ effect, a significant difference between the cooling-flow and non-cooling-flow clusters (or relaxed and non-relaxed clusters), which can explain some of the discrepancy. This lower amplitude is consistent with the lower-than-theoretically expected SZ power spectrum recently measured by the South Pole Telescope Collaboration.
11,309 citations
TL;DR: In this article, the authors used high-resolution N-body simulations to study the equilibrium density profiles of dark matter halos in hierarchically clustering universes, and they found that all such profiles have the same shape, independent of the halo mass, the initial density fluctuation spectrum, and the values of the cosmological parameters.
Abstract: We use high-resolution N-body simulations to study the equilibrium density profiles of dark matter halos in hierarchically clustering universes. We find that all such profiles have the same shape, independent of the halo mass, the initial density fluctuation spectrum, and the values of the cosmological parameters. Spherically averaged equilibrium profiles are well fitted over two decades in radius by a simple formula originally proposed to describe the structure of galaxy clusters in a cold dark matter universe. In any particular cosmology, the two scale parameters of the fit, the halo mass and its characteristic density, are strongly correlated. Low-mass halos are significantly denser than more massive systems, a correlation that reflects the higher collapse redshift of small halos. The characteristic density of an equilibrium halo is proportional to the density of the universe at the time it was assembled. A suitable definition of this assembly time allows the same proportionality constant to be used for all the cosmologies that we have tested. We compare our results with previous work on halo density profiles and show that there is good agreement. We also provide a step-by-step analytic procedure, based on the Press-Schechter formalism, that allows accurate equilibrium profiles to be calculated as a function of mass in any hierarchical model.
9,729 citations
TL;DR: GADGET-2 as mentioned in this paper is a massively parallel tree-SPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics.
Abstract: 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.
6,196 citations
TL;DR: It is shown 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.
Abstract: 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.
4,814 citations
TL;DR: A novel method of directly calculating the force on N bodies that grows only as N log N is described, using a tree-structured hierarchical subdivision of space into cubic cells, each is recursively divided into eight subcells whenever more than one particle is found to occupy the same cell.
Abstract: Until recently the gravitational N-body problem has been modelled numerically either by direct integration, in which the computation needed increases as N2, or by an iterative potential method in which the number of operations grows as N log N. Here we describe a novel method of directly calculating the force on N bodies that grows only as N log N. The technique uses a tree-structured hierarchical subdivision of space into cubic cells, each of which is recursively divided into eight subcells whenever more than one particle is found to occupy the same cell. This tree is constructed anew at every time step, avoiding ambiguity and tangling. Advantages over potential-solving codes are: accurate local interactions; freedom from geometrical assumptions and restrictions; and applicability to a wide class of systems, including (proto-)planetary, stellar, galactic and cosmological ones. Advantages over previous hierarchical tree-codes include simplicity and the possibility of rigorous analysis of error. Although we concentrate here on stellar dynamical applications, our techniques of efficiently handling a large number of long-range interactions and concentrating computational effort where most needed have potential applications in other areas of astrophysics as well.
3,750 citations