Paul Bode

Halo formation in warm dark matter models

Discrepancies have emerged between the predictions of standard cold dark matter (CDM) theory and observations of clustering on subgalactic scales. Warm dark matter (WDM) is a simple modification of CDM in which the dark matter particles have initial velocities due either to their having decoupled as thermal relics or to their having been formed via nonequilibrium decay. We investigate the nonlinear gravitational clustering of WDM with a high-resolution N-body code and identify a number of distinctive observational signatures. Relative to CDM, halo concentrations and core densities are lowered, core radii are increased, and large halos emerge with far fewer low-mass satellites. The number of small halos is suppressed, and those present are formed by top-down fragmentation of caustics, as part of a cosmic web connecting massive halos. Few small halos form outside this web. If we identify small halos with dwarf galaxies, then their number, spatial distribution, and formation epoch appear in better agreement with the observations for WDM than they are for CDM.

Statistics of Physical Properties of Dark Matter Clusters

We have identified over 2000 well-resolved cluster halos, and also their associated bound subhalos, from the output of a 10243 particle cosmological N-body simulation (of box size 320 h-1 Mpc and softening length 3.2 h-1 kpc). This has allowed us to measure halo quantities in a statistically meaningful way, and for the first time analyze their distribution for a large and well-resolved sample. We characterize each halo in terms of its morphology, concentration, spin, circular velocity, and the fraction of their mass in substructure. We also identify those halos that have not yet reached a state of dynamical equilibrium, using the virial theorem with an additional correction to account for the surface pressure at the boundary. These amount to 3.4% of our initial sample. For the virialized halos, we find a median of 5.6% of halo mass is contained within substructure, with the distribution ranging between no identified subhalos to 65%. The fraction of mass in substructure increases with halo mass with logarithmic slope of 0.44 ± 0.06. Halos tend to have a prolate morphology, becoming more so with increasing mass. Subhalos have a greater orbital angular momentum per unit mass than their host halo. Furthermore, their orbital angular momentum is typically well aligned with that of their host. Overall, we find that dimensionless properties of dark matter halos do depend on their mass, thereby demonstrating a lack of self-similarity.

Characterizing the Cluster Lens Population

We present a detailed investigation into which properties of CDM halos make them effective strong gravitational lenses. Strong-lensing cross sections of 878 clusters from an N-body simulation are measured by ray-tracing through 13,594 unique projections. We measure concentrations, axis ratios, orientations, and the substructure of each cluster, and compare the lensing-weighted distribution of each quantity to that of the cluster population as a whole. The concentrations of lensing clusters are on average 34% larger than the typical cluster in the universe. Despite this bias, the anomalously high concentrations (c > 14) recently measured by several groups appear to be inconsistent with the concentration distribution in our simulations, which predict that 0.6) lenses is in good agreement with ΛCDM, although our simulations predict more low-redshift (z < 0.6) lenses than observed.

The Cluster Mass Function from Early Sloan Digital Sky Survey Data: Cosmological Implications

The mass function of clusters of galaxies is determined from 400 deg2 of early commissioning imaging data of the Sloan Digital Sky Survey using ~300 clusters in the redshift range z = 0.1-0.2. Clusters are selected using two independent selection methods: a matched filter and a red-sequence color-magnitude technique. The two methods yield consistent results. The cluster mass function is compared with large-scale cosmological simulations. We find a best-fit cluster normalization relation of σ8Ω = 0.33 ± 0.03 (for 0.1 Ωm 0.4) or, equivalently, σ8 = (0.16/Ωm)0.6. The amplitude of this relation is significantly lower than the previous canonical value, implying that either Ωm is lower than previously expected (Ωm = 0.16 if σ8 = 1) or σ8 is lower than expected (σ8 = 0.7 if Ωm = 0.3). The shape of the cluster mass function partially breaks this classic degeneracy. We find best-fit parameters of Ωm = 0.19 ± and σ8 = 0.9 ±. High values of Ωm (0.4) and low σ8 (0.6) are excluded at 2 σ.

Cluster Alignments and Ellipticities in ΛCDM Cosmology

The ellipticities and alignments of clusters of galaxies and their evolution with redshift are examined in the context of a Λ-dominated cold dark matter cosmology. We use a large-scale, high-resolution N-body simulation to model the matter distribution in a light cone containing ~106 clusters of mass M > 2 × 1013 h-1 M☉ out to redshifts of z = 3. The best-fit three-dimensional ellipsoid of the mass distribution is determined for each cluster, and the results are used to analyze cluster ellipticities as a function of mass, radius, and redshift. A similar analysis is done in two dimensions in order to allow direct comparisons with future observations. Cluster ellipticities are determined within different radii, including 0.5, 1.0, and 1.5 h-1 comoving Mpc. We find strong cluster ellipticities: ≡ 1 - a2/a1 ~ 0.3-0.5. The mean ellipticity increases with redshift from ~ 0.3 at z = 0 to ~ 0.5 at z = 3 for both three-dimensional and two-dimensional ellipticities; the evolution is well fitted by = 0.33 + 0.05z. The ellipticities increase with cluster mass and with cluster radius; the main cluster body is more elliptical than the cluster cores, but the increase of ellipticities with redshift is preserved. Using the fitted cluster ellipsoids, we determine the alignment of clusters as a function of their separation. We find strong alignment of clusters for separations 100 h-1 Mpc; the alignment increases with decreasing separation and with increasing redshift. The evolution of clusters from highly aligned and elongated systems at early times to lower alignment and elongation at present reflects the hierarchical and filamentary nature of structure formation. These measures of cluster ellipticity and alignment will provide a new test of the current cosmological model when compared with upcoming cluster surveys.

THE MASS POWER SPECTRUM IN QUINTESSENCE COSMOLOGICAL MODELS

We present simple analytic approximations for the linear and fully evolved nonlinear mass power spectrum of matter density fluctuations for spatially flat cold dark matter (CDM) cosmological models with quintessence (Q). Quintessence is a time-evolving, spatially inhomogeneous energy component with negative pressure and an equation of state wQ < 0. It clusters gravitationally on large length scales but remains smooth like the cosmological constant on small length scales. We show that the clustering scale is determined by the Compton wavelength of the Q-field and derive a shape parameter, ΓQ, to characterize the linear mass power spectrum. The growth of linear perturbations as functions of redshift, wQ, and matter density, Ωm, is also quantified. Calibrating to N-body simulations, we construct a simple extension of Mas 1998 formula that closely approximates the nonlinear power spectrum for a range of plausible QCDM models.

Giant Arc Statistics in Concord with a Concordance Lambda Cold Dark Matter Universe

The frequency of giant arcs?highly distorted and strongly gravitationally lensed background galaxies?is a powerful test for cosmological models. Previous comparisons of arc statistics for the currently favored concordance cosmological model (lambda cold dark matter [LCDM]) with observations have shown an apparently large discrepancy in underpredicting cluster arcs. We present new ray-shooting results, based on a high-resolution (10243 particles in a 320 h-1 Mpc box) large-scale structure simulation normalized to the Wilkinson Microwave Anisotropy Probe (WMAP) observations. We follow light rays through a pseudo-three-dimensional matter distribution approximated by up to 38 lens planes and evaluate the occurrence of arcs for various source redshifts. We find that the frequency of strongly lensed background galaxies is a steep function of source redshift: the optical depth for giant arcs increases by a factor of 5 when background sources are moved from redshift zs = 1.0 to 1.5. This is a consequence of a small decrease of the critical surface mass density for lensing, combined with the very steep cluster mass function at the high-mass end plus a modest contribution from secondary lens planes. Our results are consistent with those of Bartelmann et al. if we?as they did?restrict all sources to be at zs = 1. If we allow sources extending to or beyond zs ? 1.5, the apparent discrepancy vanishes: the frequency of arcs increases by about a factor of 10 as compared to previous estimates, and results in roughly one arc per 20 deg2 over the sky, in good agreement with the observed frequency of arcs.

Physical effects on the Lyα forest flux power spectrum: damping wings, ionizing radiation fluctuations and galactic winds

We explore several physical effects on the power spectrum of the Lyα forest transmitted flux. The effects we investigate here are not usually part of hydrodynamic simulations and so need to be estimated separately. The most important effect is that of high column density absorbers with damping wings, which add power on large scales. We compute their effect using the observational constraints on their abundance as a function of column density. Ignoring their effect leads to an underestimation of the slope of the linear theory power spectrum. The second effect we investigate is that of fluctuations in the ionizing radiation field. For this purpose we use a very large high-resolution N-body simulation, which allows us to simulate both the fluctuations in the ionizing radiation and the small-scale Lyα forest within the same simulation. We find an enhancement of power on large scales for quasars and a suppression for galaxies. The strength of the effect rapidly increases with increasing redshift, allowing it to be uniquely identified in cases where it is significant. We develop templates that can be used to search for this effect as a function of quasar lifetime, quasar luminosity function and attenuation length. Finally, we explore the effects of galactic winds using hydrodynamic simulations. We find the wind effects on the Lyα forest power spectrum to be degenerate with parameters related to the temperature of the gas that are already marginalized over in cosmological fits. While more work is needed to conclusively exclude all possible systematic errors, our results suggest that, in the context of data analysis procedures, where parameters of the Lyα forest model are properly marginalized over, the flux power spectrum is a reliable tracer of cosmological information. Ke yw ords: galaxies: high-redshift ‐ intergalactic medium ‐ quasars: absorption lines ‐ cosmology: theory ‐ diffuse radiation ‐ large-scale structure of Universe.

A Simple and Accurate Model for Intracluster Gas

Starting with the well-known NFW dark matter halo distribution, we construct a simple polytropic model for the intracluster medium that is in good agreement with high-resolution numerical hydrodynamic simulations, apply this model to a very large scale concordance dark matter simulation, and compare the resulting global properties with recent observations of X-ray clusters, including the mass-temperature and luminosity-temperature relations. We make allowances for a nonnegligible surface pressure, removal of low-entropy (short cooling time) gas, energy injection due to feedback, and a relativistic (nonthermal) pressure component. A polytropic index n = 5 (Γ = 1.2) provides a good approximation to the internal gas structure of massive clusters (except in the very central regions where cooling becomes important) and allows one to recover the observed M500-T, LX-T, and T/n ∝ T0.65 relations. Using these concepts and generalizing this method so that it can be applied to fully three-dimensional N-body simulations, one can predict the global X-ray and SZE trends for any specified cosmological model. We find a good fit to observations when assuming that 12% of the initial baryonic mass condenses into stars, that the fraction of rest mass of this condensed component transferred back to the remaining gas (feedback) is 3.9 × 10-5, and that the fraction of total pressure from a nonthermal component is near 10%.

Tree Particle-Mesh: An Adaptive, Efficient, and Parallel Code for Collisionless Cosmological Simulation

An improved implementation of an N-body code for simulating collisionless cosmological dynamics is presented. TPM (tree particle-mesh) combines the PM method on large scales with a tree code to handle particle-particle interactions at small separations. After the global PM forces are calculated, spatially distinct regions above a given density contrast are located; the tree code calculates the gravitational interactions inside these denser objects at higher spatial and temporal resolution. The new implementation includes individual particle time steps within trees, an improved treatment of tidal forces on trees, new criteria for higher force resolution and choice of time step, and parallel treatment of large trees. TPM is compared to P3M and a tree code (GADGET) and is found to give equivalent results in significantly less time. The implementation is highly portable (requiring a FORTRAN compiler and MPI) and efficient on parallel machines. The source code can be found on the World Wide Web.