A Large Sky Simulation of the Gravitational Lensing of the Cosmic Microwave Background

Large scale structure deflects cosmic microwave background (CMB) photons. Since large angular scales in the large scale structure contribute significantly to the gravitational lensing effect, a realistic simulation of CMB lensing requires a sufficiently large sky area. We describe simulations that include these effects, and present both effective and multiple plane ray-tracing versions of the algorithm, which employs spherical harmonic space and does not use the flat sky approximation. We simulate lensed CMB maps with an angular resolution of ~0.9 arcmin. The angular power spectrum of the simulated sky agrees well with analytical predictions. Maps generated in this manner are a useful tool for the analysis and interpretation of upcoming CMB experiments such as PLANCK and ACT.Comment: 14 pages, 12 figures, replaced with version accepted for publication by the AP

The Tree-Particle-Mesh N-body Gravity Solver

The Tree-Particle-Mesh (TPM) N-body algorithm couples the tree algorithm for directly computing forces on particles in an hierarchical grouping scheme with the extremely efficient mesh based PM structured approach. The combined TPM algorithm takes advantage of the fact that gravitational forces are linear functions of the density field. Thus one can use domain decomposition to break down the density field into many separate high density regions containing a significant fraction of the mass but residing in a very small fraction of the total volume. In each of these high density regions the gravitational potential is computed via the tree algorithm supplemented by tidal forces from the external density distribution. For the bulk of the volume, forces are computed via the PM algorithm; timesteps in this PM component are large compared to individually determined timesteps in the tree regions. Since each tree region can be treated independently, the algorithm lends itself to very efficient parallelization using message passing. We have tested the new TPM algorithm (a refinement of that originated by Xu 1995) by comparison with results from Ferrell & Bertschinger's P^3M code and find that, except in small clusters, the TPM results are at least as accurate as those obtained with the well-established P^3M algorithm, while taking significantly less computing time. Production runs of 10^9 particles indicate that the new code has great scientific potential when used with distributed computing resources.Comment: 24 pages including 9 figures, uses aaspp4.sty; revised to match published versio

Cosmological Constraints from a Combined Analysis of the Cluster Mass Function and Microwave Background Anisotropies

We present constraints on several cosmological parameters from a combined analysis of the most recent Cosmic Microwave Background anisotropy data and the Sloan Digital Sky Survey cluster mass function. We find that the combination of the two data sets breaks several degeneracies among the parameters and provides the following constraints: $\sigma_8=0.76\pm0.09$, $\Omega_m=0.26^{+0.06}_{-0.07}$, $h=0.66^{+0.05}_{-0.06}$, $n=0.96 \pm 0.05$, $\tau_c=0.07^{+0.07}_{-0.05}$.Comment: 7 pages, 1 figur

Where are the missing baryons in clusters?

Observations of clusters of galaxies suggest that they contain significantly fewer baryons (gas plus stars) than the cosmic baryon fraction. This `missing baryon' puzzle is especially surprising for the most massive clusters which are expected to be representative of the cosmic matter content of the universe (baryons and dark matter). Here we show that the baryons may not actually be missing from clusters, but rather are extended to larger radii than typically observed. The baryon deficiency is typically observed in the central regions of clusters (~0.5 the virial radius). However, the observed gas-density profile is significantly shallower than the mass-density profile, implying that the gas is more extended than the mass and that the gas fraction increases with radius. We use the observed density profiles of gas and mass in clusters to extrapolate the measured baryon fraction as a function of radius and as a function of cluster mass. We find that the baryon fraction reaches the cosmic value near the virial radius for all groups and clusters above 5e13 solar masses. This suggests that the baryons are not missing, they are simply located in cluster outskirts. Heating processes (shock-heating of the intracluster gas, plus supernovae and AGN feedback) that cause the gas to expand are likely explanations for these results. Upcoming observations should be able to detect these baryons.Comment: Submitted to PNA

Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and its richness-dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with \Omega_m = 0.3 and, for comparison, a tilted \Omega_m = 1 model, TSCDM, are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high redshift clusters are clustered more strongly (in comoving scale) than low redshift clusters of the same mass. The increased correlations with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation-scale versus cluster mean separation relation, R_0 - d, is found to be, remarkably, independent of redshift to z <~ 2 for LCDM and z <~ 1 for TCDM (for a fixed correlation function slope and cluster mass within a fixed comoving radius). The non-evolving R_0 - d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters so that the R_0 - d relation remains essentially unchanged. The evolution of the R_0 - d relation from z ~ 0 to z ~ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ~ 0 and provide precise determination of cosmological parameters.Comment: AASTeX, 15 pages, including 5 figures, accepted version for publication in ApJ, vol.603, March 200

Accurate Realizations of the Ionized Gas in Galaxy Clusters: Calibrating Feedback

Using the full, three-dimensional potential of galaxy cluster halos (drawn from an N-body simulation of the current, most favored cosmology), the distribution of the X-ray emitting gas is found by assuming a polytropic equation of state and hydrostatic equilibrium, with constraints from conservation of energy and pressure balance at the cluster boundary. The resulting properties of the gas for these simulated redshift zero clusters (the temperature distribution, mass-temperature and luminosity-temperature relations, and the gas fraction) are compared with observations in the X-ray of nearby clusters. The observed properties are reproduced only under the assumption that substantial energy injection from non-gravitational sources has occurred. Our model does not specify the source, but star formation and AGN may be capable of providing this energy, which amounts to 3 to 5 x10^{-5} of the rest mass in stars (assuming ten percent of the gas initially in the cluster forms stars). With the method described here it is possible to generate realistic X-ray and Sunyaev-Zel'dovich cluster maps and catalogs from N-body simulations, with the distributions of internal halo properties (and their trends with mass, location, and time) taken into account.Comment: Matches ApJ published version; 30 pages, 7 figure

Templates for the Sunyaev-Zel'dovich Angular Power Spectrum

We present templates for the Sunyaev-Zel'dovich (SZ) angular power spectrum based on four models for the nonlinear gas distribution. The frequency-dependent SZ temperature fluctuations, with thermal (TSZ) and kinetic (KSZ) contributions, are calculated by tracing through a dark matter simulation, processed to include gas in dark matter halos and in the filamentary intergalactic medium. Different halo gas models are compared to study how star formation, energetic feedback, and nonthermal pressure support influence the angular power spectrum. The standard model has been calibrated to reproduce the stellar and gas fractions and X-ray scaling relations measured from low redshift clusters and groups. The other models illustrate the current theoretical and empirical uncertainties relating to properties of the intracluster medium. Relative to the standard model, their angular power spectra differ by approximately 50% (TSZ), 20% (KSZ), and 40% (SZ at 148 GHz) for l=3000, sigma_8=0.8, and homogeneous reionization at z=10. The angular power spectrum decreases in amplitude as gas mass and binding energy is removed through star formation, and as gas is pushed out to larger radii by energetic feedback. With nonthermal pressure support, less pressure is required to maintain hydrostatic equilibrium, thus reducing the thermal contribution to the SZ power. We also calculate the SZ templates as a function of sigma_8 and quantify this dependence. Assuming C_l is proprotional to (sigma_8/0.8)^alpha, the effective scaling index ranges from 7<alpha_tsz<9, 4.5<alpha_ksz<5.5, and 6.5<alpha_sz(148 GHz)<8 at l=3000 for 0.6<sigma_8<1. The template spectra are publicly available and can be used when fitting for the SZ contribution to the cosmic microwave background on arcminute scales.Comment: 14 pages, 10 figures, to be submitted to Ap

The Shape, Multiplicity, and Evolution of Superclusters in LambdaCDM Cosmology

We determine the shape, multiplicity, size, and radial structure of superclusters in the LambdaCDM concordance cosmology from z = 0 to z = 2. Superclusters are defined as clusters of clusters in our large-scale cosmological simulation. We find that superclusters are triaxial in shape; many have flattened since early times to become nearly two-dimensional structures at present, with a small fraction of filamentary systems. The size and multiplicity functions are presented at different redshifts. Supercluster sizes extend to scales of ~ 100 - 200 Mpc/h. The supercluster multiplicity (richness) increases linearly with supercluster size. The density profile in superclusters is approximately isothermal (~ R^{-2}) and steepens on larger scales. These results can be used as a new test of the current cosmology when compared with upcoming observations of large-scale surveys.Comment: 33 pages, 15 figures, accepted to ApJ; minor content changes, some figures removed to shorten pape