The Amplitude of Mass Fluctuations

We determine the linear amplitude of mass fluctuations in the universe, sigma_8, from the abundance of massive clusters at redshifts z=0.5 to 0.8. The evolution of massive clusters depends exponentially on the amplitude of mass fluctuations and thus provides a powerful measure of this important cosmological parameter. The relatively high abundance of massive clusters observed at z>0.5, and the relatively slow evolution of their abundance with time, suggest a high amplitude of mass fluctuations: sigma_8=0.9 +-10% for Omega_m=0.4, increasing slightly to sigma_8=0.95 for Omega_m=0.25 and sigma_8=1.0 for Omega_m=0.1 (flat CDM models). We use the cluster abundance observed at z=0.5 to 0.8 to derive a normalization relation from the high-redshift clusters, which is only weakly dependent on Omega_m: sigma_8*Omega_m^0.14 = 0.78 +-0.08. When combined with recent constraints from the present-day cluster mass function (sigma_8*Omega_m^0.6=0.33 +-0.03) we find sigma_8=0.98 +-0.1 and Omega_m=0.17 +-0.05. Low sigma_8 values (<0.7) are unlikely; they produce an order of magnitude fewer massive clusters than observed.Comment: 12 pages including 3 figures; updated to match published versio

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

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

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

The Mass Power Spectrum in Quintessence Cosmological Models

We present simple analytic approximations for the linear and fully evolved nonlinear mass power spectrum 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 w_Q < 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, \Gamma_Q, to characterize the linear mass power spectrum. The growth of linear perturbations as functions of redshift, w_Q, and matter density \Omega_m is also quantified. Calibrating to N-body simulations, we construct a simple extension of the formula by Ma (1998) that closely approximates the nonlinear power spectrum for a range of plausible QCDM models.Comment: 5 pages with 3 inserted postscript figures, AAS LaTeX v4.0 emulateapj.sty. Astrophysical Journal Letters, in pres

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 amount of 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 < 2% of lensing clusters should have concentrations this high. No correlation is found between lensing cross section and the amount of substructure. We introduce several types of simplified dark matter halos, and use them to isolate which properties of CDM clusters make them effective lenses. Projections of halo substructure onto small radii and the large scale mass distribution of clusters do not significantly influence cross sections. The abundance of giant arcs is primarily determined by the mass distribution within an average overdensity of ~ 10,000. A multiple lens plane ray tracing algorithm is used to show that projections of large scale structure increase the giant arc abundance by a modest amount <7%. We revisit the question of whether there is an excess of giant arcs behind high redshift clusters in the RCS survey and find that the number of high redshift (z > 0.6) lenses is in good agreement with LCDM, although our simulations predict more low redshift (z < 0.6) lenses than were observed. (abridged)Comment: 19 pages, 15 figures. Submitted to Ap

Noise in strong lensing cosmography

Giant arcs in strong lensing galaxy clusters can provide a purely geometric determination of cosmological parameters, such as the dark energy density and equation of state. We investigate sources of noise in cosmography with giant arcs, focusing in particular on errors induced by density fluctuations along the line-of-sight, and errors caused by modeling uncertainties. We estimate parameter errors in two independent ways, first by developing a Fisher matrix formalism for strong lensing parameters, and next by directly ray-tracing through N-body simulations using a multi-plane lensing code. We show that for reasonable power spectra, density fluctuations from large-scale structure produce > 100% errors in cosmological parameters derived from any single sightline, precluding the use of individual clusters or golden lenses to derive accurate cosmological constraints. Modeling uncertainties similarly can lead to large errors, and we show that the use of parametrized mass models in fitting strong lensing clusters can significantly bias the inferred cosmological parameters. We lastly speculate on means by which these errors may be corrected.Comment: 7 pages, submitted to Ap

Cluster Ellipticities as a Cosmological Probe

We investigate the dependence of ellipticities of clusters of galaxies on cosmological parameters using large-scale cosmological simulations. We determine cluster ellipticities out to redshift unity for LCDM models with different mean densities $\Omega_m$ and amplitudes of mass fluctuation $\sigma_{8,0}$. The mean ellipticity increases monotonically with redshift for all models. Larger values of $\sigma_{8,0}$, i.e., earlier cluster formation time, produce lower ellipticities. The dependence of ellipticity on $\Omega_m$ is relatively weak in the range $0.2 \leq \Omega_m \leq 0.5$ for high mass clusters. The mean ellipticity $\bar{e}(z)$ decreases linearly with the amplitude of fluctuations at the cluster redshift $z$, nearly independent of $\Omega_m$; on average, older clusters are more relaxed and are thus less elliptical. The distribution of ellipticities about the mean is approximated by a Gaussian, allowing a simple characterization of the evolution of ellipticity with redshift as a function of cosmological parameters. At $z=0$, the mean ellipticity of high mass clusters is approximated by $\bar{e}(z=0) = 0.248-0.069 \sigma_{8,0} + 0.013 \Omega_{m,0}$. This relation opens up the possibility that, when compared with future observations of large cluster samples, the mean cluster ellipticity and its evolution could be used as a new, independent tool to constrain cosmological parameters, especially the amplitude of mass fluctuations, $\sigma_{8,0}$.Comment: 16 pages, 4 figure

Historical Overview of the Human Population-Genetic Studies in Bosnia and Herzegovina: Small Country, Great Diversity

Modern Bosnia and Herzegovina is a multinational and multi-religious country, situated in the western part of the Balkan Peninsula in South-eastern Europe. According to recent archaeological findings, Bosnia and Herzegovina has been occupied by modern humans since the Palaeolithic period. The structure of Bosnia-Herzegovina’s human populations is very complex and specific, due to which it is interesting for various population-genetic surveys. The population of Bosnia and Herzegovina has been the focus of bio-anthropological and population genetics studies since the 19th century. The first known bio-anthropological analyses of Bosnia-Herzegovina population were primarily based on the observation of some phenotypic traits. Later examinations included cytogenetic and DNA based molecular markers. The results of all studies which have been done up to date showed no accented genetic difference among the populations (based on geographical regions) with quite high diversity within them. Human population of Bosnia and Herzegovina is closely related to other populations in the Balkans. However, there are still many interesting features hidden within the existing diversity of local human populations that are still waiting to be discovered and described

Evolution of the Cluster Mass and Correlation Functions in LCDM Cosmology

The evolution of the cluster mass function and the cluster correlation function from z = 0 to z = 3 are determined using 10^6 clusters obtained from high-resolution simulations of the current best-fit LCDM cosmology (\Omega_m = 0.27, \sigma_8 = 0.84, h = 0.7). The results provide predictions for comparisons with future observations of high redshift clusters. A comparison of the predicted mass function of low redshift clusters with observations from early Sloan Digital Sky Survey data, and the predicted abundance of massive distant clusters with observational results, favor a slightly larger amplitude of mass fluctuations (\sigma_8 = 0.9) and lower density parameter (\Omega_m = 0.2); these values are consistent within 1-\sigma with the current observational and model uncertainties. The cluster correlation function strength increases with redshift for a given mass limit; the clusters were more strongly correlated in the past, due to their increasing bias with redshift - the bias reaches b = 100 at z = 2 for M > 5 x 10^13 h^-1 M_sun. The richness-dependent cluster correlation function, represented by the correlation scale versus cluster mean separation relation, R0-d, is generally consistent with observations. This relation can be approximated as R_0 = 1.7 d^0.6 h^-1 Mpc for d = 20 - 60 h^-1 Mpc. The R0-d relation exhibits surprisingly little evolution with redshift for z < 2; this can provide a new test of the current LCDM model when compared with future observations of high redshift clusters.Comment: 20 pages, 9 figures, accepted for publication in Ap