Cluster Morphologies as a Test of Different Cosmological Models

We investigate how cluster morphology is affected by the cosmological constant in low-density universes. Using high-resolution cosmological N-body/SPH simulations of flat (\Omega_0 = 0.3, \lambda_0 = 0.7, \Lambda CDM) and open (\Omega_0 = 0.3, \lambda_0 = 0, OCDM) cold dark matter universes, we calculate statistical indicators to quantify the irregularity of the cluster morphologies. We study axial ratios, center shifts, cluster clumpiness, and multipole moment power ratios as indicators for the simulated clusters at z=0 and 0.5. Some of these indicators are calculated for both the X-ray surface brightness and projected mass distributions. In \Lambda CDM all these indicators tend to be larger than those in OCDM at z=0. This result is consistent with the analytical prediction of Richstone, Loeb, & Turner, that is, clusters in \Lambda CDM are formed later than in OCDM, and have more substructure at z=0. We make a Kolmogorov-Smirnov test on each indicator for these two models. We then find that the results for the multipole moment power ratios and the center shifts for the X-ray surface brightness are under the significance level (5%). We results also show that these two cosmological models can be distinguished more clearly at z=0 than z = 0.5 by these indicators.Comment: 30pages, 6figures, Accepted for publication in Ap

Graph cluster randomization: network exposure to multiple universes

A/B testing is a standard approach for evaluating the effect of online experiments; the goal is to estimate the `average treatment effect' of a new feature or condition by exposing a sample of the overall population to it. A drawback with A/B testing is that it is poorly suited for experiments involving social interference, when the treatment of individuals spills over to neighboring individuals along an underlying social network. In this work, we propose a novel methodology using graph clustering to analyze average treatment effects under social interference. To begin, we characterize graph-theoretic conditions under which individuals can be considered to be `network exposed' to an experiment. We then show how graph cluster randomization admits an efficient exact algorithm to compute the probabilities for each vertex being network exposed under several of these exposure conditions. Using these probabilities as inverse weights, a Horvitz-Thompson estimator can then provide an effect estimate that is unbiased, provided that the exposure model has been properly specified. Given an estimator that is unbiased, we focus on minimizing the variance. First, we develop simple sufficient conditions for the variance of the estimator to be asymptotically small in n, the size of the graph. However, for general randomization schemes, this variance can be lower bounded by an exponential function of the degrees of a graph. In contrast, we show that if a graph satisfies a restricted-growth condition on the growth rate of neighborhoods, then there exists a natural clustering algorithm, based on vertex neighborhoods, for which the variance of the estimator can be upper bounded by a linear function of the degrees. Thus we show that proper cluster randomization can lead to exponentially lower estimator variance when experimentally measuring average treatment effects under interference.Comment: 9 pages, 2 figure

07181 Abstracts Collection -- Parallel Universes and Local Patterns

From 1 May 2007 to 4 May 2007 the Dagstuhl Seminar 07181 ``Parallel Universes and Local Patterns\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

The Local Group as a test of cosmological models

The dynamics of the Local Group and its environment provide a unique challenge to cosmological models. The velocity field within 5h-1 Mpc of the Local Group (LG) is extremely ``cold''. The deviation from a pure Hubble flow, characterized by the observed radial peculiar velocity dispersion, is measured to be about 60km/s. We compare the local velocity field with similarly defined regions extracted from N-body simulations of Universes dominated by cold dark matter (CDM). This test is able to strongly discriminate between models that have different mean mass densities. We find that neither the Omega=1 (SCDM) nor Omega=0.3 (OCDM) cold dark matter models can produce a single candidate Local Group that is embedded in a region with such small peculiar velocities. For these models, we measure velocity dispersions between 500-700km/s and 150-300km/s respectively, more than twice the observed value. Although both CDM models fail to produce environments similar to those of our Local Group on a scale of a few Mpc, they can give rise to many binary systems that have similar orbital properties as the Milky Way--Andromeda system. The local, gravitationally induced bias of halos in the CDM ``Local Group'' environment, if defined within a sphere of 10 Mpc around each Local Group is about 1.5, independent of Omega. No biasing scheme could reconcile the measured velocity dispersions around Local Groups with the observed one. Identification of binary systems using a halo finder (named Skid (http://www-hpcc.astro.washington.edu/tools/DENMAX for a public version)) based on local density maxima instead of a simple linking algorithm, gives a much more complete sample. We show that a standard ``friend of friends'' algorithm would miss 40% of the LG candidates present in the simulations.Comment: Latex file (19 pages) + 13 figures. Submitted to New Astronomy. Two MPEG movies were not included. Also available (this time with the movies) at http://www-hpcc.astro.washington.edu/faculty/fabio/index.htm

Lensing Sunyaev-Zel'dovich Clusters

Full-sky microwave surveys like the upcoming Planck satellite mission will detect of order 10^4 galaxy clusters through their thermal Sunyaev-Zel'dovich effect. I investigate the properties of the gravitationally lensing subsample of these clusters. The main results are: (1) The combined sample comprises >~70% of the complete sample. (2) It is confined to redshifts 0.2+-0.1, and to masses (5+-3) x 10^14 solar masses. (3) Using a particular measure for the weak lensing effect, viz. the aperture mass, cluster masses can be determined with a relative accuracy of ~20% if their density profile is known. Consequently, the mass function of the combined sample can accurately be measured. (4) For low-density universes, I predict a sharp peak in the measured (aperture) mass function near 5 x 10^14 solar masses and explain its origin, showing that the peak will be absent in high-density universes. (5) The location of the peak and the exponential decrease of the mass function on its high-mass side will allow the determination of the amplitude of the dark-matter power spectrum on the cluster scale and the baryon fraction in clusters, and constrain the thermal history of the intracluster gas.Comment: submitted to Astronomy & Astrophysic

Cosmology and Cluster Halo Scaling Relations

We explore the effects of dark matter and dark energy on the dynamical scaling properties of galaxy clusters. We investigate the cluster Faber-Jackson (FJ), Kormendy and Fundamental Plane (FP) relations between the mass, radius and velocity dispersion of cluster size halos in cosmological $N$-body simulations. The simulations span a wide range of cosmological parameters, representing open, flat and closed Universes. Independently of the cosmology, we find that the simulated clusters are close to a perfect virial state and do indeed define a Fundamental Plane. The fitted parameters of the FJ, Kormendy and FP relationships do not show any significant dependence on $\Omega_m$ and/or $\Omega_{\Lambda}$. The one outstanding effect is the influence of $\Omega_{m}$ on the thickness of the Fundamental Plane. Following the time evolution of our models, we find slight changes of FJ and Kormendy parameters in high $\Omega_m$ universe, along with a slight decrease of FP fitting parameters. We also see an initial increase of the FP thickness followed by a convergence to a nearly constant value. The epoch of convergence is later for higher values of $\Omega_m$ while the thickness remains constant in the low $\Omega_m$ $\Lambda$-models. We also find a continuous increase of the FP thickness in the Standard CDM (SCDM) cosmology. There is no evidence that these differences are due to the different power spectrum slope at cluster scales. From the point of view of the FP, there is little difference between clusters that quietly accreted their mass and those that underwent massive mergers. The principal effect of strong mergers is to change significantly the ratio of the half-mass radius $r_{half}$ to the harmonic mean radius $r_h$.Comment: 24 pages, 17 figures, submitted to MNRA