Cosmological Implications of the Fundamental Relations of X-ray Clusters

Based on the two-parameter family nature of X-ray clusters of galaxies obtained in a separate paper, we discuss the formation history of clusters and cosmological parameters of the universe. Utilizing the spherical collapse model of cluster formation, and assuming that the cluster X-ray core radius is proportional to the virial radius at the time of the cluster collapse, the observed relations among the density, radius, and temperature of clusters imply that cluster formation occurs in a wide range of redshift. The observed relations favor the low-density universe. Moreover, we find that the model of $n\sim -1$ is preferable.Comment: 7 pages, 4 figures. To be published in ApJ Letter

Mass-Temperature Relation of Galaxy Clusters: A Theoretical Study

Combining conservation of energy throughout nearly-spherical collapse of galaxy clusters with the virial theorem, we derive the mass-temperature relation for X-ray clusters of galaxies $T=CM^{2/3}$. The normalization factor $C$ and the scatter of the relation are determined from first principles with the additional assumption of initial Gaussian random field. We are also able to reproduce the recently observed break in the M-T relation at T \sim 3 \keV, based on the scatter in the underlying density field for a low density $\Lambda$CDM cosmology. Finally, by combining observational data of high redshift clusters with our theoretical formalism, we find a semi-empirical temperature-mass relation which is expected to hold at redshifts up to unity with less than 20% error.Comment: 43 pages, 13 figures, One figure is added and minor changes are made. Accepted for Publication in Ap

Effective transport barriers in nontwist systems

In fluids and plasmas with zonal flow reversed shear, a peculiar kind of transport barrier appears in the shearless region, one that is associated with a proper route of transition to chaos. These barriers have been identified in symplectic nontwist maps that model such zonal flows. We use the so-called standard nontwist map, a paradigmatic example of nontwist systems, to analyze the parameter dependence of the transport through a broken shearless barrier. On varying a proper control parameter, we identify the onset of structures with high stickiness that give rise to an effective barrier near the broken shearless curve. Moreover, we show how these stickiness structures, and the concomitant transport reduction in the shearless region, are determined by a homoclinic tangle of the remaining dominant twin island chains. We use the finite-time rotation number, a recently proposed diagnostic, to identify transport barriers that separate different regions of stickiness. The identified barriers are comparable to those obtained by using finite-time Lyapunov exponents.FAPESPCNPqCAPESMCT/CNEN (Rede Nacional de Fusao)Fundacao AraucariaUS Department of Energy DE-FG05-80ET-53088Physic

Weak Lensing as a Calibrator of the Cluster Mass-Temperature Relation

The abundance of clusters at the present epoch and weak gravitational lensing shear both constrain roughly the same combination of the power spectrum normalization sigma_8 and matter energy density Omega_M. The cluster constraint further depends on the normalization of the mass-temperature relation. Therefore, combining the weak lensing and cluster abundance data can be used to accurately calibrate the mass-temperature relation. We discuss this approach and illustrate it using data from recent surveys.Comment: Matches the version in ApJL. Equation 4 corrected. Improvements in the analysis move the cluster contours in Fig1 slightly upwards. No changes in the conclusion

Normalizing the Temperature Function of Clusters of Galaxies

We re-examine the constraints which can be robustly obtained from the observed temperature function of X-ray cluster of galaxies. The cluster mass function has been thoroughly studied in simulations and analytically, but a direct simulation of the temperature function is presented here for the first time. Adaptive hydrodynamic simulations using the cosmological Moving Mesh Hydro code of Pen (1997a) are used to calibrate the temperature function for different popular cosmologies. Applying the new normalizations to the present-day cluster abundances, we find $\sigma_8=0.53\pm 0.05 \Omega_0^{-0.45}$ for a hyperbolic universe, and $\sigma_8=0.53\pm 0.05 \Omega_0^{-0.53}$ for a spatially flat universe with a cosmological constant. The simulations followed the gravitational shock heating of the gas and dark matter, and used a crude model for potential energy injection by supernova heating. The error bars are dominated by uncertainties in the heating/cooling models. We present fitting formulae for the mass-temperature conversions and cluster abundances based on these simulations.Comment: 20 pages incl 5 figures, final version for ApJ, corrected open universe \gamma relation, results unchange

Breaking Cosmological Degeneracies in Galaxy Cluster Surveys with a Physical Model of Cluster Structure

Forthcoming large galaxy cluster surveys will yield tight constraints on cosmological models. It has been shown that in an idealized survey, containing > 10,000 clusters, statistical errors on dark energy and other cosmological parameters will be at the percent level. It has also been shown that through "self-calibration", parameters describing the mass-observable relation and cosmology can be simultaneously determined, though at a loss in accuracy by about an order of magnitude. Here we examine the utility of an alternative approach of self-calibration, in which a parametrized ab-initio physical model is used to compute cluster structure and the resulting mass-observable relations. As an example, we use a modified-entropy ("pre-heating") model of the intracluster medium, with the history and magnitude of entropy injection as unknown input parameters. Using a Fisher matrix approach, we evaluate the expected simultaneous statistical errors on cosmological and cluster model parameters. We study two types of surveys, in which a comparable number of clusters are identified either through their X-ray emission or through their integrated Sunyaev-Zel'dovich (SZ) effect. We find that compared to a phenomenological parametrization of the mass-observable relation, using our physical model yields significantly tighter constraints in both surveys, and offers substantially improved synergy when the two surveys are combined. These results suggest that parametrized physical models of cluster structure will be useful when extracting cosmological constraints from SZ and X-ray cluster surveys. (abridged)Comment: 22 pages, 8 figures, accepted to Ap

Process transparency on construction sites : examples from construction companies in Brazil

Process transparency is the core concept in Visual Management (VM), which is one of the founding blocks of the Toyota Production System. This paper presents the preliminary results of a collaborative research conducted between Brazil and the UK, as part of a research effort focused on the application of Visual Management in construction. How process transparency is realized on construction sites is the main research question of the paper. The use of this concept and the implementation of the transparency theory were investigated through multiple case studies, carried out in nine different construction companies. The findings are explained through six theoretical transparency increasing approaches. The affecting parameters in the application of, the management’s perception of and several methods in process transparency in construction were identified. Further work, especially exploring the functions of process transparency on construction sites and reflecting the worker perception of the issue, is necessary to elaborate the process transparency concept

Constraints on Cosmological Parameters from Future Galaxy Cluster Surveys

We study the expected redshift evolution of galaxy cluster abundance between 0 < z < 3 in different cosmologies, including the effects of the cosmic equation of state parameter w=p/rho. Using the halo mass function obtained in recent large scale numerical simulations, we model the expected cluster yields in a 12 deg^2 Sunyaev-Zeldovich Effect (SZE) survey and a deep 10^4 deg^2 X-ray survey over a wide range of cosmological parameters. We quantify the statistical differences among cosmologies using both the total number and redshift distribution of clusters. Provided that the local cluster abundance is known to a few percent accuracy, we find only mild degeneracies between w and either Omega_m or h. As a result, both surveys will provide improved constraints on Omega_m and w. The Omega_m-w degeneracy from both surveys is complementary to those found either in studies of CMB anisotropies or of high-redshift Supernovae (SNe). As a result, combining these surveys together with either CMB or SNe studies can reduce the statistical uncertainty on both w and Omega_m to levels below what could be obtained by combining only the latter two data sets. Our results indicate a formal statistical uncertainty of about 3% (68% confidence) on both Omega_m and w when the SZE survey is combined with either the CMB or SN data; the large number of clusters in the X-ray survey further suppresses the degeneracy between w and both Omega_m and h. Systematics and internal evolution of cluster structure at the present pose uncertainties above these levels. We briefly discuss and quantify the relevant systematic errors. By focusing on clusters with measured temperatures in the X-ray survey, we reduce our sensitivity to systematics such as non-standard evolution of internal cluster structure.Comment: ApJ, revised version. Expanded discussion of systematics; Press-Schechter mass function replaced by fit from simulation

Non-extensive processes associated with heating of the Galactic disc

We analyse the mechanisms ruling galactic disc heating through the dynamics of space velocities $U$, $V$ and $W$, extracted from the Geneva-Copenhagen catalogue. To do this, we use a model based on non-extensive statistical mechanics, where we derive the probability distribution functions that quantify the non-Gaussian effects. Furthermore, we find that the deviation $q-1$ at a given stellar age follows non-random behaviour. As a result, the $q$-index behaviour indicates that the vertical component $W$, perpendicular to the Galactic plane, does not ``heat up'' at random, which is in disagreement with previous works that attributed the evolution of $W$ to randomness. Finally, our results bring a new perspective to this matter and open the way for studying Galactic kinematic components through the eyes of more robust statistical models that consider non-Gaussian effects.Comment: 7 pages, 3 figures, 2 tables. Accepted to EP

Statics and dynamics of an Ashkin-Teller neural network with low loading

An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns built from the two types of neurons, with different degrees of (in)dependence is studied. In particular, thermodynamic properties including the existence and stability of Mattis states are discussed. Furthermore, the dynamic behaviour is examined by deriving flow equations for the macroscopic overlap. It is found that for linked patterns the model shows better retrieval properties than a corresponding Hopfield model.Comment: 20 pages, 6 figures, Latex with postscript figures in one tar.gz fil