High-Resolution Simulations of Cosmic Microwave Background non-Gaussian Maps in Spherical Coordinates

We describe a new numerical algorithm to obtain high-resolution simulated maps of the Cosmic Microwave Background (CMB), for a broad class of non-Gaussian models. The kind of non-Gaussianity we account for is based on the simple idea that the primordial gravitational potential is obtained by a non-linear but local mapping from an underlying Gaussian random field, as resulting from a variety of inflationary models. Our technique, which is based on a direct realization of the potential in spherical coordinates and fully accounts for the radiation transfer function, allows to simulate non-Gaussian CMB maps down to the Planck resolution ($\ell_{\rm max} \sim 3,000$), with reasonable memory storage and computational time.Comment: 9 pages, 5 figures. Submitted to ApJ. A version with higher quality figures is available at http://www.pd.infn.it/~liguori/content.htm

Optical vortex mode generation by nanoarrays with a tailored geometry

Light generated with orbital angular momentum, commonly known as an optical vortex, is widely achieved by modifying the phase structure of a conventional laser beam through the utilization of a suitable optical element. In recent research, a process has been introduced that can produce electromagnetic radiation with a helical wave-front directly from a source. The chirally driven optical emission originates from a hierarchy of tailored nanoscale chromophore arrays arranged with a specific propeller-like geometry and symmetry. In particular, a nanoarray composed of n particles requires each component to be held in a configuration with a rotation and associated phase shift of 2 π/n radians with respect to its neighbor. Following initial electronic excitation, each such array is capable of supporting delocalized doubly degenerate excitons, whose azimuthal phase progression is responsible for the helical wave-front. Under identified conditions, the relaxation of the electronically-excited nanoarray produces structured light in a spontaneous manner. Nanoarrays of escalating order, i.e. those containing an increasing number of components, enable access to a set of topological charges of higher order. Practical considerations for the development of this technique are discussed, and potential new applications are identified. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE)

The Cluster Distribution as a Test of Dark Matter Models. IV: Topology and Geometry

We study the geometry and topology of the large-scale structure traced by galaxy clusters in numerical simulations of a box of side 320 $h^{-1}$ Mpc, and compare them with available data on real clusters. The simulations we use are generated by the Zel'dovich approximation, using the same methods as we have used in the first three papers in this series. We consider the following models to see if there are measurable differences in the topology and geometry of the superclustering they produce: (i) the standard CDM model (SCDM); (ii) a CDM model with $\Omega_0=0.2$ (OCDM); (iii) a CDM model with a `tilted' power spectrum having $n=0.7$ (TCDM); (iv) a CDM model with a very low Hubble constant, $h=0.3$ (LOWH); (v) a model with mixed CDM and HDM (CHDM); (vi) a flat low-density CDM model with $\Omega_0=0.2$ and a non-zero cosmological $\Lambda$ term ($\Lambda$CDM). We analyse these models using a variety of statistical tests based on the analysis of: (i) the Euler-Poincar\'{e} characteristic; (ii) percolation properties; (iii) the Minimal Spanning Tree construction. Taking all these tests together we find that the best fitting model is $\Lambda$CDM and, indeed, the others do not appear to be consistent with the data. Our results demonstrate that despite their biased and extremely sparse sampling of the cosmological density field, it is possible to use clusters to probe subtle statistical diagnostics of models which go far beyond the low-order correlation functions usually applied to study superclustering.Comment: 17 pages, 7 postscript figures, uses mn.sty, MNRAS in pres

Topology of Neutral Hydrogen Within the Small Magellanic Cloud

In this paper, genus statistics have been applied to an HI column density map of the Small Magellanic Cloud in order to study its topology. To learn how topology changes with the scale of the system, we provide the study of topology for column density maps at varying resolution. To evaluate the statistical error of the genus we randomly reassign the phases of the Fourier modes while keeping the amplitudes. We find, that at the smallest scales studied ($40 {pc}\leq\lambda\leq 80 {pc}$) the genus shift is in all regions negative, implying a clump topology. At the larger scales ($110 {pc}\leq\lambda\leq 250 {pc}$) the topology shift is detected to be negative in 4 cases and positive (``swiss cheese'' topology) in 2 cases. In 4 regions there is no statistically significant topology shift at large scales

Cluster Correlations in the Zel'dovich Approximation

We show how to simulate the clustering of rich clusters of galaxies using a technique based on the Zel'dovich approximation. This method well reproduces the spatial distribution of clusters obtainable from full N-body simulations at a fraction of the computational cost. We use an ensemble of large--scale simulations to assess the level and statistical significance of cluster clustering in open, tilted and flat versions of the Cold Dark Matter (CDM) model, as well as a model comprising a mixture of Cold and Hot Dark Matter (CHDM). We find the open and flat CDM models are excluded by the data. The tilted CDM model with a slight tilt is in marginal agreement, while larger tilt produces the right amount of clustering; CHDM is the best of all our models at reproducing the observations of cluster clustering. We find that {\em all} our models display a systematically weaker relationship between clustering length and mean cluster separation than seems to be implied by observations. We also note that the cluster bias factor, is not constant in any of the models, showing that one needs to be very careful when relating cluster clustering statistics to primordial density fluctuations.Comment: 9 pages including 6 figures, uuencoded compressed postscript file, Ref. DFUPG 85-9

Small Deviations from Gaussianity and The Galaxy Cluster Abundance Evolution

We raise the hypothesis that the density fluctuations field which originates the growth of large scale structures is a combination of two or more distributions. By applying the statistical analysis of finite mixture distributions to a specific combination of Gaussian plus non-Gaussian random fields, we studied the case where just a small departure from Gaussianity is allowed. Our results suggest that even a very small level of non-Gaussianity may introduce significant changes in the cluster abundance evolution rate.Comment: 10 pages with 2 figures, accepted for publication in Ap

Moments of the Cluster Distribution as a Test of Dark Matter Models

We estimate the variance and the skewness of the cluster distribution in several dark matter (DM) models. The cluster simulations are based on the Zel'dovich approximation, the low computational cost of which allows us to run 50 random realizations of each model. We compare our results with those coming from a similar analysis of a redshift sample of Abell/ACO clusters. Within the list of the considered models, we find that only the model based on Cold+Hot DM (with $\Omega_{\rm hot}=0.3$) provides a good fit to the data. The standard CDM model and the low-density ($\Omega_{\circ}=0.2$) CDM models, both with and without a cosmological constant term ($\Omega_\Lambda =0.8$) are ruled out. The tilted CDM model with primordial spectral index $n=0.7$ and a low Hubble constant ($h=0.3$) CDM model are only marginally consistent with the data.Comment: 11 pages + 1 figure, uuencoded compressed postscript, ApJ Letters in press. Replaced because results are changed for the $\Lambda$CDM mode

The Cluster Distribution as a Test for Dark Matter Models. I: Clustering Properties

We present extended simulations of the distribution of galaxy clusters in different dark matter models, using an optimized version of the Zel'dovich approximation. Six different dark matter models are studied: Standard CDM, Open CDM, Tilted CDM, Cold + Hot DM, low-density CDM with cosmological constant, and low Hubble constant ($h=0.3$) CDM. We compare simulations with an Abell/ACO redshift sample. We find that the models that best reproduce the clustering of the real data sets are the Cold + Hot DM model and the CDM model with a cosmological constant. The probability density function of all models and data is always well approximated by a lognormal distribution. We also find that the linear biasing parameter for the simulated clusters is nearly constant over a large range of scales, but its value depends on the model. We also note that the abundances of clusters predicted by the Press-Schechter theory provide strong constraints on these models: only the Cold + Hot DM model and the low-H CDM model appear to produce the correct number-density of clusters. Taking this constraint together with the cluster clustering statistics leads one to conclude that the best of our models is the Cold + Hot DM scenario.Comment: 13 pages+8 figures, uuencoded compressed postscript. MNRAS submitted. Replaced because of problems in the uuencoding procedur

Angular Distribution of Clustersin Skewed CDM Models

We perform a detailed investigation of the statistical properties of the projected distribution of galaxy clusters obtained in Cold Dark Matter (CDM) models with both Gaussian and skewed primordial density fluctuations. We use N-body simulations to construct a set artificial Lick maps. An objective cluster--finding algorithm is used to identify clusters of different richness. For Gaussian models, the overall number of clusters is too small in the standard CDM case, but a model with higher normalisation fares much better; non--Gaussian models with negative skewness also fit faily well. We apply several statistical tests to compare real and simulated cluster samples, such as the 2-point correlation function, the minimal spanning tree construction, the multifractal analysis and the skewness of cell counts. The emerging picture is that Gaussian models, even with a higher normalization, are in trouble. Skew-positive models are also ruled out, while skew-negative models can reproduce the observed clustering of galaxy clusters in the CDM framework.Comment: To be compiled with LaTeX, with the A4.STY macro, included at the bottom of the text fil