7,473 research outputs found

    Line-of-sight percolation

    Full text link
    Given ω≥1\omega\ge 1, let Z(ω)2Z^2_{(\omega)} be the graph with vertex set Z2Z^2 in which two vertices are joined if they agree in one coordinate and differ by at most ω\omega in the other. (Thus Z(1)2Z^2_{(1)} is precisely Z2Z^2.) Let pc(ω)p_c(\omega) be the critical probability for site percolation in Z(ω)2Z^2_{(\omega)}. Extending recent results of Frieze, Kleinberg, Ravi and Debany, we show that \lim_{\omega\to\infty} \omega\pc(\omega)=\log(3/2). We also prove analogues of this result on the nn-by-nn grid and in higher dimensions, the latter involving interesting connections to Gilbert's continuum percolation model. To prove our results, we explore the component of the origin in a certain non-standard way, and show that this exploration is well approximated by a certain branching random walk.Comment: Revised and expanded (section 2.3 added). To appear in Combinatorics, Probability and Computing. 27 pages, 4 figure

    Continuum Line-of-Sight Percolation on Poisson-Voronoi Tessellations

    Full text link
    In this work, we study a new model for continuum line-of-sight percolation in a random environment driven by the Poisson-Voronoi tessellation in the dd-dimensional Euclidean space. The edges (one-dimensional facets, or simply 1-facets) of this tessellation are the support of a Cox point process, while the vertices (zero-dimensional facets or simply 0-facets) are the support of a Bernoulli point process. Taking the superposition ZZ of these two processes, two points of ZZ are linked by an edge if and only if they are sufficiently close and located on the same edge (1-facet) of the supporting tessellation. We study the percolation of the random graph arising from this construction and prove that a 0-1 law, a subcritical phase as well as a supercritical phase exist under general assumptions. Our proofs are based on a coarse-graining argument with some notion of stabilization and asymptotic essential connectedness to investigate continuum percolation for Cox point processes. We also give numerical estimates of the critical parameters of the model in the planar case, where our model is intended to represent telecommunications networks in a random environment with obstructive conditions for signal propagation.Comment: 30 pages, 4 figures. Accepted for publication in Advances in Applied Probabilit

    Projection Effects of Galaxy Clusters

    Get PDF
    Dark matter halos are used as cosmological probes of the universe. From the halo mass function, we can obtain energy density parameters. However, in the observation of halos there are projection effects that make it difficult to count the number of galaxies in a halo. These projection effects include uncertainty about the radius of each halo and the line of sight distance. The line of sight distance is measured from the halo center. Distances are determined with redshift. We can use simulation data so we know everything about a halo and then compare different methods of counting galaxies. For simplicity, we used a fixed line of sight distance and assumed we knew the halo center. We compared galaxy counts from catalogs using different line of sight distances, with and without percolation, and fixed vs iterative radii. Percolation is counting a galaxy towards the more massive halo when the galaxy is within the radius of multiple halos to prevent halo radii from blowing up. The catalog without percolation has more galaxies at low masses but has little effect at high halo masses. We have found that the projection effects are dominated by galaxies within 15 Mpc/h

    The Aquarius Superclusters - I. Identification of Clusters and Superclusters

    Get PDF
    We study the distribution of galaxies and galaxy clusters in a 10^deg x 6^deg field in the Aquarius region. In addition to 63 clusters in the literature, we have found 39 new candidate clusters using a matched-filter technique and a counts-in-cells analysis. From redshift measurements of galaxies in the direction of these cluster candidates, we present new mean redshifts for 31 previously unobserved clusters, while improved mean redshifts are presented for 35 other systems. About 45% of the projected density enhancements are due to the superposition of clusters and/or groups of galaxies along the line of sight, but we could confirm for 72% of the cases that the candidates are real physical associations similar to the ones classified as rich galaxy clusters. On the other hand, the contamination due to galaxies not belonging to any concentration or located only in small groups along the line of sight is ~ 10%. Using a percolation radius of 10 h^{-1} Mpc (spatial density contrast of about 10), we detect two superclusters of galaxies in Aquarius, at z = 0.086 and at z = 0.112, respectively with 5 and 14 clusters. The latter supercluster may represent a space overdensity of about 160 times the average cluster density as measured from the Abell et al. (1989) cluster catalog, and is possibly connected to a 40 h^{-1} Mpc filament from z ~ 0.11 to 0.14.Comment: LateX text (21 pages) and 12 (ps/eps/gif) figures; figures 5a, 5b and 6 are not included in the main LateX text; to be published in the Astronomical Journal, March issu

    Quantifying the Bull's Eye Effect

    Full text link
    We have used N-body simulations to develop two independent methods to quantify redshift distortions known as the Bull's Eye effect (large scale infall plus small scale virial motion). This effect depends upon the mass density, Ω0\Omega_0, so measuring it can in principle give an estimate of this important cosmological parameter. We are able to measure the effect and distinguish between its strength for high and low values of Ω0\Omega_0. Unlike other techniques which utilize redshift distortions, one of our methods is relatively insensitive to bias. In one approach, we use path lengths between contour crossings of the density field. The other is based upon percolation. We have found both methods to be successful in quantifying the effect and distinguishing between values of Ω0\Omega_0. However, only the path lengths method exhibits low sensitivity to bias.Comment: 21 pages, 5 figures, 3 tables; Replaced version - minor corrections, replaced figure 2; To appear in ApJ, Jan. 20, 200

    Binary Galaxies in the Local Supercluster and Its Neighborhood

    Full text link
    We report a catalog of 509 pairs identified among 10403 nearby galaxies with line-of-sight velocities V_LG < 3500 km/s.We selected binary systems in accordance with two criteria (bounding and temporal), which require the physical pair of galaxies to have negative total energy and its components to be located inside the zero-velocity surface. We assume that individual galaxy masses are proportional to their total K-band luminosities, M = L_K x 6M/L. The catalog gives the magnitudes and morphological types of galaxies and also the projected (orbital) masses and pair isolation indices. The component line-of-sight velocity differences and projected distances of the binary systems considered have power-law distributions with the median values of 35 km/s and 123 kpc, respectively. The median mass-to-K-band luminosity ratio is equal to 11 M/L, and its uncertainty is mostly due to the errors of measured velocities. Our sample of binary systems has a typical density contrast of d ro/ro_c ~ 500 and a median crossing time of about 3.5 Gyr. We point out the substantial fraction of binary systems consisting of late-type dwarf galaxies, where the luminosities of both components are lower than that of the Small Magellanic Cloud. The median projected distance for 41 such pairs is only 30 kpc, and the median difference of their line-of-sight velocities is equal to 14 km/s which is smaller than the typical error for radial-velocity (30 km/s). This specific population of gas-rich dwarf binary galaxies such as I Zw 18 may be at the stage immediately before merging of its components. Such objects, which are usually lost in flux-limited (and not distance-limited) samples deserve a thorough study in the HI radio line with high spatial and velocity resolution.Comment: published in Astrophysical Bulletin, 2008, Vol. 63, No. 4, pp. 299-34

    Discovery of Extreme Examples of Superclustering in Aquarius

    Get PDF
    We report the discovery of two highly extended filaments and one extremely high density knot within the region of Aquarius. The supercluster candidates were chosen via percolation analysis of the Abell and ACO catalogs and include only the richest clusters (R >= 1). The region examined is a 10x45 degree strip and is now 87% complete in cluster redshift measurements to mag_10 = 18.3. In all, we report 737 galaxy redshifts in 46 cluster fields. One of the superclusters, dubbed Aquarius, is comprised of 14 Abell/ACO clusters and extends 110h^-1Mpc in length only 7 degrees off the line-of-sight. On the near-end of the Aquarius filament, another supercluster, dubbed Aquarius-Cetus, extends for 75h^-1Mpc perpendicular to the line-of-sight. After fitting ellipsoids to both Aquarius and Aquarius-Cetus, we find axis ratios (long-to- midlength axis) of 4.3 for Aquarius and 3.0 for Aquarius-Cetus. We fit ellipsoids to all N>=5 clumps of clusters in the Abell/ACO measured-z cluster sample. The frequency of filaments with axis ratios >=3.0 (~20%) is nearly identical with that found among `superclusters' in Monte Carlo simulations of random and random- clumped clusters, however, so the rich Abell/ACO clusters have no particular tendency toward filamentation. The Aquarius filament also contains a `knot' of 6 clusters at Z ~0.11, with five of the clusters near enough togeteher to represent an apparent overdensity of 150. There are three other R >= 1 cluster density enhancements similar to this knot at lower redshifts: Corona Borealis, the Shapely Concentration, and another grouping of seven clusters in Microscopium. All four of these dense superclusters appear near the point of breaking away from the Hubble Flow, and some may now be in collapse, but there is little evidence of any being virialized.Comment: 45 pages (+ e-tables), 7 figures, AASTeX Accepted for Publication in Ap
    • …
    corecore