7,473 research outputs found
Line-of-sight percolation
Given , let be the graph with vertex set
in which two vertices are joined if they agree in one coordinate and differ by
at most in the other. (Thus is precisely .) Let
be the critical probability for site percolation in
. 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 -by- 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
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
-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 of these two processes,
two points of 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
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
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
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, , 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 . 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 . 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
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
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
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