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

Noncommutative ball maps

In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. These types of functions have recently been used in the study of dimension-free linear system engineering problems. In this paper we characterize NC analytic maps that send dimension-free matrix balls to dimension-free matrix balls and carry the boundary to the boundary; such maps we call "NC ball maps". We find that up to normalization, an NC ball map is the direct sum of the identity map with an NC analytic map of the ball into the ball. That is, "NC ball maps" are very simple, in contrast to the classical result of D'Angelo on such analytic maps over C. Another mathematically natural class of maps carries a variant of the noncommutative distinguished boundary to the boundary, but on these our results are limited. We shall be interested in several types of noncommutative balls, conventional ones, but also balls defined by constraints called Linear Matrix Inequalities (LMI). What we do here is a small piece of the bigger puzzle of understanding how LMIs behave with respect to noncommutative change of variables.Comment: 46 page

Projection, Spatial Correlations, and Anisotropies in a Large and Complete Sample of Abell Clusters

An analysis of R >= 1 Abell clusters is presented for samples containing recent redshifts from the MX Northern Abell Cluster Survey. The newly obtained redshifts from the MX Survey as well as those from the ESO Nearby Abell Cluster Survey (ENACS) provide the necessary data for the largest magnitude-limited correlation analysis of rich clusters in the entire sky (excluding the galactic plane) to date. We find 19.4 <= r_0 <= 23.3 h^-1Mpc, -1.92 <= gamma <= -1.83 for four different subsets of Abell/ACO clusters, including a large sample (N=104) of cD clusters. We have used this dataset to look for line-of-sight anisotropies within the Abell/ACO catalogs. We show that the strong anisotropies present in previously studied Abell cluster datasets are not present in our R >= 1 samples. There are, however, indications of residual anisotropies which we show are the result of two elongated superclusters, Ursa Majoris and Corona Borealis, whose axes lie near the line-of-sight. After rotating these superclusters so that their semi-major axes are prependicular to the line-of-sight, we find no anisotropies as indicated by the correlation function. The amplitude and slope of the two-point correlation function remain the same before and after these rotations. We also remove a subset of R = 1 Abell/ACO clusters that show sizable foreground/background galaxy contamination and again find no change in the amplitude or slope of the correlation function. We conclude that the correlation length of R >= 1 Abell clusters is not artificially enhanced by line-of-sight anisotropies.Comment: 37 pages, 8 figures, AASTeX Accepted for publication in Ap

Infall Regions and Scaling Relations of X-ray Selected Groups

We use the Fifth Data Release of the Sloan Digital Sky Survey to study X-ray-selected galaxy groups and compare their properties to clusters. We search for infall patterns around the groups and use these to measure group mass profiles to large radii. In previous work, we analyzed infall patterns for an X-ray-selected sample of 72 clusters from the ROSAT All-Sky Survey. Here, we extend this approach to a sample of systems with smaller X-ray fluxes selected from the 400 Square Degree serendipitous survey of clusters and groups in ROSAT pointed observations. We identify 16 groups with SDSS DR5 spectroscopy, search for infall patterns, and compute mass profiles out to 2-6 Mpc from the group centers with the caustic technique. No other mass estimation methods are currently available at such large radii for these low-mass groups, because the virial estimate requires dynamical equilibrium and the gravitational lensing signal is too weak. Despite the small masses of these groups, most display recognizable infall patterns. We use caustic and virial mass estimates to measure the scaling relations between different observables, extending these relations to smaller fluxes and luminosities than many previous surveys. Close inspection reveals that three of the groups are subclusters in the outskirts of larger clusters. A fourth group is apparently undergoing a group-group merger. These four merging groups represent the most extreme outliers in the scaling relations. Excluding these groups, we find $L_X\propto\sigma_p^{3.4\pm1.6}$, consistent with previous determinations for both clusters and groups. Understanding cluster and group scaling relations is crucial for measuring cosmological parameters from clusters.Comment: published in AJ Feb 2010, significantly revised in response to referee report, title edite

The architecture of Abell 1386 and its relationship to the Sloan Great Wall

We present new radial velocities from AAOmega on the Anglo-Australian Telescope for 307 galaxies (b_J < 19.5) in the region of the rich cluster Abell 1386. Consistent with other studies of galaxy clusters that constitute sub-units of superstructures, we find that the velocity distribution of A1386 is very broad (21,000--42,000 kms^-1, or z=0.08--0.14) and complex. The mean redshift of the cluster that Abell designated as number 1386 is found to be ~0.104. However, we find that it consists of various superpositions of line-of-sight components. We investigate the reality of each component by testing for substructure and searching for giant elliptical galaxies in each and show that A1386 is made up of at least four significant clusters or groups along the line of sight whose global parameters we detail. Peculiar velocities of brightest galaxies for each of the groups are computed and found to be different from previous works, largely due to the complexity of the sky area and the depth of analysis performed in the present work. We also analyse A1386 in the context of its parent superclusters: Leo A, and especially the Sloan Great Wall. Although the new clusters may be moving toward mass concentrations in the Sloan Great Wall or beyond, many are most likely not yet physically bound to it.Comment: 21 pages, 9 figures, includes the full appendix table. Accepted for publication in MNRA

Diffuse steep-spectrum sources from the 74 MHz VLSS survey

Galaxy clusters grow by a sequence of mergers with other clusters and galaxy groups. During these mergers, shocks and/or turbulence are created within the intracluster medium (ICM). In this process, particles could be accelerated to highly relativistic energies. The synchrotron radiation from these particles is observed in the form of radio relics and halos that are generally characterized by a steep radio spectral index. Shocks can also revive fossil radio plasma from a previous episode of AGN activity, creating a so-called radio phoenix. Here we present multi-frequency radio observations of diffuse steep-spectrum radio sources selected from the 74 MHz VLSS survey. Previous GMRT observations showed that some of these sources had filamentary and elongated morphologies, which are expected for radio relics. We carried out radio continuum observations at 325 MHz with the GMRT. Observations with the VLA and WSRT were taken at 1.4 GHz in full polarization mode. Optical images around the radio sources were taken with the WHT and INT telescopes. Most of the sources in our sample consist of old radio plasma from AGNs located in small galaxy clusters. The sources can be classified as AGN relics or radio phoenices. The spectral indices across most of the radio sources display large variations. We conclude that diffuse steep-spectrum radio sources are not only found in massive X-ray luminous galaxy clusters but also in smaller systems. Future low-frequency surveys will uncover large numbers of steep-spectrum radio relics related to previous episodes of AGN activity. [abridged]Comment: 15 pages, 15 figures, accepted for publication in A&A on December 9, 201

Environmental Dependence of Local Luminous Infrared Galaxies

We study the environmental dependence of local luminous infrared galaxies (LIRGs) and ultraluminous infrared galaxies (ULIRGs) found in the Sloan Digital Sky Survey (SDSS) data. The LIRG and ULIRG samples are constructed by cross-correlating spectroscopic catalogs of galaxies of the SDSS Data Release 7 and the Infrared Astronomical Satellite Faint Source Catalog. We examine the effects of the large-scale background density (Sigma_5), galaxy clusters, and the nearest neighbor galaxy on the properties of infrared galaxies (IRGs). We find that the fraction of LIRGs plus ULIRGs among IRGs (f_(U)LIRGs) and the infrared luminosity (L_IR) of IRGs strongly depend on the morphology of and the distance to the nearest neighbor galaxy: the probability for an IRG to be a (U)LIRG (f_(U)LIRGs) and its L_IR both increase as it approaches a late-type galaxy, but decrease as it approaches an early-type galaxy (within half the virial radius of its neighbor). We find no dependence of f_(U)LIRGs on the background density (surface galaxy number density) at fixed stellar mass of galaxies. The dependence of f_(U)LIRGs on the distance to galaxy clusters is also found to be very weak, but in highest-density regions such as the center of galaxy clusters, few (U)LIRGs are found. These environmental dependence of LIRGs and ULIRGs and the evolution of star formation rate (SFR)-environment relation from high redshifts to low redshifts seem to support the idea that galaxy-galaxy interactions/merging play a critical role in triggering the star formation activity of LIRGs and ULIRGs.Comment: 14 pages, 17 figures. To appear in A&A. Paper with high resolution figures is available at http://astro.kias.re.kr/~hshwang/doc/ms_hwang_lirg.pd

The 2MASS Redshift Survey - Description and Data Release

We present the results of the 2MASS Redshift Survey (2MRS), a ten-year project to map the full three-dimensional distribution of galaxies in the nearby Universe. The 2 Micron All-Sky Survey (2MASS) was completed in 2003 and its final data products, including an extended source catalog (XSC), are available on-line. The 2MASS XSC contains nearly a million galaxies with Ks <= 13.5 mag and is essentially complete and mostly unaffected by interstellar extinction and stellar confusion down to a galactic latitude of |b|=5 deg for bright galaxies. Near-infrared wavelengths are sensitive to the old stellar populations that dominate galaxy masses, making 2MASS an excellent starting point to study the distribution of matter in the nearby Universe. We selected a sample of 44,599 2MASS galaxies with Ks =5 deg (>= 8 deg towards the Galactic bulge) as the input catalog for our survey. We obtained spectroscopic observations for 11,000 galaxies and used previously-obtained velocities for the remainder of the sample to generate a redshift catalog that is 97.6% complete to well-defined limits and covers 91% of the sky. This provides an unprecedented census of galaxy (baryonic mass) concentrations within 300 Mpc. Earlier versions of our survey have been used in a number of publications that have studied the bulk motion of the Local Group, mapped the density and peculiar velocity fields out to 50 Mpc, detected galaxy groups, and estimated the values of several cosmological parameters. Additionally, we present morphological types for a nearly-complete sub-sample of 20,860 galaxies with Ks = 10 deg.Comment: Accepted for publication in The Astrophysical Journal Supplement Series. The 2MRS catalogs and a version of the paper with higher-resolution figures can be found at http://tdc-www.harvard.edu/2mrs

NC ball maps and changes of variables

In this dissertation, we analyze problems set in a dimension-free, noncommutative setting. To be more specific, we use a class of functions defined by power series in noncommutative variables and evaluate these functions on sets of matrices of all sizes - hence the dimension-free term. These types of functions have recently been used in the study of dimension-free linear system engineering problems [HP07], [CHSY03]. Here we analyze a class of functions called NC analytic with the intention of understanding changes of variables in dimension-free classes of problems in matrix variables. To this end, we force geometric constraints on our analytic functions and ask how this affects the algebraic structure of the series defining them. In particular, we present a characterization of maps that send dimension-free matrix balls to dimension-free matrix balls and carry the boundary to the boundary. We study this problem in various cases restricting the variables (and matrices) to have additional symmetric structure and in cases where the variables (and matrices) have no such restrictions. These characterizations are then used to study the more general question of understanding when a dimension-free set is bianalytic to a dimension-free ball. In addition to our study of NC analytic functions, we present a result on a representation of noncommutative rational expressions. Recently there have been studies linking convexity of noncommutative rational functions to linear matrix inequalities, LMIs [HMV06]. The algorithm presented in the final chapter of the thesis presents a necessary step to automatically converting inequalities involving convex rational expressions into LMI

Noncommutative ball maps

Abstract. In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. These types of functions have recently been used in the study of dimension-free linear system engineering problems [HMPV], [OHMP]. In this paper we characterize NC analytic maps that send dimension-free matrix balls to dimensionfree matrix balls and carry the boundary to the boundary; such maps we call ”NC ball maps”. We find that up to normalization, an NC ball map is the direct sum of the identity map with an NC analytic map of the ball into the ball. That is, “NC ball maps ” are very simple, in contrast to the classical result of D’Angelo on such analytic maps in C. Another mathematically natural class of maps carries a variant of the noncommutative distinguished boundary to the boundary, but on these our results are limited. We shall be interested in several types of noncommutative balls, conventional ones, but also balls defined by constraints called Linear Matrix Inequalities (LMI). What we do here is a small piece of the bigger puzzle of understanding how LMIs behave with respect to noncommutative change of variables. 1