Effects of Noise on Galaxy Isophotes

The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis which is based on a set of non-parametric shape descriptors known as the Minkowski Functionals (MFs). These functionals are extremely versatile and under some conditions give a complete description of the geometrical properties of objects. We believe that MFs could be a useful tool to extract information about the shapes of galaxies, clusters of galaxies and superclusters. The information revealed by MFs can be utilized along with the knowledge obtained from currently popular methods and thus could improve our understanding of the true shapes of cosmological objects.Comment: 3 pages, 1 figure, to appear in "The IGM/Galaxy Connection - The Distribution of Baryons at z=0" Conference Proceeding

Topology and Geometry of the CfA2 Redshift Survey

We analyse the redshift space topology and geometry of the nearby Universe by computing the Minkowski functionals of the Updated Zwicky Catalogue (UZC). The UZC contains the redshifts of almost 20,000 galaxies, is 96% complete to the limiting magnitude m_Zw=15.5 and includes the Center for Astrophysics (CfA) Redshift Survey (CfA2). From the UZC we can extract volume limited samples reaching a depth of 70 hMpc before sparse sampling dominates. We quantify the shape of the large-scale galaxy distribution by deriving measures of planarity and filamentarity from the Minkowski functionals. The nearby Universe shows a large degree of planarity and a small degree of filamentarity. This quantifies the sheet-like structure of the Great Wall which dominates the northern region (CfA2N) of the UZC. We compare these results with redshift space mock catalogues constructed from high resolution N-body simulations of two Cold Dark Matter models with either a decaying massive neutrino (tauCDM) or a non-zero cosmological constant (LambdaCDM). We use semi-analytic modelling to form and evolve galaxies in these dark matter-only simulations. We are thus able, for the first time, to compile redshift space mock catalogues which contain galaxies, along with their observable properties, rather than dark matter particles alone. In both models the large scale galaxy distribution is less coherent than the observed distribution, especially with regard to the large degree of planarity of the real survey. However, given the small volume of the region studied, this disagreement can still be a result of cosmic variance.Comment: 14 pages including 10 figures. Accepted for publication in Monthly Notice

Minkowski functionals in cosmology

Minkowski functionals provide a novel tool to characterize the large-scale galaxy distribution in the Universe. Here we give a brief tutorial on the basic features of these morphological measures and indicate their practical application for simulation data and galaxy redshift catalogues as examples

Minkowski Functionals of Abell/ACO Clusters

We determine the Minkowski functionals for a sample of Abell/ACO clusters, 401 with measured and 16 with estimated redshifts. The four Minkowski functionals (including the void probability function and the mean genus) deliver a global description of the spatial distribution of clusters on scales from $10$ to 60\hMpc with a clear geometric interpretation. Comparisons with mock catalogues of N--body simulations using different variants of the CDM model demonstrate the discriminative power of the description. The standard CDM model and the model with tilted perturbation spectrum cannot generate the Minkowski functionals of the cluster data, while a model with a cosmological constant and a model with breaking of the scale invariance of perturbations (BSI) yield compatible results.Comment: 10 pages, 13 Postscript figures, uses epsf.sty and mn.sty (included), submitted to MNRA

Minkowski Functionals of SDSS galaxies I : Analysis of Excursion Sets

We present a first morphometric investigation of a preliminary sample from the SDSS of 154287 galaxies with apparent magnitude 14.5<m_r<17.5 and redshift 0.001<z<0.4. We measure the Minkowski Functionals, which are a complete set of morphological descriptors. To account for the complicated wedge--like geometry of the present survey data, we construct isodensity contour surfaces from the galaxy positions in redshift space and employ two complementary methods of computing the Minkowski Functionals. We find that the observed Minkowski Functionals for SDSS galaxies are consistent with the prediction of a Lambda--dominated spatially--flat Cold Dark Matter model with random--Gaussian initial conditions, within the cosmic variance estimated from the corresponding mock catalogue. We expect that future releases of the SDSS survey will allow us to distinguish morphological differences in the galaxy distribution with regard to different morphological type and luminosity ranges.Comment: 35 pages, 13 figures, accepted for publication in PASJ. For preprint with higher-resolution PS files, see http://www.a.phys.nagoya-u.ac.jp/~hikage/MFs/mf_sdss.ps.g

Morphological fluctuations of large-scale structure: the PSCz survey

In a follow-up study to a previous analysis of the IRAS 1.2Jy catalogue, we quantify the morphological fluctuations in the PSCz survey. We use a variety of measures, among them the family of scalar Minkowski functionals. We confirm the existence of significant fluctuations that are discernible in volume-limited samples out to 200Mpc/h. In contrast to earlier findings, comparisons with cosmological N-body simulations reveal that the observed fluctuations roughly agree with the cosmic variance found in corresponding mock samples. While two-point measures, e.g. the variance of count-in-cells, fluctuate only mildly, the fluctuations in the morphology on large scales indicate the presence of coherent structures that are at least as large as the sample

Searching for Signatures of Cosmic String Wakes in 21cm Redshift Surveys using Minkowski Functionals

Minkowski Functionals are a powerful tool for analyzing large scale structure, in particular if the distribution of matter is highly non-Gaussian, as it is in models in which cosmic strings contribute to structure formation. Here we apply Minkowski functionals to 21cm maps which arise if structure is seeded by a scaling distribution of cosmic strings embeddded in background fluctuations, and then test for the statistical significance of the cosmic string signals using the Fisher combined probability test. We find that this method allows for detection of cosmic strings with $G \mu > 5 \times 10^{-8}$, which would be improvement over current limits by a factor of about 3.Comment: Matches published versio

Disentangling the Cosmic Web I: Morphology of Isodensity Contours

We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.Comment: 26 pages including 12 figures. Accepted for publication in Ap