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 used in the Morphological Analysis of Cosmic Microwave Background Anisotropy Maps

We present a novel approach to quantifying the morphology of Cosmic Microwave Background (CMB) anisotropy maps. As morphological descriptors, we use shape parameters known as Minkowski functionals. Using the mathematical framework provided by the theory of integral geometry on arbitrary curved supports, we point out the differences to their characterization and interpretation in the case of flat space. With restrictions of real data -- such as pixelization and incomplete sky coverage, to mention just a few -- in mind, we derive and test unbiased estimators for all Minkowski functionals. Various examples, among them the analysis of the four-year COBE DMR data, illustrate the application of our method.Comment: 14 pages, 13 figures, most of which look better in color. Uses AMSTeX, epsf.sty, mncite.sty. Very minor changes to match version accepted for publication in MNRA

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

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

Two-State Migration of DNA in a structured Microchannel

DNA migration in topologically structured microchannels with periodic cavities is investigated experimentally and with Brownian dynamics simulations of a simple bead-spring model. The results are in very good agreement with one another. In particular, the experimentally observed migration order of Lambda- and T2-DNA molecules is reproduced by the simulations. The simulation data indicate that the mobility may depend on the chain length in a nonmonotonic way at high electric fields. This is found to be the signature of a nonequilibrium phase transition between two different migration states, a slow one and a fast one, which can also be observed experimentally under appropriate conditions.Comment: Revised edition corresponding to the comments by the referees, submitted to Physical Review

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

A global descriptor of spatial pattern interaction in the galaxy distribution

We present the function J as a morphological descriptor for point patterns formed by the distribution of galaxies in the Universe. This function was recently introduced in the field of spatial statistics, and is based on the nearest neighbor distribution and the void probability function. The J descriptor allows to distinguish clustered (i.e. correlated) from ``regular'' (i.e. anti-correlated) point distributions. We outline the theoretical foundations of the method, perform tests with a Matern cluster process as an idealised model of galaxy clustering, and apply the descriptor to galaxies and loose groups in the Perseus-Pisces Survey. A comparison with mock-samples extracted from a mixed dark matter simulation shows that the J descriptor can be profitably used to constrain (in this case reject) viable models of cosmic structure formation.Comment: Significantly enhanced version, 14 pages, LaTeX using epsf, aaspp4, 7 eps-figures, accepted for publication in the Astrophysical Journa

Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?

In this paper, we investigate the utility of Minkowski Functionals as a probe of cold/hot disk-like structures in the CMB. In order to construct an accurate estimator, we resolve a long-standing issue with the use of Minkowski Functionals as probes of the CMB sky -- namely that of systematic differences ("residuals") when numerical and analytical MF are compared. We show that such residuals are in fact by-products of binning, and not caused by pixelation or masking as originally thought. We then derive a map-independent estimator that encodes the effects of binning, applicable to beyond our present work. Using this residual-free estimator, we show that small disk-like effects (as claimed by Vielva et al.) can be detected only when a large sample of such maps are averaged over. In other words, our estimator is noise-dominated for small disk sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to the WMAP7 data to obtain a null result.Comment: 15 pages, 13 figure