arXiv subjects

Jens Schmalzing

Publications and source records attributed to Jens Schmalzing.

16 recordsLinked to original sources

arXiv2005

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.

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arXiv2004

An Analysis of the Large Scale N-body Simulation using the Minkowski Functionals

We analyze the Minkowski functionals with a large $N$-body simulation of a standard $Λ$CDM model, focusing on transition scales between linear and non-linear gravitational evolution. We numerically calculate the Minkowski functionals with sufficient accuracies to investigate the transition scales, 10--$50\himpc$. The results are compared with analytic formulae of linear and second-order perturbation theories. We first show that the skewness parameters of the density fluctuations, which are important in second-order analytic formulae of the Minkowski functionals, are in good agreement with the perturbation theory. Considering relative differences between the Minkowski functionals of the analytic formulae and that of the simulation data, we evaluate accuracy levels of the predictions of the perturbation theory. When the straightforward threshold $ν$ by density value is used in Minkowski functionals, the accuracy of the second-order perturbation theory is within 10% for smoothing length $R > 15\himpc$, and within a several % for $R > 20\himpc$. The accuracies of the linear theory are 2--5 times worse than that. When the rescaled threshold by volume fraction, $ν_{\rm f}$ is used, accuracies of both linear and second-order theories are within a few % on all scales of $10\himpc < R < 50\himpc$.

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arXiv2001

Cosmic Microwave Background polarization and the ionization history of the Universe

We point out that polarization measurements as planned for the upcoming PLANCK mission can significantly enhance the accuracy of cosmic parameter estimation compared to the temperature anisotropy spectrum alone. In order to illustrate this, we consider a standard cosmological model and several modifications that adjust one parameter each to fit the recently published Maxima-1 data. While all models produce acceptable fits as far as the power spectrum is concerned, their corresponding polarization spectra differ widely. The strongest differences are expected for a model with delayed recombination, reflecting the fact that polarization measurements are most sensitive to the processes governing the epoch of recombination.

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arXiv2000

Constraints on the redshift of reionization from CMB data

We use the recent CMB power spectrum measurement by the Maxima experiment (Hanany et al. 2000) to constrain the redshift of reionization z_re. This becomes possible by combining the CMB data with cosmological parameters from various independent measurements, including Big Bang Nucleosynthesis (BBN) and X-ray cluster data. Most notably, our results provide a robust lower bound on z_re. We find that z_re>15 (8) at the 68% (95%) confidence level, unless the Hubble constant is larger than 75 km/s/Mpc.

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arXiv2000

Effects of weak lensing on the topology of CMB maps

We investigate the non-Gaussian signatures in Cosmic Microwave Background (CMB) maps induced by the intervening large-scale structure through weak lensing. In order to measure the deviation from the Gaussian behavior of the intrinsic temperature anisotropies, we use a family of three morphological descriptors, the so-called Minkowski functionals. We show analytically how these quantities depend on the temperature threshold, and compare the results to numerical experiments including the instrumental effects of Planck. Minkowski functionals can directly measure the statistical properties of the displacement field and hence provide useful constraints on large-scale structure formation in the past.

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arXiv2000

On non-Gaussianity in the Cosmic Microwave Background

We consider a cosmological model with non-Gaussian initial perturbations, which in principle could be generated in non-standard inflationary scenarios with two or more scalar fields. In particular we focus our attention on the model proposed by Linde & Mukhanov (1997) perturbations are quadratic in a Gaussian field. These perturbations, if they exist, have to be observable as a non-Gaussian distribution of the CMB signal on the sky. In order to efficiently pick up the non-Gaussian signal in CMB maps of degree resolution, one can use Minkowski Functionals and peak statistics. Our paper contains the theoretical predictions of the properties for Minkowski Functionals and distributions of peaks of the CMB anisotropy in the model with "squared" Gaussian statistics. Likelihood comparison of the four-year COBE DMR data to this non-Gaussian model and the standard Gaussian model does not select any of them as most likely. We also suggest an efficient algorithm for fast simulation of CMB maps on the whole sky. Using a cylindrical partition of the sphere, we rewrite the spherical harmonics analysis as a Fourier transform in flat space, which makes the problem accessible to numerically advantageous FFT methods.

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arXiv1999

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.

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arXiv1999

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.

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arXiv1999

Quantifying the evolution of higher-order clustering

We use a high-resolution dissipationless simulation to study the evolution of the dark matter and halo distributions in a spatially flat cosmological model dominated by a cosmological constant $Λ$ and cold dark matter ($Λ$CDM). In order to quantify the evolution of structure, we calculate the Minkowski functionals of the halos and the dark matter component at various redshifts. A comparison of Minkowski functionals and the more standard correlation function analysis shows that the Minkowski functionals contain information about correlation functions of arbitrary order. While little evolution of the Minkowski functionals of halos between $z=4$ and $z=0$ is observed, we find that the Minkowski functionals of the dark matter evolve rapidly with time. The difference of the Minkowski functionals of halos and dark matter can be interpreted as a scale dependent bias. This implies that scale-dependent bias is a property of not only the two-point halo correlation function, but also of correlation functions of higher order.

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arXiv1998

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.

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arXiv1998

Fluctuations in the IRAS 1.2 Jy Catalogue

An analysis of the IRAS 1.2 Jy redshift catalogue with emphasis on the separate examination of northern and southern parts (in galactic coordinates) is performed using a complete set of morphological descriptors (Minkowski functionals), nearest neighbour distributions and the variance of the galaxy counts. We find large fluctuations in the clustering properties as seen in a large difference between the northern and southern parts of the catalogue on scales of 100Mpc/h. These fluctuations remain discernible even on the scale of 200Mpc/h. We also identify sparse sampling as a major source of ``apparent homogenization''. Tests on observational selection effects concerning luminosity, colour and redshift-space distortion support the significance of these large-scale fluctuations.

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arXiv1997

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.

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arXiv1997

Minkowski Functionals in Cosmology: An Overview

Minkowski functionals have recently been introduced into cosmology as novel tools for studying the large-scale distribution of matter in the Universe. We present a brief overview of the method, including its mathematical foundations as well as some completed and upcoming applications.

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arXiv1997

The Significance of the Fluctuations in the IRAS 1.2 Jy Galaxy Catalogue

In an analysis of the IRAS 1.2 Jy redshift catalogue, with emphasis on the separate examination of northern and southern parts (in galactic coordinates), we found that the clustering of galaxies differs significantly between north and south, showing fluctuations in the clustering properties at least on scales of 100 Mpc/h (Kerscher et al. 1997, astro-ph/9704028). We give a brief description of our morphological method which is based on Minkowski functionals and show the results obtained from the IRAS 1.2 Jy galaxy catalogue. We discuss several error estimates and select different subsamples from the 1.2 Jy catalogue according to flux and colour and validate the results for the whole sample. Furthermore we look closer at the spatial origin of the fluctuation and we compare with optically selected galaxies from the CfA1 survey.

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arXiv1997

Koenderink filters and the Microwave Background

We introduce Koenderink filters as novel tools for statistical cosmology. Amongst several promising applications, they provide a test for the Gaussianity of random fields. We focus on this application and present some preliminary results from an analysis of the Cosmic Microwave Background (CMB).

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arXiv1997

Beyond genus statistics: a unifying approach to the morphology of cosmic structure

The genus statistics of isodensity contours has become a well-established tool in cosmology. In this Letter we place the genus in the wider framework of a complete family of morphological descriptors. These are known as the Minkowski functionals, and we here apply them for the first time to isodensity contours of a continuous random field. By taking two equivalent approaches, one through differential geometry, the other through integral geometry, we derive two complementary formulae suitable for numerically calculating the Minkowski functionals. As an example we apply them to simulated Gaussian random fields and compare the outcome to the analytically known results, demonstrating that both are indeed well suited for numerical evaluation. The code used for calculating all Minkowski functionals is available from the authors.

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