arXiv subjects

Peter Schneider

Publications and source records attributed to Peter Schneider.

At least 145 records · Page 8Linked to original sources

arXiv2007

Localisations and Completions of Skew Power Series Rings

This paper is a natural continuation of the study of skew power series rings A initiated in [P. Schneider and O. Venjakob, On the codimension of modules over skew power series rings with applications to Iwasawa algebras, J. Pure Appl. Algebra 204 (2005), 349 - 367.]. We construct skew Laurent series rings B and show the existence of some canonical Ore sets S for the skew power series rings A such that a certain completion of the localisation A_S is isomorphic to B. This is applied to certain Iwasawa algebras. Finally we introduce subrings of overconvergent skew Laurent series rings.

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arXiv2007

Weak lensing goes bananas: What flexion really measures

In weak gravitational lensing, the image distortion caused by shear measures the projected tidal gravitational field of the deflecting mass distribution. To lowest order, the shear is proportional to the mean image ellipticity. If the image sizes are not small compared to the scale over which the shear varies, higher-order distortions occur, called flexion. For ordinary weak lensing, the observable quantity is not the shear, but the reduced shear, owing to the mass-sheet degeneracy. Likewise, the flexion itself is unobservable. Rather, higher-order image distortions measure the reduced flexion, i.e., derivatives of the reduced shear. We derive the corresponding lens equation in terms of the reduced flexion and calculate the resulting relation between brightness moments of source and image. Assuming an isotropic distribution of source orientations, estimates for the reduced shear and flexion are obtained; these are then tested with simulations. In particular, the presence of flexion affects the determination of the reduced shear. The results of these simulations yield the amount of bias of the estimators, as a function of the shear and flexion. We point out and quantify a fundamental limitation of the flexion formalism, in terms of the product of reduced flexion and source size. If this product increases above the derived threshold, multiple images of the source are formed locally, and the formalism breaks down. Finally, we show how a general (reduced) flexion field can be decomposed into its four components: two of them are due to a shear field, carrying an E- and B-mode in general. The other two components do not correspond to a shear field; they can also be split up into corresponding E- and B-modes.

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arXiv2006

Report by the ESA-ESO Working Group on Fundamental Cosmology

ESO and ESA agreed to establish a number of Working Groups to explore possible synergies between these two major European astronomical institutions. This Working Group's mandate was to concentrate on fundamental questions in cosmology, and the scope for tackling these in Europe over the next ~15 years. One major resulting recommendation concerns the provision of new generations of imaging survey, where the image quality and near-IR sensitivity that can be attained only in space are naturally matched by ground-based imaging and spectroscopy to yield massive datasets with well-understood photometric redshifts (photo-z's). Such information is essential for a range of new cosmological tests using gravitational lensing, large-scale structure, clusters of galaxies, and supernovae. Great scope in future cosmology also exists for ELT studies of the intergalactic medium and space-based studies of the CMB and gravitational waves; here the synergy is less direct, but these areas will remain of the highest mutual interest to the agencies. All these recommended facilities will produce vast datasets of general applicability, which will have a tremendous impact on broad areas of astronomy.

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arXiv2006

The ring statistics - how to separate E- and B-modes of cosmic shear correlation functions on a finite interval

Aims. One of the main probes for systematic errors in the cosmic shear signal are the division of the shear field into E- and B-mode shear, where gravitational lensing only produces the former. As shown in a recent note, all currently used E-/B-mode separation methods for the shear correlation functions xi_pm require them to be measured to arbitrarily small and/or large separations which is of course not feasible in practice. Methods. We derive second-order shear statistics which provide a clean separation into E- and B-modes from measurements of xi_pm(theta) over a finite interval only. We call these new statistics the circle and ring statistics, respectively; the latter is obtained by an integral over the former. The mathematical properties of these new shear statistics are obtained, as well as specific expressions for applying them to observed data. Results. It is shown that an E-/B-mode separation can be performed on measurements of xi_pm over a finite interval in angular separation, using the ring statistics. We furthermore generalize this result to derive the most general class of second-order shear statistics which provide a separation of E- and B-mode shear on a given angular interval theta_min <= theta <= theta_max. Our results will be of practical use particularly for future cosmic shear surveys where highly precise measurements of the shear will become available and where control of systematics will be mandatory.

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arXiv2006

E- and B-mode mixing from incomplete knowledge of the shear correlation

Aims. We quantify the mixing of the measured cosmic-shear E- and B-modes caused by the lack of shear-correlation measurements on small and large scales, arising from a lack of close projected galaxy pairs and the finite field size, respectively. Methods. We calculate the aperture-mass statistics and the E-/B-mode shear-correlation functions xi_{E, B +/-} where small- and large-scale cutoffs are taken into account. We assess the deviation of the obtained E-mode to the true E-mode and the introduction of a spurious B-mode. Results. The measured aperture-mass dispersion is underestimated by more than 10% on scales smaller than 12 times the lower cutoff. For a precise measurement of the E- and B-modes at the percent level using a combination of xi_{E, B +} and xi_{E, B -}, a field as large as 7 (2.4) degrees is necessary for ground-based (space-based) observations.

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arXiv2006

GaBoDS: The Garching-Bonn Deep Survey -- IX. A sample of 158 shear-selected mass concentration candidates

The aim of the present work is the construction of a mass-selected galaxy cluster sample based on weak gravitational lensing methods. This sample will be subject to spectroscopic follow-up observations. We apply the mass aperture statistics and a derivative of it to 19 square degrees of high quality, single colour wide field imaging data obtained with the WFI@MPG/ESO 2.2m telescope. For the statistics a family of filter functions is used that approximates the expected tangential radial shear profile and thus allows for the efficient detection of mass concentrations. We identify 158 possible mass concentrations. This is the first time that such a large and blindly selected sample is published. 72 of the detections are associated with concentrations of bright galaxies. For about 22 of those we found spectra in the literature, indicating or proving that the galaxies seen are indeed spatially concentrated. 15 of those were previously known to be clusters or have meanwhile been secured as such. We currently follow-up a larger number of them spectroscopically to obtain deeper insight into their physical properties. The remaining 55% of the possible mass concentrations found are not associated with any optical light, or could not be classified unambiguously. We show that those "dark" detections are to a significant degree due to noise, and appear preferentially in shallow data.

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arXiv2006

DEMON: a Proposal for a Satellite-Borne Experiment to study Dark Matter and Dark Energy

We outline a novel satellite mission concept, DEMON, aimed at advancing our comprehension of both dark matter and dark energy, taking full advantage of two complementary methods: weak lensing and the statistics of galaxy clusters. We intend to carry out a 5000 sqdeg combined IR, optical and X-ray survey with galaxies up to a redshift of z~2 in order to determine the shear correlation function. We will also find ~100000 galaxy clusters, making it the largest survey of this type to date. The DEMON spacecraft will comprise one IR/optical and eight X-ray telescopes, coupled to multiple cameras operating at different frequency bands. To a great extent, the technology employed has already been partially tested on ongoing missions, therefore ensuring improved reliability.

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arXiv2005

Banach-Hecke algebras and p-adic Galois Representations

We take some initial steps towards illuminating the (hypothetical) $p$-adic local Langlands functoriality principle relating Galois representations of a $p$-adic field $L$ and admissible unitary Banach space representations of $G(L)$ when $G$ is a split reductive group over $L$. The outline of our work is derived from Breuil's remarkable insights into the nature of the correspondence between 2-dimensional crystalline Galois representations of the Galois group of $\Qdss_p$ and Banach space representations of $GL_{2}(\Qdss_p)$.

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arXiv2005

Trends in Space Astronomy and Cosmic Vision 2015-2025

As a short introduction to the astronomy session, the response of the community to the Call for Themes issued by ESA and the specific themes selected by the Astronomy Working Group are briefly presented in connection with the four grand themes finally selected for the ESA Science Programme. They are placed in the context of the main discoveries of the past decade and the astronomy projects currently in their development or definition phase. Finally, possible strategies for their implementation are summarised.

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arXiv2005

Weak Gravitational Lensing

This review forms the Weak Lensing part of the Saas-Fee Advanced Course on Gravitational Lensing. It describes the basicsm applications and results of weak lensing. Contents: (1) Introduction (2) The principles of weak gravitational lensing (3) Observational issues and challenges (4) Clusters of galaxies: Introduction, and strong lensing (5) Mass reconstructions from weak lensing (6) Cosmic shear -- lensing by the LSS (7) Large-scale structure lensing: results (8) The mass of, and associated with galaxies (9) Additional issues in cosmic shear (10) Concluding remarks.

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arXiv2005

Cosmological parameters from combined second- and third-order aperture mass statistics of cosmic shear

We present predictions for cosmological parameter constraints from combined measurements of second- and third-order statistics of cosmic shear. We define the generalized third-order aperture mass statistics and show that it contains much more information about the bispectrum of the projected matter density than the skewness of the aperture mass. From theoretical models as well as from LCDM ray-tracing simulations, we calculate and and their dependence on cosmological parameters. The covariances including shot noise and cosmic variance of M_ap^2, M_ap^3 and their cross-correlation are calculated using ray-tracing simulations. We perform an extensive Fisher matrix analysis, and for various combinations of cosmological parameters, we predict 1-sigma-errors corresponding to measurements from a deep 29 square degree cosmic shear survey. Although the parameter degeneracies can not be lifted completely, the (linear) combination of second- and third-order aperture mass statistics reduces the errors significantly. The strong degeneracy between Omega_m and sigma_8, present for all second-order cosmic shear measures, is diminished substantially, whereas less improvement is found for the near-degenerate pair consisting of the shape parameter Gamma and the spectral index n_s. Uncertainties in the source galaxy redshift z_0 increase the errors of all other parameters.

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arXiv2005

The three-point correlation function of cosmic shear. II: Relation to the bispectrum of the projected mass density and generalized third-order aperture measures

We study the relation of the three-point cosmic shear statistics to the third-order statistical properties of the underlying convergence, expressed in terms of its bispectrum. Explicit relations for the natural components of the shear three-point correlation function in terms of the bispectrum are derived. The behavior of the correlation function under parity transformation is obtained and found to agree with previous results. We find that in contrast to the two-point shear correlation function, the three-point function at a given angular scale θis not affected by power in the bispectrum on much larger scales. These relations are then inverted to obtain the bispectrum in terms of the three-point shear correlator; two different expressions, corresponding to different natural components of the shear correlator, are obtained and can be used to separate E and B-mode shear contributions. These relations allow us to explicitly show that correlations containing an odd power of B-mode shear vanish for parity-symmetric fields. Generalizing a recent result by Jarvis et al., we derive expressions for the third-order aperture measures, employing multiple angular scales, in terms of the (natural components of the) three-point shear correlator and show that they contain essentially all the information about the underlying bispectrum. We discuss the many useful features these (generalized) aperture measures have that makes them convenient for future analyses of the skewness of the cosmic shear field (and any other polar field, such as the polarization of the Cosmic Microwave Background). (Abridged)

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arXiv2005

Galaxy-galaxy-galaxy lensing: Third-order correlations between the galaxy and mass distributions in the Universe

Galaxy-galaxy lensing (GGL) measures the 2-point cross-correlation between galaxies and mass in the Universe. In this work we seek to generalise this effect by considering the third-order correlations between galaxies and mass: galaxy-galaxy-galaxy lensing. Third-order correlations in the cosmic shear field have recently been reported in the VIRMOS-DESCART and CTIO surveys. Such data should also be ideal for measuring galaxy-galaxy-galaxy lensing. Indeed, the effects of these higher-order correlations may have already been detected in recent studies of galaxy-galaxy lensing. In this paper we lay out the basic relations for third-order cross correlations and their projections and introduce a new set of scale dependent third-order bias parameters. We define three new observables: two galaxy-shear-shear correlation functions, $G_{\pm}$, and a galaxy-galaxy-shear correlation, ${\cal G}$. We relate these to the various projected cross-bispectra and give practical estimators for their measurement. We note that the observational signature of these correlators is simply the excess shear-shear correlation measured about foreground galaxies (for $G_{\pm}$) and the average tangential shear around foreground galaxy pairs (for $\cal G$). Finally we derive expressions for the third order aperture mass statistics in terms of both the cross-bispectra and the real-space correlation functions. (Abridged)

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arXiv2004

The galaxy-dark matter bias in the Garching-Bonn Deep Survey

We measured the bias and correlation factor of galaxies with respect to the dark matter using the aperture statistics including the aperture mass from weak gravitational lensing. The analysis was performed for three galaxy samples selected by R-band magnitudes; the median redshifts of the samples were $\ave{z}=0.34,0.49$ and 0.65, respectively. The brightest sample has the strongest peak in redshift and can therefore be most accurately represented by a single redshift. The data used is the GaBoDS, and the COMBO-17 survey for an accurate estimate of the redshift distribution of the galaxies. Assuming the currently favoured $Λ\rm CDM$ model as cosmology, we obtained values for the linear stochastic galaxy-dark matter bias on angular scales $1^\prime\leθ\le20^\prime$. Averaging the measurements for the bias over the range $4^\prime\le θ_{\rm ap}\le 18^\prime$, weighting with the cosmic variance error, yields $b=0.89(5), 0.79(5), 0.89(5)$, respectively ($1σ$). As for the correlation factor $r$ we see, as Hoekstra et al. (2002), a slight increase to $r=1$ in the last angular bin from an almost constant value on smaller scales; the weighted average here over the same range as before is $r=0.8(1), 0.8(1), 0.5(1)$, respectively (abridged).

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arXiv2004

Galaxy-galaxy lensing studies from COMBO-17

We study the dark matter halos of galaxies with galaxy-galaxy lensing using the COMBO-17 survey. This survey offers an unprecedented data set for studying lens galaxies at z=0.2-0.7 including redshift information and spectral classification from 17 optical filters for objects brighter than R=24. So far, redshifts and classification for the lens galaxies have mainly been available for local surveys like the Sloan Digital Sky Survey (SDSS). Further, redshifts for the source galaxies have typically not been available at all but had to be estimated from redshift probability distribution which -- for faint surveys -- even had to be extrapolated. To study the dark matter halos we parametrize the lens galaxies as singular isothermal spheres (SIS) or by Navarro-Frenk-White (NFW) profiles. In both cases we find a dependence of the velocity dispersion or virial radius, respectively, on lens luminosity and colour. For the SIS model, we are able to reproduce the Tully-Fisher/Faber-Jackson relation on a scale of 150h^-1kpc. For the NFW profile we also calculate virial masses, mass-to-light ratios and rotation velocities. Finally, we investigate differences between the three survey fields used here.

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arXiv2004

On the dimension theory of skew power series rings

The first purpose of this paper is to set up a general notion of skew power series rings S over a coefficient ring R, which are then studied by filtered ring techniques. The second subject consists of investigating the class of S-modules which are finitely generated as R-module. In the case that S and R are Auslander regular we show in particular that the codimension of M as S-module is one higher than the codimension of M as R-module. Furthermore its class in the Grothendieck group of S-modules of codimension at most one less vanishes, which is in the spirit of the Gersten conjecture for commutative regular local rings. Finally we apply these results to Iwasawa algebras of p-adic Lie groups.

math.RA↗

arXiv2004

Duality for admissible locally analytic representations

We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of a p-adic analytic group G. A naive contragredient does not exist. As a best approximation, we construct an involutive "duality" functor from the bounded derived category of modules over the distribution algebra of G with coadmissible cohomology to itself. On the subcategory corresponding to complexes of smooth representations, this functor induces the usual smooth contragredient (with a degree shift). Although we construct our functor in general we obtain its involutivity, for technical reasons, only in the case of locally Qp-analytic groups.

math.NT↗

arXiv2004

The covariance of cosmic shear correlation functions and cosmological parameter estimates using redshift information

Cosmological weak lensing by the large scale structure of the Universe, cosmic shear, is coming of age as a powerful probe of the parameters describing the cosmological model and matter power spectrum. It complements CMB studies, by breaking degeneracies and providing a cross-check. An important measure of the cosmic shear signal are the shear correlation functions; these can be directly calculated from data, and compared with theoretical expectations for different cosmological models and matter power spectra. We present a Monte Carlo method to quickly simulate mock cosmic shear surveys. One application of this method is in the determination of the full covariance matrix for the correlation functions; this includes redshift binning and is applicable to arbitrary survey geometries. Terms arising from shot noise and cosmic variance (dominant on small and large scales respectively) are accounted for naturally. As an illustration of the use of such covariance matrices, we consider to what degree confidence regions on parameters are tightened when redshift binning is employed. The parameters considered are those commonly discussed in cosmic shear analyses - the matter density parameter, dark energy density parameter (classical cosmological constant), power spectrum normalisation and shape parameter. We incorporate our covariance matrices into a likelihood treatment, and also use the Fisher formalism to explore a larger region of parameter space (abridged).

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