A new measure for cosmic shear

We consider here a new statistical measure for cosmic shear, the aperture mass Map, which is defined as a spatially filtered projected density field and which can be measured directly from the image distortions of high-redshift galaxies. By selecting an appropriate spatial filter function, the dispersion of the aperture mass is a convolution of the power spectrum of the projected density field with a narrow kernel, so that provides a well localized estimate of the power spectrum at wavenumbers s~5/theta. We calculate for various cosmological models, using the fully non-linear power spectrum of the cosmic density fluctuations. The non-linear evolution yields a significant increase of relative to the linear growth on scales below ~0.5 degree. The third-order moment of Map can be used to define a skewness, which is a measure of the non-Gaussianity of the density field. We present the first calculation of the skewness of the shear in the frame of quasi-linear theory of structure growth. We show that it yields a sensitive measure of the cosmological model; in particular, it is independent of the normalization of the power spectrum. Several practical estimates for are constructed and their dispersions calculated. We show that one sq.deg. of a high-quality image is sufficient to detect the cosmic shear with the Map-statistics on scales below ~10 arcmin, and to estimate its amplitude with an accuracy of ~30% on scales below ~5 arcmin. (abbreviated)Comment: 34 pages, plain TeX, including 9 figures, submitted to MNRA

Weak gravitational lensing with SKA

SIGLEAvailable from: http://www.mpa-garching.mpg.de / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A simultaneous maximum likelihood approach for galaxy-galaxy lensing and cluster lens reconstruction

In a previous paper we investigated means for constraining the mass distribution of cluster galaxies by weak lensing. We concluded that a comprehensive method should treat the lensing effects of individual cluster galaxies and those resulting from a general cluster component simultaneously. To this end we now develop a non-parametric maximum likelihood cluster reconstruction algorithm that can implicitly take into account the presence of cluster galaxies. The method includes an entropy-like regularization prescription and directly uses the ellipticities of individual source galaxy images as observables rather than relying on an averaged ellipticity field. The mass distribution of cluster galaxies is described by parametrized models. For each set of galaxy parameters the cluster reconstruction algorithm allows to determine the best representation of the global underlying cluster component that is consistent with the presence of the cluster galaxies and the observed image ellipticities of background galaxies. Tests with simulations yielded convincing and robust results. We applied the method to a WFPC2 image of the cluster Cl0939+4713 and obtained a detection of the lensing effects of luminous elliptical cluster galaxies. We consider this application as a successful test of our technique. However, the small size of the image we analysed does not yet allow to draw strong conclusions regarding the mass distribution of cluster galaxies. (orig.)30 refs.Available from TIB Hannover: RR 4697(1090) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Detection of (dark) matter concentrations via weak gravitational lensing

The distortion of images of faint background galaxies by (weak) gravitational lensing can be used to measure the mass distribution of the deflector. Reconstruction methods for the mass profile of lensing clusters have been developed and successfully tested. Alternatively, the image distortions can be used to define a weighted mean of the mass inside a circular aperture, as was first suggested by Kaiser. This 'aperture mass' has the advantage that strict error bars can be obtained from the data itself, and that a strict lower limit of the lens mass inside a circle can be obtained. The aperture mass can thus be used to detect dark matter concentration. Keeping in mind that wide-field cameras will become increasingly available, this method can be used to search for mass concentrations on wide-field images. To do this, the aperture mass measure is generalized to account for different weighting functions. For each such weighting function, a signal-to-noise ratio can be calculated. For an assumed mass profile of the density concentrations, the weighting function can be chosen such as to maximize the resulting signal-to-noise ratio. Assuming that dark matter halos can be approximated by an isothermal profile over a large range of radius, a weighting function is constructed which is adapted to this density profile and which yields a smooth signal-to-noise map. Numerical simulations which adopt parameters characteristic of 4-m class telescopes are then used to show that dark halos with a velocity dispersion in excess of #approx# 600 km/s can be reliably detected as significant peaks in the signal-to-noise map. The effects of seeing and an anisotropic PSF are then investigated and shown to be less important than might be feared. It is thus suggested that the method of aperture mass measures developed here can be used to obtain a mass-selected sample of dark halos, in contrast to flux-selected samples. Shear fields around high-redshift bright QSOs as detected by Fort et al. provide a first successful application of this strategy. The simplicity of the method allows its routine application to wide-field images of sufficient depth and image quality. (orig.)Available from TIB Hannover: RR 4697(917) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Diffuse X-ray emission around high-redshift, radio-loud QSOs

We announce the detection of correlations on angular scales of >or#approx#10' between optically bright, high-redshift, radio-loud QSOs with diffuse X-ray emission seen by ROSAT in the All-Sky Survey. These correlations reach significance levels of up to 99.8%. A comparison of the results with a sample of contol fields, bootstrapping analyses, and Kolmogorov-Smirnov tests provide unambiguous support for the statistical significance of the correlations found. We argue that the detected enhanced diffuse X-ray emission is in the foreground of the QSOs, and that it is probably due to galaxy clusters which magnify the QSOs by their gravitational lensing effect, thereby giving rise to a magnification bias in the background source sample. A comparison of the results presented below with correlations previously found between the same QSO sample and either Lick or IRAS galaxies provides further evidence for this interpretation, and identifies positions in the sky where weak gravitational lensing may be detected by searching for coherent distortions of background galaxy images. (orig.)Available from TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Cosmic shear and biasing

The correlation between cosmic shear as measured by the image distortion of high-redshift galaxies and the number counts of foreground galaxies is calculated. For a given power spectrum of the cosmic density fluctuations, this correlation is proportional to the bias factor, which can thus directly be measured. In addition, this correlation provides a first-order measure of cosmic shear and is therefore easier to observe than quadratic measures hitherto proposed. Analytic approximations show that the expected signal-to-noise ratio of the correlation is large, so that a significant detection is possible with a moderate amount of data; in particular, it is predicted that the ongoing ESO imaging survey (EIS) will be able to detect this correlation on scales of #propor to#10' at a 3-#sigma# level, and at with higher significance on smaller angular scales. (orig.)Available from TIB Hannover: RR 4697(1041) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

The cosmological lens equation and the equivalent single-plane graviational lens

The gravitational lens equation resulting from a single (non-linear) mass concentration (the main lens) plus inhomogeneities of the large-scale structure is shown to be strictly equivalent to the single-plane gravitational lens equation without the cosmological perturbations. The deflection potential (and, by applying the Poisson equation, also the mass distribution) of the equivalent single-plane lens is derived. If the main lens is described by elliptical isopotential curves plus a shear term, the equivalent single-plane lens will be of the same form. Due to the equivalence shown, the determination of the Hubble constant from time delay measurements is affected by the same mass-sheet invariance transformation as for the single-plane lens. If the lens strength is fixed (e.g., by measuring the velocity dispersion of stars in the main lens), the determination of H_0 is affected by inhomogeneous matter between us and the lens. The orientation of the mass distribution relative to the image positions is the same for the cosmological lens situation and the single-plane case. In particular this implies that cosmic shear cannot account for a misalignment of the observed galaxy orientation relative to the best-fitting lens model. (orig.)Available from TIB Hannover: RR 4697(1034) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Cosmological applications of gravitational lensing

The last decade has seen an enormous increase of activity in the field of gravitational lensing, mainly driven by improvements of observational capabilities. I will review the basics of gravitational lens theory, just enough to understand the rest of this contribution, and will then concentrate on several of the main applications in cosmology. Cluster lensing, and weak lensing, will constitute the main part of this review. (orig.)Available from TIB Hannover: RR 4697(901) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

A new finite-field mass reconstruction algorithm

A new method for the reconstruction of the projected mass distribution of clusters of galaxies from the image distortion of background galaxies is discussed. This method is essentially equivalent to the one we developed previously, i.e., the noise-filtering method, but has several practical advantages: (1) It is much easier to implement; (2) it can be easily applied to wide-field images, since the constraints on the number of gridpoints are much weaker than for the previous method, and (3) it can be easily generalized to more complicated field geometries, such as that of the wide field planetary camera 2 (WFPC2) onboard HST. We have tested the performance of our new inversion method (for which a FORTRAN-77 implementation is available from the authors) using simulated data, demonstrating that it fares very favourably. (orig.)19 refs.Available from TIB Hannover: RR 4697(1077) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Cluster mass profiles from weak lensing II

When a cluster gravitationally lenses faint background galaxies, its tidal gravitational field distorts their shapes (shear effect) and its magnification effect changes the observed number density. In Schneider, King and Erben (2000) we developed likelihood techniques to compare the constraints on cluster mass profiles that can be obtained using the shear and magnification information. This work considered circularly symmetric power-law models for clusters at fairly low redshifts where the redshift distribution of source galaxies could be neglected. Here this treatment is extended to encompass NFW profiles which are a good description of clusters from cosmological N-body simulations, and NFW clusters at higher redshifts where the influence of various scenarios for the knowledge of the redshift distribution are examined. Since in reality the overwhelming majority of clusters have ellipsoidal rather than spherical profiles, the singular isothermal ellipsoid (SIE) is investigated. We also briefly consider the impact of substructure on such a likelihood analysis. In general, we find that the shear information provides a better constraint on the NFW profile under consideration, so this becomes the focus of what follows. The ability to differentiate between the NFW and power-law profiles strongly depends on the size of the data field, and on the number density of galaxies for which an ellipticity can be measured. Combining Monte Carlo simulations with likelihood techniques is a very suitable way to predict whether profiles will be distinguishable, given the field of view and depth of the observations. For higher redshift NFW profiles, there is very little reduction (#propor to#1.5%) in the dispersion of parameter estimates when spectroscopic redshifts, as opposed to photometric redshift estimates, are available for the galaxies used in the lensing analysis. (orig.)SIGLEAvailable from: http://www.mpa-garching.mpg.de / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman