No Arabic abstract
After a brief introduction to gravitational lensing theory, a rough overview of the types of gravitational lensing statistics that have been performed so far will be given. I shall then concentrate on recent results of galaxy-galaxy lensing, which indicate that galactic halos extend much further than can be probed via rotation of stars and gas.
We introduce the skew-spectrum statistic for weak lensing convergence $kappa$ maps and test it against state-of-the-art high-resolution all-sky numerical simulations. We perform the analysis as a function of source redshift and smoothing angular scale for individual tomographic bins. We also analyse the cross-correlation between different tomographic bins. We compare the numerical results to fitting-functions used to model the bispectrum of the underlying density field as a function of redshift and scale. We derive a closed form expression for the skew-spectrum for gravity-induced secondary non-Gaussianity. We also compute the skew-spectrum for the projected $kappa$ inferred from Cosmic Microwave Background (CMB) studies. As opposed to the low redshift case we find the post-Born corrections to be important in the modelling of the skew-spectrum for such studies. We show how the presence of a mask and noise can be incorporated in the estimation of a skew-spectrum.
The galaxy cluster 1E0657-56 (z = 0.296) is remarkably well-suited for addressing outstanding issues in both galaxy evolution and fundamental physics. We present a reconstruction of the mass distribution from both strong and weak gravitational lensing data. Multi-color, high-resolution HST ACS images allow detection of many more arc candidates than were previously known, especially around the subcluster. Using the known redshift of one of the multiply imaged systems, we determine the remaining source redshifts using the predictive power of the strong lens model. Combining this information with shape measurements of weakly lensed sources, we derive a high-resolution, absolutely-calibrated mass map, using no assumptions regarding the physical properties of the underlying cluster potential. This map provides the best available quantification of the total mass of the central part of the cluster. We also confirm the result from Clowe et al. (2004,2006a).
Weak gravitational lensing is considered to be one of the most powerful tools to study the mass and the mass distribution of galaxy clusters. However, the mass-sheet degeneracy transformation has limited its success. We present a novel method for a cluster mass reconstruction which combines weak and strong lensing information on common scales and can, as a consequence, break the mass-sheet degeneracy. We extend the weak lensing formalism to the inner parts of the cluster and combine it with the constraints from multiple image systems. We demonstrate the feasibility of the method with simulations, finding an excellent agreement between the input and reconstructed mass also on scales within and beyond the Einstein radius. Using a single multiple image system and photometric redshift information of the background sources used for weak and strong lensing analysis, we find that we are effectively able to break the mass-sheet degeneracy, therefore removing one of the main limitations on cluster mass estimates. We conclude that with high resolution (e.g. HST) imaging data the method can more accurately reconstruct cluster masses and their profiles than currently existing lensing techniques.
Statistical isotropy (SI) has been one of the simplifying assumptions in cosmological model building. Experiments like WMAP and PLANCK are attempting to test this assumption by searching for specific signals in the Cosmic Microwave Background (CMB) two point correlation function. Modifications to this correlation function due to gravitational lensing by the large scale structure (LSS) surrounding us have been ignored in this context. Gravitational lensing will induce signals which mimic isotropy violation even in an isotropic universe. The signal detected in the Bipolar Spherical Harmonic (BipoSH) coefficients $A^{20}_{ll}$ by the WMAP team may be explained by accounting for the lensing modifications to these coefficients. Further the difference in the amplitude of the signal detected in the V-band and W-band maps can be explained by accounting for the differences in the designed angular sensitivity of the instrumental beams. The arguments presented in this article have crucial implications for SI violation studies. Constraining SI violation will only be possible by complementing CMB data sets with all sky measurements of the large scale dark matter distribution. Till that time, the signal detected in the BipoSH coefficients from WMAP-7 could also be yet another suggested evidence of strong deviations from the standard $Lambda$CDM cosmology based on homogeneous and isotropic FRW models.
We study the morphology of convergence maps by perturbatively reconstructing their Minkowski Functionals (MFs). We present a systematics study using a set of three generalised skew-spectra as a function of source redshift and smoothing angular scale. Using an approach based on pseudo-$S_{ell}$s (PSL) we show how these spectra will allow reconstruction of MFs in the presence of an arbitrary mask and inhomogeneous noise in an unbiased way. Our theoretical predictions are based on a recently introduced fitting function to the bispectrum. We compare our results against state-of-the art numerical simulations and find an excellent agreement. The reconstruction can be carried out in a controlled manner as a function of angular harmonics $ell$ and source redshift $z_s$ which allows for a greater handle on any possible sources of non-Gaussianity. Our method has the advantage of estimating the topology of convergence maps directly using shear data. We also study weak lensing convergence maps inferred from Cosmic Microwave Background (CMB) observations; and we find that, though less significant at low redshift, the post-Born corrections play an important role in any modelling of the non-Gaussianity of convergence maps at higher redshift. We also study the cross-correlations of estimates from different tomographic bins.