Weak Lensing Flexion Study

Abstract

In this thesis, I studied the higher order weak gravitational lensing effect,flexion, and some of its potential applications in cosmology.<br /> Flexion, as a new subject in lensing, has shown its advantages in various studies (at least theoretically). Flexion is more sensitive to small-scale variations in the potential than shear, and therefore has a higher signal-to-noise, in some regions than the shear.<br /> In Chapter 1, I briefly introduced the standard model of cosmology, the Lambda CDM model. Although supported by most observations, such as CMB and large-scale galaxy surveys, the Lambda CDM model still has several unsolved problems. The very big unknowns are the nature of dark energy and dark matter, which comprise more than 95% of the content of the whole universe. In order to understand that, we need to know how the universe evolves and how the matter is distributed in the universe.<br /> Gravitational lensing offers a powerful tool to study the matter distribution in the universe. I presented the basic concepts and definitions of gravitational lensing in Chapter 2, focusing on weak lensing. The central observation in weak lensing studies is the ellipticity of background galaxies. Due to mass-sheet degeneracy, the ellipticity is only an estimate of a reduced shear. Further, I present some lensing statistical quantities since a single image does not provide enough information. There are the 2-point correlation functions and aperture mass which are widely used in weak lensing studies. Various approaches are used to analyze different properties on different scales, such as cosmic shear, cluster mass reconstruction and galaxy-galaxy lensing.<br /> In Chapter 3, I introduced the higher-order weak lensing effect -- flexion -- and studied the effect of flexion in weak gravitational lensing. A general flexion field can be decomposed into a pair of components which is due to a shear field and a pair of components not related to shear. The former pair can be further separated into flexion due to an E- and B-mode shear, with only the E-mode flexion expected to arise from gravitational lensing. For the second pair of components are most due to noise or intrinsic shape effects of source. Owing to the mass-sheet degeneracy, only reduced flexion can be measured. The second-order lens equation is given as well as the relations between the brightness moments of source and image in terms of the reduced shear and the reduced flexion. I present approximate estimates for the reduced shear and flexion using these moments equations. In a number of numerical tests I have studied the bias of the reduced flexion estimators. The product of flexion and source size matters in the accuracy of estimates. I also pointed out a limit where the flexion formalism ceases to be valid, namely when the product of source size and flexion is sufficiently large that parts of the source are multiply imaged locally, i.e., where a caustic cuts through the source. I gave this limitation in some cases and also a complete classification of the critical curves of the second-order lens equation employed in flexion studies.<br /> Chapter 4 deals with galaxy clusters, which are an important probe of the matter content of the universe. I present some methods for cluster mass reconstruction, especially detailed the method which combines strong lensing, weak lensing shear and flexion information. This method allows one to extend the weak lensing analysis into the inner part of the clusters and of substructures within the clusters. We tested the method with numerical simulations, finding an agreement between the input and reconstructed mass also on the substructures. Using flexion allows us to obtain a significant improvement on the results of inner part of clusters and resolve the substructures. We conclude that with high resolution imaging data the method can accurately reconstruct cluster masses and substructures.<br /> In Chapter 5, I showed preliminary results on galaxy-galaxy lensing. The spin-1 flexion can be decomposed into radial and tangential components, which respond to different properties of the galaxy halo. The ratio of tangential flexion to radial flexion can be used to measure the ellipticity of dark matter halos. In an ideal numerical test, the result perfectly agrees with the input value. I also presented an aperture statistics for the radial flexion, which can be used for substructure detections.