Abstract:
The correlation between source galaxies and lensing potentials causes a systematic effect on measurements of cosmic shear statistics, known as the source-lens clustering (SLC) effect. The SLC effect on the skewness of lensing convergence, $S_3$, is examined using a nonlinear semi-analytic approach and is checked against numerical simulations. The semi-analytic calculations have been performed in a wide variety of generic models for the redshift distribution of source galaxies and power-law models for the bias parameter between the galaxy and dark matter distributions. The semi-analytic predictions are tested successfully against numerical simulations. We find the relative amplitude of the SLC effect on $S_3$ to be of the order of five to forty per cent. It depends significantly on the redshift distribution of sources and on the way the bias parameter evolves. We discuss possible measurement strategies to minimize the SLC effects.

Abstract:
We investigate an analytic model to compute nonlinear power spectrum of dark matter, galaxies and their cross-correlation. The model is based on Press-Schechter halos, which cluster and have realistic dark matter profiles. The total power spectrum is a sum of two contributions, one from correlations betwen the halos and one from correlations within the same halo. We show that such a model can give dark matter power spectra which match well with the results of N-body simulations, provided that concentration parameter decreases with the halo mass. Galaxy power spectrum differs from dark matter power spectrum because pair weighted number of galaxies increases less rapidly than the halo mass, as predicted by theoretical models and observed in clusters. In this case the resulting power spectrum becomes a power law with the slope closed to the observed. Such a model also predicts a later onset of nonlinear clustering compared to the dark matter, which is needed to reconcile the CDM models with the data. Generic prediction of this model is that bias is scale dependent and nonmonotonic. For red or elliptical galaxies bias in power spectrum may be scale dependent even on very large scales. Our predictions for galaxy-dark matter correlations, which can be observed through the galaxy-galaxy lensing, show that these cannot be interpreted simply as an average halo profile of a typical galaxy, because different halo masses dominate at different scales and because larger halos host more than one galaxy. We discuss the prospects of using cross-correlations in combination with galaxy clustering to determine the dark matter power spectrum (ABRIDGED).

Abstract:
We examine scatter and bias in weak lensing selected clusters, employing both an analytic model of dark matter haloes and numerical mock data of weak lensing cluster surveys. We pay special attention to effects of the diversity of dark matter distributions within clusters. We find that peak heights of the lensing convergence map correlates rather poorly with the virial mass of haloes. The correlation is tighter for the spherical overdensity mass with a higher mean interior density. We examine the dependence of the halo shape on the peak heights, and find that the rms scatter caused by the halo diversity scales linearly with the peak heights with the proportionality factor of 0.1-0.2. The noise originated from the halo shape is found to be comparable to the source galaxy shape noise and the cosmic shear noise. We find the significant halo orientation bias, i.e., weak lensing selected clusters on average have their major axes aligned with the line-of-sight direction. We compute the orientation bias using an analytic triaxial halo model and obtain results quite consistent with the ray-tracing results. We develop a prescription to analytically compute the number count of weak lensing peaks taking into account all the main sources of scatters in peak heights. We find that the improved analytic predictions agree well with the simulation results for high S/N peaks. We also compare the expected number count with our weak lensing analysis results for 4 sq deg of Subaru/Suprime-Cam observations and find a good agreement.

Abstract:
We present a quantitative analysis of the largest contiguous maps of projected mass density obtained from gravitational lensing shear. We use data from the 154 deg2 covered by the Canada-France-Hawaii Telescope Lensing Survey. Our study is the first attempt to quantitatively characterize the scientific value of lensing maps, which could serve in the future as a complementary approach to the study of the dark universe with gravitational lensing. We show that mass maps contain unique cosmological information beyond that of traditional two-points statistical analysis techniques. Using a series of numerical simulations, we first show how, reproducing the CFHTLenS observing conditions, gravitational lensing inversion provides a reliable estimate of the projected matter distribution of large scale structure. We validate our analysis by quantifying the robustness of the maps with various statistical estimators. We then apply the same process to the CFHTLenS data. We find that the 2-points correlation function of the projected mass is consistent with the cosmological analysis performed on the shear correlation function discussed in the CFHTLenS companion papers. The maps also lead to a significant measurement of the third order moment of the projected mass, which is in agreement with analytic predictions, and to a marginal detection of the fourth order moment. Tests for residual systematics are found to be consistent with zero for the statistical estimators we used. A new approach for the comparison of the reconstructed mass map to that predicted from the galaxy distribution reveals the existence of giant voids in the dark matter maps as large as 3 degrees on the sky. Our analysis shows that lensing mass maps can be used for new techniques such as peak statistics and the morphological analysis of the projected dark matter distribution.

Abstract:
We present a set of predictions for weak lensing correlation functions in the context of modified gravity models, including a prescription for the impact of the nonlinear power spectrum regime in these models. We consider the DGP and f(R) models, together with dark energy models with the same expansion history. We use the requirement that gravity is close to GR on small scales to estimate the non-linear power for these models. We then calculate weak lensing statistics, showing their behaviour as a function of scale and redshift, and present predictions for measurement accuracy with future lensing surveys, taking into account cosmic variance and galaxy shape noise. We demonstrate the improved discriminatory power of weak lensing for testing modified gravities once the nonlinear power spectrum contribution has been included. We also examine the ability of future lensing surveys to constrain a parameterisation of the non-linear power spectrum, including sensitivity to the growth factor.

Abstract:
The magnifications of the images in a strong gravitational lens system are sensitive to small mass clumps in the lens potential; this effect has been used to infer the amount of substructure in galaxy dark matter halos. I study the theory of substructure lensing to identify important general features, and to compute analytic cross sections that will facilitate further theoretical studies. I show that the problem of a clump anywhere along the line of sight to a lens can be mapped onto an equivalent problem of a clump in a simple convergence and shear field; clumps at arbitrary redshifts are therefore not hard to handle in calculations. For clumps modeled as singular isothermal spheres (SIS), I derive simple analytic estimates of the cross section for magnification perturbations of a given strength. The results yield two interesting conceptual points. First, lensed images with positive parity are always made brighter by SIS clumps; images with negative parity can be brightened but are much more likely to be dimmed. Second, the clumps need not lie within the lens galaxy; they can be moved in redshift by several tenths and still have a significant lensing effect. Isolated small halos are expected to be common in hierarchical structure formation models, but it is not yet known whether they are abundant enough compared with clumps inside lens galaxies to affect the interpretation of substructure lensing.

Abstract:
We investigate the galaxy population in simulated proto-cluster regions using a semi-analytic model of galaxy formation, coupled to merger trees extracted from N-body simulations. We select the most massive clusters at redshift $z=0$ from our set of simulations, and follow their main progenitors back in time. The analysis shows that proto-cluster regions are dominated by central galaxies and their number decreases with time as many become satellites, clustering around the central object. In agreement with observations, we find an increasing velocity dispersion with cosmic time, the increase being faster for satellites. The analysis shows that proto-clusters are very extended regions, $\gtrsim 20 \, Mpc$ at $z \gtrsim 1$. The fraction of galaxies in proto-cluster regions that are not progenitor of cluster galaxies varies with redshift, stellar mass and area considered. It is about 20-30 per cent for galaxies with stellar mass $\sim 10^9\,{\rm M}_{\sun}$, while negligible for the most massive galaxies considered. Nevertheless, these objects have properties similar to those of progenitors. We investigate the building-up of the passive-sequence in clusters, and find that their progenitors are on average always active at any redshift of interest of proto-clusters. The main mechanism which quenches their star formation is the removal of the hot gas reservoir at the time of accretion. The later galaxies are accreted (become satellite), and the more the cold gas available, the longer the time spent as active. Central galaxies are active over all redshift range considered, although a non-negligible fraction of them become passive at redshift $z<1$, due to strong feedback from Active Galactic Nuclei.

Abstract:
Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically the deflection law of a point-mass. MONDian lensing is consistent with general relativity, in so far as the deflection experienced by a photon is twice that experienced by a massive particle moving at the speed of light. With the deflection law in place and no invisible matter, MOND can be tested wherever lensing is observed. The implications are that either MONDian lensing is completely non-linear or that MOND is not an accurate description of the universe.

Abstract:
Measuring dark matter substructure within galaxy cluster haloes is a fundamental probe of the Lambda-CDM model of structure formation. Gravitational lensing is a technique for measuring the total mass distribution which is independent of the nature of the gravitating matter, making it a vital tool for studying these dark-matter dominated objects. We present a new method for measuring weak gravitational lensing flexions, the gradients of the lensing shear field, to measure mass distributions on small angular scales. While previously published methods for measuring flexions focus on measuring derived properties of the lensed images, such as shapelet coefficients or surface brightness moments, our method instead fits a mass-sheet-transformation-invariant Analytic Image Model (AIM) to the each galaxy image. This simple parametric model traces the distortion of lensed image isophotes and constrains the flexion fields. We test the AIM method using simulated data images with realistic noise and a variety of unlensed image properties, and show that it successfully reproduces the input flexion fields. We also apply the AIM method for flexion measurement to Hubble Space Telescope observations of Abell 1689, and detect mass structure in the cluster using flexions measured with the AIM method.

Abstract:
We investigate the gravitational lensing properties of dark matter halos with Burkert profiles. We derive an analytic expression for the lens equation and use it to compute the magnification, impact parameter and image separations for strong lensing. For the scaling relation that provides the best fits to spiral-galaxy rotation curve data, Burkert halos will not produce strong lensing, even if this scaling relation extends up to masses of galaxy clusters. Tests of a simple model of an exponential stellar disk superimposed on a Burkert-profile halo demonstrate that strong lensing is unlikely without an additional concentration of mass in the galaxy center (e.g. a bulge). The fact that most strong lenses on galactic scales are elliptical galaxies suggests that a strong central concentration of baryons is required to produce image splitting. This solution is less attractive for clusters of galaxies, which are generally considered to be dark-matter dominated even at small radii. There are three possible implications of these results: (1) dark halos may have a variety of inner profiles (2) dark matter halos may not follow a single scaling relation from galaxy scale up to cluster scale and/or (3) the splitting of images (even by clusters of galaxies) may in general be due to the central concentration of baryonic material in halos rather than dark matter.