Focus on Gravitational Lensing

Weak gravitational lensing is a powerful tool for studying both the geometry\nand the dynamics of the Universe. Its power spectrum contains information on\nthe sources emitting photons and on the large--scale structures that these\nhotons cross. We calculate the weak lensing cosmic convergence and shear power\nspectra, in linear theory and Limber's approximation, for two different classes\nof cosmological models: the standard \\LambdaCDM and Unified Dark Matter (UDM)\nmodels. The latter models attempt to solve the problems of the dark matter in\nthe dynamics of galaxies and galaxy clusters and of the late-time acceleration\nof the Universe expansion by introducing a scalar field that mimics both dark\nmatter and dark energy. A crucial feature of the UDM models is the speed of\nsound c_\\infty, that is the value of the sound speed at late times, on which\nstructure formation depends. In this paper, we provide the predictions of the\nUDM models for the weak lensing signal,with various values of c_\\infty. We\nconsider both the Cosmic Microwave Background and background galaxies at\ndifferent redshifts as sources for the weak lensing power spectra. We find that\nthe power spectra in UDM models are more sensitive to the variations of\nc_\\infty for sources located at low redshifts. Moreover, we find that for\nc_\\infty>10^{-3} (in units of the speed of light), the UDM weak lensing\nconvergence power spectrum C^{\\kappa\\kappa}(l) for background galaxies is\nstrongly suppressed with respect to the \\LambdaCDM spectrum, particularly at\nsmall angular scales l\\gtrsim100.\n

This paper reviews statistical methods recently developed to reconstruct and analyze dark matter mass maps from weak lensing observations. The field of weak lensing is motivated by the observations made in the last decades showing that the visible matter represents only about 4-5% of the Universe, the rest being dark. The Universe is now thought to be mostly composed by an invisible, pressureless matter -potentially relic from higher energy theories- called "dark matter" (20-21%) and by an even more mysterious term, described in Einstein equations as a vacuum energy density, called "dark energy" (70%). This "dark" Universe is not well described or even understood, so this point could be the next breakthrough in cosmology. Weak gravitational lensing is believed to be the most promising tool to understand the nature of dark matter and to constrain the cosmological model used to describe the Universe. Gravitational lensing is the process in which light from distant galaxies is bent by the gravity of intervening mass in the Universe as it travels towards us. This bending causes the image of background galaxies to appear slightly distorted and can be used to extract significant results for cosmology. Future weak lensing surveys are already planned in order to cover a large fraction of the sky with large accuracy. However this increased accuracy also places greater demands on the methods used to extract the available information. In this paper, we will first describe the important steps of the weak lensing processing to reconstruct the dark matter distribution from shear estimation. Then we will discuss the problem of statistical estimation in order to set constraints on the cosmological model. We review the methods which are currently used especially new methods based on sparsity.

Clusters of galaxies are excellent locations to probe the distribution of baryons and dark matter (DM) over a wide range of scales. We study a sample of seven massive, relaxed galaxy clusters with centrally-located brightest cluster galaxies (BCGs) at z=0.2-0.3. Using the observational tools of strong and weak gravitational lensing, combined with resolved stellar kinematics within the BCG, we measure the total radial density profile, comprising both dark and baryonic matter, over scales of ~3-3000 kpc. Lensing-derived mass profiles typically agree with independent X-ray estimates within ~15%, suggesting that departures from hydrostatic equilibrium are small and that the clusters in our sample (except A383) are not strongly elongated along the line of sight. The inner logarithmic slope gamma_tot of the total density profile measured over r/r200=0.003-0.03, where rho_tot ~ r^(-gamma_tot), is found to be nearly universal, with a mean <gamma_tot> = 1.16 +- 0.05 (random) +0.05-0.07 (systematic) and an intrinsic scatter of < 0.13 (68% confidence). This is further supported by the very homogeneous shape of the observed velocity dispersion profiles, obtained via Keck spectroscopy, which are mutually consistent after a simple scaling. Remarkably, this slope agrees closely with numerical simulations that contain only dark matter, despite the significant contribution of stellar mass on the scales we probe. The Navarro-Frenk-White profile characteristic of collisionless cold dark matter is a better description of the total mass density at radii >~ 5-10 kpc than that of dark matter alone. Hydrodynamical simulations that include baryons, cooling, and feedback currently provide a poorer match. We discuss the significance of our findings for understanding the assembly of BCGs and cluster cores, particularly the influence of baryons on the inner DM halo. [abridged]

The nature of the dark matter remains a mystery. The possibility of an unstable dark matter particle decaying to invisible daughter particles has been explored many times in the past few decades. Meanwhile, weak gravitational lensing shear has gained a lot of attention as a probe of dark energy. Weak lensing is a useful tool for constraining the stability of the dark matter. In the coming decade a number of large, galaxy imaging surveys will be undertaken and will measure the statistics of cosmological weak lensing with unprecedented precision. Weak lensing statistics are sensitive to unstable dark matter in at least two ways. Dark matter decays alter the matter power spectrum and change the angular diameter distance-redshift relation. We show how measurements of weak lensing shear correlations may provide the most restrictive, model-independent constraints on the lifetime of unstable dark matter. Our results rely on assumptions regarding nonlinear evolution of density fluctuations in scenarios of unstable dark matter and one of our aims is to stimulate interest in theoretical work on nonlinear structure growth in unstable dark matter models.

Gravitational lensing offers a unique tool to study dark matter on a broad range of scales, from galaxies to clusters, to the large-scale matter distribution in the Universe. Density fluctuations on large scales have a small amplitude, hence their lensing effects are weak. In this chapter, after introducing the concepts of weak gravitational lensing – which are quite different from those used in strong lensing – I will concentrate on three main topics: the mass distribution of galaxy clusters as obtained from combining strong and weak lensing results, the lensing effects of the large-scale matter distribution in the Universe and lessons to be learned from them, and the weak lensing studies of the mass profiles in the outskirts of galaxies, together with the correlation of galaxies and the underlying dark matter distribution. Introduction Since gravitational light deflection is independent of the nature and state of matter, and in particular is equally sensitive to luminous and dark matter, it provides a unique tool for studying the total mass distribution of objects in the Universe. The study of the mass properties in the inner part of galaxies is covered by other chapters in this volume, as well as that of stellar- and planetary-mass objects. In my chapter, the mass distribution on larger scales is treated, namely that of galaxy clusters (Section 5.3), the statistical properties of the mass of galaxies, groups and clusters on large scales (Section 5.5), and that of the large-scale structure in the Universe in Section 5.4. In preparing this chapter, I have assumed that the reader has read the contribution by Sherry Suyu (Chapter 1, this volume), where the basic theory of gravitational lensing is treated thoroughly, or is otherwise familiar with the concepts of gravitational lensing. Furthermore, I assume a certain familiarity with the cosmological standard model. It should also be mentioned here that I have written about these topics before, with extended lecture notes published as Schneider (2006). For more details on many issues discussed below, I refer the reader to this work. For the same reason, only a few papers from before 2005 are cited. I have made no efforts to present a balanced, or even complete presentation of the subject; therefore, I apologize to all those colleagues whose work has not been discussed or cited.

We investigate whether the shapes of galaxy clusters inferred from weak gravitational lensing can be used as a test of the nature of dark matter. We analyse mock weak lensing data, with gravitational lenses extracted from cosmological simulations run with two different dark matter models: cold dark matter (CDM) and self-interacting dark matter (SIDM). We fit elliptical Navarro–Frenk–White profiles to the shear fields of the simulated clusters. Despite large differences in the distribution of 3D shapes between CDM and SIDM, we find that the distributions of weak-lensing-inferred cluster shapes are almost indistinguishable. We trace this information loss to two causes. First, weak lensing measures the shape of the projected mass distribution, not the underlying 3D shape, and projection effects wash out some of the difference. Secondly, weak lensing is most sensitive to the projected shape of clusters, on a scale approaching the virial radius ($\sim\! 1.5 \mathrm{\, Mpc}$), whereas SIDM shapes differ most from CDM in the inner halo. We introduce a model for the mass distribution of galaxy clusters where the ellipticity of the mass distribution can vary with distance to the centre of the cluster. While this mass distribution does not enable weak lensing data to distinguish between CDM and SIDM with cluster shapes (the ellipticity at small radii is poorly constrained by weak lensing), it could be useful when modelling combined strong and weak gravitational lensing of clusters.

We describe a method to estimate the mass distribution of a gravitational lens and the position of the sources from combined strong and weak lensing data. The algorithm combines weak and strong lensing data in a unified way producing a solution which is valid in both the weak and strong lensing regimes. We study how the result depends on the relative weighting of the weak and strong lensing data and on choice of basis to represent the mass distribution. We find that combining weak and strong lensing information has two major advantages: it eliminates the need for priors and/or regularization schemes for the intrinsic size of the background galaxies (this assumption was needed in previous strong lensing algorithms) and it corrects for biases in the recovered mass in the outer regions where the strong lensing data is less sensitive. The code is implemented into a software package called WSLAP (Weak & Strong Lensing Analysis Package) which is publicly available at this http URL

Cosmology with weak lensing surveys

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.

Weak gravitational lensing is rapidly becoming one of the principal probes of dark matter and dark energy in the universe. In this brief review we outline how weak lensing helps determine the structure of dark matter halos, measure the expansion rate of the universe, and distinguish between modified gravity and dark energy explanations for the acceleration of the universe. We also discuss requirements on the control of systematic errors so that the systematics do not appreciably degrade the power of weak lensing as a cosmological probe.

We present a detailed analysis of the baryonic and dark matter distribution in the lensing cluster Abell 611 (z = 0.288), with the goal of determining the dark matter profile over an unprecedented range of cluster-centric distance. By combining three complementary probes of the mass distribution, weak lensing from multi-color Subaru imaging, strong lensing constraints based on the identification of multiply imaged sources in Hubble Space Telescope images, and resolved stellar velocity dispersion measures for the brightest cluster galaxy secured using the Keck telescope, we extend the methodology for separating the dark and baryonic mass components introduced by Sand et al. Our resulting dark matter profile samples the cluster from ∼3 kpc to 3.25 Mpc, thereby providing an excellent basis for comparisons with recent numerical models. We demonstrate that only by combining our three observational techniques can degeneracies in constraining the form of the dark matter profile be broken on scales crucial for detailed comparisons with numerical simulations. Our analysis reveals that a simple Navarro–Frenk–White (NFW) profile is an unacceptable fit to our data. We confirm earlier claims based on less extensive analyses of other clusters that the inner profile of the dark matter profile deviates significantly from the NFW form and find a inner logarithmic slope β flatter than 0.3 (68%; where ρDM ∝ r−β at small radii). In order to reconcile our data with cluster formation in a ΛCDM cosmology, we speculate that it may be necessary to revise our understanding of the nature of baryon–dark matter interactions in cluster cores. Comprehensive weak and strong lensing data, when coupled with kinematic information on the brightest cluster galaxy, can readily be applied to a larger sample of clusters to test the universality of these results.

In this work, I shall figure out the general structure of dark fabric matter, and the direct interactions of the celestial objects, ordinary matter, and ordinary energy with dark fabric matter and energy. Dark Fabric matter and energy is a hidden dimension of the parallel universes, visible Universe, galaxies, Atoms, molecules, ordinary matter, celestial objects, stellar systems, and Planetary systems. The Main Structure of Dark fabric matter consists of the Dark matter particles called Fabriton particles, Dark Matter Strings, and Dark Matter Webs. The dark matter particles are named fabriton particles. Fabriton means Fast actively binding reacting in total objects naturally. Fabriton is a good proposed name for dark matter particles to be recognized among subatomic particles. The mystery of Dark matter and the dark energy could be solved here entirely. Einstein and Newton built clear mathematical equations to describe the nature of gravity, after them many other people worked warmly to resolve the reality of gravity, dark matter, and dark energy. Gravity is the ripples, curvatures, gravitational waves, and tunnels that form rapidly in the structure of dark fabric matter and energy when celestial objects and ordinary matter particles pass through it directly.

We present a weak gravitational lensing analysis of 22 early-type strong lens galaxies, based on deep HST images obtained as part of the Sloan Lens ACS Survey. Using the most advanced techniques to control systematic uncertainties related to the variable PSF and charge transfer efficiency of the ACS, we detect weak lensing signal out to 300 kpc/h. We analyze blank control fields from the COSMOS survey in the same manner, inferring that the residual systematic uncertainty in the tangential shear is <0.3%. A joint strong and weak lensing analysis shows that the average total mass density profile is consistent with isothermal over two decades in radius (3-300 kpc/h, approximately 1-100 Reff). This finding extends by over an order of magnitude in radius previous results, based on strong lensing and/or stellar dynamics, that luminous and dark component ``conspire'' to form an isothermal mass distribution. In order to disentangle the contributions of luminous and dark matter, we fit a two-component mass model (R^1/4 + NFW) to the weak and strong lensing constraints. It provides a good fit to the data with only two free parameters; i) the average stellar mass-to-light ratio M_*/L_V=4.48 +- 0.46 hMo/Lo, in agreement with that expected for an old stellar population; ii) the average virial mass-to-light ratio M_vir/L_V = 246+101-87 hMo/Lo. [abridged]

Measuring the three-dimensional (3D) distribution of mass on galaxy cluster scales is a crucial test of thecold dark matter (� CDM) model, providing constraints on the nature of dark mat- ter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spher- ical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. We recently introduced a Markov Chain Monte Carlo method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true shape uncertainty present in nature. In this paper we apply that method to weak lensing data obtained with the ESO/MPG Wide Field Imager for galaxy clusters A1689, A1835 and A2204, under a range of Bayesian priors derived from theory and from independent X-ray and strong lensing observations. For Abell 1689, using a simple strong lensing prior we find marginalized mean parameter values M200 = (0.83 ± 0.16) × 10 15 h −1 Mand C = 12.2 ± 6.7, which are marginally consistent with the mass- concentration relation predicted inCDM. With the same strong lensing prior we find for Abell 1835 M200 = (0.67 ± 0.22) × 10 15 h −1 Mand C = 7.1 +10.6

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.