4 pages, 3 figures, to appear in the proceedings of "Panoramic Views of Galaxy Formation and Evolution", 1st Subaru International Conference held in Hayama, Japan 11-16 December 2007
To set useful limits on the abundance of small-scale dark matter halos (subhalos) in a galaxy scale, we have carried out mid-infrared imaging and integral-field spectroscopy for a sample of quadruple lens systems showing anomalous flux ratios. These observations using Subaru have been successful for distinguishing millilensing by subhalos from microlensing by stars. Current status for our lensing analysis of dark matter substructure is reported.
Multiply-imaged quasar lenses can be used to constrain the substructure mass fraction in galaxy-sized dark matter halos via anomalous flux ratios in lensed images. The flux ratios, however, can be affected by both the substructure in the lens halo and by isolated small-mass halos along the entire line-of-sight to the lensed source. While lensing by dark matter clumps near the lens galaxy is more efficient than elsewhere, the cumulative effect of all objects along the line-of-sight could be significant. Here we estimate the potential contribution of isolated clumps to the substructure lensing s…
In recent years, gravitational lensing has been used as a means to detect substructure in galaxy-sized halos, via anomalous flux ratios in quadruply-imaged lenses. In addition to causing anomalous flux ratios, substructure may also perturb the positions of lensed images at observable levels. In this paper, we numerically investigate the scale of such astrometric perturbations using realistic models of substructure distributions. Substructure distributions that project clumps near the Einstein radius of the lens result in perturbations that are the least degenerate with the best-fit smooth macr…
It has been argued that the flux anomalies detected in gravitationally lensed QSOs are evidence for substructures in the foreground lensing haloes. In this paper we investigate this issue in greater detail focusing on the Cusp relation which corresponds to images of a source located to the cusp of the inner caustic curve. We use numerical simulations combined with a Monte Carlo approach to study the effects of the expected power law distribution of substructures within LCDM haloes on the multiple images. Generally, the high number of anomalous flux ratios in the cusp configurations is unlikely…
We explore the effect of substructure in dark matter halos on the power spectrum and bispectrum of matter fluctuations and weak lensing shear. By experimenting with substructure in a cosmological N = 512^3 simulation, we find that when a larger fraction of the host halo mass is in subhalos, the resulting power spectrum has less power at 1 < k < 100 h Mpc^{-1} and more power at k > 100 h Mpc^{-1}. We explain this effect using an analytic halo model including subhalos, which shows that the 1 < k < 100 h Mpc^{-1} regime depends sensitively on the radial distribution of subhalo centers while the i…
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 the…
We present high-resolution mass reconstructions for five massive cluster-lenses spanning a redshift range from $z = 0.18$--0.57 utilising archival {\it Hubble Space Telescope} ({\it HST}) data and applying galaxy-galaxy lensing techniques. These detailed mass models were obtained from the observations by combining constraints from the strong and weak lensing regimes. We ascribe local weak distortions in the shear maps to perturbations induced by the presence of galaxy haloes around individual bright early-type cluster member galaxies. This technique constrains the mass enclosed within an apert…
In this work we investigate the gravitationally lensed system B1422+231. High--quality VLBI image positions, fluxes and shapes as well as an optical HST lens galaxy position are used. First, two simple and smooth models for the lens galaxy are applied to fit observed image positions and fluxes; no even remotely acceptable model was found. Such models also do not accurately reproduce the image shapes. In order to fit the data successfully, mass substructure has to be added to the lens, and its level is estimated. To explore expectations about the level of substructure in galaxies and its influe…
Spatially resolved spectroscopic data from the CIRPASS integral field unit (IFU) on Gemini are used to measure the gravitational lensing of the 4-image quasar Q2237+0305 on different size scales. A method for measuring the substructure present in the lens using observations at multiple wavelengths is demonstrated to be very effective and independent of many of the degeneracies inherent in previous methods. The magnification ratios of the QSO's narrow line region (NLR) and broad line region (BLR) are measured and found to be disagree with each other and with the published radio and mid-infrared…
We show how observations of multiply-imaged quasars at high redshift can be used as a probe of dark matter clumps (subhalos with masses ~ 10^9 solar masses) within the virialized extent of more massive lensing halos. A large abundance of such satellites is predicted by numerical simulations of galaxy formation in cold dark matter (CDM) cosmogonies. Small-scale structure within galaxy halos affects the flux ratios of the images without appreciably changing their positions. We use numerical simulations to quantify the effect of dark matter substructure on the distribution of magnifications, and …
It is widely recognized that cold dark matter models predict abundant dark matter substructure in halos of all sizes. Galaxy-galaxy lensing provides a unique opportunity to directly measure the presence and the mass of such substructures in clusters of galaxies. Here we present the mass function of substructures obtained from lensing in massive HST cluster lenses, and compare it with that obtained from high-resolution cosmological N-body simulations. We find excellent agreement in the slope and amplitude in the mass range 10^{11} - 10^{12.5} solar masses probed by the observations, highlightin…
Flux ratio `anomalies' in quadruply-imaged gravitational lenses can be explained with galactic substructure of the sort predicted by CDM, but the strength and uniqueness of that hypothesis needs to be further assessed. A good way to do that is to use the physical scale associated with the size of the source quasar, and its dependence on wavelength. We develop an analytic toy model to study finite source effects in substructure lensing and identify general principles. We find that image positions and magnifications are basically independent of source size until the source is large enough to int…
We present high-resolution mass reconstructions for five massive cluster-lenses spanning a redshift range from z = 0.18 - 0.57 utilizing archival Hubble Space Telescope data and applying galaxy-galaxy lensing techniques. These detailed mass models were obtained by combining constraints from the observed strong and weak lensing regimes. Quantifying the local weak distortions in the shear maps in terms of perturbations induced by the presence of galaxy halos around individual bright early-type cluster member galaxies, we estimate the fraction of mass in the central regions of these clusters that…
Weak gravitational lensing can be used to directly measure the mass along a line-of-sight without any dependence on the dynamical state of the mass, and thus can be used to measure the masses of clusters even if they are not relaxed. One common technique used to measure cluster masses is fitting azimuthally-averaged gravitational shear profiles with a spherical mass model. In this paper we quantify how asphericity and projected substructure in clusters can affect the virial mass and concentration measured with this technique by simulating weak lensing observations on 30 independent lines-of-si…
The gravitational lensing constraints on the small mass end of the LCDM mass function are discussed. Here a conservative approach is taken where only the most difficult to explain image flux anomalies in strong QSO lenses are emphasized. Numerical simulations are performed to compare predictions for the LCDM small scale mass function with the observed flux ratios. It is found that the cusp caustic lens anomalies and the disagreements between monochromatic flux ratios and simple lens models can be explained without any substructure in the primary lenses' dark matter halos. Extragalactic LCDM ha…
We investigate the extended source size effects on gravitational lensing in which a lens consists of a smooth potential and small mass clumps (``substructure lensing''). We first consider a lens model that consists of a clump modeled as a singular isothermal sphere (SIS) and a primary lens modeled as an external background shear and convergence. For this simple model, we derive analytic formulae for (de)magnification of circularly symmetric top-hat sources with three types of parity for their lensed images, namely, positive, negative, and doubly negative parities. Provided that the source size…
Galactic sized gravitational lenses are simulated by combining a cosmological N-body simulation and models for the baryonic component of the galaxy. The lens caustics, critical curves, image locations and magnification ratios are calculated by ray-shooting on an adaptive grid. When the source is near a cusp in a smooth lens' caustic the sum of the magnifications of the three closest images should be close to zero. It is found that in the observed cases this sum is generally too large to be consistent with the simulations implying that there is not enough substructure in the simulations. This s…
Gravitational lensing of a background source by a foreground galaxy lens occasionally produces four images of the source. The cusp and the fold relations impose conditions on the ratios of magnifications of these four-image lenses. In this theoretical investigation, we explore the sensitivity of these relations to the presence of substructure in the lens. Starting with a smooth lens potential, we add varying amounts of substructure, while keeping the source position fixed, and find that the fold relation is a more robust indicator of substructure than the cusp relation for the images. This rob…
We investigate how ellipticity, asymmetries and substructures separately affect the ability of galaxy clusters to produce strong lensing events, i.e. gravitational arcs, and how they influence the arc morphologies and fluxes. This is important for those studies aiming, for example, at constraining cosmological parameters from statistical lensing, or at determining the inner structure of galaxy clusters through gravitational arcs. We do so by creating two-dimensional gradually smoothed, differently elliptical and asymmetric versions of some numerical models. On average, we find that the contrib…
Since dark matter clusters and groups may have substructure, we have examined the sextupole content of Hubble images looking for a curvature signature in background galaxies that would arise from galaxy-galaxy lensing. We describe techniques for extracting and analyzing sextupole and higher weakly lensed moments. Indications of substructure, via spatial clumping of curved background galaxies, were observed in the image of CL0024 and then surprisingly in both Hubble deep fields. We estimate the dark cluster masses in the deep field. Alternatives to a lensing hypothesis appear improbable, but be…
We address the question of how well the density profile of galaxy clusters can be determined by combining strong lensing and velocity dispersion data. We use cosmological dark matter simulations of clusters to test the reliability of the method, producing mock catalogues of tangential and radial gravitational arcs and simulating the radial velocity dispersion profile of the cluster brightest central galaxy. The density profiles of the simulated clusters closely follow the NFW form, but we find that the recovered values of the inner slope are systematically underestimated, by about 0.4 in the m…
We analyse the number density and radial distribution of substructures and satellite galaxies using cosmological simulations that follow the gas dynamics of a baryonic component, including shock heating, radiative cooling and star formation within the hierarchical concordance LCDM model. We find that the dissipation of the baryons greatly enhances the survival of subhaloes, expecially in the galaxy core, resulting in a radial distribution of satellite galaxies that closely follows the overall mass distribution in the inner part of the halo. Hydrodynamical simulations are necessary to resolve t…
We present a study of the lens properties of quadruply imaged systems, lensed by numerically simulated galaxies. We investigate a simulated elliptical and disc galaxy drawn from high resolution simulations of galaxy formation in a concordance $Λ$CDM universe. The simulations include the effects of gas dynamics, star formation and feedback processes. Flux-ratio anomalies observed in strong gravitational lensing potentially provide an indicator for the presence of mass substructure in lens galaxies as predicted from CDM simulations. We particularly concentrate on the prediction that, for an idea…
Recent years have seen a series of large-scale photometric surveys with the aim of detecting substructure in nearby dwarf galaxies. Some of these objects display a varying distribution of each stellar population, reflecting their star formation histories. Also, dwarf galaxies are dominated by dark matter, therefore luminous substructure may represent a perturbation in the underlying dark material. Substructure can also be the effect of tidal interaction, such as the disruption of the Sagittarius dSph by the Milky Way. Therefore, substructure in dwarf galaxies manifests the stellar, structural …
Gravitational lensing of background compact objects like active galactic nuclei and quasars, by extended intermediate mass lenses such as globular clusters and and dark matter clumps with masses 10^5 - 10^8 M_sun, is considered. It is shown that observational study of the galaxy-quasar's associations is a powerful direct observational test of the nature of massive galaxy haloes. Optical interferometric observations with VLTI and Keck instruments are able to constrain masses and number of substructure halo objects. Evidence of gravitational lensing by globular clusters in haloes of spiral and e…
Various differences in galaxy cluster properties derived from X-ray and weak lensing observations have been highlighted in the literature. One such difference is the observation of mass concentrations in lensing maps which have no X-ray counterparts (e.g. Jee, White, Ford et al. 2005). We investigate this issue by identifying substructures in maps of projected total mass (analogous to weak lensing mass reconstructions) and maps of projected X-ray surface brightness for three simulated clusters. We then compare the 2D mass substructures with both 3D subhalo data and the 2D X-ray substructures. …
We present mid-infrared imaging at 11.7 mu m for the quadruple lens systems, PG1115+080 and B1422+231, using the cooled mid-infrared camera and spectrometer (COMICS) attached on the Subaru telescope. These lensed QSOs are characterized by their anomalous optical and radio flux ratios as obtained for (A1, A2) images of PG1115+080 and (A, B, C) images of B1422+231, respectively, i.e., such flux ratios are hardly reproduced by lens models with smooth mass distribution. Our mid-infrared observations for these images have revealed that the mid-infrared flux ratio A2/A1 of PG1115+080 is virtually co…
We have examined the spatial distribution of substructure in clusters of galaxies using Einstein X-ray observations. Subclusters are found to have a markedly anisotropic distribution that reflects the surrounding matter distribution on supercluster scales. Our results suggest a picture in which cluster formation proceeds by mergers of subclusters along large-scale filaments. The implications of such an anisotropic formation process for the shapes, orientations and kinematics of clusters are discussed briefly.
Recently, ``CDM crisis'' is under discussion. The main point of this crisis is that number of substructures presented by cosmological N-body simulations based on CDM scenario for structure formation is much larger than observed substructures. Therefore, it is crucial for this crisis to discriminate whether expected number of CDM substructures really exist but non-luminous or do not exist. In this paper, we present a new idea to detect such invisible substructures by utilizing a gravitational lensing. Here, we consider quasars that are gravitationally lensed by a foreground galaxy. A substructu…
We present the results of a weak lensing survey of six high-redshift (z > 0.5), X-ray selected clusters of galaxies. We have obtained ultra-deep R-band images of each cluster with the Keck Telescope, and have measured a weak lensing signal from each cluster. From the background galaxy ellipticities we create two-dimensional maps of the surface mass density of each cluster. We find that the substructure seen in the mass reconstructions typically agree well with substructure in both the cluster galaxy distributions and X-ray images of the clusters. We also measure the one-dimensional radial prof…
Large galaxies are thought to form hierarchically, from the accretion and disruption of many smaller galaxies. Such a scenario should naturally lead to galactic phase-space distributions containing some degree of substructure. We examine the errors in mass estimates of galaxies and their dark halos made using the projected phase-space distribution of a tracer population (such as a globular cluster system or planetary nebulae) due to falsely assuming that the tracers are distributed randomly. The level of this uncertainty is assessed by applying a standard mass estimator to samples drawn from 1…
Clusters of galaxies form through major merger and/or absorption of smaller groups. In fact, some characteristic structures such as cold fronts, which are likely relevant to moving substructures, are found by {\it Chandra}. It is expected that moving substructures generate turbulence in the intracluster medium (ICM). Such turbulence probably plays a crucial role in mixture and transport of gas energy and heavy elements, and particle acceleration. The {\it Astro-E2} satellite, which is planned to be launched in 2005, will detect broadened lines due to turbulent motion. In order to explore the a…
We investigate the formation of clusters of galaxies in an expanding universe using a new code that regrids at a region of high density. In particular we investigate two models for the initial conditions, both with the standard CDM power spectrum - one has $Ω= 1$ and the other $Ω= 0.2$. Both universes have $H_0 = 100 \kms\mpc^{-1}$ and $Λ= 0$. The level of substructure in the final cluster can be used as a discriminant of the cosmic density. We discuss various statistics which can be measured observationally from clusters of galaxies, that can be used to discriminate between the two models. We…
Gravitational lensing in clusters of galaxies is an efficient tool to probe the mass distribution of galaxies and clusters, high redshift objects thanks to the gravitational amplification, and the geometry of the universe. We review some important aspects of cluster lensing and related issues in observational cosmology.
We have run high resolution N-body models simulating the encounter of a dwarf galaxy with a bright elliptical galaxy. The dwarf absorbs orbital angular momentum and shows counter-rotating features in the external regions of the galaxy. To explain the core-envelope kinematic decoupling observed in some dwarf galaxies in high-density environments requires nearly head-on collisions and very little dark matter bound to the dwarf. These kinematic structures appear under rather restrictive conditions. As a consequence, in a cluster like Virgo ~1% of dwarf galaxies may present counter-rotation formed…
We study luminosity and morphology segregation of over 3000 cluster galaxies in an ensemble cluster of 59 rich, nearby galaxy clusters observed in the ESO Nearby Cluster Survey (ENACS). Within this sample we identify those galaxies that are in substructures. We compare the distribution of projected clustercentric distance, R, and 'normalized' relative line-of-sight velocity, v, of several subsamples, using the 2D Kolmogorov-Smirnov test. We find evidence of luminosity segregation only for the ellipticals outside substructure and brighter than M_R = -22.0 +/- 0.1 (h0=100 km/s/Mpc). We confirm t…
One of the generic predictions of modern cosmological models is that large galaxies should have experienced many mergers with smaller galaxies at some point in their past. Debris from such encounters will leave spatially distinct substructure in the stellar haloes of nearby galaxies, detectable for a few orbital periods after the final merger. In the case of the Milky Way, kinematic data from surveys such as RAVE and satellite missions such as GAIA will allow us to probe much more of the merger history, and to connect the properties of the stellar halo with those of local dwarf galaxies. To es…
We discuss whether one should expect that multiply imaged QSOs can be understood with `simple' lens models which contain a handful of parameters. Whereas for many lens systems such simple mass models yield a remarkably good description of the observed properties, there are some systems which are notoriously difficult to understand quantitatively. We argue that at least in one case (B 1422+231) these difficulties are not due to a `wrong' parametrization of the lens model, but that the discrepancy between observed and model-predicted flux ratios are due to substructure in the lens. Similar to mi…
Formation theories for central dominant galaxies in clusters require them to be located at the minimum of the cluster gravitational potential. However, 32\% (8 out of 25) of the clusters with more than 50 measured redshifts have central galaxies with significant velocity offsets (with respect to other cluster members). By studying their velocity distributions and correlations between velocity and position, I show that the presence of a large peculiar velocity is strongly correlated with the presence of substructure in these massive systems. About 85\% (21 of 25) of all well-studied clusters sh…
The different regimes of gravitational lensing constitutes an interesting tool in order to map the mass distribution in galaxy clusters on different scales. In this proceedings article, I review some work I have performed on this topic. More precisely, I will focus on : (i) galaxy scale substructures, using weak galaxy-galaxy lensing in order to study how does the environment shape their properties; (ii) the mass profile of Abell~1689 as probed combining strong and weak lensing; (iii) the slope of the inner dark matter distribution in Abell~1703 as measured by strong lensing. The lensing resul…
We study the anomalous flux ratio which is observed in some four-image lens systems, where the source lies close to a fold caustic. In this case two of the images are close to the critical curve and their flux ratio should be equal to unity, instead in several cases the observed value differs significantly. The most plausible solution is to invoke the presence of substructures, as for instance predicted by the Cold Dark Matter scenario, located near the two images. In particular, we analyze the two fold lens systems PG1115+080 and B1555+375, for which there are not yet satisfactory models whic…
Gravitational lenses are a unique new constraint on the structure of galaxies. We review the evidence that most lenses are early-type galaxies, the optical properties of the lens galaxies, the evidence against constant M/L models, recent work on the axis ratios of the mass distribution, and the role stellar dynamics plays in gravitational lensing.
A homogeneous sample of galaxy redshifts in the core regions (R < 0.5 h$^{-1}$ Mpc) of 12 clusters is used to measure the frequency of substructure with different tests. In 50 % of the cases substructure is detected, a frequency which agrees well with previous studies of cluster cores. Magnitude information and rough morphological classes are also available for 80 % of the sample, allowing us to confirm that bright galaxies (M < -22 mag) have a significantly lower velocity dispersion than the rest. Elliptical galaxies are the main responsibles for this luminosity segregation in velocity space,…
Gravitational lenses with anomalous flux ratios are often cited as possible evidence for dark matter satellites predicted by simulations of hierarchical merging in cold dark matter cosmogonies. We show that the fraction of quads with anomalous flux ratios depends primarily on the total mass and spatial extent of the satellites, and the characteristic lengthscale R of their distribution. If R is 100 kpc, then for a moderately elliptical galaxy with a line-of-sight velocity dispersion of 250 km/s, a mass of 3 x 10^9 solar masses in highly-concentrated (Plummer model) satellites is needed for 20%…
We present Subaru spectroscopy of the early-type lensing galaxies in the lens systems HST14113+5211 (z=0.464) and B2045+265 (z=0.868), being aimed at measuring the velocity dispersion of the lensing galaxies as an important component to their mass distributions and internal dynamics. For HST14113+5211 we have obtained 174+/-20km/s (1-sigma) inside an aperture of 0.9", and for B2045+265 we have obtained 213+/-23km/s inside an aperture of 1.2". To extract the significance of these information on the mass distributions and stellar dynamics of the lensing galaxies, we construct two alternative mod…
We perform three dimensional hydrodynamical simulations of a moving substructure in a cluster of galaxies. We investigate dynamical evolution of the intracluster medium (ICM) in and around the substructure moving radially in the larger cluster's gravitational potential, and its observational consequences. After the substructure passes the larger cluster's center, a bow shock and clear contact discontinuity form in front of it. The contact discontinuity looks like a sharp cold front in the X-ray image synthesized from the simulation results. This agrees with a structure found in 1E 0657-56. The…
We give a non-exhaustive review of the use of strong gravitational lensing in placing constraints on the quantity of dark and visible mass in galaxies. We discuss development of the methodology and summarise some recent results.
In addition to the determination of the mass distribution of lenses (see P. Schneider, this conference), strong and weak lensing can also be powerfull tools to analyse the redshift distribution of faint galaxies. In this review, I summarize the present status of redshifts of galaxies beyond $B=25$ as they are inferred by spectroscopy of magnified galaxies, lensing inversion and magnification bias.
The lensing cross section of triaxial halos depends on the relative orientation between a halo's principal axes and its line of sight. Consequently, a lensing subsample of randomly oriented halos is not, in general,randomly oriented. Using an isothermal mass model for the lensing galaxies and their host halos, we show that the lensing subsample of halos that produces doubles is preferentially aligned along the lines of sight, whereas halos that produce quads tend to be projected along their middle axes. These preferred orientations result in different projected ellipticity distributions for qu…
We present results of a weak gravitational lensing survey of six X-ray selected high-redshift clusters of galaxies. We find that the masses of the clusters derived from weak lensing are comparable to those derived from the X-ray observations. We show that many of the clusters have significant substructure not observed in the X-ray observations and that for the more massive clusters a singular isothermal sphere does not provide a good fit to the radial mass profile.
We present a high resolution dark matter reconstruction of the z=0.165 Abell 901/902 supercluster from a weak lensing analysis of the HST STAGES survey. We detect the four main structures of the supercluster at high significance, resolving substructure within and between the clusters. We find that the distribution of dark matter is well traced by the cluster galaxies, with the brightest cluster galaxies marking out the strongest peaks in the dark matter distribution. We also find a significant extension of the dark matter distribution of Abell 901a in the direction of an infalling X-ray group …
We investigate how strong gravitational lensing in the concordance LCDM cosmology is affected by the stellar mass in galaxies. We extend our previous studies, based on ray-tracing through the Millennium Simulation, by including the stellar components predicted by galaxy formation models. We find that the inclusion of these components greatly enhances the probability for strong lensing compared to a `dark matter only' universe. The identification of the `lenses' associated with strong-lensing events reveals that the stellar mass of galaxies (i) significantly enhances the strong-lensing cross-se…
We show that dark matter substructure in galaxy-scale halos perturbs the time delays between images in strong gravitational lens systems. The variance of the effect depends on the subhalo mass function, scaling as the product of the substructure mass fraction and a characteristic mass of subhalos (namely <m^2>/<m>). Time delay perturbations therefore complement gravitational lens flux ratio anomalies and astrometric perturbations by measuring a different moment of the subhalo mass function. Unlike flux ratio anomalies, "time delay millilensing" is unaffected by dust extinction or stellar micro…
This paper is intended as an introduction to the theory of weak lensing. A review of the inversion formula introduced by Kaiser and Squires is presented. We then prove the formula of the aperture densitometry method in a simple way that allows a clear understanding of where the various terms come from. This is particularly useful to quantitatively measure masses in any region of a lens. We then summarize what has been learned from observations of strong lensing about the dark matter distribution; weak lensing should provide similar information on larger scales in clusters of galaxies.
Very deep galaxy surveys have revealed a considerably large population of faint galaxies, which leads to the speculation that all distant objects are moderately magnified by the gravitational lensing effects of galaxies (Fried 1997). In this letter, we present a simple estimate of the lensing amplitudes by all galaxies up to redshift $z=2$ in terms of galaxy merging and answer the question whether the sky is fully covered by the lensing cross-sections of galaxies. It is shown that, as a result of the combination of the increase of galaxy number density and the decrease of galaxy velocity dispe…
A large fraction of known galaxy-lens systems require a component of external shear to explain the observed image geometries. In most cases, this shear can be attributed to a nearby group of galaxies. We discuss how the dark-matter mass distribution of groups of galaxies can influence the external shear for strongly lensed sources and Calculate the expected weak lensing signal from groups for various mass profiles.
Analysing the weak lensing distortions of the images of faint background galaxies provides a means to constrain the mass distribution of cluster galaxies and potentially to test the extent of their dark matter halos as a function of the density of the environment. Here I describe simulations of observational data and present a maximum likelihood method to infer the average properties of an ensemble of cluster galaxies.
We use weak lensing shear measurements of six z>0.5 clusters of galaxies to derive the mean lensing redshift of the background galaxies used to measure the shear. Five of these clusters are compared to X-ray mass models and verify a mean lensing redshift for a 23<R<26.3, R-I<0.9 background galaxy population in good agreement with photometric redshift surveys of the HDF-S. The lensing strength of the six clusters is also analyzed as a function of the magnitude of the background galaxies, and an increase in shear with increasing magnitude is detected at moderate significance. The change in the s…
We present a list of clusters that have had their dark matter content measured using weak gravitational lensing. The list consists of 139 clusters, with weak lensing measurements reported in 64 different publications. Details are provided about the selection criteria and some basic properties of the sample, such as the redshift distribution. An electronic, sortable version of this list with links to public database information on the clusters and publications is provided at http://folk.uio.no/hdahle/WLclusters.html
Very deep imaging data of three optically luminous radio-loud quasars with redshifts between z=0.9 and z=1.36 are presented. The data are complete for galaxies down to R=26. There is no evidence for excess numbers of galaxies around the quasars; foreground galaxy clusters are excluded by the data as well as clusters with richness classes greater than 1 associated with the quasars. We find clear evidence for gravitational lensing for two quasars. It is further shown that due to the high surface density of galaxies all distant (z>1) objects are moderately affected by gravitational lensing; the a…
If the statistics of quasar lensing are to be used to constrain the cosmological model, the various potential systematic uncertainties in the deflector population must be accounted for. One ambiguity in the lensing properties of the dominant deflectors - elliptical galaxies - is their dynamical normalisation. Assuming they can be modelled as isothermal spheres, it is shown that their mass normalisation is sufficiently high that current upper limits on the cosmological constant remain valid, and in fact probably strengthened, even if ellipticals have significant core radii.
