Double lenses

The analysis of the shear induced by a single cluster on the images of a large number of background galaxies is all centered around the curl-free character of a well-known vector field that can be derived from the data. Such basic property breaks down when the source galaxies happen to be observed through two clusters at different redshifts, partially aligned along the line of sight. In this paper we address the study of double lenses and obtain five main results. (i) First we generalize the procedure to extract the available information, contained in the observed shear field, from the case of a single lens to that of a double lens. (ii) Then we evaluate the possibility of detecting the signature of double lensing given the known properties of the distribution of clusters of galaxies. (iii) As a different astrophysical application, we demonstrate how the method can be used to detect the presence of a dark cluster that might happen to be partially aligned with a bright cluster studied in terms of statistical lensing. (iv) In addition, we show that the redshift distribution of the source galaxies, which in principle might also contribute to break the curl-free character of the shear field, actually produces systematic effects typically two orders of magnitude smaller than the double lensing effects we are focusing on. (v) Remarkably, a discussion of relevant contributions to the noise of the shear measurement has brought up an intrinsic limitation of weak lensing analyses, since one specific contribution, associated with the presence of a non-vanishing two-galaxy correlation function, turns out not to decrease with the density of source galaxies (and thus with the depth of the observations).Comment: 40 pages, 15 figures. Accepted for publication in ApJ main journa

Quiet Planting in the Locked Constraint Satisfaction Problems

We study the planted ensemble of locked constraint satisfaction problems. We describe the connection between the random and planted ensembles. The use of the cavity method is combined with arguments from reconstruction on trees and first and second moment considerations; in particular the connection with the reconstruction on trees appears to be crucial. Our main result is the location of the hard region in the planted ensemble. In a part of that hard region instances have with high probability a single satisfying assignment.Comment: 21 pages, revised versio

The Effects of Massive Substructures on Image Multiplicities in Gravitati onal Lenses

Surveys for gravitational lens systems have typically found a significantly larger fraction of lenses with four (or more) images than are predicted by standard ellipsoidal lens models (50% versus 25-30%). We show that including the effects of smaller satellite galaxies, with an abundance normalized by the observations, significantly increases the expected number of systems with more than two images and largely explains the discrepancy. The effect is dominated by satellites with ~20% the luminosity of the primary lens, in rough agreement with the typical luminosities of the observed satellites. We find that the lens systems with satellites cannot, however, be dropped from estimates of the cosmological model based on gravitational lens statistics without significantly biasing the results.Comment: 23 pages, 7 figures, more discussion of sis vs sie and inclusion of uncorrelated contribution

Effect of Peculiar Motion in Weak Lensing

We study the effect of peculiar motion in weak gravitational lensing. We derive a fully relativistic formula for the cosmic shear and the convergence in a perturbed Friedmann Universe. We find a new contribution related to galaxies peculiar velocity. This contribution does not affect cosmic shear in a measurable way, since it is of second order in the velocity. However, its effect on the convergence (and consequently on the magnification, which is a measurable quantity) is important, especially for redshifts z < 1. As a consequence, peculiar motion modifies also the relation between the shear and the convergence.Comment: 11 pages, 7 figures; v2: discussion on the reduced shear added (5.C), additional references, version accepted in PRD; v3: mistakes corrected in eqs. (26), (31), (33) and (44); results unchange

Distance-Redshift in Inhomogeneous Omega0=1Omega_0=1 Friedmann-Lemaitre-Robertson-Walker Cosmology

Distance--redshift relations are given in terms of associated Legendre functions for partially filled beam observations inspatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies. These models are dynamically pressure-free, flat FLRW on large scales but, due to mass inhomogeneities, differ in their optical properties. The partially filled beam area-redshift equation is a Lame$^{\prime}$ equation for arbitrary FLRW and is shown to simplify to the associated Legendre equation for the spatially flat, i.e. $\Omega_0=1$ case. We fit these new analytic Hubble curves to recent supernovae (SNe) data in an attempt to determine both the mass parameter $\Omega_m$ and the beam filling parameter $\nu$. We find that current data are inadequate to limit $\nu$. However, we are able to estimate what limits are possible when the number of observed SNe is increased by factor of 10 or 100, sample sizes achievable in the near future with the proposed SuperNova Acceleration Probe satellite.Comment: 9 pages, 3 figure

Weak Lensing Analysis of the z~0.8 cluster CL 0152-1357 with the Advanced Camera for Surveys

We present a weak lensing analysis of the X-ray luminous cluster CL 0152-1357 at z~0.84 using HST/ACS observations. The unparalleled resolution and sensitivity of ACS enable us to measure weakly distorted, faint background galaxies to the extent that the number density reaches ~175 arcmin^-2. The PSF of ACS has a complicated shape that also varies across the field. We construct a PSF model for ACS from an extensive investigation of 47 Tuc stars in a modestly crowded region. We show that this model PSF excellently describes the PSF variation pattern in the cluster observation when a slight adjustment of ellipticity is applied. The high number density of source galaxies and the accurate removal of the PSF effect through moment-based deconvolution allow us to restore the dark matter distribution of the cluster in great detail. The direct comparison of the mass map with the X-ray morphology from Chandra observations shows that the two peaks of intracluster medium traced by X-ray emission are lagging behind the corresponding dark matter clumps, indicative of an on-going merger. The overall mass profile of the cluster can be well described by an NFW profile with a scale radius of r_s =309+-45 kpc and a concentration parameter of c=3.7+-0.5. The mass estimates from the lensing analysis are consistent with those from X-ray and Sunyaev-Zeldovich analyses. The predicted velocity dispersion is also in good agreement with the spectroscopic measurement from VLT observations. In the adopted WMAP cosmology, the total projected mass and the mass-to-light ratio within 1 Mpc are estimated to be 4.92+-0.44 10^14 solar mass and 95+-8 solar mass/solar luminosity, respectively.Comment: Accepted for publication in Astrophysical Journal. 58 pages, 26 figures. Figures have been degraded to meet size limit; a higher resolution version available at http://acs.pha.jhu.edu/~mkjee/ms_cl0152.pd

The GALATEA Test-Facility for High Purity Germanium Detectors

GALATEA is a test facility designed to investigate bulk and surface effects in high purity germanium detectors. A vacuum tank houses an infrared screened volume with a cooled detector inside. A system of three stages allows an almost complete scan of the detector. The main feature of GALATEA is that there is no material between source and detector. This allows the usage of alpha and beta sources as well as of a laser beam to study surface effects. A 19-fold segmented true-coaxial germanium detector was used for commissioning

Large-Scale QSO-Galaxy Correlations and Weak Lensing

Several recent studies show that bright, intermediate and high redshift optically and radio selected QSOs are positively correlated with nearby galaxies on a range of angular scales up to a degree. Obscuration by unevenly distributed Galactic dust can be ruled out as the cause, leaving weak statistical lensing as the physical process responsible. However the amplitude of correlations on < 1 degree scales is at least a factor of a few larger than lensing model predictions. A possible way to reconcile the observations and theory is to revise the weak lensing formalism. We extend the standard lensing formulation to include the next higher order term (second order) in the geodesic equation of motion for photons. We derive relevant equations applicable in the weak lensing regime, and discuss qualitative properties of the updated formulation. We then perform numerical integrations of the revised equation and study the effect of the extra term using two different types of cosmic mass density fluctuations. We find that nearby large-scale coherent structures increase the amplitude of the predicted lensing-induced correlations between QSOs and foreground galaxies by ~ 10% (not a factor of several required by observations), while the redshift of the optimal, i.e. `most correlated' structures is moved closer to the observer compared to what is predicted using the standard lensing equation.Comment: extended Section 2; 20 pages, including 4 figures, accepted to Ap