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

Parametric Strong Gravitational Lensing Analysis of Abell 1689

(Abridged) We measure the mass distribution of galaxy cluster Abell 1689 within 0.3 Mpc/h_70 of the cluster centre using its strong lensing effect on 32 background galaxies. The multiple images are based on those of Broadhurst et al. 2005 with some modifications. The cluster profile is explored further out to ~2.5 Mpc/h_70 with weak lensing shear measurements from Broadhurst et al. 2005b. The masses of ~200 cluster galaxies are measured with Fundamental Plane in order to accurately model the small scale mass structure in the cluster. The galaxies are modelled as elliptical truncated isothermal spheres. The dark matter component of the cluster is described by either non-singular isothermal ellipsoids (NSIE) or elliptical versions of the universal dark matter profile (ENFW). We use two dark matter haloes to model the smooth DM in the cluster. The total mass profile is well described by either an NSIS profile with sigma=1514+-18 km/s and core radius of r_c=71+-5kpc/h_70, or an NFW profile with C=6.0+-0.5 and r_200=2.82+-0.11 Mpc/h_70. The errors are assumed to be due to the error in assigning masses to the individual galaxies in the galaxy component. The derived total mass is in good agreement with the mass profile of Broadhurst et al. 05. Using also weak lensing we can constrain the profile further out to r~2.5 Mpc/h_70. The best fit parameters are then sigma=1499+-15 km/s and r_c=66+-5 kpc/h_70 for the NSIS profile and C=7.6+-0.5 and r_200=2.55+-0.07 Mpc/h_70 for the NFW profile. Using the same image configuration as Broadhurst et al. 2005 we obtain a strong lensing model that is superior to that of Broadhurst et al. 2005 (rms of 2.7'' compared to 3.2'').Comment: 43 pages, 22 figures, submitted to the Monthly Notices of the Royal Astronomical Society after the first referee report. Full resolution paper available from http://www.usm.uni-muenchen.de/~halkola/A1689

Implementation of robust image artifact removal in SWarp through clipped mean stacking

We implement an algorithm for detecting and removing artifacts from astronomical images by means of outlier rejection during stacking. Our method is capable of addressing both small, highly significant artifacts such as cosmic rays and, by applying a filtering technique to generate single frame masks, larger area but lower surface brightness features such as secondary (ghost) images of bright stars. In contrast to the common method of building a median stack, the clipped or outlier-filtered mean stacked point-spread function (PSF) is a linear combination of the single frame PSFs as long as the latter are moderately homogeneous, a property of great importance for weak lensing shape measurement or model fitting photometry. In addition, it has superior noise properties, allowing a significant reduction in exposure time compared to median stacking. We make publicly available a modified version of SWarp that implements clipped mean stacking and software to generate single frame masks from the list of outlier pixels.Comment: PASP accepted; software for download at http://www.usm.uni-muenchen.de/~dgruen

Cosmic variance of the galaxy cluster weak lensing signal

Intrinsic variations of the projected density profiles of clusters of galaxies at fixed mass are a source of uncertainty for cluster weak lensing. We present a semi-analytical model to account for this effect, based on a combination of variations in halo concentration, ellipticity and orientation, and the presence of correlated haloes. We calibrate the parameters of our model at the 10 per cent level to match the empirical cosmic variance of cluster profiles at M_200m=10^14...10^15 h^-1 M_sol, z=0.25...0.5 in a cosmological simulation. We show that weak lensing measurements of clusters significantly underestimate mass uncertainties if intrinsic profile variations are ignored, and that our model can be used to provide correct mass likelihoods. Effects on the achievable accuracy of weak lensing cluster mass measurements are particularly strong for the most massive clusters and deep observations (with ~20 per cent uncertainty from cosmic variance alone at M_200m=10^15 h^-1 M_sol and z=0.25), but significant also under typical ground-based conditions. We show that neglecting intrinsic profile variations leads to biases in the mass-observable relation constrained with weak lensing, both for intrinsic scatter and overall scale (the latter at the 15 per cent level). These biases are in excess of the statistical errors of upcoming surveys and can be avoided if the cosmic variance of cluster profiles is accounted for.Comment: 14 pages, 6 figures; submitted to MNRA

A Comparison of Simple Mass Estimators for Galaxy Clusters

High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an isothermal cluster potential, (2) the dynamical mass obtained from the measured velocity dispersion under the assumption of an isothermal cluster potential, and (3) the classical virial estimator. The clusters consist of order 2.5e+05 particles of mass m_p \simeq 10^{10} \Msun, have triaxial mass distributions, and significant substructure exists within their virial radii. Not surprisingly, the level of agreement between the mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. The virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by of order 10%. This result suggests that, at least in the limit of ideal data, the virial estimator is quite robust to deviations from pure spherical symmetry and the presence of substructure. The dynamical mass estimate based upon a measurement of the cluster velocity dispersion and an assumption of an isothermal potential yields a poor measurement of the total mass. The weak lensing estimate yields a very good measurement of the total mass, provided the mean shear used to determine the equivalent cluster velocity dispersion is computed from an average of the lensing signal over the entire cluster (i.e. the mean shear is computed interior to the virial radius). [abridged]Comment: Accepted for publication in The Astrophysical Journal. Complete paper, including 3 large colour figures can also be obtained from http://bu-ast.bu.edu/~brainerd/preprints

Weak Lensing Reconstruction and Power Spectrum Estimation: Minimum Variance Methods

Large-scale structure distorts the images of background galaxies, which allows one to measure directly the projected distribution of dark matter in the universe and determine its power spectrum. Here we address the question of how to extract this information from the observations. We derive minimum variance estimators for projected density reconstruction and its power spectrum and apply them to simulated data sets, showing that they give a good agreement with the theoretical minimum variance expectations. The same estimator can also be applied to the cluster reconstruction, where it remains a useful reconstruction technique, although it is no longer optimal for every application. The method can be generalized to include nonlinear cluster reconstruction and photometric information on redshifts of background galaxies in the analysis. We also address the question of how to obtain directly the 3-d power spectrum from the weak lensing data. We derive a minimum variance quadratic estimator, which maximizes the likelihood function for the 3-d power spectrum and can be computed either from the measurements directly or from the 2-d power spectrum. The estimator correctly propagates the errors and provides a full correlation matrix of the estimates. It can be generalized to the case where redshift distribution depends on the galaxy photometric properties, which allows one to measure both the 3-d power spectrum and its time evolution.Comment: revised version, 36 pages, AAS LateX, submitted to Ap

The sizes of galaxy halos in galaxy cluster Abell 1689

The multiple images observed in galaxy cluster Abell 1689 provide strong constraints not only on the mass distribution of the cluster but also on the ensemble properties of the cluster galaxies. Using parametric strong lensing models for the cluster, and by assuming well motivated scaling laws between the truncation radius s and the velocity dispersion sigma of a cluster galaxy we are able to derive sizes of the dark matter halos of cluster galaxies. For the scaling law expected for galaxies in the cluster environment (s propto sigma), we obtain s = 64^{+15}_{-14} (sigma / 220 km/s) kpc. For the scaling law used for galaxies in the field with s propto sigma^2 we find s = 66^{+18}_{-16} (sigma / 220 km/s)^2 kpc. Compared to halos of field galaxies, the cluster galaxy halos in Abell 1689 are strongly truncated.Comment: 12 pages, 4 figures. Accepted for publication in the Ap

Spanning Trees in Random Satisfiability Problems

Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning trees in the associated factor graph. We introduce a modified survey propagation algorithm which returns null edges of the factor graph and helps us to find satisfiable spanning trees. This allows us to study organization of satisfiable spanning trees in the space spanned by spanning trees.Comment: 12 pages, 5 figures, published versio

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

HST/ACS weak lensing analysis of the galaxy cluster RDCS 1252.9-2927 at z=1.24

We present a weak lensing analysis of one of the most distant massive galaxy cluster known, RDCS 1252.9-2927 at z=1.24, using deep images from the Advanced Camera for Survey (ACS) on board the Hubble Space Telescope (HST). By taking advantage of the depth and of the angular resolution of the ACS images, we detect for the first time at z>1 a clear weak lensing signal in both the i (F775W) and z (F850LP) filters. We measure a 5-\sigma signal in the i band and a 3-\sigma signal in the shallower z band image. The two radial mass profiles are found to be in very good agreement with each other, and provide a measurement of the total mass of the cluster inside a 1Mpc radius of M(<1Mpc) = (8.0 +/- 1.3) x 10^14 M_\odot in the current cosmological concordance model h =0.70, \Omega_m=0.3, \Omega_\Lambda=0.7, assuming a redshift distribution of background galaxies as inferred from the Hubble Deep Fields surveys. A weak lensing signal is detected out to the boundary of our field (3' radius, corresponding to 1.5Mpc at the cluster redshift). We detect a small offset between the centroid of the weak lensing mass map and the brightest cluster galaxy, and we discuss the possible origin of this discrepancy. The cumulative weak lensing radial mass profile is found to be in good agreement with the X-ray mass estimate based on Chandr and XMM-Newton observations, at least out to R_500=0.5Mpc.Comment: 38 pages, ApJ in press. Full resolution images available at http://www.eso.org/~prosati/RDCS1252/Lombardi_etal_accepted.pd