Weak Lensing Mass Reconstruction Research Articles

Weak lensing mass reconstructions of the ESO Distant Cluster Survey

We present weak lensing mass reconstructions for the 20 high-redshift clusters in the ESO Distant Cluster Survey. The weak lensing analysis was performed on deep, 3-color optical images taken with VLT/FORS2, using a composite galaxy catalog with separate shape estimators measured in each passband. We find that the EDisCS sample is composed primarily of clusters that are less massive than those in current X-ray selected samples at similar redshifts, but that all of the fields are likely to contain massive clusters rather than superpositions of low mass groups. We find that 7 of the 20 fields have additional massive structures which are not associated with the clusters and which can affect the weak lensing mass determination. We compare the mass measurements of the remaining 13 clusters with luminosity measurements from cluster galaxies selected using photometric redshifts and find evidence of a dependence of the cluster mass-to-light ratio with redshift. Finally we determine the noise level in the shear measurements for the fields as a function of exposure time and seeing and demonstrate that future ground-based surveys which plan to perform deep optical imaging for use in weak lensing measurements must achieve point-spread functions smaller than a median of FWHM.

Mass-sheet degeneracy: Fundamental limit on the cluster mass reconstruction from statistical (weak) lensing

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, weak lensing mass reconstructions are plagued by the so-called mass-sheet degeneracy--the surface mass density \kappa of the cluster can be determined only up to a degeneracy transformation \kappa \to \kappa' = \lambda \kappa + (1 -\lambda), where \lambda is an arbitrary constant. This transformation fundamentally limits the accuracy of cluster mass determinations if no further assumptions are made. We describe here a method to break the mass-sheet degeneracy in weak lensing mass maps using distortion and redshift information of background galaxies and illustrate this by two simple toy models. Compared to other techniques proposed in the past, it does not rely on any assumptions on cluster potential; it can be easily applied to non-parametric mass-reconstructions and no assumptions on boundary conditions have to be made. In addition it does not make use of weakly constrained information (such as the source number counts, used in the magnification effect). Our simulations show that we are effectively able to break the mass-sheet degeneracy for supercritical lenses, but that for undercritical lenses the mass-sheet degeneracy is very difficult to be broken, even under idealised conditions.

Weak‐Lensing Mass Reconstruction of the Interacting Cluster 1E 0657−558: Direct Evidence for the Existence of Dark Matter

We present a weak-lensing mass reconstruction of the interacting cluster 1E 0657-558, in which we detect both the main cluster and a subcluster. The subcluster is identified as a smaller cluster that has just undergone initial infall and pass-through of the primary cluster and has been previously identified in both optical surveys and X-ray studies. The X-ray gas has been separated from the galaxies by ram pressure-stripping during the pass-through. The detected mass peak is located between the X-ray peak and galaxy concentration, although the position is consistent with the galaxy centroid within the errors of the mass reconstruction. We find that the mass peak for the main cluster is in good spatial agreement with the cluster galaxies and is offset from the X-ray halo at 3.4 σ significance, and we determine that the mass-to-light ratios of the two components are consistent with those of relaxed clusters. The observed offsets of the lensing mass peaks from the peaks of the dominant visible mass component (the X-ray gas) directly demonstrate the presence, and dominance, of dark matter in this cluster. This proof of dark matter existence holds true even under the assumption of modified Newtonian dynamics (MOND); based on the observed gravitational shear-optical light ratios and the mass peak-X-ray gas offsets, the dark matter component in a MOND regime would have a total mass that is at least equal to the baryonic mass of the system.

Searching for Dark Matter Halos in the Suprime-Cam 2 Square Degree Field

We report the first result of a weak gravitational lensing survey on a 2.1 deg2 Rc-band image taken with a wide-field camera (Suprime-Cam) on the prime focus of the 8.2 m Subaru Telescope. The weak lensing mass reconstruction is applied to the data to search for dark matter halos of cluster scale M ≥ 1014 M☉. The reconstructed convergence field is divided by 1 σ noise to obtain the signal-to-noise ratio (S/N) map of the detection. Local maxima and minima are searched on the S/N map, and the probability distribution function (PDF) of the peaks is created to compare with model predictions. We found excess over noise PDF created from the randomized realization on both the positive and negative sides. Negative peaks imply the presence of voids in the dark matter distribution, and this is the first report of the detection. Positive peaks, on the other hand, represent the dark matter halos, and the number count of the halos on the 2.1 deg2 image is 4.9 ± 2.3 for S/N > 5, where the Gaussian smoothing radius of the convergence map is 1'. The result is consistent with the prediction assuming the Press-Schechter mass function and the Navarro-Frenk-White halo profile under the cluster-normalized cold dark matter cosmology. Although the present statistics are not enough because of the limited field of view, this work demonstrates that dark matter halo count via weak lensing is a promising way to test the paradigm of structure formation and the cosmological model.

Weak Gravitational Lensing by the Nearby Cluster Abell 3667.

We present two weak lensing reconstructions of the nearby (zcl=0.055) merging cluster Abell 3667, based on observations taken approximately 1 yr apart under different seeing conditions. This is the lowest redshift cluster with a weak lensing mass reconstruction to date. The reproducibility of features in the two mass maps demonstrates that weak lensing studies of low-redshift clusters are feasible. These data constitute the first results from an X-ray luminosity-selected weak lensing survey of 19 low-redshift (z<0.1) southern clusters.

Aperture multipole moments from weak gravitational lensing

The projected mass of a gravitational lens inside (circular) apertures can be derived from the measured shear inside an annulus which is caused by the tidal field of the deflecting mass distribution. Here we show that also the multipoles of the two-dimensional mass distribution can be derived from the shear in annuli. We derive several expressions for these mass multipole moments in terms of the shear, which allow large flexibility in the choice of a radial weight function. In contrast to determining multipole moments from weak-lensing mass reconstructions, this approach allows to quantify the signal-to-noise ratio of the multipole moments directly from the observed galaxy ellipticities, and thus to estimate the significance of the multipole detection. Radial weight functions can therefore be chosen such as to optimize the significance of the detection given an assumed radial mass profile. Application of our formulae to numerically simulated clusters demonstrates that the quadrupole moment of realistic cluster models can be detected with high signal-to-noise ratio S/N; in about 85 per cent of the simulated cluster fields S/N >~ 3. We also show that the shear inside a circular annulus determines multipole moments inside and outside the annulus. This is relevant for clusters whose central region is too bright to allow the observation of the shear of background galaxies, or which extend beyond the CCD. We also generalize the aperture mass equation to the case of `radial' weight functions which are constant on arbitrarily-shaped curves which are not necessarily self-similar.