We present results from a comprehensive lensing analysis in HST data, of the complete Cluster Lensing And Supernova survey with Hubble (CLASH) cluster sample. We identify new multiple-images previously undiscovered, allowing improved or first constraints on the cluster inner mass distributions and profiles. We combine these strong-lensing constraints with weak-lensing shape measurements within the HST FOV to jointly constrain the mass distributions. The analysis is performed in two different common parameterizations (one adopts light-traces-mass for both galaxies and dark matter while the other adopts an analytical, elliptical NFW form for the dark matter), to provide a better assessment of the underlying systematics -which is most important for deep, cluster-lensing surveys, especially when studying magnified high-redshift objects. We find that the typical (median), relative systematic differences throughout the central FOV are ∼ 40% in the (dimensionless) mass density, κ, and ∼ 20% in the magnification, µ. We show maps of these differences for each cluster, as well as the mass distributions, critical curves, and 2D integrated mass profiles. For the Einstein radii (z s = 2) we find that all typically agree within 10% between the two models, and Einstein masses agree, typically, within ∼ 15%. At larger radii, the total projected, 2D integrated mass profiles of the two models, within r ∼ 2 , differ by ∼ 30%. Stacking the surface-density profiles of the sample from the two methods together, we obtain an average slope of d log(Σ)/d log(r) ∼ −0.64 ± 0.1, in the radial range [5,350] kpc. Lastly, we also characterize the behavior of the average magnification, surface density, and shear differences between the two models, as a function of both the radius from the center, and the best-fit values of these quantities. All mass models and magnification maps are made publicly available for the community.

We derive an accurate mass distribution of the galaxy cluster MACS J1206.2-0847 (z = 0.439) from a combined weak-lensing distortion, magnification, and strong-lensing analysis of wide-field Subaru BV R c I c z ′ imaging and our recent 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble (CLASH) program. We find good agreement in the regions of overlap between several weak and strong lensing mass reconstructions using a wide variety of modeling methods, ensuring consistency. The Subaru data reveal the presence of a surrounding large scale structure with the major axis running approximately north-west south-east (NW-SE), aligned with the cluster and its brightest galaxy shapes, showing elongation with a ∼ 2 : 1 axis ratio in the plane of the sky. Our full-lensing mass profile exhibits a shallow profile slope d ln Σ/d ln R ∼ −1 at cluster outskirts (R > ∼ 1 Mpc h −1 ), whereas the mass distribution excluding the NW-SE excess regions steepens further out, well described by the Navarro-Frenk-White form. Assuming a spherical halo, we obtain a virial mass M vir = (1.1±0.2±0.1)×10 15 M ⊙ h −1 and a halo concentration c vir = 6.9±1.0±1.2 (c vir ∼ 5.7 when the central 50 kpc h −1 is excluded), which falls in the range 4 < ∼ c < ∼ 7 of average c(M, z) predictions for relaxed clusters from recent Λ cold dark matter simulations. Our full lensing results are found to be in agreement with X-ray mass measurements where the data overlap, and when combined with Chandra gas mass measurements, yield a cumulative gas mass fraction of 13.7 +4.5 −3.0 % at 0.7 Mpc h −1 (≈ 1.7 r 2500 ), a typical value observed for high mass clusters.

We perform a strong lensing analysis of the merging galaxy cluster MACS J0416.1−2403 (M0416; z = 0.42) in recent CLASH/HST observations. We identify 70 new multiple images and candidates of 23 background sources in the range 0.7 z phot 6.14 including two probable high-redshift dropouts, revealing a highly elongated lens with axis ratio 5:1, and a major axis of ∼100 (z s ∼ 2). Compared to other well-studied clusters, M0416 shows an enhanced lensing efficiency. Although the critical area is not particularly large ( 0.6 ; z s ∼ 2), the number of multiple images, per critical area, is anomalously high. We calculate that the observed elongation boosts the number of multiple images, per critical area, by a factor of ∼2.5×, due to the increased ratio of the caustic area relative to the critical area. Additionally, we find that the observed separation between the two main mass components enlarges the critical area by a factor of ∼2. These geometrical effects can account for the high number (density) of multiple images observed. We find in numerical simulations that only ∼4% of the clusters (with M vir 6 × 10 14 h −1 M ) exhibit critical curves as elongated as in M0416.

In the strong lensing regime non-parametric lens models struggle to achieve sufficient angular resolution for a meaningful derivation of the central cluster mass distribution. The problem lies mainly with cluster members which perturb lensed images and generate additional images, requiring high resolution modelling, even though we mainly wish to understand the relatively smooth cluster component. In practice the required resolution for a fully non-parametric mass map is not achievable because the separation between lensed images is several times larger than the deflection angles by member galaxies, even for the most impressive data. Here we bypass this limitation by incorporating a simple physical prior for member galaxies, using their observed positions and their luminosity scaled masses. This high frequency contribution is added to a relatively coarse Gaussian pixel grid used to model the more smoothly varying cluster mass distribution, extending our established WSLAP code (Diego et al. 2007). We test this new code (WSLAP+) with an empirical simulation based on A1689, using all the pixels belonging to multiply-lensed images and the observed member galaxies. Dealing with the cluster members this way leads to stable convergent solutions, without resorting to regularization, reproducing well smooth input cluster distributions and substructures. We highlight the ability of this method to recover "dark" sub-components and other differences between the distributions of cluster mass and member galaxies. Such anomalies can provide clues to the nature of invisible dark matter, but are hard to discover using parametrized models where substructures are modelled on the basis of the visible data. With our increased resolution and stability we show, for the first time, that non-parametric models can be made sufficiently precise to locate multiply-lensed systems, thereby achieving fully self-consistent solutions without reliance on input systems from less objective means.

The cosmic microwave background (CMB) is affected by the total radiation density around the time of decoupling. At that epoch, neutrinos comprised a significant fraction of the radiative energy, but there could also be a contribution from primordial gravitational waves with frequencies greater than ∼ 10 −15 Hz. If this cosmological gravitational wave background (CGWB) were produced under adiabatic initial conditions, its effects on the CMB and matter power spectrum would mimic massless non-interacting neutrinos. However, with homogenous initial conditions, as one might expect from certain models of inflation, pre big-bang models, phase transitions and other scenarios, the effect on the CMB would be distinct. We present updated observational bounds for both initial conditions using the latest CMB data at small scales from the South Pole Telescope (SPT) in combination with Wilkinson Microwave Anisotropy Probe (WMAP), current measurements of the baryon acoustic oscillations, and the Hubble parameter. With the inclusion of the data from SPT the adiabatic bound on the CGWB density is improved by a factor of 1.7 to 10 6 Ωgwh 2 8.7 at the 95% confidence level (C. L.), with weak evidence in favor of an additional radiation component consistent with previous analyses. The constraint can be converted into an upper limit on the tension of horizon-sized cosmic strings that could generate this gravitational wave component, with Gµ 2 × 10 −7 at 95% C. L., for string tension Gµ. The homogeneous bound improves by a factor of 3.5 to 10 6 Ωgwh 2 1.0 at 95% C. L., with no evidence for such a component from current data.