Gravitational lensing by clusters of galaxies offers a powerful probe of their structure and mass distribution. Deriving a lens magnification map for a galaxy cluster is a classic inversion problem and many methods have been developed over the past two decades to solve it. Several research groups have developed techniques independently to map the predominantly dark matter distribution in cluster lenses. While these methods have all provided remarkably high precision mass maps, particularly with exquisite imaging data from the Hubble Space Telescope (HST), the reconstructions themselves have never been directly compared. In this paper, we report the results of comparing various independent lens modeling techniques employed by individual research groups in the community. Here we present for the first time a detailed and robust comparison of methodologies for fidelity, accuracy and precision. For this collaborative exercise, the lens modeling community was provided simulated cluster images -of two clusters Ares and Hera -that mimic the depth and resolution of the ongoing HST Frontier Fields. The results of the submitted reconstructions with the un-blinded true mass profile of these two clusters are presented here. Parametric, free-form and hybrid techniques have been deployed by the participating groups and we detail the strengths and trade-offs in accuracy and systematics that arise for each methodology. We note in conclusion that lensing reconstruction methods produce reliable mass distributions that enable the use of clusters as extremely valuable astrophysical laboratories and cosmological probes.

Galaxy cluster Abell 3827 hosts the stellar remnants of four almost equally bright elliptical galaxies within a core of radius 10 kpc. Such corrugation of the stellar distribution is very rare, and suggests recent formation by several simultaneous mergers. We map the distribution of associated dark matter, using new Hubble Space Telescope imaging and VLT/MUSE integral field spectroscopy of a gravitationally lensed system threaded through the cluster core. We find that each of the central galaxies retains a dark matter halo, but that (at least) one of these is spatially offset from its stars. The best-constrained offset is 1.62 +0.47 −0.49 kpc, where the 68% confidence limit includes both statistical error and systematic biases in mass modelling. Such offsets are not seen in field galaxies, but are predicted during the long infall to a cluster, if dark matter self-interactions generate an extra drag force. With such a small physical separation, it is difficult to definitively rule out astrophysical effects operating exclusively in dense cluster core environments -but if interpreted solely as evidence for self-interacting dark matter, this offset implies a cross-section σ DM /m ∼ (1.7 ± 0.7) × 10 −4 cm 2 /g ×(t infall /10 9 yrs) −2 , where t infall is the infall duration.

We detect a dip of 20-45% in the surface brightness and number counts of NVSS sources smoothed to a few degrees at the location of the WMAP cold spot. The dip has structure on scales of ∼ 1 • to 10 • . Together with independent all-sky wavelet analyses, our results suggest that the dip in extragalactic brightness and number counts and the WMAP cold spot are physically related, i.e., that the coincidence is neither a statistical anomaly nor a WMAP foreground correction problem. If the cold spot does originate from structures at modest redshifts, as we suggest, then there is no remaining need for non-Gaussian processes at the last scattering surface of the CMB to explain the cold spot. The late integrated Sachs-Wolfe effect, already seen statistically for NVSS source counts, can now be seen to operate on a single region. To create the magnitude and angular size of the WMAP cold spot requires a ∼ 140 Mpc radius completely empty void at z≤1 along this line of sight. This is far outside the current expectations of the concordance cosmology, and adds to the anomalies seen in the CMB.Subject headings: large-scale structure of the universe -cosmic microwave background -radio continuum: galaxies IntroductionThe detection of an extreme "cold spot" (Vielva et al. 2004) in the foreground-corrected WMAP images was an exciting but unexpected finding. At 4 • resolution, Cruz et al. (2005) determine an amplitude of -73 µK, which reduces to -20 µK at ∼10 • scales (Cruz et al. 1

A galaxy cluster acts as a cosmic telescope over background galaxies but also as a cosmic microscope magnifying the imperfections of the lens. The diverging magnification of lensing caustics enhances the microlensing effect of substructure present within the lensing mass. Fine-scale structure can be accessed as a moving background source brightens and disappears when crossing these caustics. The recent discovery of a distant lensed star near the Einstein radius of the galaxy cluster MACSJ1149.5+2223 allows the rare opportunity to reach subsolar-mass microlensing through a supercritical column of cluster matter. Here we compare these observations with high-resolution raytracing simulations that include stellar microlensing set by the observed intracluster starlight and also primordial black holes that may be responsible for the recently observed LIGO events. We explore different scenarios with microlenses from the intracluster medium and black holes, including primordial ones, and examine strategies to exploit these unique alignments. We find that the best constraints on the fraction of compact dark matter in the small-mass regime can be obtained in regions of the cluster where the intracluster medium plays a negligible role. This new lensing phenomenon should be widespread and can be detected within modest-redshift lensed galaxies so that the luminosity distance is not prohibitive for detecting individual magnified stars. High-cadence Hubble Space Telescope monitoring of several such optimal arcs will be rewarded by an unprecedented mass spectrum of compact objects that can contribute to uncovering the nature of dark matter.

Although high-resolution N-body simulations make robust empirical predictions for the density distribution within cold dark matter halos, these studies have yielded little physical insight into the origins of the distribution. We investigate the problem using analytic and semi-analytic approaches. Simple analytic considerations suggest that the inner slope of dark matter halos cannot be steeper than alpha=2 (rho ~ r^-alpha), with alpha=1.5-1.7 being a more realistic upper limit. Our analysis suggests that any number of effects, both real (angular momentum from tidal torques, secondary perturbations) and artificial (two-body interactions, the accuracy of the numerical integrator, round-off errors), will result in shallower slopes. We also find that the halos should exhibit a well-defined relation between r_peri/r_apo and j_theta/j_r. We derive this relation analytically and speculate that it may be "universal". Using a semi-analytic scheme based on Ryden & Gunn (1987), we further explore the relationship between the specific angular momentum distribution in a halo and its density profile. For now we restrict ourselves to halos that form primarily via nearly-smooth accretion of matter, and only consider the specific angular momentum generated by secondary perturbations associated with the cold dark matter spectrum of density fluctuations. Compared to those formed in N-body simulations, our ``semi-analytic'' halos are more extended, have flatter rotation curves and have higher specific angular momentum, even though we have not yet taken into account the effects of tidal torques. Whether the density profiles of numerical halos is indeed the result of loss in angular momentum outside the central region, and whether this loss is a feature of hierarchical merging and major mergers in particular, is under investigation.Comment: 50 pages, incl. 9 figs; accepted to Ap

For 18 well-observed gravitationally lensed QSOs, we compare new non-parametric mass profiles for the lensing galaxies with stellar-population models derived from published HST photometry. The large volume of parameter space searched -with respect to the possible star formation histories -allows us to infer robust estimates and uncertainties for the stellar masses. The most interesting results are: (1) the transition from little or no dark matter in the inner regions ( ∼ < r e ) to dark matter dominating on the ∼ 5r e scale (∼ 20kpc) is clearly seen in massive ellipticals; (2) Such a trend is not seen in lower-mass galaxies, so that the stellar content dominates the mass budget out to ∼ 5r e ; (3) the radial gradient in the dark-matter fraction for these intermediate redshift galaxies agrees with published data on nearby galaxies. This result can help reconcile the discrepancies found in recent estimates of dark matter in elliptical galaxies using different techniques (e.g. Planetary nebulae versus X-ray). The observed trend suggests the stellar component in massive galaxies extends further out in terms of the dark matter scale radius.

We present a simultaneous analysis of 10 galaxy lenses having time delay measurements. For each lens, we derive a detailed free-form mass map, with uncertainties, and with the additional requirement of a shared value of the Hubble parameter across all the lenses. We test the prior involved in the lens reconstruction against a galaxy-formation simulation. Assuming a concordance cosmology, we obtain .

We introduce and implement two novel ideas for modeling lensed quasars. The first idea is to require different lenses to agree about H 0 . This means that some models for one lens can be ruled out by data on a different lens. We explain using two worked examples. One example models 1115+080, 1608+656 (time-delay quads) and 1933+503 (a prospective time-delay system) all together, yielding time-delay predictions for the third lens and a 90%-confidence estimate of H 0 −1 = 14.6 +9.4 −1.7 Gyr (H 0 = 67 + 9 −26 km s −1 Mpc −1 ) assuming (Ω M = 0.3, Ω Λ = 0.7). The other example models the time-delay doubles 1520+530, 1600+434, 1830-211, and 2149-275, which gives H 0 −1 = 14.5 +3.3 −1.5 Gyr (H 0 = 67 + 8 −13 km s −1 Mpc −1 ). Our second idea is to write the whole modeling software as a highly interactive Java applet, which can be used both for coarse-grained results inside a browser and for fine-grained results on a workstation. Several obstacles come up in trying to implement a numerically-intensive method thus, but we overcome them.