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The Hubble Frontier Fields data, along with multiple data sets obtained by other telescopes, have provided some of the most extensive constraints on cluster lenses to date. Multiple lens modelling teams analyzed the fields and made public a number of deliverables. By comparing these results, we can then undertake a unique and vital test of the state of cluster lens modelling. Specifically, we see how well the different teams can reproduce similar magnifications and mass profiles. We find that the circularly averaged mass profiles of the fields are remarkably constrained (scatter |$\lt 5{{\ \rm per\ cent}}$|⁠) at distances of 1 arcmin from the cluster core, yet magnifications can vary significantly. Averaged across the six fields, we find a bias of −6 per  cent (−17 per cent) and a scatter of ∼40 per cent (∼65 per cent) at a modest magnification of 3 (10). Statistical errors reported by individual teams are often significantly smaller than the differences among all the teams, indicating the importance of continued systematics studies in cluster lensing. [ABSTRACT FROM AUTHOR]

Cluster lensing has become an important tool in the search for high-redshift galaxies through its ability to magnify sources. In order to determine the intrinsic properties of these galaxies, lensing mass models must be constructed to determine the magnification of the images. These models are traditionally 2D, focusing on the mass within the cluster and either ignoring or approximating any contribution from line-of-sight galaxies. In this paper, we present the first full set of 3D mass models of the six Hubble Frontier Fields and use them to test for systematic biases in magnifications due to using the traditional 2D approach. We find that omitting foreground or background galaxies causes image position offsets between 0.1 and 0.4 arcsec, a non-negligible fraction of the typical 0.3–0.7 arcsec residuals of current state-of-the-art models. We also find that median image magnifications can shift by up to 6 per cent, though it is dependent on the field. This can be alleviated in some cases by approximating the mass in the lensing plane, but a 5 per cent magnification bias still exists in other cases; image position offsets are also improved, but are still present at 0.10 arcsec. [ABSTRACT FROM AUTHOR]

Gravitational lens modelling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the source and constraining lens model parameters. Using test data for four canonical lens configurations, we explore statistical and systematic uncertainties associated with gridding, source regularization, interpolation errors, noise, and telescope pointing. Specifically, we compare two gridding schemes in the source plane: a fully adaptive grid that follows the lens mapping but is irregular, and an adaptive Cartesian grid. We also consider regularization schemes that minimize derivatives of the source (using two finite difference methods) and introduce a scheme that minimizes deviations from an analytic source profile. Careful choice of gridding and regularization can reduce ‘discreteness noise’ in the χ2 surface that is inherent in the pixel-based methodology. With a gridded source, some degree of interpolation is unavoidable, and errors due to interpolation need to be taken into account (especially for high signal-to-noise data). Different realizations of the noise and telescope pointing lead to slightly different values for lens model parameters, and the scatter between different ‘observations’ can be comparable to or larger than the model uncertainties themselves. The same effects create scatter in the lensing magnification at the level of a few per cent for a peak signal-to-noise ratio of 10, which decreases as the data quality improves. [ABSTRACT FROM PUBLISHER]

In strong gravitational lens systems, the light bending is usually dominated by one main galaxy, but may be affected by other mass along the line of sight (LOS). Shear and convergence can be used to approximate the contributions from less significant perturbers (e.g. those that are projected far from the lens or have a small mass), but higher order effects need to be included for objects that are closer or more massive. We develop a framework for multiplane lensing that can handle an arbitrary combination of tidal planes treated with shear and convergence and planes treated exactly (i.e. including higher order terms). This framework addresses all of the traditional lensing observables including image positions, fluxes, and time delays to facilitate lens modelling that includes the non-linear effects due to mass along the LOS. It balances accuracy (accounting for higher order terms when necessary) with efficiency (compressing all other LOS effects into a set of matrices that can be calculated up front and cached for lens modelling). We identify a generalized multiplane mass sheet degeneracy, in which the effective shear and convergence are sums over the lensing planes with specific, redshift-dependent weighting factors. [ABSTRACT FROM PUBLISHER]

ABSTRACT We investigate the properties of dark matter substructure in the gravitational lens HE 0435−1223 ( zl=0.455) via its effects on the positions and flux ratios of the quadruply imaged background quasar ( zs= 1.689). We start with a smooth mass model, add individual, truncated isothermal clumps near the lensed images and use the Bayesian evidence to compare the quality of different models. Compared with smooth models, models with at least one clump near image A are strongly favoured. The mass of this clump within its Einstein radius is log10( MAEin) = 7.65+0.87− 0.84 (in units of h−170 M⊙). The Bayesian evidence provides weaker support for a second clump near image B, with log10( MBEin) = 6.55+1.01− 1.51. We also examine models with a full population of substructure, and find the mass fraction in substructure at the Einstein radius to be fsub> rsim 0.000 77, assuming the total clump masses follow a mass function d N/d M∝ M−1.9 over the range M= 107-1010 M⊙. Few-clump and population models produce similar Bayesian evidence values, so neither type of model is objectively favoured. [ABSTRACT FROM AUTHOR]

Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the parameter space. I study the statistical uncertainty in the evidence computed with nested sampling. I examine the uncertainty estimator from Skilling and introduce a new estimator based on a detailed analysis of the statistical properties of nested sampling. Both perform well in test cases and make it possible to obtain the statistical uncertainty in the evidence with no additional computational cost. [ABSTRACT FROM AUTHOR]

In strong gravitational lensing, the multiple images we see correspond to light rays that leave the source in slightly different directions. If the source emission is anisotropic, the images may differ from conventional lensing predictions (which assume isotropy). To identify scales on which source anisotropy may be important, we study the angle δ between the light rays emerging from the source, for different lensing configurations. If the lens has a power-law profile , the angle δ initially increases with lens redshift and then either diverges (for a steep profile ), remains constant (for an isothermal profile ), or vanishes (for a shallow profile ) as . The scaling with lens mass is roughly . The results for an Navarro–Frenk–White (NFW) profile are qualitatively similar to those for a shallow power law, with δ peaking at about half the redshift of the source (not half the distance). In practice, beaming could modify the statistics of beamed sources lensed by massive clusters: for an opening angle , there is a probability as high as that one of the lensed images may be missed (for ). Differential absorption within active galactic nuclei (AGNs) could modify the flux ratios of AGNs lensed by clusters; a sample of AGNs lensed by clusters could provide further constraints on the sizes of absorbing regions. Source anisotropy is not likely to be a significant effect in galaxy-scale strong lensing. [ABSTRACT FROM AUTHOR]

Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton, Gaudi & Petters, this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies. [ABSTRACT FROM AUTHOR]

We study microlensing of the faint images that form close to the centres of strong gravitational lens galaxies. These central images, which have finally begun to yield to observations, naturally appear in dense stellar fields and may be particularly sensitive to fine granularity in the mass distribution. The microlensing magnification maps for overfocused (i.e. demagnified) images differ strikingly from those for magnified images. In particular, the familiar ‘fold’ and ‘cusp’ features of maps for magnified images are only present for certain values of the fraction f of the surface mass density contained in stars. For central images, the dispersion in microlensing magnifications is generally larger than for normal (minimum and saddle) images, especially when the source is comparable to or larger than the stellar Einstein radius. The dispersion depends in a complicated way on f; this behaviour may hold the key to using microlensing as a probe of the relative densities of stars and dark matter in the cores of distant galaxies. Quantitatively, we predict that the central image C in PMN J1632−0033 has a magnification dispersion of 0.6 mag for , or 0.3 mag for . For comparison, the dispersions are 0.5–0.6 mag for image B and 0.05–0.1 mag for image A, if ; and just 0.1 mag for B and 0.008 mag for A if . (The dispersions can be extrapolated to larger sources sizes as .) Thus, central images are more susceptible than other lensed images to microlensing and hence good probes for measuring source sizes. [ABSTRACT FROM AUTHOR]

Microlensing promises to be a powerful tool for studying distant galaxies and quasars. As the data and models improve, there are systematic effects that need to be explored. Quasar continuum and broad-line regions may respond differently to microlensing due to their different sizes; to understand this effect, we study microlensing of finite sources by a mass function of stars. We find that microlensing is insensitive to the slope of the mass function but does depend on the mass range. For negative-parity images, diluting the stellar population with dark matter increases the magnification dispersion for small sources and decreases it for large sources. This implies that the quasar continuum and broad-line regions may experience very different microlensing in negative-parity lensed images. We confirm earlier conclusions that the surface brightness profile and geometry of the source have little effect on microlensing. Finally, we consider non-circular sources. We show that elliptical sources that are aligned with the direction of shear have larger magnification dispersions than sources with perpendicular alignment, an effect that becomes more prominent as the ellipticity increases. Elongated sources can lead to more rapid variability than circular sources, which raises the prospect of using microlensing to probe source shape. [ABSTRACT FROM AUTHOR]

Flux ratio ‘anomalies’ in quadruply imaged gravitational lenses can be explained with galactic substructure of the sort predicted by ΛCDM, but the strength and uniqueness of that hypothesis need to be further assessed. A good way to do that is to use the physical scale associated with the size of the source quasar, and its dependence on wavelength. We develop a toy model to study finite source effects in substructure lensing. Treating substructure as a singular isothermal sphere allows us to compute the images of a finite source analytically, and then to explore how the image configurations and magnifications depend on source position and size. Although simplified, our model yields instructive general principles: image positions and magnifications are basically independent of source size until the source is large enough to intersect a substructure caustic; even sources that are much larger than the substructure Einstein radius can be perturbed at a detectable level; and, most importantly, there is a tremendous amount to be learned from comparing image positions and magnifications at wavelengths that correspond to different source sizes. In a separate analysis, we carefully study four observed radio lenses to determine which of the images are anomalous. In B0712+472, the evidence for a radio flux ratio anomaly is marginal, but if the anomaly is real then image C is probably the culprit. In B1422+231, the anomaly is in image A. Interestingly, B2045+265 and B1555+375 both appear to have two anomalous images. Coincidentally, in each system one of the anomalies is in image C, and the other is in either image A or image B (both possibilities lead to acceptable models). It remains to be seen whether ΛCDM predicts enough substructure to explain multiple anomalies in multiple lenses. When we finally join our modelling results and substructure theory, we obtain lower bounds on the masses of the substructures responsible for the observed anomalies. The mass bounds are broadly consistent with expectations for ΛCDM. Perhaps more importantly, we outline various systematic effects in the mass bounds; poor knowledge of whether the substructure lies within the main lens galaxy or elsewhere along the line of sight appears to be the dominant systematic. [ABSTRACT FROM AUTHOR]

We study the impact of lens galaxy environments on the image separation distribution of lensed quasars. We account for both environmental convergence and shear, using a joint distribution derived from galaxy formation models calibrated by galaxy–galaxy lensing data and number counts of massive elliptical galaxies. We find that the external field enhances lensing probabilities, particularly, at large image separations; the increase is ∼30 per cent at and ∼200 per cent at , when we adopt a power-law source luminosity function . The enhancement is mainly driven by convergence, which boosts both the image separation and magnification bias (for a fixed lens galaxy mass). These effects have been neglected in previous studies of lens statistics. Turning the problem around, we derive the posterior convergence and shear distributions and point out that they are strong functions of image separation; lens systems with larger image separations are more likely to lie in dense environments. [ABSTRACT FROM AUTHOR]

It has been known for over a decade that many four-image gravitational lenses exhibit anomalous radio flux ratios. These anomalies can be explained by adding a clumpy cold dark matter (CDM) component to the background galactic potential of the lens. As an alternative, Evans & Witt (2003) recently suggested that smooth multipole perturbations provide a reasonable alternative to CDM substructure in some but not all cases. We generalize their method in two ways so as to determine whether multipole models can explain highly anomalous systems. We carry the multipole expansion to higher order, and also include external tidal shear as a free parameter. Fitting for the shear proves crucial to finding a physical (positive-definite density) model. For B1422+231, working to order (and including shear) yields a model that is physical but implausible. Going to higher order reduces global departures from ellipticity, but at the cost of introducing small-scale wiggles in proximity to the bright images. These localized undulations are more pronounced in B2045+265, where multipoles are required to smooth out large-scale deviations from elliptical symmetry. Such modes surely cannot be taken at face value; they must indicate that the models are trying to reproduce some other sort of structure. Our formalism naturally finds models that fit the data exactly, but we use B0712+472 to show that measurement uncertainties have little effect on our results. Finally, we consider the system B1933+503, where two sources are lensed by the same foreground galaxy. The additional constraints provided by the images of the second source render the multipole model unphysical. We conclude that external shear must be taken into account to obtain plausible models, and that a purely smooth angular structure for the lens galaxy does not provide a viable alternative to the prevailing CDM clump hypothesis. [ABSTRACT FROM AUTHOR]

Studies of strong gravitational lensing in current and upcoming wide and deep photometric surveys, and of stellar kinematics from (integral-field) spectroscopy at increasing redshifts, promise to provide valuable constraints on galaxy density profiles and shapes. However, both methods are affected by various selection and modelling biases, which we aim to investigate in a consistent way. In this first paper in a series, we develop a flexible but efficient pipeline to simulate lensing by realistic galaxy models. These galaxy models have separate stellar and dark matter components, each with a range of density profiles and shapes representative of early-type, central galaxies without significant contributions from other nearby galaxies. We use Fourier methods to calculate the lensing properties of galaxies with arbitrary surface density distributions, and Monte Carlo methods to compute lensing statistics such as point-source lensing cross-sections. Incorporating a variety of magnification bias modes lets us examine different survey limitations in image resolution and flux. We rigorously test the numerical methods for systematic errors and sensitivity to basic assumptions. We also determine the minimum number of viewing angles that must be sampled in order to recover accurate orientation-averaged lensing quantities. We find that for a range of non-isothermal stellar and dark matter density profiles typical of elliptical galaxies, the combined density profile and corresponding lensing properties are surprisingly close to isothermal around the Einstein radius. The converse implication is that constraints from strong lensing and/or stellar kinematics, which are indeed consistent with isothermal models near the Einstein radius, cannot trivially be extrapolated to smaller and larger radii. [ABSTRACT FROM AUTHOR]

Many current and future astronomical surveys will rely on samples of strong gravitational lens systems to draw conclusions about galaxy mass distributions. We use a new strong lensing pipeline (presented in Paper I of this series) to explore selection biases that may cause the population of strong lensing systems to differ from the general galaxy population. Our focus is on point-source lensing by early-type galaxies with two mass components (stellar and dark matter) that have a variety of density profiles and shapes motivated by observational and theoretical studies of galaxy properties. We seek not only to quantify but also to understand the physics behind selection biases related to: galaxy mass, orientation and shape; dark matter profile parameters such as inner slope and concentration; and adiabatic contraction. We study how all of these properties affect the lensing Einstein radius, total cross-section, quad/double ratio and image separation distribution, with a flexible treatment of magnification bias to mimic different survey strategies. We present our results for two families of density profiles: cusped and deprojected Sérsic models. While we use fixed lens and source redshifts for most of the analysis, we show that the results are applicable to other redshift combinations, and we also explore the physics of how our results change for very different redshifts. We find significant (factors of several) selection biases with mass; orientation, for a given galaxy shape at fixed mass; cusped dark matter profile inner slope and concentration; concentration of the stellar and dark matter deprojected Sérsic models. Interestingly, the intrinsic shape of a galaxy does not strongly influence its lensing cross-section when we average over viewing angles. Our results are an important first step towards understanding how strong lens systems relate to the general galaxy population. [ABSTRACT FROM AUTHOR]

We report Atacama Large Millimeter/Submillimeter Array (ALMA) observations of the dust continuum and [C ii ] emission of the host galaxy of J0439+1634, a gravitationally lensed quasar at z = 6.5. Gravitational lensing boosts the source-plane resolution to ∼0.″15 (∼0.8 kpc). The lensing model derived from the ALMA data is consistent with the fiducial model in Fan et al. based on HST imaging. The host galaxy of J0439+1634 can be well-fitted by a Sérsic profile consistent with an exponential disk, both in the far-infrared (FIR) continuum and the [C ii ] emission. The overall magnification is 4.53 ± 0.05 for the continuum and 3.44 ± 0.05 for the [C ii ] line. The host galaxy of J0439+1634 is a compact ultraluminous infrared galaxy, with a total star formation rate (SFR) of 1.56 × 103M⊙ yr−1 after correcting for lensing and an effective radius of 0.74 kpc. The resolved regions in J0439+1634 follow the "[C ii ] deficit," where the [C ii ]-to-FIR ratio decreases with FIR surface brightness. The reconstructed velocity field of J0439+1634 appears to be rotation-like. The maximum line-of-sight rotation velocity is 130 km s−1 at a radius of 2 kpc. However, our data cannot be fit by an axisymmetric thin rotating disk, and the inclination of the rotation axis, i, remains unconstrained. We estimate the dynamical mass of the host galaxy to be. J0439+1634 is likely to have a high gas-mass fraction and an oversized SMBH compared to local relations. The SFR of J0439+1634 reaches the maximum possible values, and the SFR surface density is close to the highest value seen in any star-forming galaxy currently known in the universe. [ABSTRACT FROM AUTHOR]

In the cold dark matter (CDM) picture of structure formation, galaxy mass distributions are predicted to have a considerable amount of structure on small scales. Strong gravitational lensing has proven to be a useful tool for studying this small-scale structure. Much of the attention has been given to detecting individual dark matter subhaloes through lens modelling, but recent work has suggested that the full population of subhaloes could be probed using a power spectrum analysis. In this paper, we quantify the power spectrum of small-scale structure in simulated galaxies, with the goal of understanding theoretical predictions and setting the stage for using measurements of the power spectrum to test dark matter models. We use a sample of simulated galaxies generated from the galacticus semi-analytic model to determine the power spectrum distribution first in the CDM paradigm and then in a warm dark matter scenario. We find that a measurement of the slope and amplitude of the power spectrum on galaxy strong lensing scales (k ∼ 1 kpc−1) could be used to distinguish between CDM and alternate dark matter models, especially if the most massive subhaloes can be directly detected via gravitational imaging. [ABSTRACT FROM AUTHOR]

The free streaming length of dark matter particles determines the abundance of structure on sub-galactic scales. We present a statistical technique, amendable to any parametrization of subhalo density profile and mass function, to probe dark matter on these scales with quadrupole image lenses. We consider a warm dark matter particle with a mass function characterized by a normalization and free streaming scale m hm. We forecast bounds on dark matter warmth for 120–180 lenses, attainable with future surveys, at typical lens (source) redshifts of 0.5 (1.5) in early-type galaxies with velocity dispersions of  220–270 km s-1. We demonstrate that limits on m hm deteriorate rapidly with increasing uncertainty in image fluxes, underscoring the importance of precise measurements and accurate lens models. For our forecasts, we assume the deflectors in the lens sample do not exhibit complex morphologies, so we neglect systematic errors in their modelling. Omitting the additional signal from line-of-sight haloes, our constraints underestimate the true power of the method. Assuming cold dark matter, for a low normalization, corresponding to the destruction of all subhaloes within the host scale radius, we forecast 2σ bounds on m hm (thermal relic mass) of 107.5 (5.0), 108 (3.6), and |$10^{8.5} \ (2.7) \ {\rm M}_{\odot } \left(\rm {keV}\right)$| for flux errors of |$2{{\ \rm per\ cent}}$|⁠, |$4{{\ \rm per\ cent}}$|⁠, and |$8{{\ \rm per\ cent}}$|⁠. With a higher normalization, these constraints improve to 107.2 (6.6), 107.5 (5.3), and |$10^{7.8} \ (4.3) \ {\rm M}_{\odot } \left(\rm {keV}\right)$| with 120 systems. We are also able to measure the normalization of the mass function, which has implications for baryonic feedback models and tidal stripping. [ABSTRACT FROM AUTHOR]

Lines of sight with multiple projected cluster-scale gravitational lenses have high total masses and complex lens plane interactions that can boost the area of magnification, or étendue, making detection of faint background sources more likely than elsewhere. To identify these new “compound” cosmic telescopes, we have found directions in the sky with the highest integrated mass densities, as traced by the projected concentrations of luminous red galaxies (LRGs). We use new galaxy spectroscopy to derive preliminary magnification maps for two such lines of sight with total mass exceeding ∼3 × 1015M☼. From 1151 MMT Hectospec spectra of galaxies down to iAB = 21.2, we identify two to three group- and cluster-scale halos in each beam. These are well traced by LRGs. The majority of the mass in beam J085007.6+360428 (0850) is contributed by Zwicky 1953, a massive cluster at z = 0.3774, whereas beam J130657.5+463219 (1306) is composed of three halos with virial masses of 6 × 1014-2 × 1015M☼, one of which is A1682. The magnification maps derived from our mass models based on spectroscopy and Sloan Digital Sky Survey photometry alone display substantial étendue: the 68% confidence bands on the lens plane area with magnification exceeding 10 for a source plane of zs = 10 are [1.2, 3.8] arcmin2 for 0850 and [2.3, 6.7] arcmin2 for 1306. In deep Subaru Suprime-Cam imaging of beam 0850, we serendipitously discover a candidate multiply imaged V-dropout source at zphot = 5.03. The location of the candidate multiply imaged arcs is consistent with the critical curves for a source plane of z = 5.03 predicted by our mass model. Incorporating the position of the candidate multiply imaged galaxy as a constraint on the critical curve location in 0850 narrows the 68% confidence band on the lens plane area with μ > 10 and zs = 10 to [1.8, 4.2] arcmin2, an étendue range comparable to that of MACS 0717+3745 and El Gordo, two of the most powerful single cluster lenses known. The significant lensing power of our beams makes them powerful probes of reionization and galaxy formation in the early universe. [ABSTRACT FROM AUTHOR]

The best gravitational lenses for detecting distant galaxies are those with the largest mass concentrations and the most advantageous configurations of that mass along the line of sight. Our new method for finding such gravitational telescopes uses optical data to identify projected concentrations of luminous red galaxies (LRGs). LRGs are biased tracers of the underlying mass distribution, so lines of sight with the highest total luminosity in LRGs are likely to contain the largest total mass. We apply this selection technique to the Sloan Digital Sky Survey and identify the 200 fields with the highest total LRG luminosities projected within a 3.5 radius over the redshift range 0.1 ⩽ z ⩽ 0.7. The redshift and angular distributions of LRGs in these fields trace the concentrations of non-LRG galaxies. These fields are diverse; 22.5% contain one known galaxy cluster and 56.0% contain multiple known clusters previously identified in the literature. Thus, our results confirm that these LRGs trace massive structures and that our selection technique identifies fields with large total masses. These fields contain two to three times higher total LRG luminosities than most known strong-lensing clusters and will be among the best gravitational lensing fields for the purpose of detecting the highest redshift galaxies. [ABSTRACT FROM AUTHOR]

We present the discovery of a Type Ia supernova (SN) at redshift z = 1.914 from the CANDELS multi-cycle treasury program on the Hubble Space Telescope (HST). This SN was discovered in the infrared using the Wide- Field Camera 3, and it is the highest-redshift Type Ia SN yet observed. We classify this object as a SN Ia by comparing its light curve and spectrum with those of a large sample of Type Ia and core-collapse SNe. Its apparent magnitude is consistent with that expected from the ΛCDM concordance cosmology.We discuss the use of spectral evidence for classification of z > 1.5 SNe Ia using HST grism simulations, finding that spectral data alone can frequently rule out SNe II, but distinguishing between SNe Ia and SNe Ib/c can require prohibitively long exposures. In such cases, a quantitative analysis of the light curve may be necessary for classification. Our photometric and spectroscopic classification methods can aid the determination of SN rates and cosmological parameters from the full high-redshift CANDELS SN sample. [ABSTRACT FROM AUTHOR]

We investigate the gravitational lensing properties of lines of sight containing multiple cluster-scale halos, motivated by their ability to lens very high redshift (z ∼ 10) sources into detectability. We control for the total mass along the line of sight, isolating the effects of distributing the mass among multiple halos and of varying the physical properties of the halos. Our results show that multiple-halo lines of sight can increase the magnified source-plane region compared to the single cluster lenses typically targeted for lensing studies and thus are generally better fields for detecting very high redshift sources. The configurations that result in optimal lensing cross sections benefit from interactions between the lens potentials of the halos when they overlap somewhat on the sky, creating regions of high magnification in the source plane not present when the halos are considered individually. The effect of these interactions on the lensing cross section can even be comparable to changing the total mass of the lens from 1015M☼ to 3 × 1015M☼. The gain in lensing cross section increases as the mass is split into more halos, provided that the lens potentials are projected close enough to interact with each other. A nonzero projected halo angular separation, equal halo mass ratio, and high projected halo concentration are the best mass configurations, whereas projected halo ellipticity, halo triaxiality, and the relative orientations of the halos are less important. Such high-mass, multiple-halo lines of sight exist in the Sloan Digital Sky Survey. [ABSTRACT FROM AUTHOR]

Gravitational lensing is a powerful tool for the study of the distribution of dark matter in the Universe. The cold-dark-matter model of the formation of large-scale structures (that is, clusters of galaxies and even larger assemblies) predicts the existence of quasars gravitationally lensed by concentrations of dark matter so massive that the quasar images would be split by over 7?arcsec. Numerous searches for large-separation lensed quasars have, however, been unsuccessful. All of the roughly 70 lensed quasars known, including the first lensed quasar discovered, have smaller separations that can be explained in terms of galaxy-scale concentrations of baryonic matter. Although gravitationally lensed galaxies with large separations are known, quasars are more useful cosmological probes because of the simplicity of the resulting lens systems. Here we report the discovery of a lensed quasar, SDSS J1004 + 4112, which has a maximum separation between the components of 14.62?arcsec. Such a large separation means that the lensing object must be dominated by dark matter. Our results are fully consistent with theoretical expectations based on the cold-dark-matter model. [ABSTRACT FROM AUTHOR]

Certain configurations of massive structures projected along the line of sight (LOS) maximize the number of detections of gravitationally lensed z ∼ 10 galaxies. We characterize such LOSs with the étendue σμ, the area in the source plane magnified over some threshold μ. We use the Millennium I and Millennium XXL cosmological simulations to determine the frequency of high σμ beams on the sky, their properties, and efficient selection criteria. We define the best beams as having σμ > 3 > 2000 arcsec2, for a z ∼ 10 source plane, and predict 477 ± 21 such beams on the sky. The total mass in the beam and σμ > 3 are strongly correlated. After controlling for total mass, we find a significant residual correlation between σμ > 3 and the number of cluster-scale halos (>1014M☼h–1) in the beam. Beams with σμ > 3 > 2000 arcsec2, which should be best at lensing z ∼ 10 galaxies, are 10 times more likely to contain multiple cluster-scale halos than a single cluster-scale halo. Beams containing an A1689-like massive cluster halo often have additional structures along the LOS, including at least one additional cluster-scale (M200 > 1014M☼h–1) halo 28% of the time. Selecting beams with multiple, massive structures will lead to enhanced detection of the most distant and intrinsically faint galaxies. [ABSTRACT FROM AUTHOR]