Hubble Space Telescope Frontier Fields Research Articles

New Metrics to Probe the Dynamical State of Galaxy Clusters

We present new diagnostic metrics to probe the dynamical state of galaxy clusters. These novel metrics rely on the computation of the power spectra of the matter and gas distributions and their cross-correlation derived from cluster observations. This analysis permits us to cross-correlate the fluctuations in the matter distribution, inferred from high-resolution lensing mass maps derived from Hubble Space Telescope (HST) data, with those derived from the emitted X-ray surface brightness distribution of the hot intracluster medium from the Chandra X-ray Observatory. These methodological tools allow us to quantify with unprecedented resolution the coherence with which the gas traces the mass and interrogate the assumption that the gas is in hydrostatic equilibrium with the underlying gravitational potential. We characterize departures from equilibrium as a function of scale with a new gas-mass coherence parameter. The efficacy of these metrics is demonstrated by applying them to the analysis of two representative clusters known to be in different dynamical states: the massive merging cluster A2744, from the HST Frontier Fields sample, and the dynamically relaxed cluster A383, from the Cluster Lensing and Supernova Survey with the Hubble sample. Using lensing mass maps in combination with archival Chandra data, and simulated cluster analogs available from the OMEGA500 suite, we quantify the fluctuations in the mass and X-ray surface brightness and show that new insights into the dynamical state of the clusters can be obtained from our gas-mass coherence analysis.

Probing 3D Structure with a Large MUSE Mosaic: Extending the Mass Model of Frontier Field Abell 370

We present an updated strong-lensing analysis of the massive cluster Abell 370 (A370), continuing the work first presented in Lagattuta et al. (2017). In this new analysis, we take advantage of the deeper imaging data from the Hubble Space Telescope (HST) Frontier Fields program, as well as a large spectroscopic mosaic obtained with the Multi-Unit Spectroscopic Explorer (MUSE). Thanks to the extended coverage of this mosaic, we probe the full 3D distribution of galaxies in the field, giving us a unique picture of the extended structure of the cluster and its surroundings. Our final catalog contains 584 redshifts, representing the largest spectroscopic catalog of A370 to date. Constructing the model, we measure a total mass distribution that is quantitatively similar to our previous work -- though to ensure a low rms error in the model fit, we invoke a significantly large external shear term. Using the redshift catalog, we search for other bound groups of galaxies, which may give rise to a more physical interpretation of this shear. We identify three structures in narrow redshift ranges along the line of sight, highlighting possible infalling substructures into the main cluster halo. We also discover additional substructure candidates in low-resolution imaging at larger projected radii. More spectroscopic coverage of these regions (pushing close to the A370 virial radius) and more extended, high-resolution imaging will be required to investigate this possibility, further advancing the analysis of these interesting developments.

An Evaluation of 10 Lensing Models of the Frontier Fields Cluster MACS J0416.1-2403

Abstract Galaxy clusters can act as gravitational lenses and magnify the universe behind them, allowing us to see deep into the early universe. The Hubble Space Telescope Frontier Fields program uses six galaxy clusters imaged by Hubble to discover and study galaxies at z ∼ 5–10. Seven independent teams developed lens models and derived magnifications for each galaxy cluster, based on positional and redshift constraints from the best available data at the time. In this work we evaluate 10 models for MACS J0416.1-2403 that were made public in 2015 by contrasting them with new spectroscopic redshifts that were measured in 2016. We developed an independent comparison method that uses the source plane root-mean-square as a metric of lensing model performance. Our analysis quantifies the ability of models to predict unknown multiple images. We examine the source plane scatter of multiply imaged systems and explore the dependence of the scatter on the location and the redshift of the background sources. The analysis we present evaluates the performance of the different algorithms in the specific case of the MACS J0416.1-2403 models.

Globular cluster population of the HST Frontier Fields galaxy J07173724+3744224

We present the first measurement of the globular cluster population surrounding the elliptical galaxy J07173724+3744224 (z=0.1546). This galaxy is located in the foreground in the field-of-view of the Hubble Space Telescope (HST) Frontier Fields observations of galaxy cluster MACS J0717.5+3745 (z=0.5458). Based on deep HST ACS F435W, F606W, and F814W images, we find a total globular cluster population of N_tot = 3441 +/- 1416. Applying the appropriate extinction correction and filter transformation from ACS F814W to the Johnson V-band, we determine that the host galaxy has an absolute magnitude of M_V = -22.2. The specific frequency was found to be S_N = 4.5 +/- 1.8. The radial profile of the globular cluster system was best fit using a powerlaw of the form $\sigma\sim R^{-0.6}$, with the globular cluster population found to be more extended than the halo light of the host galaxy ($\sigma_{halo}\sim R^{-1.7}$). The F435W-F814W colour distribution suggests a bimodal population, with red globular clusters 1-3x more abundant than blue clusters. These results are consistent with the host elliptical galaxy J07173724+3744224 having formed its red metal-rich GCs in situ, with the blue metal-poor globular clusters accreted from low-mass galaxies.

Little Blue Dots in the Hubble Space Telescope Frontier Fields: Precursors to Globular Clusters?

Abstract Galaxies with stellar masses and specific star formation rates yr−1 were examined on images of the Hubble Space Telescope Frontier Field Parallels for Abell 2744 and MACS J0416.1-02403. They appear as unresolved “Little Blue Dots” (LBDs). They are less massive and have higher specific star formation rates (sSFRs) than “blueberries” studied by Yang et al. and higher sSFRs than “Blue Nuggets” studied by Tacchella et al. We divided the LBDs into three redshift bins and, for each, stacked the B435, V606, and I814 images convolved to the same stellar point-spread function (PSF). Their radii were determined from PSF deconvolution to be ∼80 to ∼180 pc. The high sSFRs suggest that their entire stellar mass has formed in only 1% of the local age of the universe. The sSFRs at similar epochs in local dwarf galaxies are lower by a factor of ∼100. Assuming that the star formation rate is for efficiency , gas mass M gas, and free-fall time, t ff, the gas mass and gas-to-star mass ratio are determined. This ratio exceeds 1 for reasonable efficiencies, and is likely to be ∼5 even with a high of 0.1. We consider whether these regions are forming today’s globular clusters. With their observed stellar masses, the maximum likely cluster mass is , but if star formation continues at the current rate for before feedback and gas exhaustion stop it, then the maximum cluster mass could become .

The Star Formation Main Sequence in the Hubble Space Telescope Frontier Fields

Abstract We investigate the relation between star formation rate (SFR) and stellar mass (M), i.e., the main sequence (MS) relation of star-forming galaxies, at in the first four Hubble Space Telescope (HST) Frontier Fields, on the basis of rest-frame UV observations. Gravitational lensing combined with deep HST observations allows us to extend the analysis of the MS down to at and at higher redshifts, a factor of ∼10 below most previous results. We perform an accurate simulation to take into account the effect of observational uncertainties and correct for the Eddington bias. This step allows us to reliably measure the MS and in particular its slope. While the normalization increases with redshift, we fit an unevolving and approximately linear slope. We nicely extend to lower masses the results of brighter surveys. Thanks to the large dynamic range in mass and by making use of the simulation, we analyzed any possible mass dependence of the dispersion around the MS. We find tentative evidence that the scatter decreases with increasing mass, suggesting a larger variety of star formation histories in low-mass galaxies. This trend agrees with theoretical predictions and is explained as either a consequence of the smaller number of progenitors of low-mass galaxies in a hierarchical scenario and/or of the efficient but intermittent stellar feedback processes in low-mass halos. Finally, we observe an increase in the SFR per unit stellar mass with redshift milder than predicted by theoretical models, implying a still incomplete understanding of the processes responsible for galaxy growth.

Thick Disks in the Hubble Space Telescope Frontier Fields

Abstract Thick disk evolution is studied using edge-on galaxies in two Hubble Space Telescope Frontier Field Parallels. The galaxies were separated into 72 clumpy types and 35 spiral types with bulges. Perpendicular light profiles in F435W, F606W, and F814W (B, V, and I) passbands were measured at 1 pixel intervals along the major axes and fitted to sech2 functions convolved with the instrument line spread function (LSF). The LSF was determined from the average point spread function of ∼20 stars in each passband and field, convolved with a line of uniform brightness to simulate disk blurring. A spread function for a clumpy disk was also used for comparison. The resulting scale heights were found to be proportional to galactic mass, with the average height for a 1010±0.5 M ⊙ galaxy at z = 2 ± 0.5 equal to 0.63 ± 0.24 kpc. This value is probably the result of a blend between thin and thick disk components that cannot be resolved. Evidence for such two-component structure is present in an inverse correlation between height and midplane surface brightness. Models suggest that the thick disk is observed best between the clumps, and there the average scale height is 1.06 ± 0.43 kpc for the same mass and redshift. A 0.63 ± 0.68 mag V − I color differential with height is also evidence for a mixture of thin and thick components.

The Frontier Fields lens modelling comparison project

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.

Hubble Frontier Fields: systematic errors in strong lensing models of galaxy clusters – implications for cosmography

Strong gravitational lensing by galaxy clusters is a fundamental tool to study dark matter and constrain the geometry of the Universe. Recently, the Hubble Space Telescope Frontier Fields programme has allowed a significant improvement of mass and magnification measurements but lensing models still have a residual root mean square between 0.2 arcsec and few arcsec- onds, not yet completely understood. Systematic errors have to be better understood and treated in order to use strong lensing clusters as reliable cosmological probes. We have analysed two simulated Hubble-Frontier-Fields-like clusters from the Hubble Frontier Fields Comparison Challenge, Ares and Hera. We use several estimators (relative bias on magnification, den- sity profiles, ellipticity and orientation) to quantify the goodness of our reconstructions by comparing our multiple models, optimized with the parametric software LENSTOOL , with the input models. We have quantified the impact of systematic errors arising, first, from the choice of different density profiles and configurations and, secondly, from the availability of con- straints (spectroscopic or photometric redshifts, redshift ranges of the background sources) in the parametric modelling of strong lensing galaxy clusters and therefore on the retrieval of cosmological parameters. We find that substructures in the outskirts have a significant im- pact on the position of the multiple images, yielding tighter cosmological contours. The need for wide-field imaging around massive clusters is thus reinforced. We show that competitive cosmological constraints can be obtained also with complex multimodal clusters and that photometric redshifts improve the constraints on cosmological parameters when considering a narrow range of (spectroscopic) redshifts for the sources.

The Frontier Fields: Survey Design and Initial Results

Abstract What are the faintest distant galaxies we can see with the Hubble Space Telescope (HST) now, before the launch of the James Webb Space Telescope? This is the challenge taken up by the Frontier Fields, a Director’s discretionary time campaign with HST and the Spitzer Space Telescope to see deeper into the universe than ever before. The Frontier Fields combines the power of HST and Spitzer with the natural gravitational telescopes of massive high-magnification clusters of galaxies to produce the deepest observations of clusters and their lensed galaxies ever obtained. Six clusters—Abell 2744, MACSJ0416.1-2403, MACSJ0717.5+3745, MACSJ1149.5+2223, Abell S1063, and Abell 370—have been targeted by the HST ACS/WFC and WFC3/IR cameras with coordinated parallel fields for over 840 HST orbits. The parallel fields are the second-deepest observations thus far by HST with 5σ point-source depths of ∼29th ABmag. Galaxies behind the clusters experience typical magnification factors of a few, with small regions magnified by factors of 10–100. Therefore, the Frontier Field cluster HST images achieve intrinsic depths of ∼30–33 mag over very small volumes. Spitzer has obtained over 1000 hr of Director’s discretionary imaging of the Frontier Field cluster and parallels in IRAC 3.6 and 4.5 μm bands to 5σ point-source depths of ∼26.5, 26.0 ABmag. We demonstrate the exceptional sensitivity of the HST Frontier Field images to faint high-redshift galaxies, and review the initial results related to the primary science goals.

Mapping substructure in the HST Frontier Fields cluster lenses and in cosmological simulations

We map the lensing-inferred substructure in the first three clusters observed by the Hubble Space Telescope Frontier Fields Initiative (HSTFF): Abell 2744 (z = 0.308), MACSJ0416, (z = 0.396) and MACSJ1149 (z = 0.543). Statistically resolving dark-matter subhaloes down to ~10^{9.5} solar masses, we compare the derived subhalo mass functions (SHMFs) to theoretical predictions from analytical models and with numerical simulations in a Lambda Cold Dark Matter (LCDM) cosmology. Mimicking our observational cluster member selection criteria in the HSTFF, we report excellent agreement in both amplitude and shape of the SHMF over four decades in subhalo mass (10^{9-13} solar masses). Projection effects do not appear to introduce significant errors in the determination of SHMFs from simulations. We do not find evidence for a substructure crisis, analogous to the missing satellite problem in the Local Group, on cluster scales, but rather excellent agreement of the count-matched HSTFF SHMF down to M_{sub halo}/M_{halo} ~ 10^{-5}. However, we do find discrepancies in the radial distribution of sub haloes inferred from HSTFF cluster lenses compared to determinations from simulated clusters. This suggests that although the selected simulated clusters match the HSTFF sample in mass, they do not adequately capture the dynamical properties and complex merging morphologies of these observed cluster lenses. Therefore, HSTFF clusters are likely observed in a transient evolutionary stage that is presently insufficiently sampled in cosmological simulations. The abundance and mass function of dark matter substructure in cluster lenses continues to offer an important test of the LCDM paradigm, and at present we find no tension between model predictions and observations.

GLOBULAR CLUSTERS, ULTRACOMPACT DWARFS, AND DWARF GALAXIES IN ABELL 2744 AT A REDSHIFT OF 0.308

ABSTRACT We report a photometric study of globular clusters (GCs), ultracompact dwarfs (UCDs), and dwarf galaxies in the giant merging galaxy cluster Abell 2744 at z = 0.308. Color–magnitude diagrams of the point sources derived from deep F814W (rest frame r′) and F105W (rest frame I) images of Abell 2744 in the Hubble Space Telescope Frontier Field show a rich population of point sources, which have colors that are similar to those of typical GCs. These sources are as bright as (26.0 < F814W(Vega) ≤ 29.5) mag, being mostly UCDs and bright GCs in Abell 2744. The luminosity function (LF) of these sources shows a break at (F814W ≈ 28.0) mag, indicating a boundary between UCDs and bright GCs. The numbers of GCs and UCDs are estimated to be 1,711,640+589,760 −430,500 and 147 ± 26, respectively. The clustercentric radial number density profiles of the UCDs and bright GCs show similar slopes, but these profiles are much steeper than those of the dwarf galaxies and the mass density profile based on gravitational lensing analysis. We derive an LF of the red sequence galaxies for mag. The faint end of this LF is fit well by a flat power law with , showing no faint upturn. These results support the galaxy-origin scenario for bright UCDs: they are the nuclei of dwarf galaxies that are stripped when they pass close to the center of massive galaxies or a galaxy cluster, while some of the faint UCDs are at the bright end of the GCs.

FRONTIER FIELDS CLUSTERS: DEEP CHANDRA OBSERVATIONS OF THE COMPLEX MERGER MACS J1149.6+2223

ABSTRACT The Hubble Space Telescope Frontier Fields cluster MACS J1149.6+2223 is one of the most complex merging clusters, believed to consist of four dark matter halos. We present results from deep (365 ks) Chandra observations of the cluster, which reveal the most distant cold front (z = 0.544) discovered to date. In the cluster outskirts, we also detect hints of a surface brightness edge that could be the bow shock preceding the cold front. The substructure analysis of the cluster identified several components with large relative radial velocities, thus indicating that at least some collisions occur almost along the line of sight. The inclination of the mergers with respect to the plane of the sky poses significant observational challenges at X-ray wavelengths. MACS J1149.6+2223 possibly hosts a steep-spectrum radio halo. If the steepness of the radio halo is confirmed, then the radio spectrum, combined with the relatively regular ICM morphology, could indicate that MACS J1149.6+2223 is an old merging cluster.

CONSTRAINING THE WARM DARK MATTER PARTICLE MASS THROUGH ULTRA-DEEP UV LUMINOSITY FUNCTIONS AT z = 2

ABSTRACT We compute the mass function of galactic dark matter halos for different values of the warm dark matter (WDM) particle mass m X and compare it with the number density of ultra-faint galaxies derived from the deepest UV luminosity function available so far at redshift z ≈ 2. The magnitude limit M UV = −13 reached by such observations allows us to probe the WDM mass functions down to scales close to or smaller than the half-mass mode mass scale ∼109 M ⊙. This allowed for an efficient discrimination among predictions for different m X which turn out to be in practice independent of the star formation efficiency η adopted to associate the observed UV luminosities of galaxies to the corresponding dark matter halo masses. Adopting a conservative approach to take into account the existing theoretical uncertainties in the galaxy halo mass function, we obtain a robust limit m X ≥ 1.8 keV for the mass of thermal relic WDM particles when comparing with the measured abundance of the faintest galaxies, while m X ≥ 1.5 keV is obtained when we compare with the Schechter fit to the observed luminosity function. The corresponding lower limit for sterile neutrinos depends on the modeling of the production mechanism; for instance m sterile ≳ 4 keV holds for the Shi–Fuller mechanism. We discuss the impact of observational uncertainties on the above bound on m X . In the cold dark matter (CDM) limit m X ≫ 1 keV ?> we recover the generic CDM result that very inefficient star formation efficiency is required to match the observed galaxy abundances. As a baseline for comparison with forthcoming observational results from the Hubble Space Telescope Frontier Field project, we provide predictions for the number density of faint galaxies with M UV = −13 for different values of the WDM particle mass and of the star formation efficiency η, which are valid up to z ≈ 4.

Hubble Frontier Fields: predictions for the return of SN Refsdal with the MUSE and GMOS spectrographs

We present a high-precision mass model of the galaxy cluster MACSJ1149.6+2223, based on a strong-gravitational-lensing analysis of Hubble Space Telescope Frontier Fields (HFF) imaging data and spectroscopic follow-up with Gemini/GMOS and VLT/MUSE. Our model includes 12 new multiply imaged galaxies, bringing the total to 22, comprised of 65 individual lensed images. Unlike the first two HFF clusters, Abell 2744 and MACSJ0416.1-2403, MACSJ1149 does not reveal as many multiple images in the HFF data. Using the Lenstool software package and the new sets of multiple images, we model the cluster with several cluster-scale dark-matter halos and additional galaxy-scale halos for the cluster members. Consistent with previous analyses, we find the system to be complex, composed of five cluster-scale halos. Their spatial distribution and lower mass, however, makes MACSJ1149 a less powerful lens. Our best-fit model predicts image positions with an RMS of 0.91". We measure the total projected mass inside a 200~kpc aperture as ($1.840\pm 0.006$)$\times 10^{14}$M$_{\odot}$, thus reaching again 1% precision, following our previous HFF analyses of MACSJ0416.1-2403 and Abell 2744. In light of the discovery of the first resolved quadruply lensed supernova, SN Refsdal, in one of the multiply imaged galaxies identified in MACSJ1149, we use our revised mass model to investigate the time delays and predict the rise of the next image between November 2015 and January 2016.

The Local Group as a time machine: studying the high-redshift Universe with nearby galaxies

We infer the UV luminosities of Local Group galaxies at early cosmic times (z ∼ 2 and z ∼ 7) by combining stellar population synthesis modelling with star formation histories derived from deep colour–magnitude diagrams constructed from Hubble Space Telescope (HST) observations. Our analysis provides a basis for understanding high-z galaxies – including those that may be unobservable even with the James Webb Space Telescope (JWST) – in the context of familiar, well-studied objects in the very low-z Universe. We find that, at the epoch of reionization, all Local Group dwarfs were less luminous than the faintest galaxies detectable in deep HST observations of blank fields. We predict that JWST will observe z ∼ 7 progenitors of galaxies similar to the Large Magellanic Cloud today; however, the HST Frontier Fields initiative may already be observing such galaxies, highlighting the power of gravitational lensing. Consensus reionization models require an extrapolation of the observed blank-field luminosity function (LF) at z ≈ 7 by at least 2 orders of magnitude in order to maintain reionization. This scenario requires the progenitors of the Fornax and Sagittarius dwarf spheroidal galaxies to be contributors to the ionizing background at z ∼ 7. Combined with numerical simulations, our results argue for a break in the UV LF from a faint-end slope of α ∼ −2 at MUV ≲ −13 to α ∼ −1.2 at lower luminosities. Applied to photometric samples at lower redshifts, our analysis suggests that HST observations in lensing fields at z ∼ 2 are capable of probing galaxies with luminosities comparable to the expected progenitor of Fornax.

Hubble Frontier Fields: a high-precision strong-lensing analysis of the massive galaxy cluster Abell 2744 using ∼180 multiple images

We present a high-precision mass model of galaxy cluster Abell 2744, based on a strong gravitational-lensing analysis of the Hubble Space Telescope Frontier Fields (HFF) imaging data, which now include both Advanced Camera for Surveys and Wide Field Camera 3 observations to the final depth. Taking advantage of the unprecedented depth of the visible and near-infrared data, we identify 34 new multiply imaged galaxies, bringing the total to 61, comprising 181 individual lensed images. In the process, we correct previous erroneous identifications and positions of multiple systems in the northern part of the cluster core. With the lenstool software and the new sets of multiple images, we model the cluster using two cluster-scale dark matter haloes plus galaxy-scale haloes for the cluster members. Our best-fitting model predicts image positions with an rms error of 0.79 arcsec, which constitutes an improvement by almost a factor of 2 over previous parametric models of this cluster. We measure the total projected mass inside a 200 kpc aperture as (2.162 ± 0.005) × 1014 M⊙, thus reaching 1 per cent level precision for the second time, following the recent HFF measurement of MACSJ0416.1−2403. Importantly, the higher quality of the mass model translates into an overall improvement by a factor of 4 of the derived magnification factor. Together with our previous HFF gravitational lensing analysis, this work demonstrates that the HFF data enables high-precision mass measurements for massive galaxy clusters and the derivation of robust magnification maps to probe the early Universe.

ACCOUNTING FOR COSMIC VARIANCE IN STUDIES OF GRAVITATIONALLY LENSED HIGH-REDSHIFT GALAXIES IN THE HUBBLE FRONTIER FIELD CLUSTERS

Strong gravitational lensing provides a powerful means for studying faint galaxies in the distant universe. By magnifying the apparent brightness of background sources, massive clusters enable the detection of galaxies fainter than the usual sensitivity limit for blank fields. However, this gain in effective sensitivity comes at the cost of a reduced survey volume and, in this {\it Letter}, we demonstrate there is an associated increase in the cosmic variance uncertainty. As an example, we show that the cosmic variance uncertainty of the high redshift population viewed through the Hubble Space Telescope Frontier Field cluster Abell 2744 increases from ~35% at redshift z~7 to >~65% at z~10. Previous studies of high redshift galaxies identified in the Frontier Fields have underestimated the cosmic variance uncertainty that will affect the ultimate constraints on both the faint end slope of the high-redshift luminosity function and the cosmic star formation rate density, key goals of the Frontier Field program.

The effect of large-scale structure on the magnification of high-redshift sources by cluster lenses

Cluster gravitational lensing surveys like the Hubble Space Telescope Frontier Fields survey will detect distant galaxies 10-50 times fainter than any yet discovered. Using these surveys to measure the luminosity function of such faint, distant galaxies, however, requires that magnification maps built from the constraints of strongly-lensed images be accurate. For models that assume the cluster and nearby (correlated) structures are the only significant sources of lensing, a potential source of error in these maps comes from the fact that light rays also suffer weak deflections by uncorrelated large-scale structure along the line-of-sight, i.e. cosmic weak lensing (CWL). To demonstrate the magnitude of this effect, we calculate the magnification change which results when the same cluster-lens is placed along different lines of sight. Using a simple density profile for a cluster-lens at z~0.3-0.5 and the power spectrum of the matter density fluctuations responsible for CWL, we show that the typical magnifications of ~5(10) of sources at z=6-10 can differ by ~10-20(20-30)% from one line-of-sight to another. However, these fluctuations rise to greater than order unity near critical curves, indicating that CWL tends to make its greatest contribution to the most magnified images. We conclude that the neglect of CWL in determining the intrinsic luminosities of highly-magnified galaxies may introduce errors significant enough to warrant further effort to include this contribution in cluster-lens modeling. We suggest that methods of modeling CWL in galaxy-strong-lensing systems should be generalized to cluster-lensing systems.

Mass and magnification maps for the Hubble Space Telescope Frontier Fields clusters: implications for high-redshift studies

Extending over three Hubble Space Telescope (HST) cycles, the Hubble Frontier Fields (HFF) initiative constitutes the largest commitment ever of HST time to the exploration of the distant Universe via gravitational lensing by massive galaxy clusters. We here present models of the mass distribution in the six HFF cluster lenses, derived from a joint strong- and weak-lensing analysis anchored by a total of 88 multiple-image systems identified in existing HST data. The resulting maps of the projected mass distribution and of the gravitational magnification effectively calibrate the HFF clusters as gravitational telescopes. Allowing the computation of search areas in the source plane, these maps are provided to the community to facilitate the exploitation of forthcoming HFF data for quantitative studies of the gravitationally lensed population of background galaxies. Our models of the gravitational magnification afforded by the HFF clusters allow us to quantify the lensing-induced boost in sensitivity over blank-field observations and predict that galaxies at $z>10$ and as faint as m(AB)=32 will be detectable, up to 2 magnitudes fainter than the limit of the Hubble Ultra Deep Field.