Strong Lensing Model Research Articles

CLASH-VLT: INSIGHTS ON THE MASS SUBSTRUCTURES IN THE FRONTIER FIELDS CLUSTER MACS J0416.1–2403 THROUGH ACCURATE STRONG LENS MODELING

We present a detailed mass reconstruction and a novel study on the substructure properties in the core of the CLASH and Frontier Fields galaxy cluster MACS J0416.1-2403. We show and employ our extensive spectroscopic data set taken with the VIMOS instrument as part of our CLASH-VLT program, to confirm spectroscopically 10 strong lensing systems and to select a sample of 175 plausible cluster members to a limiting stellar mass of log(M_*/M_Sun) ~ 8.6. We reproduce the measured positions of 30 multiple images with a remarkable median offset of only 0.3" by means of a comprehensive strong lensing model comprised of 2 cluster dark-matter halos, represented by cored elliptical pseudo-isothermal mass distributions, and the cluster member components. The latter have total mass-to-light ratios increasing with the galaxy HST/WFC3 near-IR (F160W) luminosities. The measurement of the total enclosed mass within the Einstein radius is accurate to ~5%, including systematic uncertainties. We emphasize that the use of multiple-image systems with spectroscopic redshifts and knowledge of cluster membership based on extensive spectroscopic information is key to constructing robust high-resolution mass maps. We also produce magnification maps over the central area that is covered with HST observations. We investigate the galaxy contribution, both in terms of total and stellar mass, to the total mass budget of the cluster. When compared with the outcomes of cosmological $N$-body simulations, our results point to a lack of massive subhalos in the inner regions of simulated clusters with total masses similar to that of MACS J0416.1-2403. Our findings of the location and shape of the cluster dark-matter halo density profiles and on the cluster substructures provide intriguing tests of the assumed collisionless, cold nature of dark matter and of the role played by baryons in the process of structure formation.

MUSE integral-field spectroscopy towards the Frontier Fields cluster Abell S1063

We present the first observations of the Frontier Fields Cluster Abell S1063 taken with the newly commissioned Multi Unit Spectroscopic Explorer (MUSE) integral field spectrograph. Because of the relatively large field of view (1 arcmin^2), MUSE is ideal to simultaneously target multiple galaxies in blank and cluster fields over the full optical spectrum. We analysed the four hours of data obtained in the Science Verification phase on this cluster and measured redshifts for 53 galaxies. We confirm the redshift of five cluster galaxies, and determine the redshift of 29 other cluster members. Behind the cluster, we find 17 galaxies at higher redshift, including three previously unknown Lyman-alpha emitters at z>3, and five multiply-lensed galaxies. We report the detection of a new z=4.113 multiply lensed galaxy, with images that are consistent with lensing model predictions derived for the Frontier Fields. We detect C III], C IV, and He II emission in a multiply lensed galaxy at z=3.116, suggesting the likely presence of an active galactic nucleus. We also created narrow-band images from the MUSE datacube to automatically search for additional line emitters corresponding to high-redshift candidates, but we could not identify any significant detections other than those found by visual inspection. With the new redshifts, it will become possible to obtain an accurate mass reconstruction in the core of Abell S1063 through refined strong lensing modelling. Overall, our results illustrate the breadth of scientific topics that can be addressed with a single MUSE pointing. We conclude that MUSE is a very efficient instrument to observe galaxy clusters, enabling their mass modelling, and to perform a blind search for high-redshift galaxies.

LENS MODELS AND MAGNIFICATION MAPS OF THE SIX HUBBLE FRONTIER FIELDS CLUSTERS

We present strong-lensing models, as well as mass and magnification maps, for the cores of the six HST Frontier Fields galaxy clusters. Our parametric lens models are constrained by the locations and redshifts of multiple image systems of lensed background galaxies. We use a combination of photometric redshifts and spectroscopic redshifts of the lensed background sources obtained by us (for Abell 2744 and Abell S1063), collected from the literature, or kindly provided by the lensing community. Using our results, we (1) compare the derived mass distribution of each cluster to its light distribution, (2) quantify the cumulative magnification power of the HFF clusters, (3) describe how our models can be used to estimate the magnification and image multiplicity of lensed background sources at all redshifts and at any position within the cluster cores, and (4) discuss systematic effects and caveats resulting from our modeling methods. We specifically investigate the effect of the use of spectroscopic and photometric redshift constraints on the uncertainties of the resulting models. We find that the photometric redshift estimates of lensed galaxies are generally in excellent agreement with spectroscopic redshifts, where available. However, the flexibility associated with relaxed redshift priors may cause the complexity of large-scale structure that is needed to account for the lensing signal to be underestimated. Our findings thus underline the importance of spectroscopic arc redshifts, or tight photometric redshift constraints, for high precision lens models. All products from our best-fit lens models (magnification, convergence, shear, deflection field) and model simulations for estimating errors are made available via the Mikulski Archive for Space Telescopes.

Characterizing SL2S galaxy groups using the Einstein radius

We analyzed the Einstein radius, $\theta_E$, in our sample of SL2S galaxy groups, and compared it with $R_A$ (the distance from the arcs to the center of the lens), using three different approaches: 1.- the velocity dispersion obtained from weak lensing assuming a Singular Isothermal Sphere profile ($\theta_{E,I}$), 2.- a strong lensing analytical method ($\theta_{E,II}$) combined with a velocity dispersion-concentration relation derived from numerical simulations designed to mimic our group sample, 3.- strong lensing modeling ($\theta_{E,III}$) of eleven groups (with four new models presented in this work) using HST and CFHT images. Finally, $R_A$ was analyzed as a function of redshift $z$ to investigate possible correlations with L, N, and the richness-to-luminosity ratio (N/L). We found a correlation between $\theta_{E}$ and $R_A$, but with large scatter. We estimate $\theta_{E,I}$ = (2.2 $\pm$ 0.9) + (0.7 $\pm$ 0.2)$R_A$, $\theta_{E,II}$ = (0.4 $\pm$ 1.5) + (1.1 $\pm$ 0.4)$R_A$, and $\theta_{E,III}$ = (0.4 $\pm$ 1.5) + (0.9 $\pm$ 0.3)$R_A$ for each method respectively. We found a weak evidence of anti-correlation between $R_A$ and $z$, with Log$R_A$ = (0.58$\pm$0.06) - (0.04$\pm$0.1)$z$, suggesting a possible evolution of the Einstein radius with $z$, as reported previously by other authors. Our results also show that $R_A$ is correlated with L and N (more luminous and richer groups have greater $R_A$), and a possible correlation between $R_A$ and the N/L ratio. Our analysis indicates that $R_A$ is correlated with $\theta_E$ in our sample, making $R_A$ useful to characterize properties like L and N (and possible N/L) in galaxy groups. Additionally, we present evidence suggesting that the Einstein radius evolves with $z$.

Strong Gravitational Lensing in the Einstein-Proca Theory

Adopting the strong field limit approach, we investigate the strong gravitational lensing of a spherically symmetric spacetime in the Einstein-Proca theory. With the strong field limit coefficient, three observable quantities are obtained, which are the innermost relativistic image, the deflection angle and the ratio of the flux. Comparing the observable value and the theoretical value of the strong gravitational lensing, we can verify the effectiveness of the strong gravitational lensing model.

Enabling non-parametric strong lensing models to derive reliable cluster mass distributions – wslap+

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 modeling, even though we mainly wish to understand the relatively smooth cluster component. The required resolution is not achievable because the separation between lensed images is several times larger than the deflection angles by member galaxies, even for the deepest 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 galaxy contribution is added to a relatively coarse Gaussian pixel grid for modeling the cluster mass distribution, extending our established WSLAP code (Diego et al. 2007). We test this new code with a simulation based on A1689, using the pixels belonging to multiply-lensed images and the observed member galaxies. Dealing with the cluster members this way leads to convergent solutions, without resorting to regularization, reproducing well the input cluster and substructures. We highlight the ability of this method to recover dark sub-components of the cluster, unrelated to 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 defined by 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.

CLASH-VLT: spectroscopic confirmation of az= 6.11 quintuply lensed galaxy in the Frontier Fields cluster RXC J2248.7-4431

We present VIsible Multi-Object Spectrograph (VIMOS) observations of a z 6 galaxy quintuply imaged by the Frontier Fields galaxy cluster RXC J2248.7-4431 (z=0.348). This sub-L^*, high-z galaxy has been recently discovered by Monna et al. (2013) using dropout techniques with the 16-band HST photometry acquired as part of the Cluster Lensing And Supernova survey with Hubble (CLASH). Obtained as part of the CLASH-VLT survey, the VIMOS medium-resolution spectra of this source show a very faint continuum between ~8700A and ~9300A and a prominent emission line at 8643A, which can be readily identified with Lyman-alpha at z=6.110. The emission line exhibits an asymmetric profile, with a more pronounced red wing. The rest-frame equivalent width of the line is EW=79+-10A. After correcting for magnification, the star-formation rate (SFR) estimated from the Lya line is SFR(Lya)=11 M_{sol}/yr and that estimated from the UV data is SFR(UV)=3 M_{sol}/yr. We estimate that the effective radius of the source is R_e<~0.4 kpc, which implies a star formation surface mass density Sigma_{SFR}>6 M_{sol}/yr/kpc^2 and, using the Kennicutt-Schmidt relation, a gas surface mass density Sigma_{gas}>10^3 M_{sol}/pc^2. Our results support the idea that this magnified, distant galaxy is a young and compact object with 0.4 L^* at z=6, with comparable amount of mass in gas and stars. Future follow-up observations with ALMA will provide valuable insight into the SFR and molecular gas content of this source. In the spirit of the Frontier Fields initiative, we also publish the redshifts of several multiply imaged sources and other background objects which will help improving the strong lensing model of this galaxy cluster.

The Dark Halo – Spheroid Conspiracy

AbstractObservational results from strong lensing and dynamical modeling indicate that the total density profiles of early-type galaxies are close to isothermal, i.e. ρtot ∝ rγ with γ ≈ −2. To understand the origin of this universal slope we study a set of simulated spheroids formed in cosmological hydrodynamical zoom-in simulations (see Oser et al. 2010 for more details). We find that the total stellar plus dark matter density profiles of all our simulations on average can be described by a power law with a slope of γ ≈ −2.1, with a tendency towards steeper slopes for more compact, lower mass ellipticals, while the total intrinsic velocity dispersion is flat for all simulations, independent of the values of γ. Our results are in good agreement with observations of Coma cluster ellipticals (Thomas et al. 2007) and results from strong lensing (Sonnenfeld et al. 2012). We find that for z ≳ 2 the majority of the stellar build-up occurs through in-situ star formation, i.e. the gas falls to the center of the galaxy and forms stars, causing the galaxy to be more compact and thus the stellar component to be more dominant. As a result, the total density slopes at z ≈ 2 are generally steeper (around γ ≈ −3). Between z = 2 and z = 0 galaxies grow mostly through dry merging, with each merging event shifting the slope more towards γ ≈ −2. We conclude from our simulations that the steepness of the slope of present day galaxies is a signature of the importance of mostly dry mergers in the formation of an elliptical, and suggest that all elliptical galaxies will with time end up in a configuration with a density slope of γ ≈ −2. For a more detailed analysis with a larger sample of simulations see Remus et al. (2013).

ON THE AVERAGE DENSITY PROFILE OF DARK-MATTER HALOS IN THE INNER REGIONS OF MASSIVE EARLY-TYPE GALAXIES

We study a sample of 39 massive early-type lens galaxies at redshift z < 0.3 to determine the slope of the average dark-matter density profile in the innermost regions. We keep the strong lensing and stellar population synthesis modeling as simple as possible to measure the galaxy total and luminous masses. By rescaling the values of the Einstein radius and dark-matter projected mass with the values of the luminous effective radius and mass, we combine all the data of the galaxies in the sample. We find that between 0.3 and 0.9 times the value of the effective radius the average logarithmic slope of the dark-matter projected density profile is -1.0 +/- 0.2 (i.e., approximately isothermal) or -0.7 +/- 0.5 (i.e., shallower than isothermal), if, respectively, a constant Chabrier or heavier, Salpeter-like stellar IMF is adopted. These results provide positive evidence of the influence of the baryonic component on the contraction of the galaxy dark-matter halos, compared to the predictions of dark matter-only cosmological simulations, and open a new way to test models of structure formation and evolution within the standard LCDM cosmological scenario.

A HIGH-RESOLUTION MASS MAP OF GALAXY CLUSTER SUBSTRUCTURE: LensPerfect ANALYSIS OF A1689

We present a strong lensing (SL) mass model of A1689 which resolves substructures an estimated 25 kpc across within the central ∼400 kpc diameter. We achieve this resolution by perfectly reproducing the observed (strongly lensed) input positions of 168 multiple images of 55 knots residing within 135 images of 42 galaxies. Our model makes no assumptions about light tracing mass, yet we reproduce the brightest visible structures with some slight deviations. A1689 remains one of the strongest known lenses on the sky, with an Einstein radius of RE = 470 ± 12 (143+3−4 kpc) for a lensed source at zs = 2. We find that a single Navarro–Frenk–White (NFW) or Sérsic profile yields a good fit simultaneously (with only slight tension) to both our SL mass model and published weak lensing (WL) measurements at larger radius (out to the virial radius). According to this NFW fit, A1689 has a mass of Mvir = 2.0+0.5−0.3 × 1015 M☉ h−170 (M200 = 1.8+0.4−0.3 × 1015 M☉ h−170) within the virial radius rvir = 3.0 ± 0.2 Mpc h−170 (r200 = 2.4+0.1−0.2 Mpc h−170), and a central concentration cvir = 11.5+1.5−1.4 (c200 = 9.2 ± 1.2). Our SL model prefers slightly higher concentrations than previous SL models, bringing our SL + WL constraints in line with other recent derivations. Our results support those of previous studies which find A1689 has either an anomalously large concentration or significant extra mass along the line of sight (perhaps in part due to triaxiality). If clusters are generally found to have higher concentrations than realized in simulations, this could indicate that they formed earlier, perhaps as a result of early dark energy.

CENTRAL DARK MATTER TRENDS IN EARLY-TYPE GALAXIES FROM STRONG LENSING, DYNAMICS, AND STELLAR POPULATIONS

We analyze the correlations between central dark matter (DM) content of early-type galaxies and their sizes and ages, using a sample of intermediate-redshift (z ~ 0.2) gravitational lenses from the SLACS survey, and by comparing them to a larger sample of z ~ 0 galaxies. We decompose the deprojected galaxy masses into DM and stellar components using combinations of strong lensing, stellar dynamics, and stellar populations modeling. For a given stellar mass, we find that for galaxies with larger sizes, the DM fraction increases and the mean DM density decreases, consistently with the cuspy halos expected in cosmological formation scenarios. The DM fraction also decreases with stellar age, which can be partially explained by the inverse correlation between size and age. The residual trend may point to systematic dependencies on formation epoch of halo contraction or stellar initial mass functions. These results are in agreement with recent findings based on local galaxies by Napolitano, Romanowsky & Tortora (2010) and suggest negligible evidence of galaxy evolution over the last ~ 2.5 Gyr other than passive stellar aging.

Weighing simulated galaxy clusters using lensing and X-ray

<i>Context. <i/>Among the methods employed to measure the mass of galaxy clusters, the techniques based on lensing and X-ray analyses are perhaps the most widely used; however, the comparison between these mass estimates is often difficult and, in several clusters, the results apparently inconsistent.<i>Aims. <i/>We aim at investigating potential biases in lensing and X-ray methods to measure the cluster mass profiles.<i>Methods. <i/>We performed realistic simulations of lensing and X-ray observations that were subsequently analyzed using observational techniques. The resulting mass estimates were compared with the input models. Three clusters obtained from state-of-the-art hydrodynamical simulations, each of which projected along three independent lines-of-sight, were used for this analysis.<i>Results. <i/>We find that strong lensing models can be trusted over a limited region around the cluster core. Extrapolating the strong lensing mass models to outside the Einstein ring can lead to significant biases in the mass estimates, if the BCG is not modeled properly, for example. Weak-lensing mass measurements can be strongly affected by substructures, depending on the method implemented to convert the shear into a mass estimate. Using nonparametric methods which combine weak and strong lensing data, the projected masses within <i>R<i/><sub>200<sub/> can be constrained with a precision of ~10%. Deprojection of lensing masses increases the scatter around the true masses by more than a factor of two because of cluster triaxiality. X-ray mass measurements have much smaller scatter (about a factor of two less than the lensing masses), but they are generally biased toward low values between 5 and 10%. This bias is entirely ascribable to bulk motions in the gas of our simulated clusters. Using the lensing and the X-ray masses as proxies for the true and the hydrostatic equilibrium masses of the simulated clusters and by averaging over the cluster sample, we are able to measure the lack of hydrostatic equilibrium in the systems we have investigated.<i>Conclusions. <i/>Although the comparison between lensing and X-ray masses may be difficult in individual systems due to triaxiality and substructures, using a large number of clusters with both lensing and X-ray observations may lead to important information about their gas physics and allow use of lensing masses to calibrate the X-ray scaling relations.

Keck spectroscopic survey of strongly lensed galaxies in Abell 1703: further evidence of a relaxed, unimodal cluster

Context. Strong gravitational lensing is a unique tool that can be used to accurately model the inner mass distribution of massive galaxy clusters. In particular, clusters with large Einstein radii provide a wealth of multiply imaged systems in the cluster core. Measuring the redshift of these multiple images provides strong constraints for precisely determining the shape of the central dark matter profile. Aims. This paper presents a spectroscopic survey of strongly lensed galaxies in the massive cluster lens Abell 1703, which displays a large Einstein radius (28 at z = 2.8) and numerous strongly-lensed systems including a central ring-like configuration. Methods. We used the LRIS spectrograph on Keck to target multiple images and lensed galaxy candidates, and used the measured spectroscopic redshifts to constrain the mass distribution of the cluster using a parametric model. Results. The spectroscopic data enable us to measure accurate redshifts for 7 sources at z > 2 , all of which are in good agreement with their photometric redshifts. We update the identification of multiply imaged systems by discovering 3 new systems and identifying a radial counter image. We also report the discovery of a remarkably bright ~3.6 L∗ i-band dropout at z = 5.827 in our mask and it is only moderately magnified by the cluster (μ ~ 3.0 ± 0.08). The improved parametric mass model, including 16 multiple systems with 10 spectroscopic redshifts, further constrains the smooth cluster-scale mass distribution with a generalized NFW profile of best-fit logarithmic slope α = 0.92 ± 0.04, concentration c_(200) = 4.72 ± 0.40 and scale radius r_s = 476 ± 45 kpc. The overall rms in the image plane is 1.3. Conclusions. Our strong-lensing model allows us to predict a large-scale shear signal that is consistent with weak-lensing measurements inferred from Subaru data out to 4 Mpc h^(−1). Also considering the strong-lensing modeling requires a single dark matter clump, this suggests that Abell 1703 is a relaxed, unimodal cluster. This unique cluster could be probed further using deep X-ray, SZ, and dynamics analysis for a detailed study of the physics in a relaxed cluster.

A MULTIPLY IMAGED LUMINOUS INFRARED GALAXY BEHIND THE BULLET CLUSTER (1E0657-56)

We present evidence for a Spitzer-selected luminous infrared galaxy (LIRG) behind the Bullet Cluster (1E0657-56). The galaxy, originally identified as a multiply imaged source using Infrared Array Camera (IRAC) photometry, has a spectral energy distribution consistent with a highly extincted (AV ~ 3.3), strongly star forming galaxy at z = 2.7. Using our strong gravitational lensing model presented in a previous paper, we find that the magnifications are |μ| 10-50 for the three images of the galaxy. The brightest and faintest images differ by a factor of 3.2 in magnification. The implied infrared luminosity is consistent with the galaxy being a LIRG, with a stellar mass of M * ~ 2 × 1010 M ☉ and a star formation rate (SFR) of ~90 M ☉ yr–1. With lensed fluxes at 24 μm of 0.58 mJy and 0.39 mJy in the two brightest images, this galaxy presents a unique opportunity for detailed study of an obscured starburst with a SFR comparable to that of L* galaxies at z > 2.

Probing the slope of cluster mass profile with gravitational Einstein rings: application to Abell 1689

Abstract The strong lensing modelling of gravitational ‘rings’ formed around massive galaxies is sensitive to the amplitude of the external shear and convergence produced by nearby mass condensations. In current wide-field surveys, it is now possible to find out a large number of rings, typically 10 gravitational rings per square degree. We propose here, to systematically study gravitational rings around galaxy clusters to probe the cluster mass profile beyond the cluster strong lensing regions. For cluster of galaxies with multiple arc systems, we show that rings found at various distances from the cluster centre can improve the modelling by constraining the slope of the cluster mass profile. We outline the principle of the method with simple numerical simulations and we apply it to three rings discovered recently in Abell 1689. In particular, the lens modelling of the three rings confirms that the cluster is bimodal, and favours a slope of the mass profile steeper than isothermal at a cluster radius ∼300 kpc. These results are compared with previous lens modelling of Abell 1689 including weak lensing analysis. Because of the difficulty arising from the complex mass distribution in Abell 1689, we argue that the ring method will be better implemented on simpler and relaxed clusters.

Separating Baryons and Dark Matter in Cluster Cores: A Full Two‐dimensional Lensing and Dynamic Analysis of Abell 383 and MS 2137−23

We utilize existing data for the galaxy clusters MS 2137–23 and Abell 383 to present improved measures of the distribution of dark and baryonic material in the clusters' central regions. Our method, based on the combination of gravitational lensing and dynamical data, is uniquely capable of separating the distribution of dark and baryonic components at scales below 100 kpc. Our mass models include pseudoelliptical generalized NFW profiles for constraining the inner dark matter slope. We find that a variety of strong-lensing models fit the available data, including some with dark matter profiles as steep as expected from recent simulations. However, when combined with stellar velocity dispersion data for the brightest member, shallower inner slopes than predicted by numerical simulations are preferred, in general agreement with our earlier work in these clusters. For Abell 383, the preferred shallow inner slopes are statistically a good fit only when the multiple-image position uncertainties associated with our lens model are assumed to be 0.5, to account for unknown substructure. No statistically satisfactory fit was obtained matching both the multiple-image lensing data and the velocity dispersion profile of the brightest cluster galaxy in MS 2137–23. This suggests that the mass model we are using, which comprises a pseudoelliptical generalized NFW profile and a brightest cluster galaxy component, may inadequately represent the inner cluster regions. This may arise due to halo triaxiality or by the gravitational interaction of baryons and dark matter in cluster cores. The progress made via this detailed study highlights the key role that complementary observations of lensed features and stellar dynamics offer in understanding the interaction between dark and baryonic matter on nonlinear scales in the central regions of clusters.

A Bayesian approach to strong lensing modelling of galaxy clusters

In this paper, we describe a procedure for modelling strong lensing galaxy clusters with parametric methods, and to rank models quantitatively using the Bayesian evidence. We use a publicly available Markov chain Monte-Carlo (MCMC) sampler (‘bayesys’), allowing us to avoid local minima in the likelihood functions. To illustrate the power of the MCMC technique, we simulate three clusters of galaxies, each composed of a cluster-scale halo and a set of perturbing galaxy-scale subhalos. We ray-trace three light beams through each model to produce a catalogue of multiple images, and then use the MCMC sampler to recover the model parameters in the three different lensing configurations. We find that, for typical Hubble Space Telescope (HST)-quality imaging data, the total mass in the Einstein radius is recovered with ∼1–5% error according to the considered lensing configuration. However, we find that the mass of the galaxies is strongly degenerated with the cluster mass when no multiple images appear in the cluster centre. The mass of the galaxies is generally recovered with a 20% error, largely due to the poorly constrained cut-off radius. Finally, we describe how to rank models quantitatively using the Bayesian evidence. We confirm the ability of strong lensing to constrain the mass profile in the central region of galaxy clusters in this way. Ultimately, such a method applied to strong lensing clusters with a very large number of multiple images may provide unique geometrical constraints on cosmology. The implementation of the MCMC sampler used in this paper has been done within the framework of the lenstool software package, which is publicly availablewww.oamp.fr/cosmology/lenstool..

MS 2053.7−0449: Confirmation of a Bimodal Mass Distribution from Strong Gravitational Lensing

We present the first strong-lensing study of the mass distribution in the cluster MS 2053-04 based on HST archive data. This massive, X-ray luminous cluster has a redshift z = 0.583 and is composed of two structures that are gravitationally bound to each other. The cluster has one multiply imaged system composed of a double gravitational arc. We have performed a parametric strong-lensing mass reconstruction using NFW density profiles to model the cluster potential. We also included perturbations from 23 galaxies, modeled like elliptical singular isothermal spheres, that are approximately within 1' × 1' around the cluster center. These galaxies were constrained in both the geometric and dynamical parameters with observational data. Our analysis predicts a third image that is slightly demagnified. We found a candidate for this counterimage near the expected position and with the same F702W - F814W colors as the gravitational arcs in the cluster. The results from the strong-lensing model show the complex structure in this cluster, the asymmetry and the elongation in the mass distribution, and are consistent with previous spectrophotometric results that indicate that the cluster has a bimodal mass distribution. Finally, the derived mass profile was used to estimate the mass within the arcs and for comparison with X-ray estimates.

The Sizes of Galaxy Halos in Galaxy Cluster Abell 1689

The multiple images observed in galaxy cluster Abell 1689 provide strong constraints not only on the mass distribution of the cluster but also on the ensemble properties of the cluster galaxies. Using parametric strong lensing models for the cluster, and by assuming well motivated scaling laws between the truncation radius s and the velocity dispersion sigma of a cluster galaxy we are able to derive sizes of the dark matter halos of cluster galaxies. For the scaling law expected for galaxies in the cluster environment (s propto sigma), we obtain s = 64^{+15}_{-14} (sigma / 220 km/s) kpc. For the scaling law used for galaxies in the field with s propto sigma^2 we find s = 66^{+18}_{-16} (sigma / 220 km/s)^2 kpc. Compared to halos of field galaxies, the cluster galaxy halos in Abell 1689 are strongly truncated.

Parametric strong gravitational lensing analysis of Abell 1689

We have derived the mass distribution of galaxy cluster Abell 1689 within 0.3 h−170 Mpc of the cluster centre using its strong lensing (SL) effect on 32 background galaxies, which are mapped in altogether 107 multiple images. The multiple images are based on some from the literature with modifications to both include new and exclude some of the original image systems. The cluster profile is explored further out to ∼2.5 h−170 Mpc with weak lensing (WL) shear measurements from the literature. The masses of ∼200 cluster galaxies are measured with the Fundamental Plane (FP) in order to model accurately the small-scale mass structure in the cluster. The cluster galaxies are modelled as elliptical truncated isothermal spheres. The scalings of the truncation radii with the velocity dispersions of galaxies are assumed to match those of: (i) field galaxies; and (ii) theoretical expectations for galaxies in dense environments. The dark matter (DM) component of the cluster is described by either non-singular isothermal ellipsoids (NSIE) or elliptical versions of the universal DM profile (elliptical Navarro, Frenk & White, ENFW). To account for substructure in the DM we allow for two DM haloes. The fitting of a non-singular isothermal sphere (NSIS) to the smooth DM component results in a velocity dispersion of 1450+39−31 km s−1 and a core radius of 77+10−8 h−170 kpc, while a Navarro, Frenk & White (NFW) profile has an r200 of 2.86 ± 0.16 h−170 Mpc(M200= 3.2 × 1015 M⊙ h70) and a concentration of 4.7+0.6−0.5. The total mass profile is well described by either a NSIS profile with σ= 1514+18−17 km s−1 and a core radius of rc= 71 ± 5 h−170 kpc, or an NFW profile with C= 6.0 ± 0.5 and r200= 2.82 ± 0.11 h−170 Mpc(M200= 3.0 × 1015 M⊙ h70). The errors are assumed to be due to the error in assigning masses to the individual galaxies in the galaxy component. Their small size is due to the very strong constraints imposed by multiple images and the ability of the smooth DM component to adjust to uncertainties in the galaxy masses. The agreement in the total mass profile between this work and that of the literature is better than 1σ at all radii, despite the considerable differences in the methodology used. Using the same image configuration as used in the literature, we obtain a SL model that is superior to some in the literature (rms of 2.7 compared to 3.2 arcsec). This is very surprising considering the larger freedom in the surface mass profile in their grid modelling. The difference is most likely a result of the careful inclusion of the cluster galaxies. Using also WL shear measurements from the literature, we can constrain the profile further out to r∼ 2.5 h−170 Mpc. The best-fitting parameters change to σ= 1499 ± 15 km s−1 and rc= 66 ± 5 h−170 kpc for the NSIS profile and C= 7.6 ± 0.5 and r200= 2.55 ± 0.07 h−170 Mpc(M200= 2.3 × 1015 M⊙ h70) for the NFW profile.