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L. Bradley

Publications and source records attributed to L. Bradley.

At least 37 records · Page 2Linked to original sources

Optimisation of the design for the LOFT Large Area Detector Module

LOFT (Large Observatory for X-ray Timing) is an X-ray timing observatory that, with four other candidates, was considered by ESA as an M3 mission (with launch in 2022-2024) and has been studied during an extensive assessment phase. Its pointed instrument is the Large Area Detector (LAD), a 10 m 2 -class instrument operating in the 2-30 keV range, which is designed to perform X-ray timing of compact objects with unprecedented resolution down to millisecond time scales. Although LOFT was not downselected for launch, during the assessment most of the trade-offs have been closed, leading to a robust and well documented design that will be reproposed in future ESA calls. The building block of the LAD instrument is the Module, and in this paper we summarize the rationale for the module concept, the characteristics of the module and the trade-offs/optimisations which have led to the current design.

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The MUSIC of CLASH: predictions on the concentration-mass relation

We present the results of a numerical study based on the analysis of the MUSIC-2 simulations, aimed at estimating the expected concentration-mass relation for the CLASH cluster sample. We study nearly 1400 halos simulated at high spatial and mass resolution, which were projected along many lines-of-sight each. We study the shape of both their density and surface-density profiles and fit them with a variety of radial functions, including the Navarro-Frenk-White, the generalised Navarro-Frenk-White, and the Einasto density profiles. We derive concentrations and masses from these fits and investigate their distributions as a function of redshift and halo relaxation. We use the X-ray image simulator X-MAS to produce simulated Chandra observations of the halos and we use them to identify objects resembling the X-ray morphologies and masses of the clusters in the CLASH X-ray selected sample. We also derive a concentration-mass relation for strong-lensing clusters. We find that the sample of simulated halos which resemble the X-ray morphology of the CLASH clusters is composed mainly by relaxed halos, but it also contains a significant fraction of un-relaxed systems. For such a sample we measure an average 2D concentration which is ~11% higher than found for the full sample of simulated halos. After accounting for projection and selection effects, the average NFW concentrations of CLASH clusters are expected to be intermediate between those predicted in 3D for relaxed and super-relaxed halos. Matching the simulations to the individual CLASH clusters on the basis of the X-ray morphology, we expect that the NFW concentrations recovered from the lensing analysis of the CLASH clusters are in the range [3-6], with an average value of 3.87 and a standard deviation of 0.61. Simulated halos with X-ray morphologies similar to those of the CLASH clusters are affected by a modest orientation bias.

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CLASH: The Concentration-Mass Relation of Galaxy Clusters

We present a new determination of the concentration-mass relation for galaxy clusters based on our comprehensive lensing analysis of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble (CLASH). Our sample spans a redshift range between 0.19 and 0.89. We combine weak lensing constraints from the Hubble Space Telescope (HST) and from ground-based wide field data with strong lensing constraints from HST. The result are reconstructions of the surface-mass density for all CLASH clusters on multi-scale grids. Our derivation of NFW parameters yields virial masses between 0.53 x 10^15 and 1.76 x 10^15 M_sol/h and the halo concentrations are distributed around c_200c ~ 3.7 with a 1-sigma significant negative trend with cluster mass. We find an excellent 4% agreement between our measured concentrations and the expectation from numerical simulations after accounting for the CLASH selection function based on X-ray morphology. The simulations are analyzed in 2D to account for possible biases in the lensing reconstructions due to projection effects. The theoretical concentration-mass (c-M) relation from our X-ray selected set of simulated clusters and the c-M relation derived directly from the CLASH data agree at the 90% confidence level.

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Intra Cluster Light properties in the CLASH-VLT cluster MACS J1206.2-0847

We aim at constraining the assembly history of clusters by studying the intra cluster light (ICL) properties, estimating its contribution to the fraction of baryons in stars, f*, and understanding possible systematics/bias using different ICL detection techniques. We developed an automated method, GALtoICL, based on the software GALAPAGOS to obtain a refined version of typical BCG+ICL maps. We applied this method to our test case MACS J1206.2-0847, a massive cluster located at z=0.44, that is part of the CLASH sample. Using deep multi-band SUBARU images, we extracted the surface brightness (SB) profile of the BCG+ICL and we studied the ICL morphology, color, and contribution to f* out to R500. We repeated the same analysis using a different definition of the ICL, SBlimit method, i.e. a SB cut-off level, to compare the results. The most peculiar feature of the ICL in MACS1206 is its asymmetric radial distribution, with an excess in the SE direction and extending towards the 2nd brightest cluster galaxy which is a Post Starburst galaxy. This suggests an interaction between the BCG and this galaxy that dates back to t <= 1.5 Gyr. The BCG+ICL stellar content is 8% of M_(*,500) and the (de-) projected baryon fraction in stars is f*=0.0177 (0.0116), in excellent agreement with recent results. The SBlimit method provides systematically higher ICL fractions and this effect is larger at lower SB limits. This is due to the light from the outer envelopes of member galaxies that contaminate the ICL. Though more time consuming, the GALtoICL method provides safer ICL detections that are almost free of this contamination. This is one of the few ICL study at redshift z > 0.3. At completion, the CLASH/VLT program will allow us to extend this analysis to a statistically significant cluster sample spanning a wide redshift range: 0.2<z<0.6.

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CLASH: Extending galaxy strong lensing to small physical scales with distant sources highly-magnified by galaxy cluster members

We present a strong lensing system in which a double source is imaged 5 times by 2 early-type galaxies. We take advantage in this target of the multi-band photometry obtained as part of the CLASH program, complemented by the spectroscopic data of the VLT/VIMOS and FORS2 follow-up campaign. We use a photometric redshift of 3.7 for the source and confirm spectroscopically the membership of the 2 lenses to the galaxy cluster MACS J1206.2-0847 at redshift 0.44. We exploit the excellent angular resolution of the HST/ACS images to model the 2 lenses in terms of singular isothermal sphere profiles and derive robust effective velocity dispersions of (97 +/- 3) and (240 +/- 6) km/s. The total mass distribution of the cluster is also well characterized by using only the local information contained in this lensing system, that is located at a projected distance of more than 300 kpc from the cluster luminosity center. According to our best-fitting lensing and composite stellar population models, the source is magnified by a total factor of 50 and has a luminous mass of about (1.0 +/- 0.5) x 10^{9} M_{Sun}. By combining the total and luminous mass estimates of the 2 lenses, we measure luminous over total mass fractions projected within the effective radii of 0.51 +/- 0.21 and 0.80 +/- 0.32. With these lenses we can extend the analysis of the mass properties of lens early-type galaxies by factors that are about 2 and 3 times smaller than previously done with regard to, respectively, velocity dispersion and luminous mass. The comparison of the total and luminous quantities of our lenses with those of astrophysical objects with different physical scales reveals the potential of studies of this kind for investigating the internal structure of galaxies. These studies, made possible thanks to the CLASH survey, will allow us to go beyond the current limits posed by the available lens samples in the field.

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Characterizing faint galaxies in the reionization epoch: LBT confirms two L<0.2L* sources at z=6.4 behind the CLASH/Frontier Fields cluster MACS0717.5+3745

We report the LBT/MODS1 spectroscopic confirmation of two images of faint Lyman alpha emitters at $z=6.4$ behind the Frontier Fields galaxy cluster MACSJ0717.5+3745. A wide range of lens models suggests that the two images are highly magnified, with a strong lower limit of mu>5. These are the faintest z>6 candidates spectroscopically confirmed to date. These may be also multiple images of the same z=6.4 source as supported by their similar intrinsic properties, but the lens models are inconclusive regarding this interpretation. To be cautious, we derive the physical properties of each image individually. Thanks to the high magnification, the observed near-infrared (restframe ultraviolet) part of the spectral energy distributions and Ly-alpha lines are well detected with S/N(m_1500)>~10 and S/N(Ly-alpha)~10-15. Adopting mu>5, the absolute magnitudes, M_1500, and Ly-alpha fluxes, are fainter than -18.7 and 2.8x10^(-18)erg/s/cm2, respectively. We find a very steep ultraviolet spectral slope beta=-3.0+/-0.5 (F_lambda=lambda^(beta)), implying that these are very young, dust-free and low metallicity objects, made of standard stellar populations or even extremely metal poor stars (age<~30Myr, E(B-V)=0 and metallicity 0.0-0.2 Z/Zsolar). The objects are compact (< 1 kpc^(2)), and with a stellar mass M* < 10^(8) M_solar. The very steep beta, the presence of the Ly-alpha line and the intrinsic FWHM (<300 km/s) of these newborn objects do not exclude a possible leakage of ionizing radiation. We discuss the possibility that such faint galaxies may resemble those responsible for cosmic reionization.

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Type-Ia Supernova Rates to Redshift 2.4 from CLASH: the Cluster Lensing And Supernova survey with Hubble

We present the supernova (SN) sample and Type-Ia SN (SN Ia) rates from the Cluster Lensing And Supernova survey with Hubble (CLASH). Using the Advanced Camera for Surveys and the Wide Field Camera 3 on the Hubble Space Telescope (HST), we have imaged 25 galaxy-cluster fields and parallel fields of non-cluster galaxies. We report a sample of 27 SNe discovered in the parallel fields. Of these SNe, ~13 are classified as SN Ia candidates, including four SN Ia candidates at redshifts z > 1.2. We measure volumetric SN Ia rates to redshift 1.8 and add the first upper limit on the SN Ia rate in the range 1.8 < z < 2.4. The results are consistent with the rates measured by the HST/GOODS and Subaru Deep Field SN surveys. We model these results together with previous measurements at z < 1 from the literature. The best-fitting SN Ia delay-time distribution (DTD; the distribution of times that elapse between a short burst of star formation and subsequent SN Ia explosions) is a power law with an index of -1.00 +0.06(0.09) -0.06(0.10) (statistical) +0.12 -0.08 (systematic), where the statistical uncertainty is a result of the 68% and 95% (in parentheses) statistical uncertainties reported for the various SN Ia rates (from this work and from the literature), and the systematic uncertainty reflects the range of possible cosmic star-formation histories. We also test DTD models produced by an assortment of published binary population synthesis (BPS) simulations. The shapes of all BPS double-degenerate DTDs are consistent with the volumetric SN Ia measurements, when the DTD models are scaled up by factors of 3-9. In contrast, all BPS single-degenerate DTDs are ruled out by the measurements at a >99% significance level.

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CLASH: Photometric redshifts with 16 HST bands in galaxy cluster fields

The Cluster Lensing And Supernovae survey with Hubble (CLASH) is an Hubble Space Telescope (HST) Multi-Cycle Treasury program observing 25 massive galaxy clusters. CLASH observations are carried out in 16 bands from UV to NIR to derive accurate and reliable estimates of photometric redshifts. We present the CLASH photometric redshifts and study the photometric redshift accuracy of the arcs in more detail for the case of MACS1206.2-0847. We use the publicly available Le Phare and BPZ photometric redshift codes on 17 CLASH galaxy clusters. Using Le Phare code for objects with StoN>=10, we reach a precision of 3%(1+z) for the strong lensing arcs, which is reduced to 2.4%(1+z) after removing outliers. For galaxies in the cluster field the corresponding values are 4%(1+z) and 3%(1+z). Using mock galaxy catalogues, we show that 3%(1+z) precision is what one would expect from the CLASH photometry when taking into account extinction from dust, emission lines and the finite range of SEDs included in the photo-z template library. We study photo-z results for different aperture photometry and find that the SExtractor isophotal photometry works best. Le Phare and BPZ give similar photo-z results for the strong lensing arcs as well as galaxies of the cluster field. Results are improved when optimizing the photometric aperture shape showing an optimal aperture size around 1" radius giving results which are equivalent to isophotal photometry. Tailored photometry of the arcs improve the photo-z results.

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CLASH: z ~ 6 young galaxy candidate quintuply lensed by the frontier field cluster RXC J2248.7-4431

We present a quintuply lensed z ~ 6 candidate discovered in the field of the galaxy cluster RXC J2248.7-4431 (z ~ 0.348) targeted within the Cluster Lensing and Supernova survey with Hubble (CLASH) and selected in the deep HST Frontier Fields survey. Thanks to the CLASH 16-band HST imaging, we identify the quintuply lensed z ~ 6 candidate as an optical dropout in the inner region of the cluster, the brightest image having magAB=24.81+-0.02 in the f105w filter. We perform a detailed photometric analysis to verify its high-z and lensed nature. We get as photometric redshift z_phot ~ 5.9, and given the extended nature and NIR colours of the lensed images, we rule out low-z early type and galactic star contaminants. We perform a strong lensing analysis of the cluster, using 13 families of multiple lensed images identified in the HST images. Our final best model predicts the high-z quintuply lensed system with a position accuracy of 0.8''. The magnifications of the five images are between 2.2 and 8.3, which leads to a delensed UV luminosity of L_1600 ~ 0.5L*_1600 at z=6. We also estimate the UV slope from the observed NIR colours, finding a steep beta=-2.89+-0.38. We use singular and composite stellar population SEDs to fit the photometry of the hiz candidate, and we conclude that it is a young (age <300 Myr) galaxy with mass of M ~ 10^8Msol, subsolar metallicity (Z<0.2Zsol) and low dust content (AV ~ 0.2-0.4).

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CLASH-VLT: spectroscopic confirmation of a z=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.

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CLASH-VLT: The mass, velocity-anisotropy, and pseudo-phase-space density profiles of the z=0.44 galaxy cluster MACS 1206.2-0847

We use an unprecedented data-set of about 600 redshifts for cluster members, obtained as part of a VLT/VIMOS large programme, to constrain the mass profile of the z=0.44 cluster MACS J1206.2-0847 over the radial range 0-5 Mpc (0-2.5 virial radii) using the MAMPOSSt and Caustic methods. We then add external constraints from our previous gravitational lensing analysis. We invert the Jeans equation to obtain the velocity-anisotropy profiles of cluster members. With the mass-density and velocity-anisotropy profiles we then obtain the first determination of a cluster pseudo-phase-space density profile. The kinematics and lensing determinations of the cluster mass profile are in excellent agreement. This is very well fitted by a NFW model with mass M200=(1.4 +- 0.2) 10^15 Msun and concentration c200=6 +- 1, only slightly higher than theoretical expectations. Other mass profile models also provide acceptable fits to our data, of (slightly) lower (Burkert, Hernquist, and Softened Isothermal Sphere) or comparable (Einasto) quality than NFW. The velocity anisotropy profiles of the passive and star-forming cluster members are similar, close to isotropic near the center and increasingly radial outside. Passive cluster members follow extremely well the theoretical expectations for the pseudo-phase-space density profile and the relation between the slope of the mass-density profile and the velocity anisotropy. Star-forming cluster members show marginal deviations from theoretical expectations. This is the most accurate determination of a cluster mass profile out to a radius of 5 Mpc, and the only determination of the velocity-anisotropy and pseudo-phase-space density profiles of both passive and star-forming galaxies for an individual cluster [abridged]

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Evidence for Ubiquitous, High-EW Nebular Emission in z~7 Galaxies: Towards a Clean Measurement of the Specific Star Formation Rate using a Sample of Bright, Magnified Galaxies

Growing observational evidence now indicates that nebular line emission has a significant impact on the rest-frame optical fluxes of z~5-7 galaxies observed with Spitzer. This line emission makes z~5-7 galaxies appear more massive, with lower specific star formation rates. However, corrections for this line emission have been very difficult to perform reliably due to huge uncertainties on the overall strength of such emission at z>~5.5. Here, we present the most direct observational evidence yet for ubiquitous high-EW [OIII]+Hbeta line emission in Lyman-break galaxies at z~7, while also presenting a strategy for an improved measurement of the sSFR at z~7. We accomplish this through the selection of bright galaxies in the narrow redshift window z~6.6-7.0 where the IRAC 4.5 micron flux provides a clean measurement of the stellar continuum light. Observed 4.5 micron fluxes in this window contrast with the 3.6 micron fluxes which are contaminated by the prominent [OIII]+Hbeta lines. To ensure a high S/N for our IRAC flux measurements, we consider only the brightest (H_{160}<26 mag) magnified galaxies we have identified in CLASH and other programs targeting galaxy clusters. Remarkably, the mean rest-frame optical color for our bright seven-source sample is very blue, [3.6]-[4.5]=-0.9+/-0.3. Such blue colors cannot be explained by the stellar continuum light and require that the rest-frame EW of [OIII]+Hbeta be greater than 637 Angstroms for the average source. The bluest four sources from our seven-source sample require an even more extreme EW of 1582 Angstroms. Our derived lower limit for the mean [OIII]+Hbeta EW could underestimate the true EW by ~2x based on a simple modeling of the redshift distribution of our sources. We can also set a robust lower limit of >~4 Gyr^-1 on the specific star formation rates based on the mean SED for our seven-source sample. (abridged)

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Constraining the luminosity function of faint undetected i-dropout galaxies

We present a new technique to quantify the light contribution coming from the faint high redshift ($z\sim6$) galaxies below the detection threshold of imaging data, set conventionally at S/N=4.5. We illustrate the technique with an application to Hubble Space Telescope Advanced Camera for Surveys images in the F775W and F850LP filters of the Ultra Deep Field parallel field NICP12. The aim of this analysis is to extend by a few magnitudes the faint end of the luminosity function at $z\sim6$. After masking all the detected sources in the field we apply a Fast Fourier Transform to obtain the spatial power spectrum of the background signal. The power spectrum permits us to separate the background noise signal, the residuals due to the data reduction of the wide field, and the overall signal produced by faint galaxies. The ratio of the signal in the i_775 and z_850 bands is used to estimate the contribution of the faint i-dropout objects. We rely on extensive Monte Carlo simulations to characterize various sources of uncertainty and quantify the number of faint i-dropout galaxies in the field. The analysis allows us to put constraints on the luminosity function at $z\sim6$ down to z_850= 30 mag, 2.5 mag fainter than with standard techniques on the same data. The data are consistent with a faint end slope of the luminosity function of $α= -1.9$. Assuming a specific set of values for the clumping factor, escape fraction, and spectral energy distribution, we find that the $z\sim6$ undetected galaxies down to z_850=30 mag could have driven cosmic reionization.

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On-Orbit Degradation of Solar Instruments

We present the lessons learned about the degradation observed in several space solar missions, based on contributions at the Workshop about On-Orbit Degradation of Solar and Space Weather Instruments that took place at the Solar Terrestrial Centre of Excellence (Royal Observatory of Belgium) in Brussels on 3 May 2012. The aim of this workshop was to open discussions related to the degradation observed in Sun-observing instruments exposed to the effects of the space environment. This article summarizes the various lessons learned and offers recommendations to reduce or correct expected degradation with the goal of increasing the useful lifespan of future and ongoing space missions.

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The Cluster Lensing and Supernova Survey with Hubble (CLASH): Strong Lensing Analysis of Abell 383 from 16-Band HST WFC3/ACS Imaging

We examine the inner mass distribution of the relaxed galaxy cluster Abell 383 in deep 16-band HST/ACS+WFC3 imaging taken as part of the CLASH multi-cycle treasury program. Our program is designed to study the dark matter distribution in 25 massive clusters, and balances depth with a wide wavelength coverage to better identify lensed systems and generate precise photometric redshifts. This information together with the predictive strength of our strong-lensing analysis method identifies 13 new multiply-lensed images and candidates, so that a total of 27 multiple-images of 9 systems are used to tightly constrain the inner mass profile, $d\log Σ/d\log r\simeq -0.6\pm 0.1$ (r<160 kpc). We find consistency with the standard distance-redshift relation for the full range spanned by the lensed images, 1.01<z<6.03, with the higher redshift sources deflected through larger angles as expected. The inner mass profile derived here is consistent with the results of our independent weak-lensing analysis of wide-field Subaru images, with good agreement in the region of overlap. The overall mass profile is well fitted by an NFW profile with M_{vir}=(5.37^{+0.70}_{-0.63}\pm 0.26) x 10^{14}M_{\odot}/h and a relatively high concentration, c_{vir}=8.77^{+0.44}_{-0.42}\pm 0.23, which lies above the standard c-M relation similar to other well-studied clusters. The critical radius of Abell 383 is modest by the standards of other lensing clusters, r_{E}\simeq16\pm2\arcsec (for z_s=2.55), so the relatively large number of lensed images uncovered here with precise photometric redshifts validates our imaging strategy for the CLASH survey. In total we aim to provide similarly high-quality lensing data for 25 clusters, 20 of which are X-ray selected relaxed clusters, enabling a precise determination of the representative mass profile free from lensing bias. (ABRIDGED)

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CLASH: Discovery of a Bright z~6.2 Dwarf Galaxy Quadruply Lensed by MACS J0329.6-0211

We report the discovery of a z_{phot}=6.18^{+0.05}_{-0.07} (95% confidence level) dwarf galaxy, lensed into four images by the galaxy cluster MACS J0329.6-0211 (z_{l}=0.45). The galaxy is observed as a high-redshift dropout in HST/ACS/WFC3 CLASH and Spitzer/IRAC imaging. Its redshift is securely determined due to a clear detection of the Lyman-break in the 18-band photometry, making this galaxy one of the highest-redshift multiply-lensed objects known to date with an observed magnitude of F125W=24.00\pm0.04 AB mag for its highest-magnified image. We also present the first strong-lensing analysis of this cluster uncovering 15 additional multiply-imaged candidates of five lower-redshift sources spanning the range z_{s}~2-4. The mass model independently supports the high photometric redshift and reveals magnifications of 11.6^{+8.9}_{-4.1}, 17.6^{+6.2}_{-3.9}, 3.9^{+3.0}_{-1.7}, and 3.7^{+1.3}_{-0.2}, respectively, for the four images of the high-redshift galaxy. With this we construct a source image with a physical resolution of ~200 pc when the universe was ~0.9 Gyr old, where the z~6.2 galaxy occupies a source-plane area of approximately 2.2 kpc^{2}. Modeling the observed spectral energy distribution using population synthesis models, we find a demagnified stellar mass of ~10^{9} {M}_{sun}, subsolar metallicity (Z/Z_{sun}~0.5), low dust content (A_{V}~0.1 mag), a demagnified star formation rate (SFR) of ~3.2 {M}_{sun} yr^{-1}, and a specific SFR of ~3.4 Gyr^{-1}, all consistent with the properties of local dwarf galaxies.

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CLASH: New Multiple-Images Constraining the Inner Mass Profile of MACS J1206.2-0847

We present a strong-lensing analysis of the galaxy cluster MACS J1206.2-0847 ($z$=0.44) using UV, Optical, and IR, HST/ACS/WFC3 data taken as part of the CLASH multi-cycle treasury program, with VLT/VIMOS spectroscopy for some of the multiply-lensed arcs. The CLASH observations, combined with our mass-model, allow us to identify 47 new multiply-lensed images of 12 distant sources. These images, along with the previously known arc, span the redshift range $1\la z\la5.5$, and thus enable us to derive a detailed mass distribution and to accurately constrain, for the first time, the inner mass-profile of this cluster. We find an inner profile slope of $d\log Σ/d\log θ\simeq -0.55\pm 0.1$ (in the range [1\arcsec, 53\arcsec], or $5\la r \la300$ kpc), as commonly found for relaxed and well-concentrated clusters. Using the many systems uncovered here we derive credible critical curves and Einstein radii for different source redshifts. For a source at $z_{s}\simeq2.5$, the critical curve encloses a large area with an effective Einstein radius of $θ_{E}=28\pm3\arcsec$, and a projected mass of $1.34\pm0.15\times10^{14} M_{\odot}$. From the current understanding of structure formation in concordance cosmology, these values are relatively high for clusters at $z\sim0.5$, so that detailed studies of the inner mass distribution of clusters such as MACS J1206.2-0847 can provide stringent tests of the $Λ$CDM paradigm.

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