arXiv subjects

Jack Sayers

Publications and source records attributed to Jack Sayers.

At least 73 records · Page 4Linked to original sources

arXiv2016

Peculiar Velocity Constraints from Five-Band SZ Effect Measurements Towards RX J1347.5-1145 with MUSIC and Bolocam from the CSO

We present Sunyaev-Zel'dovich (SZ) effect measurements from wide-field images towards the galaxy cluster RX J1347.5-1145 obtained from the Caltech Submillimeter Observatory with the Multiwavelength Submillimeter Inductance Camera (MUSIC) at 147, 213, 281, and 337 GHz and with Bolocam at 140 GHz. As part of our analysis, we have used higher frequency data from Herschel-SPIRE and previously published lower frequency radio data to subtract the signal from the brightest dusty star-forming galaxies behind RX J1347.5-1145 and from the AGN in RX J1347.5-1145's BCG. Using these five-band SZ effect images, combined with X-ray spectroscopic measurements of the temperature of the intra-cluster medium (ICM) from Chandra, we constrain the ICM optical depth to be $τ_e = 7.33^{+0.96}_{-0.97} \times 10^{-3}$ and the ICM line of sight peculiar velocity to be $v_{pec} = -1040^{+870}_{-840}$ km s$^{-1}$. The errors for both quantities are limited by measurement noise rather than calibration uncertainties or astrophysical contamination, and significant improvements are possible with deeper observations. Our best-fit velocity is in good agreement with one previously published SZ effect analysis and in mild tension with the other, although some or all of that tension may be because that measurement samples a much smaller cluster volume. Furthermore, our best-fit optical depth implies a gas mass slightly larger than the Chandra-derived value, implying the cluster is elongated along the line of sight.

astro-ph.CO↗

arXiv2016

The Morphologies and Alignments of Gas, Mass, and the Central Galaxies of CLASH Clusters of Galaxies

Morphology is often used to infer the state of relaxation of galaxy clusters. The regularity, symmetry, and degree to which a cluster is centrally concentrated inform quantitative measures of cluster morphology. The Cluster Lensing and Supernova survey with Hubble Space Telescope (CLASH) used weak and strong lensing to measure the distribution of matter within a sample of 25 clusters, 20 of which were deemed to be relaxed based on their X-ray morphology and alignment of the X-ray emission with the BCG. Towards a quantitative characterization of this important sample of clusters, we present uniformly estimated X-ray morphological statistics for all 25 CLASH clusters. We compare X-ray morphologies of CLASH clusters with those identically measured for a large sample of simulated clusters from the MUSIC-2 simulations, selected by mass. We confirm a threshold in X-ray surface brightness concentration of C>0.4 for cool-core clusters, where C is the ratio of X-ray emission inside 100 kpc/h70 compared to inside 500 kpc/h70. We report and compare morphologies of these clusters inferred from Sunyaev-Zeldovich Effect (SZE) maps of the hot gas and in from projected mass maps based on strong and weak lensing. We find a strong agreement in alignments of the orientation of major axes for the lensing, X-ray, and SZE maps of nearly all of the CLASH clusters at radii of 500 kpc (approximately 0.5R500 for these clusters). We also find a striking alignment of clusters shapes at the 500 kpc scale, as measured with X-ray, SZE, and lensing, with that of the near-infrared stellar light at 10 kpc scales for the 20 "relaxed" clusters. This strong alignment indicates a powerful coupling between the cluster- and galaxy-scale galaxy formation processes.

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arXiv2015

CLASH-X: A Comparison of Lensing and X-ray Techniques for Measuring the Mass Profiles of Galaxy Clusters

We present profiles of temperature (Tx), gas mass, and hydrostatic mass estimated from new and archival X-ray observations of CLASH clusters. We compare measurements derived from XMM and Chandra observations with one another and compare both to gravitational lensing mass profiles derived with CLASH HST and ground-based lensing data. Radial profiles of Chandra and XMM electron density and enclosed gas mass are nearly identical, indicating that differences in hydrostatic masses inferred from X-ray observations arise from differences in Tx measurements. Encouragingly, cluster Txs are consistent with one another at ~100-200 kpc radii but XMM Tx systematically decline relative to Chandra Tx at larger radii. The angular dependence of the discrepancy suggests additional investigation on systematics such as the XMM point spread function correction, vignetting and off-axis responses. We present the CLASH-X mass-profile comparisons in the form of cosmology-independent and redshift-independent circular-velocity profiles. Ratios of Chandra HSE mass profiles to CLASH lensing profiles show no obvious radial dependence in the 0.3-0.8 Mpc range. However, the mean mass biases inferred from the WL and SaWLens data are different. e.g., the weighted-mean value at 0.5 Mpc is = 0.12 for the WL comparison and = -0.11 for the SaWLens comparison. The ratios of XMM HSE mass profiles to CLASH lensing profiles show a pronounced radial dependence in the 0.3-1.0 Mpc range, with a weighted mean mass bias of value rising to ~0.3 at ~1 Mpc for the WL comparison and of 0.25 for SaWLens comparison. The enclosed gas mass profiles from both Chandra and XMM rise to a value 1/8 times the total-mass profiles inferred from lensing at 0.5 Mpc and remain constant outside of that radius, suggesting that [8xMgas] profiles may be an excellent proxy for total-mass profiles at >0.5 Mpc in massive galaxy clusters.

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arXiv2015

Galaxy Cluster Pressure Profiles as Determined by Sunyaev Zel'dovich Effect Observations with MUSTANG and Bolocam I: Joint Analysis Technique

We present a technique to constrain galaxy cluster pressure profiles by jointly fitting Sunyaev-Zel'dovich effect (SZE) data obtained with MUSTANG and Bolocam for the clusters Abell 1835 and MACS0647. Bolocam and MUSTANG probe different angular scales and are thus highly complementary. We find that the addition of the high resolution MUSTANG data can improve constraints on pressure profile parameters relative to those derived solely from Bolocam. In Abell 1835 and MACS0647, we find gNFW inner slopes of $γ= 0.36_{-0.21}^{+0.33}$ and $γ= 0.38_{-0.25}^{+0.20}$, respectively when $α$ and $β$ are constrained to 0.86 and 4.67 respectively. The fitted SZE pressure profiles are in good agreement with X-ray derived pressure profiles.

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arXiv2015

The Most Luminous Galaxies Discovered by WISE

We present 20 WISE-selected galaxies with bolometric luminosities L_bol > 10^14 L_sun, including five with infrared luminosities L_IR = L(rest 8-1000 micron) > 10^14 L_sun. These "extremely luminous infrared galaxies," or ELIRGs, were discovered using the "W1W2-dropout" selection criteria which requires marginal or non-detections at 3.4 and 4.6 micron (W1 and W2, respectively) but strong detections at 12 and 22 micron in the WISE survey. Their spectral energy distributions are dominated by emission at rest-frame 4-10 micron, suggesting that hot dust with T_d ~ 450K is responsible for the high luminosities. These galaxies are likely powered by highly obscured AGNs, and there is no evidence suggesting these systems are beamed or lensed. We compare this WISE-selected sample with 116 optically selected quasars that reach the same L_bol level, corresponding to the most luminous unobscured quasars in the literature. We find that the rest-frame 5.8 and 7.8 micron luminosities of the WISE-selected ELIRGs can be 30-80% higher than that of the unobscured quasars. The existence of AGNs with L_bol > 10^14 L_sun at z > 3 suggests that these supermassive black holes are born with large mass, or have very rapid mass assembly. For black hole seed masses ~ 10^3 M_sun, either sustained super-Eddington accretion is needed, or the radiative efficiency must be <15%, implying a black hole with slow spin, possibly due to chaotic accretion.

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arXiv2014

Measurements of the Sunyaev-Zel'dovich Effect in MACS J0647.7+7015 and MACS J1206.2-0847 at High Angular Resolution with MUSTANG

We present high resolution (9$^{\prime \prime}$) imaging of the Sunyaev-Zel'dovich Effect (SZE) toward two massive galaxy clusters, MACS J0647.7+7015 ($z=0.591$) and MACS J1206.2-0847 ($z=0.439$). We compare these 90 GHz measurements, taken with the MUSTANG receiver on the Green Bank Telescope, with generalized Navarro-Frenk-White (gNFW) models derived from Bolocam 140 GHz SZE data as well as maps of the thermal gas derived from {\it Chandra} X-ray observations. For MACS J0647.7+7015, we find a gNFW profile with core slope parameter $γ= 0.9$ fits the MUSTANG image with $χ^{2}_{red}=1.005$ and probability to exceed (PTE) = 0.34. For MACS J1206.2-0847, we find $γ=0.7$, $χ^{2}_{red}=0.993$, and PTE = 0.70. In addition, we find a significant ($>$3-$σ$) residual SZE feature in MACS J1206.2-0847 coincident with a group of galaxies identified in VLT data and filamentary structure found in a weak-lensing mass reconstruction. We suggest the detected sub-structure may be the SZE decrement from a low mass foreground group or an infalling group. GMRT measurements at 610 MHz reveal diffuse extended radio emission to the west, which we posit is either an AGN-driven radio lobe, a bubble expanding away from disturbed gas associated with the SZE signal, or a bubble detached and perhaps re-accelerated by sloshing within the cluster. Using the spectroscopic redshifts available, we find evidence for a foreground ($z=0.423$) or infalling group, coincident with the residual SZE feature.

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arXiv2014

An overview of the planned CCAT software system

CCAT will be a 25m diameter sub-millimeter telescope capable of operating in the 0.2 to 2.1mm wavelength range. It will be located at an altitude of 5600m on Cerro Chajnantor in northern Chile near the ALMA site. The anticipated first generation instruments include large format (60,000 pixel) kinetic inductance detector (KID) cameras, a large format heterodyne array and a direct detection multi-object spectrometer. The paper describes the architecture of the CCAT software and the development strategy.

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arXiv2014

Map-making for the Next Generation of Ground-based Submillimeter Instruments

Current ground-based submillimeter instruments (e.g. SCUBA-2, SHARC-2 and LABOCA) have hundreds to thousands of detectors, sampled at tens to hundreds of hertz, generating up to hundreds of gigabytes per night. Since noise is correlated between detectors and in time, due to atmospheric signals and temperature oscillations, naive map-making is not applicable. In addition, the size of the data sets makes direct likelihood based inversion techniques intractable. As a result, the data reduction approach for most current submm cameras is to adopt iterative methods in order to separate noise from sky signal, and hence effectively produce astronomical images. We investigate how today's map-makers scale to the next generation of instruments, which will have tens of thousands of detectors sampled at thousands of hertz, leading to data sets of challenging size. We propose strategies for reducing such large data sets.

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arXiv2014

The CCAT Software System

CCAT will be a 25-meter telescope for sub millimeter astronomy located at 5600m altitude on Cerro Chajnantor in northern Chile. CCAT will combine high sensitivity, a wide field of view, and a broad wavelength range (0.35 to 2.1mm) to provide an unprecedented capability for deep, large-area multicolor submillimeter surveys. It is planned to have a suite of instruments including large format KID cameras, a large heterodyne array and a KID-based direct detection multi-object spectrometer. The remote location drives a desire for fully autonomous observing coupled with data reduction pipelines and fast feedback to principal investigators.

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arXiv2013

A Measurement of the Kinetic Sunyaev-Zel'dovich Signal Toward MACS J0717.5+3745

We report our analysis of MACS J0717.5+3745 using 140 and 268 GHz Bolocam data collected at the Caltech Submillimeter Observatory. We detect extended Sunyaev-Zel'dovich (SZ) effect signal at high significance in both Bolocam bands, and we employ Herschel-SPIRE observations to subtract the signal from dusty background galaxies in the 268 GHz data. We constrain the two-band SZ surface brightness toward two of the sub-clusters of MACS J0717.5+3745: the main sub-cluster (named C), and a sub-cluster identified in spectroscopic optical data to have a line-of-sight velocity of +3200 km/s (named B). We determine the surface brightness in two separate ways: via fits of parametric models and via direct integration of the images. For both sub-clusters, we find consistent surface brightnesses from both analysis methods. We constrain spectral templates consisting of relativistically corrected thermal and kinetic SZ signals, using a jointly-derived electron temperature from Chandra and XMM-Newton under the assumption that each sub-cluster is isothermal. The data show no evidence for a kinetic SZ signal toward sub-cluster C, but they do indicate a significant kinetic SZ signal toward sub-cluster B. The model-derived surface brightnesses for sub-cluster B yield a best-fit line-of-sight velocity of v_z = +3450 +- 900 km/s, with (1 - Prob[v_z > 0]) = 1.3 x 10^-5 (4.2 sigma away from 0 for a Gaussian distribution). The directly integrated sub-cluster B SZ surface brightnesses provide a best-fit v_z = +2550 +- 1050 km/s, with (1 - Prob[v_z > 0]) = 2.2 x 10^-3 (2.9 sigma).

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arXiv2013

WISE Discovery of Hyper Luminous Galaxies at z=2-4 and Their Implications for Galaxy and AGN Evolution

On behalf of the WISE Science team, we present the discovery of a class of distant dust-enshrouded galaxies with extremely high luminosity. These galaxies are selected to have extreme red colors in the mid-IR using NASA's Wide-field Infrared Survey Explorer (WISE). They are faint in the optical and near-IR, predominantly at z=2-4, and with IR luminosity > $10^{13}\, L_{Sun}$, making them Hyper-Luminous Infrared Galaxies (HyLIRGs). SEDs incorporating the WISE, Spitzer, and Herschel PACS and SPIRE photometry indicate hot dust dominates the bolometric luminosity, presumably powered by AGN. Preliminary multi-wavelength follow-up suggests that they are different from normal populations in the local M-sigma relation. Their low source density implies that these objects are either intrinsically rare, or a short-lived phase in a more numerous population. If the latter is the case, these hot, dust-enshrouded galaxies may be an early stage in the interplay between AGN and galaxies.

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arXiv2013

CLASH: Complete Lensing Analysis of the Largest Cosmic Lens MACS J0717.5+3745 and Surrounding Structures

The galaxy cluster MACS J0717.5+3745 (z=0.55) is the largest known cosmic lens, with complex internal structures seen in deep X-ray, Sunyaev-Zel'dovich effect and dynamical observations. We perform a combined weak and strong lensing analysis with wide-field BVRi'z' Subaru/Suprime-Cam observations and 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble (CLASH). We find consistent weak distortion and magnification measurements of background galaxies, and combine these signals to construct an optimally estimated radial mass profile of the cluster and its surrounding large-scale structure out to 5 Mpc/h. We find consistency between strong-lensing and weak-lensing in the region where these independent data overlap, <500 kpc/h. The two-dimensional weak-lensing map reveals a clear filamentary structure traced by distinct mass halos. We model the lensing shear field with 9 halos, including the main cluster, corresponding to mass peaks detected above 2.5σ_κ. The total mass of the cluster as determined by the different methods is M_{vir}=(2.8\pm0.4) \times 10^15 M_sun. Although this is the most massive cluster known at z>0.5, in terms of extreme value statistics we conclude that the mass of MACS J0717.5+3745 by itself is not in serious tension with LambdaCDM, representing only a ~2σ departure above the maximum simulated halo mass at this redshift.

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arXiv2013

Sunyaev-Zel'dovich-Measured Pressure Profiles from the Bolocam X-ray/SZ Galaxy Cluster Sample

We describe Sunyaev-Zel'dovich (SZ) effect measurements and analysis of the intracluster medium (ICM) pressure profiles of a set of 45 massive galaxy clusters imaged using Bolocam at the Caltech Submillimeter Observatory. We have used masses determined from Chandra X-ray observations to scale each cluster's profile by the overdensity radius R500 and the mass-and-redshift-dependent normalization factor P500. We deproject the average pressure profile of our sample into 13 logarithmically spaced radial bins between 0.07R500 and 3.5R500. We find that a generalized Navarro, Frenk, and White (gNFW) profile describes our data with sufficient goodness-of-fit and best-fit parameters (C500, alpha, beta, gamma, P0 = 1.18, 0.86, 3.67, 0.67, 4.29). We also use the X-ray data to define cool-core and disturbed subsamples of clusters, and we constrain the average pressure profiles of each of these subsamples. We find that given the precision of our data the average pressure profiles of disturbed and cool-core clusters are consistent with one another at R>~0.15R500, with cool-core systems showing indications of higher pressure at R<~0.15R500. In addition, for the first time, we place simultaneous constraints on the mass scaling of cluster pressure profiles, their ensemble mean profile, and their radius-dependent intrinsic scatter between 0.1R500 and 2.0R500. The scatter among profiles is minimized at radii between ~0.2R500 and ~0.5R500, with a value of ~20%. The best-fit mass scaling has a power-law slope of 0.49, which is shallower than the nominal prediction of 2/3 from self-similar hydrostatic equilibrium models. These results for the intrinsic scatter and mass scaling are largely consistent with previous analyses, most of which have relied heavily on X-ray derived pressures of clusters at significantly lower masses and redshifts compared to our sample.

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arXiv2013

The Contribution of Radio Galaxy Contamination to Measurements of the Sunyaev-Zel'dovich Decrement in Massive Galaxy Clusters at 140 GHz with Bolocam

We describe in detail our characterization of the compact radio source population in 140 GHz Bolocam observations of a set of 45 massive galaxy clusters. We use a combination of 1.4 and 30 GHz data to select a total of 28 probable cluster-member radio galaxies and also to predict their 140 GHz flux densities. All of these galaxies are steep-spectrum radio sources and they are found preferentially in the cool-core clusters within our sample. In particular, 11 of the 12 brightest cluster member radio sources are associated with cool-core systems. Although none of the individual galaxies are robustly detected in the Bolocam data, the ensemble-average flux density at 140 GHz is consistent with, but slightly lower than, the extrapolation from lower frequencies assuming a constant spectral index. In addition, our data indicate an intrinsic scatter of 30 percent around the power-law extrapolated flux densities at 140 GHz, although our data do not tightly constrain this scatter. For our cluster sample, which is composed of high-mass and moderate-redshift systems, we find that the maximum fractional change in the Sunyaev-Zel'dovich signal integrated over any single cluster due to the presence of these radio sources is 20 percent, and only 1/4 of the clusters show a fractional change of more than 1 percent. The amount of contamination is strongly dependent on cluster morphology, and nearly all of the clusters with more than 1 percent contamination are cool-core systems. This result indicates that radio contamination is not significant compared to current noise levels in 140 GHz images of massive clusters and is in good agreement with the level of radio contamination found in previous results based on lower frequency data or simulations.

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arXiv2012

Status of MUSIC, the MUltiwavelength Sub/millimeter Inductance Camera

We present the status of MUSIC, the MUltiwavelength Sub/millimeter Inductance Camera, a new instrument for the Caltech Submillimeter Observatory. MUSIC is designed to have a 14', diffraction-limited field-of-view instrumented with 2304 detectors in 576 spatial pixels and four spectral bands at 0.87, 1.04, 1.33, and 1.98 mm. MUSIC will be used to study dusty star-forming galaxies, galaxy clusters via the Sunyaev-Zeldovich effect, and star formation in our own and nearby galaxies. MUSIC uses broadband superconducting phased-array slot-dipole antennas to form beams, lumped-element on-chip bandpass filters to define spectral bands, and microwave kinetic inductance detectors to senseincoming light. The focal plane is fabricated in 8 tiles consisting of 72 spatial pixels each. It is coupled to the telescope via an ambient temperature ellipsoidal mirror and a cold reimaging lens. A cold Lyot stop sits at the image of the primary mirror formed by the ellipsoidal mirror. Dielectric and metal mesh filters are used to block thermal infrared and out-of-band radiation. The instrument uses a pulse tube cooler and 3He/3He/4He closed-cycle cooler to cool the focal plane to below 250 mK. A multilayer shield attenuates Earth's magnetic field. Each focal plane tile is read out by a single pair of coaxes and a HEMT amplifier. The readout system consists of 16 copies of custom-designed ADC/DAC and IF boards coupled to the CASPER ROACH platform. We focus on recent updates on the instrument design and results from the commissioning of the full camera in 2012.

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arXiv2012

The First Hyper-Luminous Infrared Galaxy Discovered by WISE

We report the discovery by the Wide-field Infrared Survey Explorer of the z = 2.452 source WISE J181417.29+341224.9, the first hyperluminous source found in the WISE survey. WISE 1814+3412 is also the prototype for an all-sky sample of ~1000 extremely luminous "W1W2-dropouts" (sources faint or undetected by WISE at 3.4 and 4.6 microns and well detected at 12 or 22 microns). The WISE data and a 350 micron detection give a minimum bolometric luminosity of 3.7 x 10^13 Lsun, with ~10^14 Lsun plausible. Followup images reveal four nearby sources: a QSO and two Lyman Break Galaxies (LBGs) at z = 2.45, and an M dwarf star. The brighter LBG dominates the bolometric emission. Gravitational lensing is unlikely given the source locations and their different spectra and colors. The dominant LBG spectrum indicates a star formation rate ~300 Msun/yr, accounting for < 10% of the bolometric luminosity. Strong 22 micron emission relative to 350 microns implies that warm dust contributes significantly to the luminosity, while cooler dust normally associated with starbursts is constrained by an upper limit at 1.1 mm. Radio emission is ~10x above the far-infrared/radio correlation, indicating an active galactic nucleus is present. An obscured AGN combined with starburst and evolved stellar components can account for the observations. If the black hole mass follows the local M_BH-bulge mass relation, the implied Eddington ratio is >~4. WISE 1814+3412 may be a heavily obscured object where the peak AGN activity occurred prior to the peak era of star formation.

astro-ph.CO↗

arXiv2012

Submillimeter Follow-up of WISE-Selected Hyperluminous Galaxies

We have used the Caltech Submillimeter Observatory (CSO) to follow-up a sample of WISE-selected, hyperluminous galaxies, so called W1W2-dropout galaxies. This is a rare (~ 1000 all-sky) population of galaxies at high redshift (peaks at z=2-3), that are faint or undetected by WISE at 3.4 and 4.6 um, yet are clearly detected at 12 and 22 um. The optical spectra of most of these galaxies show significant AGN activity. We observed 14 high-redshift (z > 1.7) W1W2-dropout galaxies with SHARC-II at 350 to 850 um, with 9 detections; and observed 18 with Bolocam at 1.1 mm, with five detections. Warm Spitzer follow-up of 25 targets at 3.6 and 4.5 um, as well as optical spectra of 12 targets are also presented in the paper. Combining WISE data with observations from warm Spitzer and CSO, we constructed their mid-IR to millimeter spectral energy distributions (SEDs). These SEDs have a consistent shape, showing significantly higher mid-IR to submm ratios than other galaxy templates, suggesting a hotter dust temperature. We estimate their dust temperatures to be 60-120 K using a single-temperature model. Their infrared luminosities are well over 10^{13} Lsun. These SEDs are not well fitted with existing galaxy templates, suggesting they are a new population with very high luminosity and hot dust. They are likely among the most luminous galaxies in the Universe. We argue that they are extreme cases of luminous, hot dust-obscured galaxies (DOGs), possibly representing a short evolutionary phase during galaxy merging and evolution. A better understanding of their long-wavelength properties needs ALMA as well as Herschel data.

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arXiv2012

CLASH: Mass Distribution in and around MACS J1206.2-0847 from a Full Cluster Lensing Analysis

We derive an accurate mass distribution of the galaxy cluster MACS J1206.2-0847 (z=0.439) from a combined weak-lensing distortion, magnification, and strong-lensing analysis of wide-field Subaru BVRIz' imaging and our recent 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble (CLASH) program. We find good agreement in the regions of overlap between several weak and strong lensing mass reconstructions using a wide variety of modeling methods, ensuring consistency. The Subaru data reveal the presence of a surrounding large scale structure with the major axis running approximately north-west south-east (NW-SE), aligned with the cluster and its brightest galaxy shapes, showing elongation with a \sim 2:1 axis ratio in the plane of the sky. Our full-lensing mass profile exhibits a shallow profile slope dlnΣ/dlnR\sim -1 at cluster outskirts (R>1Mpc/h), whereas the mass distribution excluding the NW-SE excess regions steepens further out, well described by the Navarro-Frenk-White form. Assuming a spherical halo, we obtain a virial mass M_{vir}=(1.1\pm 0.2\pm 0.1)\times 10^{15} M_{sun}/h and a halo concentration c_{vir} = 6.9\pm 1.0\pm 1.2 (\sim 5.7 when the central 50kpc/h is excluded), which falls in the range 4< <7 of average c(M,z) predictions for relaxed clusters from recent Lambda cold dark matter simulations. Our full lensing results are found to be in agreement with X-ray mass measurements where the data overlap, and when combined with Chandra gas mass measurements, yield a cumulative gas mass fraction of 13.7^{+4.5}_{-3.0}% at 0.7Mpc/h (\approx 1.7r_{2500}), a typical value observed for high mass clusters.

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