arXiv subjects

Guillaume Desprez

Publications and source records attributed to Guillaume Desprez.

54 records · Page 3Linked to original sources

arXiv2024

$Λ$CDM not dead yet: massive high-z Balmer break galaxies are less common than previously reported

Early JWST observations that targeted so-called double-break sources (attributed to Lyman and Balmer breaks at $z>7$), reported a previously unknown population of very massive, evolved high-redshift galaxies. This surprising discovery led to a flurry of attempts to explain these objects' unexpected existence including invoking alternatives to the standard $Λ$CDM cosmological paradigm. To test these early results, we adopted the same double-break candidate galaxy selection criteria to search for such objects in the JWST images of the CAnadian NIRISS Unbiased Cluster Survey (CANUCS), and found a sample of 19 sources over five independent CANUCS fields that cover a total effective area of $\sim60\,$arcmin$^2$ at $z\sim8$. However, (1) our SED fits do not yield exceptionally high stellar masses for our candidates, while (2) spectroscopy of five of the candidates shows that while all five are at high redshifts, their red colours are due to high-EW emission lines in star-forming galaxies rather than Balmer breaks in massive, evolved systems. Additionally, (3) field-to-field variance leads to differences of $\sim 1.5$ dex in the maximum stellar masses measured in the different fields, suggesting that the early single-field JWST observations may have suffered from cosmic variance and/or sample bias. Finally, (4) we show that the presence of even a single massive outlier can dominate conclusions from small samples such as those in early JWST observations. In conclusion, we find that the double-break sources in CANUCS are not sufficiently massive or numerous to warrant questioning the standard $Λ$CDM paradigm.

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arXiv2024

A Steep Decline in the Galaxy Space Density Beyond Redshift 9 in the CANUCS UV Luminosity Function

We present a new sample of 158 galaxies at redshift $z>7.5$ selected from deep \jwst\ NIRCam imaging of five widely-separated sightlines in the CANUCS survey. Two-thirds of the pointings and 80\% of the galaxies are covered by 12 to 14 NIRCam filters, including seven to nine medium bands, providing accurate photometric redshifts and robustness against low redshift interlopers. A sample of 28 galaxies at $z>7.5$ with spectroscopic redshifts shows a low systematic offset and scatter in the difference between photometric and spectroscopic redshifts. We derive the galaxy UV luminosity function at redshifts 8 to 12, finding a slightly higher normalization than previously seen with \hst\ at redshifts 8 to 10. We observe a steeper decline in the galaxy space density from $z=8$ to $12$ than found by most \jwst\ Cycle 1 studies. In particular, we find only eight galaxies at $z>10$ and none at $z>12.5$, with no $z>10$ galaxies brighter than F277W AB=28 or $M_{\rm UV}=-20$ in our unmasked, delensed survey area of 53.4 square arcminutes. We attribute the lack of bright $z>10$ galaxies in CANUCS compared to GLASS and CEERS to intrinsic variance in the galaxy density along different sightlines. The evolution in the CANUCS luminosity function between $z=8$ and $12$ is comparable to that predicted by simulations that assume a standard star formation efficiency, without invoking any special adjustments.

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arXiv2024

Probing the stellar populations and star formation history of early-type galaxies at $0 < z < 1.1$ in the rest-frame ultraviolet

We measure the evolution of the rest-frame $NUV-V$ colors for early-type galaxies in clusters at $0 3$. The blue UV colors of early-type galaxies at low-intermediate redshifts are likely driven by this sub-population being enriched in helium up to $\sim44\%$. At $z>0.8$ (when the extra UV component has not yet appeared) the data allows us to constrain the star formation histories of galaxies by fitting models to the evolution of their UV colors: we find that the epoch at which the stellar populations formed ranges between $3<z_{form}<10$ (corresponding to $0.5-2.2$ Gyrs after the Big Bang) with a star-formation e-folding timescale of $τ=0.35-0.7$ Gyr, suggesting that these galaxies formed the majority of stars at very high redshift, with a brief yet intense burst of star-formation activity. The star formation history and chemical evolution of early-type galaxies resemble those of globular clusters, albeit on much larger scales.

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arXiv2024

CANUCS: An Updated Mass and Magnification Model of Abell 370 with JWST

We report an updated mass and magnification model of galaxy cluster Abell 370 using new NIRCam and NIRISS data from the CAnadian NIRISS Unbiased Cluster Survey (CANUCS). Using Lenstool and a combination of archival HST and MUSE data with new JWST data as constraints, we derive an improved gravitational lensing model and extract magnifications of background galaxies with uncertainties. Using our best fit model, we perform a search for new multiply imaged systems via predicted positions. We report no new multiply imaged systems with identifiable redshifts, likely due to already very deep HST and Spitzer data, but confirm a $z\sim8$ multiply imaged system by measuring its redshift with NIRISS and NIRSpec spectra. We find that the overall shape of the critical curve for a source at $z = 9.0$ is similar to previous models of Abell 370, with small changes. We investigate the $z\sim8$ galaxy with two images observable with an apparent magnitude in the F125W band of $26.0\pm0.2$ and $25.6\pm0.1$. After correcting for the magnifications of the images, 7.2$^{+0.2}_{-1.2}$ and 8.7$^{+0.4}_{-0.4}$, we use SED fitting to find an intrinsic stellar mass of log($M^*/M_{\odot})$ = 7.35$^{+0.04}_{-0.05}$, intrinsic SFR of 3.5$^{+2.2}_{-1.4}$ M$_{\odot}$/yr, and $M_{UV}$ of -21.3$^{+0.2}_{-0.2}$, which is close to the knee of the luminosity function at that redshift. Our model, and corresponding magnification, shear, and convergence maps are available on request and will be made publicly available on MAST in a CANUCS data release (DOI: 10.17909/ph4n-6n76).

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arXiv2024

The Firefly Sparkle: The Earliest Stages of the Assembly of A Milky Way-type Galaxy in a 600 Myr Old Universe

The most distant galaxies detected by JWST are assembling in a Universe that is less than 5\% of its present age. At these times, the progenitors of galaxies like the Milky Way are expected to be about 10,000 times less massive than they are now, with masses quite comparable to that of massive globular clusters seen in the local Universe. Composed today primarily of old stars and correlating with the properties of their parent dark matter halos, the first globular clusters are thought to have formed during the earliest stages of galaxy assembly. In this article we explore the connection between star clusters and galaxy assembly by showing JWST observations of a strongly lensed galaxy at zspec = 8.304, exhibiting a network of massive star clusters (the 'Firefly Sparkle') cocooned in a diffuse arc. The Firefly Sparkle exhibits the hallmarks expected of a future Milky Way-type galaxy captured during its earliest and most gas-rich stage of formation. The mass distribution of the galaxy seems to be concentrated in ten distinct clusters, with individual cluster masses that straddle the boundary between low-mass galaxies and high-mass globular clusters. The cluster ages suggest that they are gravitationally bound with star formation histories showing a recent starburst possibly triggered by the interaction with a companion galaxy at the same redshift at a projected distance of $\sim$2 kpc away from the Firefly Sparkle. The central star cluster shows nebular-dominated spectra consistent with high temperatures and a top-heavy initial mass function, the product of formation in a very metal poor environment. Combined with abundance matching that suggests that this is likely to be a progenitor of galaxies like our own, the Firefly Sparkle provides an unprecedented case study of a Milky Way-like galaxy in the earliest stages of its assembly in only a 600 million year old Universe.

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arXiv2024

Bursty star formation and galaxy-galaxy interactions in low-mass galaxies 1 Gyr after the Big Bang

We use CANUCS JWST/NIRCam imaging of galaxies behind the gravitationally-lensing cluster MACS J0417.5-1154 to investigate star formation burstiness in low-mass ($M_\star\sim10^8\ M_\odot$) galaxies at $z\sim4.7-6.5$. Our sample of 123 galaxies is selected using the Lyman break selection and photometric emission-line excess methods. Sixty per cent of the 123 galaxies in this sample have H$α$-to-UV flux ratios that deviate significantly from the range of $η_{1500}$ values consistent with smooth and steady star formation histories. This large fraction indicates that the majority of low-mass galaxies is experiencing bursty star formation histories at high redshift. We also searched for interacting galaxies in our sample and found that they are remarkably common ($\sim40$ per cent of the sample). Compared to non-interacting galaxies, interacting galaxies are more likely to have very low H$α$-to-UV ratios, suggesting that galaxy-galaxy interactions enhance star formation burstiness and enable faster quenching (with timescales of $\lesssim100$ Myr) that follows the rapid rise of star formation activity. Given the high frequency of galaxy-galaxy interactions and the rapid SFR fluctuations they appear to cause, we conclude that galaxy-galaxy interactions could be a leading cause of bursty star formation in low-mass, high-$z$ galaxies. They could thus play a significant role in the evolution of the galaxy population at early cosmological times.

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arXiv2024

Exposing Line Emission: A First Look At The Systematic Differences of Measuring Stellar Masses With JWST NIRCam Medium Versus Wide Band Photometry

Photometrically derived stellar masses are known to suffer from systematic uncertainties, particularly due to nebular emission contributions to the spectral energy distribution. Using \emph{JWST} NIRCam imaging from the CAnadian NIRISS Unbiased Cluster Survey (CANUCS), we introduce a comparison study of photometrically-derived redshifts and stellar masses based on two photometric catalogs of the same field spanning $\sim$0.4-4.5$μ$m: one consisting solely of wide band photometry, and another employing a combination of wide and medium band photometry. We find that \tilda70\% of galaxies have consistent photometric redshifts between both catalogs, with median stellar mass difference between the two catalogs of \lessthan\ 0.2 dex across all redshift bins. There are however a subset of galaxies (5\% at z\tilda2 up to 15\% at z\tilda6) where wide bands underestimate star formation rates and infer older stellar populations, leading to median stellar mass differences of \tilda0.7 dex. Examination of the SEDs for galaxies with inconsistent photometric redshifts shows this is caused by the inability of the wide bands to distinguish continuum emission from emission lines. Computing a stellar mass density with our sample we find that it is potentially underestimated using wide-band photometry by \tilda10-20\% at z \lessthan\ \ 4, and potentially overestimated by as much as a factor of 2-3 at z \greaterthan\ 5. These systematic differences caused by the poor spectral resolution of wide bands have implications for both ongoing and future planned observing programs which determine stellar mass and other physical properties of high redshift galaxies solely via wide band photometry.

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arXiv2024

Two rest-frame wavelength measurements of galaxy sizes at $z<1$: the evolutionary effects of emerging bulges and quenched newcomers

We analyze the size evolution of $16000$ star-forming galaxies (SFGs) and $5000$ quiescent galaxies (QGs) with mass $M_*>10^{9.5}M_\odot$ at $0.1 9$ are red and only QGs have $\logΣ_1>9.7$. The size of $M_*=M_0$ QGs grows by $50\%$ ($110\%$) in the UV (visible) light. Up to $\sim20\%$ of this increase in size of massive QGs is due to newcomers (recently quenched galaxies). However, newcomers cannot explain the observed pace in the size growth of QGs; that trend has to be dominated by processes affecting individual galaxies, such as minor mergers and accretion.

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arXiv2023

Star Formation at the Epoch of Reionization with CANUCS: The ages of stellar populations in MACS1149-JD1

We present measurements of stellar populations properties of a z = 9.1 gravitationally lensed galaxy MACS1149-JD1 using deep JWST NIRISS slitless spectroscopy as well as NIRISS and NIRCam imaging from the CAnadian NIRISS Unbiased Cluster Survey (CANUCS). The galaxy is split into four components. Three magnified ($μ$ ~ 17) star-forming components are unresolved, giving intrinsic sizes of < 50pc. In addition, the underlying extended component contains the bulk of the stellar mass, formed the majority of its stars ~ 50Myr earlier than the other three components and is not the site of the most active star formation currently. The NIRISS and NIRCam resolved photometry does not confirm a strong Balmer break previously seen in Spitzer. The NIRISS grism spectrum has been extracted for the entire galaxy and shows a clear continuum and Lyman-break, with no Lyman-$α$ detected.

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arXiv2023

JWST catches the assembly of a $z\sim5$ ultra-low-mass galaxy

Using CANUCS imaging we found an apparent major merger of two $z\sim5$ ultra-low-mass galaxies ($M_\star\sim10^{7}M_\odot$ each) that are doubly imaged and magnified $\sim$12-15$\times$ by the lensing cluster MACS 0417. Both galaxies are experiencing young ($\sim$100 Myr), synchronised bursts of star formation with $\log({\rm sSFR/Gyr^{-1}} )\sim$1.3-1.4, yet SFRs of just $\sim 0.2 M_\odot\ {\rm yr}^{-1}$. They have sub-solar ($Z\sim0.2Z_\odot$) gas-phase metallicities and are connected by an even more metal-poor star-forming bridge. The galaxy that forms from the merger will have a mass of at least $M_\star\sim 2\times10^7 M_\odot$, at least half of it formed during the interaction-induced starburst. More than half of the ionizing photons produced by the system (before and during the merger) will have been produced during the burst. This system provides the first detailed look at a merger involving two high-$z$ ultra-low-mass galaxies of the type believed to be responsible for reionizing the Universe. It suggests that such galaxies can grow via a combination of mass obtained through major mergers, merger-triggered starbursts, and long-term in-situ star formation. If such high-$z$ mergers are common, then merger-triggered starbursts could be significant contributors to the ionizing photon budget of the Universe.

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arXiv2023

Spectroscopy from Photometry: A Population of Extreme Emission Line Galaxies at $1.7 \lesssim z \lesssim 6.7$ Selected with JWST Medium Band Filters

We use JWST/NIRCam medium band photometry in a single pointing of the CAnadian NIRISS Unbiased Cluster Survey (CANUCS) to identify 118 Extreme Emission Line Galaxies (EELGs) over $1.7 \lesssim z \lesssim 6.7$, selected using a set of color cuts that target galaxies with extreme $\text{[OIII] + H}β$ and H$α$ emission. We show that our medium band color selections are able to select galaxies based on emission line equivalent width (EW), which is advantageous to more commonly used selections since it does not require strong continuum emission, and can select galaxies with faint or red continuum fluxes. The median EWs of our sample is $EW(\text{H}α) = 893 $ Å and $ EW(\text{[OIII] + H}β) = 1255 $ Å, and includes some objects with $EW(\text{[OIII] + H}β) \sim 3000$ Å. These systems are mostly compact with low stellar mass (median $\log(M_\star/M_\odot) = 8.03$), low metallicity (median $Z = 0.14 Z_\odot$), little dust (median $A_V = 0.18$ mag) and high SSFR (median $SSFR = 1.18 \times 10^{-8}/yr$). Additionally, galaxies in our sample show increasing EW(\Ha) and EW(\OIIIHb) with redshift, an anti-correlation of EW(\Ha) with stellar mass, and no correlation between EW(\OIIIHb) and stellar mass. Finally, we present NIRSpec spectroscopy of 15 of the EELGs in our sample. These spectra confirm the redshifts and EWs of the EELGs calculated from the medium bands, which demonstrates the accuracy and efficiency of our color selections. Overall, we show that there are significant advantages to using medium band photometry to identify and study EELGs at a wide range of redshifts.

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arXiv2023

The first large catalogue of spectroscopic redshifts in Webb's First Deep Field, SMACS J0723.3$-$7327

We present a spectroscopic redshift catalogue of the SMACS J0723.3$-$7327 field ("Webb's First Deep Field") obtained from JWST/NIRISS grism spectroscopy and supplemented with JWST/NIRSpec and VLT/MUSE redshifts. The catalogue contains a total of 190 sources with secure spectroscopic redshifts, including 156 NIRISS grism redshifts, 123 of which are for sources whose redshifts were previously unknown. These new grism redshifts are secured with two or more spectroscopic features (64 sources), or with a single spectral feature whose identity is secured from the object's nine-band photometric redshift (59 sources). These are complemented with 17 NIRSpec and 48 MUSE redshifts, including six new NIRSpec redshifts identified in this work. In addition to the $z_{\rm cl}=0.39$ cluster galaxy redshifts (for which we provide $\sim$40 new NIRISS absorption-line redshifts), we also find three prominent galaxy overdensities at higher redshifts - at $z=1.1$, $z=1.4$, and $z=2.0$ - that were until now not seen in the JWST/NIRSpec and VLT/MUSE data. The paper describes the characteristics of our spectroscopic redshift sample and the methodology we have employed to obtain it. Our redshift catalogue is made available to the community at https://niriss.github.io/smacs0723.

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arXiv2023

A First Look at Spatially Resolved Balmer Decrements at $1.0<z<2.4$ from JWST NIRISS Slitless Spectroscopy

We present the first results on the spatial distribution of dust attenuation at $1.0<z<2.4$ traced by the Balmer Decrement, H$α$/H$β$, in emission-line galaxies using deep JWST NIRISS slitless spectroscopy from the CAnadian NIRISS Unbiased Cluster Survey (CANUCS). H$α$ and H$β$ emission line maps of emission-line galaxies are extracted and stacked in bins of stellar mass for two grism redshift bins, $1.0<z_{grism}<1.7$ and $1.7<z_{grism}<2.4$. Surface brightness profiles for the Balmer Decrement are measured and radial profiles of the dust attenuation towards H$α$, $A_{\mathrm{H}α}$, are derived. In both redshift bins, the integrated Balmer Decrement increases with stellar mass. Lower mass ($7.6\leqslant$Log($M_{*}$/M$_{\odot}$)$<10.0$) galaxies have centrally concentrated, negative dust attenuation profiles whereas higher mass galaxies ($10.0\leqslant$Log($M_{*}$/M$_{\odot}$)$<11.1$) have flat dust attenuation profiles. The total dust obscuration is mild, with on average $0.07\pm0.07$ and $0.14\pm0.07$ mag in the low and high redshift bins respectively. We model the typical light profiles of star-forming galaxies at these redshifts and stellar masses with GALFIT and apply both uniform and radially varying dust attenuation corrections based on our integrated Balmer Decrements and radial dust attenuation profiles. If these galaxies were observed with typical JWST NIRSpec slit spectroscopy ($0.2\times0.5^{\prime\prime}$ shutters), on average, H$α$ star formation rates (SFRs) measured after slit-loss corrections assuming uniform dust attenuation will overestimate the total SFR by $6\pm21 \%$ and $26\pm9 \%$ at $1.0\leqslant z < 1.7$ and $1.7\leqslant z < 2.4$ respectively.

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arXiv2022

The Sparkler: Evolved High-Redshift Globular Clusters Captured by JWST

Using data from JWST, we analyze the compact sources ("sparkles") located around a remarkable $z_{\rm spec}=1.378$ galaxy (the "Sparkler") that is strongly gravitationally lensed by the $z=0.39$ galaxy cluster SMACS J0723.3-7327. Several of these compact sources can be cross-identified in multiple images, making it clear that they are associated with the host galaxy. Combining data from JWST's {\em Near-Infrared Camera} (NIRCam) with archival data from the {\em Hubble Space Telescope} (HST), we perform 0.4-4.4$μ$m photometry on these objects, finding several of them to be very red and consistent with the colors of quenched, old stellar systems. Morphological fits confirm that these red sources are spatially unresolved even in strongly magnified JWST/NIRCam images, while JWST/NIRISS spectra show [OIII]5007 emission in the body of the Sparkler but no indication of star formation in the red compact sparkles. The most natural interpretation of these compact red companions to the Sparkler is that they are evolved globular clusters seen at $z=1.378$. Applying \textsc{Dense Basis} SED-fitting to the sample, we infer formation redshifts of $z_{form} \sim 7-11$ for these globular cluster candidates, corresponding to ages of $\sim 3.9-4.1$ Gyr at the epoch of observation and a formation time just $\sim$0.5~Gyr after the Big Bang. If confirmed with additional spectroscopy, these red, compact "sparkles" represent the first evolved globular clusters found at high redshift, could be amongst the earliest observed objects to have quenched their star formation in the Universe, and may open a new window into understanding globular cluster formation. Data and code to reproduce our results will be made available at \faGithub\href{https://niriss.github.io/sparkler.html}{http://canucs-jwst.com/sparkler.html}.

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arXiv2021

Ionizing radiation from AGNs at z>3.3 with the Subaru Hyper Suprime-Cam Survey and the CFHT Large Area U-band Deep Survey (CLAUDS)

We use deep and wide imaging data from the CFHT Large Area U-band Deep Survey (CLAUDS) and the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) to constrain the ionizing radiation (Lyman Continuum; LyC) escape fraction from AGNs at $z \sim 3 - 4$. For 94 AGNs with spectroscopic redshifts at $3.3 < z < 4.0$, we use their U-band / i-band flux ratios to estimate LyC transmission of individual AGNs. The distribution of their LyC transmission shows values lower than the range of LyC transmission values for IGM of the same redshift range, which suggests that LyC escape fraction of AGNs at $z>3.3$ is considerably lower than unity in most cases. We do not find any trend in LyC transmission values depending on their UV luminosities. Based on the photometry of stacked images we find the average flux ratio of LyC and non-ionizing UV photons escaping from the objects $(f_{LyC}/f_{UV})^{out} = 0.182 \pm 0.043$ for AGNs at $3.3<z<3.6$, which corresponds to LyC escape fraction $f_{esc} = 0.303 \pm 0.072$ if we assume a fiducial intrinsic SED of AGN. Based on the estimated LyC escape fraction and the UV luminosity function of AGNs, we argue that UV-selected AGNs' contribution to the LyC emissivity at the epoch is minor, although the size of their contribution largely depends on the shape of the UV luminosity function.

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arXiv2021

Searching for low-redshift faint galaxies with MMT/Hectospec

We present redshifts for 2753 low-redshift galaxies between $0.03 \lesssim z_{\rm spec}\lesssim0.5$ with 18 $\leq$ $r$ $\leq$ 22 obtained with Hectospec at the Multi-Mirror Telescope (MMT). The observations targeted the XMM-LSS, ELAIS-N1 and DEEP2-3 fields, each of which covers $\sim$ 1 deg$^2$. These fields are also part of the recently completed CFHT Large Area U-band Deep Survey (CLAUDS) and on-going Hyper Suprime-Cam deep fields surveys. The efficiency of our technique for selecting low-redshift galaxies is confirmed by the redshift distribution of our sources. In addition to redshifts, these high S/N spectra are used to measure ages, metallicities, and nuclear activity levels. In combination with the photometric catalogue in $u$, $g$, $r$, $i$, $z$, $y$ down to 27 AB mag, we are able to study the galaxy population down to stellar masses of $\sim$ 10$^8 M_\odot$ . This paper presents the observational strategy, the reduction procedure and properties of the galaxy sample.

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arXiv2019

The CFHT Large Area U-band Deep Survey (CLAUDS)

The CFHT Large Area U-band Deep Survey (CLAUDS) uses data taken with the MegaCam mosaic imager on CFHT to produce images of 18.60 deg2 with median seeing of FWHM=0.92 arcsec and to a median depth of U = 27.1 AB (5 sigma in 2 arcsec apertures), with selected areas that total 1.36 deg2 reaching a median depth of U=27.7 AB. These are the deepest U-band images assembled to date over this large an area. These data are located in four fields also imaged to comparably faint levels in grizy and several narrowband filters as part of the Hyper Suprime-Cam (HSC) Subaru Strategic Program (HSC-SSP). These CFHT and Subaru datasets will remain unmatched in their combination of area and depth until the advent of the Large Synoptic Survey Telescope (LSST). This paper provides an overview of the scientific motivation for CLAUDS and gives details of the observing strategy, observations, data reduction, and data merging with the HSC-SSP. Three early applications of these deep data are used to illustrate the potential of the dataset: deep U-band galaxy number counts, z~3 Lyman break galaxy (LBG) selection, and photometric redshifts improved by adding CLAUDS U to the Subaru HSC grizy photometry.

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arXiv2018

Galaxy-galaxy lensing in the outskirts of CLASH clusters: constraints on local shear and testing mass-luminosity scaling relation

We present a selection of 24 candidate galaxy-galaxy lensing (GGLs) identified from Hubble images in the outskirts of the massive galaxy clusters from the CLASH survey. These GGLs provide insights into the mass distributions at larger scales than the strong lensing region in the cluster cores. We built parametric mass models for three of these GGLs showing simple lensing configurations, in order to assess the properties of their lens and its environment. We show that the local shear estimated from the GGLs traces the gravitational potential of the clusters at 1-2 arcmin radial distance, allowing us to derive their velocity dispersion. We also find a good agreement between the strength of the shear measured at the GGL positions through strong-lensing modelling and the value derived independently from a weak-lensing analysis of the background sources. Overall, we show the advantages of using single GGL events in the outskirts of clusters to robustly constrain the local shear, even when only photometric redshift estimates are known for the source. We argue that the mass-luminosity scaling relation of cluster members can be tested by modelling the GGLs found around them, and show that the mass parameters can vary up to $\sim$30% between the cluster and GGL models assuming this scaling relation.

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