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J. Richard

Publications and source records attributed to J. Richard.

At least 55 records · Page 3Linked to original sources

4MOST Consortium Survey 8: Cosmology Redshift Survey (CRS)

The 4MOST Cosmology Redshift Survey (CRS) will perform stringent cosmological tests via spectroscopic clustering measurements that will complement the best lensing, cosmic microwave background and other surveys in the southern hemisphere. The combination of carefully selected samples of bright galaxies, luminous red galaxies, emission-line galaxies and quasars, totalling about 8 million objects over the redshift range $z = 0.15$ to $3.5$, will allow definitive tests of gravitational physics. Many key science questions will be addressed by combining CRS spectra of these targets with data from current or future facilities such as the Large Synoptic Survey Telescope, the Square Kilometre Array and the Euclid mission.

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Deep and rapid observations of strong-lensing galaxy clusters within the sky localisation of GW170814

We present observations of two strong-lensing galaxy clusters located within the $90$ per cent credible sky localization maps released following LIGO-Virgo's discovery of the binary black hole (BH-BH) gravitational wave (GW) source GW170814. Our objectives were (1) to search for candidate electromagnetic (EM) counterparts to GW170814 under the hypothesis that it was strongly-lensed, and thus more distant and less massive than inferred by LIGO-Virgo, and (2) to demonstrate the feasibility of rapid target of opportunity observations to search for faint lensed transient point sources in crowded cluster cores located within GW sky localizations. Commencing $20$ hours after discovery, and continuing over $12$ nights, we observed Abell 3084 ($z=0.22$) and SMACSJ0304.3$-$4401 ($z=0.46$) with GMOS on the Gemini-South telescope, and Abell 3084 with MUSE on ESO's Very Large Telescope. We detect no candidate EM counterparts in these data. Calibration of our photometric analysis methods using simulations yield $5σ$ detection limits for transients in difference images of the cores of these clusters of $i=25$. This is the most sensitive photometric search to date for counterparts to GW sources, and rules out the possibility that GW170814 was lensed by these clusters with a kilonova-like EM counterpart. Based on the detector frame masses of the compact objects, and assuming that at least one Neutron Star (NS) is required in the merging system to produce a kilonova-like counterpart, implies that GW170814 was neither a NS-NS nor NS-BH merger at $z>8$ lensed by either of these clusters. Also, in the first ever emission line search for counterparts to GW sources, we detected no lines down to a $5σ$ detection limit of $5\times10^{-17}{\rm erg\,s^{-1}\,cm^{-2}}$.

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The MUSE-Wide Survey: Survey Description and First Data Release

We present the MUSE-Wide survey, a blind, 3D spectroscopic survey in the CANDELS/GOODS-S and CANDELS/COSMOS regions. Each MUSE-Wide pointing has a depth of 1 hour and hence targets more extreme and more luminous objects over 10 times the area of the MUSE-Deep fields (Bacon et al. 2017). The legacy value of MUSE-Wide lies in providing "spectroscopy of everything" without photometric pre-selection. We describe the data reduction, post-processing and PSF characterization of the first 44 CANDELS/GOODS-S MUSE-Wide pointings released with this publication. Using a 3D matched filtering approach we detected 1,602 emission line sources, including 479 Lyman-$α$ (Lya) emitting galaxies with redshifts $2.9 \lesssim z \lesssim 6.3$. We cross-match the emission line sources to existing photometric catalogs, finding almost complete agreement in redshifts and stellar masses for our low redshift (z < 1.5) emitters. At high redshift, we only find ~55% matches to photometric catalogs. We encounter a higher outlier rate and a systematic offset of $Δ$z$\simeq$0.2 when comparing our MUSE redshifts with photometric redshifts. Cross-matching the emission line sources with X-ray catalogs from the Chandra Deep Field South, we find 127 matches, including 10 objects with no prior spectroscopic identification. Stacking X-ray images centered on our Lya emitters yielded no signal; the Lya population is not dominated by even low luminosity AGN. A total of 9,205 photometrically selected objects from the CANDELS survey lie in the MUSE-Wide footprint, which we provide optimally extracted 1D spectra of. We are able to determine the spectroscopic redshift of 98% of 772 photometrically selected galaxies brighter than 24th F775W magnitude. All the data in the first data release - datacubes, catalogs, extracted spectra, maps - are available on the website https://musewide.aip.de. [abridged]

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The Shapes of the Rotation Curves of Star-forming Galaxies Over the Last $\approx$10 Gyr

We analyse maps of the spatially-resolved nebular emission of $\approx$1500 star-forming galaxies at $z\approx0.6$-$2.2$ from deep KMOS and MUSE observations to measure the average shape of their rotation curves. We use these to test claims for declining rotation curves at large radii in galaxies at $z\approx1$-$2$ that have been interpreted as evidence for an absence of dark matter. We show that the shape of the average rotation curves, and the extent to which they decline beyond their peak velocities, depends upon the normalisation prescription used to construct the average curve. Normalising in size by the galaxy stellar disk-scale length after accounting for seeing effects ($R_{\rm{d}}^{\prime}$), we construct stacked position-velocity diagrams that trace the average galaxy rotation curve out to $6R_{\rm{d}}^{\prime}$ ($\approx$13 kpc, on average). Combining these curves with average HI rotation curves for local systems, we investigate how the shapes of galaxy rotation curves evolve over $\approx$10 Gyr. The average rotation curve for galaxies binned in stellar mass, stellar surface mass density and/or redshift is approximately flat, or continues to rise, out to at least $6R_{\rm{d}}^{\prime}$. We find a trend between the outer slopes of galaxies' rotation curves and their stellar mass surface densities, with the higher surface density systems exhibiting flatter rotation curves. Drawing comparisons with hydrodynamical simulations, we show that the average shapes of the rotation curves for our sample of massive, star-forming galaxies at $z\approx0$-$2.2$ are consistent with those expected from $Λ$CDM theory and imply dark matter fractions within $6R_{\rm{d}}$ of at least $\approx60$ percent.

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Nearly all the sky is covered by Lyman-alpha emission around high redshift galaxies

Galaxies are surrounded by large reservoirs of gas, mostly hydrogen, fed by inflows from the intergalactic medium and by outflows due to galactic winds. Absorption-line measurements along the sightlines to bright and rare background quasars indicate that this circumgalactic medium pervades far beyond the extent of starlight in galaxies, but very little is known about the spatial distribution of this gas. A new window into circumgalactic environments was recently opened with the discovery of ubiquitous extended Lyman-alpha emission from hydrogen around high-redshift galaxies, facilitated by the extraordinary sensitivity of the MUSE instrument at the ESO Very Large Telescope. Due to the faintness of this emission, such measurements were previously limited to especially favourable systems or to massive statistical averaging. Here we demonstrate that low surface brightness Lyman-alpha emission surrounding faint galaxies at redshifts between 3 and 6 adds up to a projected sky coverage of nearly 100%. The corresponding rate of incidence (the mean number of Lyman-alpha emitters penetrated by any arbitrary line of sight) is well above unity and similar to the incidence rate of high column density absorbers frequently detected in the spectra of distant quasars. This similarity suggests that most circumgalactic atomic hydrogen at these redshifts has now been detected also in emission.

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The WIRCam Ultra Deep Survey (WUDS) I. Survey overview and UV luminosity functions at z~5 and z~6

The aim of this paper is to introduce the WIRCam Ultra Deep Survey (WUDS), a near-IR photometric public survey carried out at the CFH Telescope in the field of the CFHTLS-D3 field (Groth Strip). WUDS includes four near-IR bands (Y, J, H and K_s) over a field of view of ~400 arcmin^2. The typical depth of WUDS data reaches between ~26.8 in Y and J, and ~26 in H and K_s (AB, 3 sigma in 1.3 arcsec aperture). The area and depth of this survey were specifically tailored to set strong constraints on the cosmic star formation rate and the luminosity function brighter or around L* in the z~6-10 redshift domain, although these data are also useful for a variety of extragalactic projects.This first paper is intended to present the properties of WUDS: catalog building, completeness and depth, number counts, photometric redshifts, and global properties of the galaxy population. We have also concentrated on the study of galaxy samples at z~[4.5-7] in this field. UV luminosity functions were derived at z~5 and z~6 taking advantage from the fact that WUDS covers a particularly interesting regime at intermediate luminosities, which allows a combined determination of M* and Phi* with increased accuracy. Our results on the luminosity function are consistent with a small evolution of both M* and Phi* between z=5 and z=6, irrespective of the method used to derive them, either photometric redshifts applied to blindly-selected dropout samples or the classical Lyman Break Galaxy color-preselected samples. Our results lend support to higher Phi* determinations at z=6 than usually reported. The selection and combined analysis of different galaxy samples at z>7 will be presented in a forthcoming paper. WUDS is intended to provide a robust database in the near-IR for the selection of targets for detailed spectroscopic studies, in particular for the EMIR/GTC GOYA Survey (Abridged)

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Physics of a clumpy lensed galaxy at z=1.6

Observations have shown that massive star-forming clumps are present in the internal structure of high-redshift galaxies. One way to study these clumps in detail with a higher spatial resolution is by exploiting the power of strong gravitational lensing which stretches images on the sky. In this work, we present an analysis of the clumpy galaxy A68-HLS115 at $z=1.5858$, located behind the cluster Abell 68, but strongly lensed by a cluster galaxy member. Resolved observations with SINFONI/VLT in the near-infrared show Ha, Hb, [NII], and [OIII] emission lines. Combined with images covering the B band to the far-infrared and CO(2-1) observations, this makes this galaxy one of the only sources for which such multi-band observations are available and for which it is possible to study the properties of resolved star-forming clumps and to perform a detailed analysis of the integrated properties, kinematics, and metallicity. We obtain a stability of $\upsilon_{rot}/σ_0 = 2.73$ by modeling the kinematics, which means that the galaxy is dominated by rotation, but this ratio also indicates that the disk is marginally stable. We find a high intrinsic velocity dispersion of $80\pm10$ km s$^{-1}$ that could be explained by the high gas fraction of $f_{gas}=0.75\pm0.15$ observed in this galaxy. This high $f_{gas}$ and the observed sSFR of $\rm 3.12 \, Gyr^{-1}$ suggest that the disk turbulence and instabilities are mostly regulated by incoming gas. The direct measure of the Toomre stability criterion of $Q_{crit}=0.70$ could also indicate the presence of a quasi-stable thick disk. Finally, we identify three clumps in the Ha map which have similar velocity dispersions, metallicities, and seem to be embedded in the rotating disk. These three clumps contribute together to $40\%$ on the SFR(Ha) of the galaxy and show a SFR density about $100$ times higher than HII regions in the local Universe.

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Properties and redshift evolution of star-forming galaxies with high [OIII]/[OII] ratios with MUSE at 0.28<z<0.85

We present a study of the [OIII]5007/[OII]3727 (O32) ratios of star-forming galaxies drawn from MUSE data spanning a redshift range 0.28 4. Here we aim to understand the properties and the occurrences of galaxies with such high line ratios. Combining data from several MUSE GTO programmes, we select a population of star-forming galaxies with bright emission lines, from which we draw 406 galaxies for our analysis based on their position in the z-dependent star formation rate (SFR) - stellar mass (M*) plane. Out of this sample 15 are identified as extreme oxygen emitters based on their O32 ratios (3.7%) and 104 galaxies have O32>1 (26%). Our analysis shows no significant correlation between M*, SFR, and the distance from the SFR-M* relation with O32. We find a decrease in the fraction of galaxies with O32>1 with increasing M*, however, this is most likely a result of the relationship between O32 and metallicity, rather than between O32 and M*. We draw a comparison sample of local analogues with ~0.03 from SDSS, and find similar incidence rates for this sample. In order to investigate the evolution in the fraction of high O32 emitters with redshift, we bin the sample into three redshift subsamples of equal number, but find no evidence for a dependence on redshift. Furthermore, we compare the observed line ratios with those predicted by nebular models with no LyC escape and find that most of the extreme oxygen emitters can be reproduced by low metallicity models. The remaining galaxies are likely LyC emitter candidates. Finally, based on a comparison between electron temperature estimates from the [OIII4363]/[OIII]5007 ratio of the extreme oxygen emitters and nebular models, we argue that the galaxies with the most extreme O32 ratios have young light-weighted ages.

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Recovering the systemic redshift of galaxies from their Lyman-alpha line profile

The Lyman alpha (lya) line of Hydrogen is a prominent feature in the spectra of star-forming galaxies, usually redshifted by a few hundreds of km/s compared to the systemic redshift. This large offset hampers follow-up surveys, galaxy pair statistics and correlations with quasar absorption lines when only lya is available. We propose diagnostics that can be used to recover the systemic redshift directly from the properties of the lya line profile. We use spectroscopic observations of Lyman-Alpha Emitters (LAEs) for which a precise measurement of the systemic redshift is available. Our sample contains 13 sources detected between z~3 and z~6 as part of various Multi Unit Spectroscopic Explorer (MUSE) Guaranteed Time Observations (GTO). We also include a compilation of spectroscopic lya data from the literature spanning a wide redshift range (z~0-8). First, restricting our analysis to double-peaked lya spectra, we find a tight correlation between the velocity offset of the red peak with respect to the systemic redshift, Vpeak, and the separation of the peaks. Secondly, we find a correlation between Vpeak and the full width at half maximum of the lya line. Fitting formulas, to estimate systemic redshifts of galaxies with an accuracy of +-100 km/s when only the lya emission line is available, are given for the two methods.

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Strong-lensing of Gravitational Waves by Galaxy Clusters

Discovery of strongly-lensed gravitational wave (GW) sources will unveil binary compact objects at higher redshifts and lower intrinsic luminosities than is possible without lensing. Such systems will yield unprecedented constraints on the mass distribution in galaxy clusters, measurements of the polarization of GWs, tests of General Relativity, and constraints on the Hubble parameter. Excited by these prospects, and intrigued by the presence of so-called "heavy black holes" in the early detections by LIGO-Virgo, we commenced a search for strongly-lensed GWs and possible electromagnetic counterparts in the latter stages of the second LIGO observing run (O2). Here, we summarise our calculation of the detection rate of strongly-lensed GWs, describe our review of BBH detections from O1, outline our observing strategy in O2, summarize our follow-up observations of GW170814, and discuss the future prospects of detection.

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Searching for supernovae in the multiply-imaged galaxies behind the gravitational telescope A370

Strong lensing by massive galaxy clusters can provide magnification of the flux and even multiple images of the galaxies that lie behind them. This phenomenon facilitates observations of high-redshift supernovae (SNe), that would otherwise remain undetected. Type Ia supernovae (SNe Ia) detections are of particular interest because of their standard brightness, since they can be used to improve either cluster lensing models or cosmological parameter measurements. We present a ground-based, near-infrared search for lensed SNe behind the galaxy cluster Abell 370. Our survey was based on 15 epochs of J-band observations with the HAWK-I instrument on the Very Large Telescope (VLT). We use Hubble Space Telescope (HST) photometry to infer the global properties of the multiply-imaged galaxies. Using a recently published lensing model of Abell 370, we also present the predicted magnifications and time delays between the images. In our survey, we did not discover any live SNe from the 13 lensed galaxies with 47 multiple images behind Abell 370. This is consistent with the expectation of $0.09\pm0.02$ SNe calculated based on the measured star formation rate. We compare the expectations of discovering strongly lensed SNe in our survey and that performed with HST during the Hubble Frontier Fields (HFF) programme. We also show the expectations of search campaigns that can be conducted with future facilities, such as the James Webb Space Telescope (JWST) or the Wide-Field Infrared Survey Telescope (WFIRST). We show that the NIRCam instrument aboard the JWST will be sensitive to most SN multiple images in the strongly lensed galaxies and thus will be able to measure their time delays if observations are scheduled accordingly.

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Kinematics, Turbulence and Star Formation of z ~1 Strongly Lensed Galaxies seen with MUSE

We analyse a sample of 8 highly magnified galaxies at redshift 0.6<z<1.5 observed with MUSE, exploring the resolved properties of these galaxies at sub-kiloparsec scales. Combining multi-band HST photometry and MUSE spectra, we derive the stellar mass, global star formation rates, extinction and metallicity from multiple nebular lines, concluding that our sample is representative of z~1 star-forming galaxies. We derive the 2D kinematics of these galaxies from the [OII] emission and model it with a new method that accounts for lensing effects and fits multiple images simultaneously. We use these models to calculate the 2D beam-smearing correction and derive intrinsic velocity dispersion maps. We find them to be fairly homogeneous, with relatively constant velocity dispersions between 15 - 80 km/s and Gini coefficient of <0.3. We do not find any evidence for higher (or lower) velocity dispersions at the positions of bright star-forming clumps. We derive resolved maps of dust attenuation and attenuation-corrected star formation rates from emission lines for two objects in the sample. We use this information to study the relation between resolved star formation rate and velocity dispersion. We find that these quantities are not correlated, and the high-velocity dispersions found for relatively low star-forming densities seems to indicate that, at sub-kiloparsec scales, turbulence in high-z discs is mainly dominated by gravitational instability rather than stellar feedback.

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Thirty-fold: Extreme gravitational lensing of a quiescent galaxy at $z=1.6$

We report the discovery of eMACSJ1341-QG-1, a quiescent galaxy at $z=1.594$ located behind the massive galaxy cluster eMACSJ1341.9$-$2442 ($z=0.835$). The system was identified as a gravitationally lensed triple image in Hubble Space Telescope images obtained as part of a snapshot survey of the most X-ray luminous galaxy clusters at $z>0.5$ and spectroscopically confirmed in ground-based follow-up observations with the ESO/X-Shooter spectrograph. From the constraints provided by the triple image, we derive a first, crude model of the mass distribution of the cluster lens, which predicts a gravitational amplification of a factor of $\sim$30 for the primary image and a factor of $\sim$6 for the remaining two images of the source, making eMACSJ1341-QG-1 by far the most strongly amplified quiescent galaxy discovered to date. Our discovery underlines the power of SNAPshot observations of massive, X-ray selected galaxy clusters for lensing-assisted studies of faint background populations.

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KMOS LENsing Survey (KLENS) : morpho-kinematic analysis of star-forming galaxies at $z \sim 2$

We present results from the KMOS lensing survey-KLENS which is exploiting gravitational lensing to study the kinematics of 24 star forming galaxies at $1.4 10$). We derive a $\rm M_\star-σ_0$ relation, using the Tully-Fisher relation, which highlights that a different evolution of the velocity dispersion is expected depending on the stellar mass, with lower velocity dispersions for lower masses, and an increase for higher masses, stronger at higher redshift. The observed velocity dispersions from this work and from comparison samples spanning $0 2$), where we observe higher velocity dispersions for low masses ($\rm log(M_\star/M_\odot)\sim 9.6$) and lower velocity dispersions for high masses ($\rm log(M_\star/M_\odot)\sim 10.9$) than expected. This discrepancy could, for instance, suggest that galaxies at high-$z$ do not satisfy the stability criterion, or that the adopted parametrisation of the specific star formation rate and molecular properties fail at high redshift.

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The MUSE Hubble Ultra Deep Field Survey VI: The Faint-End of the Lya Luminosity Function at 2.91 < z < 6.64 and Implications for Reionisation

We present the deepest study to date of the Lya luminosity function (LF) in a blank field using blind integral field spectroscopy from MUSE. We constructed a sample of 604 Lya emitters (LAEs) across the redshift range 2.91 < z < 6.64 using automatic detection software in the Hubble Ultra Deep Field. We calculate accurate total Lya fluxes capturing low surface brightness extended Lya emission now known to be a generic property of high-redshift star-forming galaxies. We simulated realistic extended LAEs to characterise the selection function of our samples, and performed flux-recovery experiments to test and correct for bias in our determination of total Lya fluxes. We find an accurate completeness correction accounting for extended emission reveals a very steep faint-end slope of the LF, alpha, down to luminosities of log10 L erg s^-1< 41.5, applying both the 1/Vmax and maximum likelihood estimators. Splitting the sample into three broad redshift bins, we see the faint-end slope increasing from -2.03+1.42-inf at z ~ 3.44 to -2.86+0.76-inf at z ~ 5.48, however no strong evolution is seen between the 68% confidence regions in L*-alpha parameter space. Using the Lya line flux as a proxy for star formation activity, and integrating the observed LFs, we find that LAEs' contribution to the cosmic SFRD rises with redshift until it is comparable to that from continuum-selected samples by z ~ 6. This implies that LAEs may contribute more to the star-formation activity of the early Universe than previously thought - any additional interglactic medium correction would act to further boost the Lya luminosities. Finally, assuming fiducial values for the escape of Lya and LyC radiation, and the clumpiness of the IGM, we integrated the maximum likelihood LF at 5.00 < z < 6.64 and find we require only a small extrapolation beyond the data (< 1 dex in L) for LAEs alone to maintain an ionised IGM at z ~ 6.

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The MUSE Hubble Ultra Deep Field Survey: III. Testing photometric redshifts to 30th magnitude

We tested the performance of photometric redshifts for galaxies in the Hubble Ultra Deep field down to 30th magnitude. We compared photometric redshift estimates from three spectral fitting codes from the literature (EAZY, BPZ and BEAGLE) to high quality redshifts for 1227 galaxies from the MUSE integral field spectrograph. All these codes can return photometric redshifts with bias |Dzn|=|z-z_phot|/(1+z)<0.05 down to F775W=30 and spectroscopic incompleteness is unlikely to strongly modify this statement. We have, however, identified clear systematic biases in the determination of photometric redshifts: in the 0.4 3 they are systematically biased high by up to Dzn = 0.05, an offset that can in part be explained by adjusting the amount of intergalactic absorption applied. In agreement with previous studies we find little difference in the performance of the different codes, but in contrast to those we find that adding extensive ground-based and IRAC photometry actually can worsen photo-z performance for faint galaxies. We find an outlier fraction, defined through |Dzn|>0.15, of 8% for BPZ and 10% for EAZY and BEAGLE, and show explicitly that this is a strong function of magnitude. While this outlier fraction is high relative to numbers presented in the literature for brighter galaxies, they are very comparable to literature results when the depth of the data is taken into account. Finally, we demonstrate that while a redshift might be of high confidence, the association of a spectrum to the photometric object can be very uncertain and lead to a contamination of a few percent in spectroscopic training samples that do not show up as catastrophic outliers, a problem that must be tackled in order to have sufficiently accurate photometric redshifts for future cosmological surveys.

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The MUSE Hubble Ultra Deep Field Survey: II. Spectroscopic redshifts and comparisons to color selections of high-redshift galaxies

We have conducted a two-layered spectroscopic survey (1'x1' ultra deep and 3'x3' deep regions) in the Hubble Ultra Deep Field (HUDF) with the Multi Unit Spectroscopic Explorer (MUSE). The combination of a large field of view, high sensitivity, and wide wavelength coverage provides an order of magnitude improvement in spectroscopically confirmed redshifts in the HUDF; i.e., 1206 secure spectroscopic redshifts for HST continuum selected objects, which corresponds to 15% of the total (7904). The redshift distribution extends well beyond z>3 and to HST/F775W magnitudes as faint as ~30 mag (AB, 1-sigma). In addition, 132 secure redshifts were obtained for sources with no HST counterparts that were discovered in the MUSE data cubes by a blind search for emission-line features. In total, we present 1338 high quality redshifts, which is a factor of eight increase compared with the previously known spectroscopic redshifts in the same field. We assessed redshifts mainly with the spectral features [OII] at z<1.5 (473 objects) and Lya at 2.9 ~20% up to 28-29 mag and ~27 mag, respectively. We used the determined redshifts to test continuum color selection (dropout) diagrams of high-z galaxies. The selection condition for F336W dropouts successfully captures ~80% of the targeted z~2.7 galaxies. However, for higher redshift selections (F435W, F606W, and F775W dropouts), the success rates decrease to ~20-40%. We empirically redefine the selection boundaries to make an attempt to improve them to ~60%. The revised boundaries allow bluer colors that capture Lya emitters with high Lya equivalent widths falling in the broadbands used for the color-color selection. Along with this paper, we release the redshift and line flux catalog.

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Strong lensing analysis of Abell 2744 with MUSE and Hubble Frontier Fields images

We present an analysis of MUSE observations obtained on the massive Frontier Fields cluster Abell 2744. This new dataset covers the entire multiply-imaged region around the cluster core. We measure spectroscopic redshifts for HST-selected continuum sources together with line emitters blindly detected in the datacube. The combined catalog consists of 514 spectroscopic redshifts (with 414 new identifications), including 156 cluster members and 326 magnified background sources. We use this redshift information to perform a strong-lensing analysis of all multiple images previously found in the deep Frontier Field images, and add three new MUSE-detected multiply-imaged systems with no obvious HST counterpart. The combined strong lensing constraints include a total of 60 systems producing 188 images altogether, out of which 29 systems and 83 images are spectroscopically confirmed, making Abell 2744 one of the most well-constrained clusters to date. A parametric mass model including two cluster-scale components in the core and several group-scale substructures at larger radii accurately reproduces all the spectroscopic multiple systems, reaching an rms of 0.67" in the image plane. Overall, the large number of spectroscopic redshifts gives us a robust model and we estimate the systematics on the mass density and magnification within the cluster core to be typically ~9%.

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