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E. Jullo

Publications and source records attributed to E. Jullo.

At least 37 records · Page 2Linked to original sources

CONCERTO: Simulating the CO, [CII], and [CI] line emission of galaxies in a 117 $\rm deg^2$ field and the impact of field-to-field variance

In the submm regime, spectral line scans and line intensity mapping (LIM) are new promising probes for the cold gas content and star formation rate of galaxies across cosmic time. However, both of these two measurements suffer from field-to-field variance. We study the effect of field-to-field variance on the predicted CO and [CII] power spectra from future LIM experiments such as CONCERTO, as well as on the line luminosity functions (LFs) and the cosmic molecular gas mass density that are currently derived from spectral line scans. We combined a 117 $\rm deg^2$ dark matter lightcone from the Uchuu cosmological simulation with the simulated infrared dusty extragalactic sky (SIDES) approach. We find that in order to constrain the CO LF with an uncertainty below 20%, we need survey sizes of at least 0.1 $\rm deg^2$. Furthermore, accounting for the field-to-field variance using only the Poisson variance can underestimate the total variance by up to 80%. The lower the luminosity is and the larger the survey size is, the higher the level of underestimate. At $z$<3, the impact of field-to-field variance on the cosmic molecular gas density can be as high as 40% for the 4.6 arcmin$^2$ field, but drops below 10% for areas larger than 0.2 deg$^2$. However, at $z>3$ the variance decreases more slowly with survey size and for example drops below 10% for 1 deg$^2$ fields. Finally, we find that the CO and [CII] LIM power spectra can vary by up to 50% in $\rm 1 deg^2$ fields. This limits the accuracy of the constraints provided by the first 1 deg$^2$ surveys. The level of the shot noise power is always dominated by the sources that are just below the detection thresholds. We provide an analytical formula to estimate the field-to-field variance of current or future LIM experiments. The code and the full SIDES-Uchuu products (catalogs, cubes, and maps) are publicly available.

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Euclid preparation. XVIII. The NISP photometric system

Euclid will be the first space mission to survey most of the extragalactic sky in the 0.95-2.02 $μ$m range, to a 5$σ$ point-source median depth of 24.4 AB mag. This unique photometric data set will find wide use beyond Euclid's core science. In this paper, we present accurate computations of the Euclid Y_E, J_E and H_E passbands used by the Near-Infrared Spectrometer and Photometer (NISP), and the associated photometric system. We pay particular attention to passband variations in the field of view, accounting among others for spatially variable filter transmission, and variations of the angle of incidence on the filter substrate using optical ray tracing. The response curves' cut-on and cut-off wavelengths - and their variation in the field of view - are determined with 0.8 nm accuracy, essential for the photometric redshift accuracy required by Euclid. After computing the photometric zeropoints in the AB mag system, we present linear transformations from and to common ground-based near-infrared photometric systems, for normal stars, red and brown dwarfs, and galaxies separately. A Python tool to compute accurate magnitudes for arbitrary passbands and spectral energy distributions is provided. We discuss various factors from space weathering to material outgassing that may slowly alter Euclid's spectral response. At the absolute flux scale, the Euclid in-flight calibration program connects the NISP photometric system to Hubble Space Telescope spectrophotometric white dwarf standards; at the relative flux scale, the chromatic evolution of the response is tracked at the milli-mag level. In this way, we establish an accurate photometric system that is fully controlled throughout Euclid's lifetime.

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GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling

We present GIGA-Lens: a gradient-informed, GPU-accelerated Bayesian framework for modeling strong gravitational lensing systems, implemented in TensorFlow and JAX. The three components, optimization using multi-start gradient descent, posterior covariance estimation with variational inference, and sampling via Hamiltonian Monte Carlo, all take advantage of gradient information through automatic differentiation and massive parallelization on graphics processing units (GPUs). We test our pipeline on a large set of simulated systems and demonstrate in detail its high level of performance. The average time to model a single system on four Nvidia A100 GPUs is 105 seconds. The robustness, speed, and scalability offered by this framework make it possible to model the large number of strong lenses found in current surveys and present a very promising prospect for the modeling of $\mathcal{O}(10^5)$ lensing systems expected to be discovered in the era of the Vera C. Rubin Observatory, Euclid, and the Nancy Grace Roman Space Telescope.

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Euclid preparation: XIII. Forecasts for galaxy morphology with the Euclid Survey using Deep Generative Models

We present a machine learning framework to simulate realistic galaxies for the Euclid Survey. The proposed method combines a control on galaxy shape parameters offered by analytic models with realistic surface brightness distributions learned from real Hubble Space Telescope observations by deep generative models. We simulate a galaxy field of $0.4\,\rm{deg}^2$ as it will be seen by the Euclid visible imager VIS and show that galaxy structural parameters are recovered with similar accuracy as for pure analytic Sérsic profiles. Based on these simulations, we estimate that the Euclid Wide Survey will be able to resolve the internal morphological structure of galaxies down to a surface brightness of $22.5\,\rm{mag}\,\rm{arcsec}^{-2}$, and $24.9\,\rm{mag}\,\rm{arcsec}^{-2}$ for the Euclid Deep Survey. This corresponds to approximately $250$ million galaxies at the end of the mission and a $50\,\%$ complete sample for stellar masses above $10^{10.6}\,\rm{M}_\odot$ (resp. $10^{9.6}\,\rm{M}_\odot$) at a redshift $z\sim0.5$ for the wide (resp. deep) survey. The approach presented in this work can contribute to improving the preparation of future high-precision cosmological imaging surveys by allowing simulations to incorporate more realistic galaxies.

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Testing the 10 spectrograph units for DESI: approach and results

The recently commissioned Dark Energy Spectroscopic Instrument (DESI) will measure the expansion history of the Universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasars over 14000 sqdeg will be measured during the life of the experiment. A new prime focus corrector for the KPNO Mayall telescope delivers light to 5000 fiber optic positioners. The fibers in turn feed ten broad-band spectrographs. A consortium of Aix-Marseille University (AMU) and CNRS laboratories (LAM, OHP and CPPM) together with LPNHE (CNRS, IN2P3, Sorbonne Université and Université de Paris) and the WINLIGHT Systems company based in Pertuis (France), were in charge of integrating and validating the performance requirements of the ten full spectrographs, equipped with their cryostats, shutters and other mechanisms. We present a summary of our activity which allowed an efficient validation of the systems in a short-time schedule. We detail the main results. We emphasize the benefits of our approach and also its limitations.

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Euclid preparation: XI. Mean redshift determination from galaxy redshift probabilities for cosmic shear tomography

The analysis of weak gravitational lensing in wide-field imaging surveys is considered to be a major cosmological probe of dark energy. Our capacity to constrain the dark energy equation of state relies on the accurate knowledge of the galaxy mean redshift $\langle z \rangle$. We investigate the possibility of measuring $\langle z \rangle$ with an accuracy better than $0.002\,(1+z)$, in ten tomographic bins spanning the redshift interval $0.2 99.8\%$. The zPDF approach could also be successful if we debias the zPDF using a spectroscopic training sample. This approach requires deep imaging data, but is weakly sensitive to spectroscopic redshift failures in the training sample. We improve the debiasing method and confirm our finding by applying it to real-world weak-lensing data sets (COSMOS and KiDS+VIKING-450).

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SPIDERS: overview of the X-ray galaxy cluster follow-up and the final spectroscopic data release

SPIDERS (The SPectroscopic IDentification of eROSITA Sources) is a large spectroscopic programme for X-ray selected galaxy clusters as part of the Sloan Digital Sky Survey-IV (SDSS-IV). We describe the final dataset in the context of SDSS Data Release 16 (DR16): the survey overall characteristics, final targeting strategies, achieved completeness and spectral quality, with special emphasis on its use as a galaxy cluster sample for cosmology applications. SPIDERS now consists of about 27,000 new optical spectra of galaxies selected within 4,000 photometric red sequences, each associated with an X-ray source. The excellent spectrograph efficiency and a robust analysis pipeline yield a spectroscopic redshift measurement success rate exceeding 98%, with a median velocity accuracy of 20 km s$^{-1}$ (at $z=0.2$). Using the catalogue of 2,740 X-ray galaxy clusters confirmed with DR16 spectroscopy, we reveal the three-dimensional map of the galaxy cluster distribution in the observable Universe up to $z\sim0.6$. We highlight the homogeneity of the member galaxy spectra among distinct regions of the galaxy cluster phase space. Aided by accurate spectroscopic redshifts and by a model of the sample selection effects, we compute the galaxy cluster X-ray luminosity function and we present its lack of evolution up to $z=0.6$. Finally we discuss the prospects of forthcoming large multiplexed spectroscopic programmes dedicated to follow up the next generation of all-sky X-ray source catalogues.

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Euclid Preparation IV. Impact of undetected galaxies on weak-lensing shear measurements

In modern weak-lensing surveys, the common approach to correct for residual systematic biases in the shear is to calibrate shape measurement algorithms using simulations. These simulations must fully capture the complexity of the observations to avoid introducing any additional bias. In this paper we study the importance of faint galaxies below the observational detection limit of a survey. We simulate simplified Euclid VIS images including and excluding this faint population, and measure the shift in the multiplicative shear bias between the two sets of simulations. We measure the shear with three different algorithms: a moment-based approach, model fitting, and machine learning. We find that for all methods, a spatially uniform random distribution of faint galaxies introduces a shear multiplicative bias of the order of a few times $10^{-3}$. This value increases to the order of $10^{-2}$ when including the clustering of the faint galaxies, as measured in the Hubble Space Telescope Ultra-Deep Field. The magnification of the faint background galaxies due to the brighter galaxies along the line of sight is found to have a negligible impact on the multiplicative bias. We conclude that the undetected galaxies must be included in the calibration simulations with proper clustering properties down to magnitude 28 in order to reach a residual uncertainty on the multiplicative shear bias calibration of a few times $10^{-4}$, in line with the $2\times10^{-3}$ total accuracy budget required by the scientific objectives of the Euclid survey. We propose two complementary methods for including faint galaxy clustering in the calibration simulations.

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Testing gravity with galaxy-galaxy lensing and redshift-space distortions using CFHT-Stripe 82, CFHTLenS and BOSS CMASS datasets

The combination of Galaxy-Galaxy Lensing (GGL) and Redshift Space Distortion of galaxy clustering (RSD) is a privileged technique to test General Relativity predictions, and break degeneracies between the growth rate of structure parameter $f$ and the amplitude of the linear power-spectrum $σ_8$. We perform a joint GGL and RSD analysis on 250 sq. degrees using shape catalogues from CFHTLenS and CFHT-Stripe 82, and spectroscopic redshifts from the BOSS CMASS sample. We adjust a model that includes non-linear biasing, RSD and Alcock-Paczynski effects. We find $f(z=0.57) =0.95\pm0.23$, $σ_8(z=0.57)=0.55\pm0.07$ and $Ω_{\rm m} = 0.31\pm0.08$, in agreement with Planck cosmological results 2018. We also estimate the probe of gravity $E_{\rm G} = 0.43\pm0.10$ in agreement with $Λ$CDM-GR predictions of $E_{\rm G} = 0.40$. This analysis reveals that RSD efficiently decreases the GGL uncertainty on $Ω_{\rm m}$ by a factor of 4, and by 30\% on $σ_8$. We use an N-body simulation supplemented by an abundance matching prescription for CMASS to build a set of overlapping lensing and clustering mocks. Together with additional spectroscopic data, this helps us to quantify and correct several systematic errors, such as photometric redshifts. We make our mock catalogues available on the Skies and Universe database.

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Growing a `Cosmic Beast': Observations and Simulations of MACS J0717.5+3745

We present a gravitational lensing and X-ray analysis of a massive galaxy cluster and its surroundings. The core of MACS\,J0717.5+3745 ($M(R<1\,{\rm Mpc})\sim$\,$2$$\times$$10^{15}\,\msun$, $z$=$0.54$) is already known to contain four merging components. We show that this is surrounded by at least seven additional substructures with masses ranging from $3.8-6.5\times10^{13}\,\msun$, at projected radii $1.6$ to $4.9$\,Mpc. We compare MACS\,J0717 to mock lensing and X-ray observations of similarly rich clusters in cosmological simulations. The low gas fraction of substructures predicted by simulations turns out to match our observed values of $1$--$4\%$. Comparing our data to three similar simulated halos, we infer a typical growth rate and substructure infall velocity. That suggests MACS\,J0717 could evolve into a system similar to, but more massive than, Abell\,2744 by $z=0.31$, and into a $\sim$\,$10^{16}\,\msun$ supercluster by $z=0$. The radial distribution of infalling substructure suggests that merger events are strongly episodic; however we find that the smooth accretion of surrounding material remains the main source of mass growth even for such massive clusters.

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Probing galaxy assembly bias with LRG weak lensing observations

In Montero-Dorta et al. 2017, we show that luminous red galaxies (LRGs) from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) at $z\sim0.55$ can be divided into two groups based on their star formation histories. So-called fast-growing LRGs assemble $80\%$ of their stellar mass at $z\sim5$, whereas slow-growing LRGs reach the same evolutionary state at $z\sim1.5$. We further demonstrate that these two subpopulations present significantly different clustering properties on scales of $\sim1 - 30 \mathrm{Mpc}$. Here, we measure the mean halo mass of each subsample using the galaxy-galaxy lensing technique, in the $\sim190°^2$ overlap of the LRG catalogue and the CS82 and CFHTLenS shear catalogues. We show that fast- and slow-growing LRGs have similar lensing profiles, which implies that they live in haloes of similar mass: $\log\left(M_{\rm halo}^{\rm fast}/h^{-1}\mathrm{M}_{\odot}\right) = 12.85^{+0.16}_{-0.26}$ and $\log\left(M_{\rm halo}^{\rm slow}/h^{-1}\mathrm{M}_{\odot}\right) =12.92^{+0.16}_{-0.22}$. This result, combined with the clustering difference, suggests the existence of galaxy assembly bias, although the effect is too subtle to be definitively proven given the errors on our current weak-lensing measurement. We show that this can soon be achieved with upcoming surveys like DES.

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The VIMOS Public Extragalactic Redshift Survey (VIPERS). Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at $0.5 < z < 1.2$

We carry out a joint analysis of redshift-space distortions and galaxy-galaxy lensing, with the aim of measuring the growth rate of structure; this is a key quantity for understanding the nature of gravity on cosmological scales and late-time cosmic acceleration. We make use of the final VIPERS redshift survey dataset, which maps a portion of the Universe at a redshift of $z \simeq 0.8$, and the lensing data from the CFHTLenS survey over the same area of the sky. We build a consistent theoretical model that combines non-linear galaxy biasing and redshift-space distortion models, and confront it with observations. The two probes are combined in a Bayesian maximum likelihood analysis to determine the growth rate of structure at two redshifts $z=0.6$ and $z=0.86$. We obtain measurements of $fσ_8(0.6) = 0.48 \pm 0.12$ and $fσ_8(0.86) = 0.48 \pm 0.10$. The additional galaxy-galaxylensing constraint alleviates galaxy bias and $σ_8$ degeneracies, providing direct measurements of $[f(0.6),σ_8(0.6)] = [0.93 \pm 0.22, 0.52 \pm 0.06]$ and $f(0.86),σ_8(0.86)] = [0.99 \pm 0.19, 0.48 \pm 0.04]$. These measurements are statistically consistent with a Universe where the gravitational interactions can be described by General Relativity, although they are not yet accurate enough to rule out some commonly considered alternatives. Finally, as a complementary test we measure the gravitational slip parameter, $E_G$ , for the first time at $z>0.6$. We find values of $\smash{\overline{E}_G}(0.6) = 0.16 \pm 0.09$ and $\smash{\overline{E}_G}(0.86) = 0.09 \pm 0.07$, when $E_G$ is averaged over scales above $3 h^{-1} \rm{Mpc}$. We find that our $E_G$ measurements exhibit slightly lower values than expected for standard relativistic gravity in a ΛCDM background, although the results are consistent within $1-2σ$.

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Herschel and Hubble study of a lensed massive dusty starbursting galaxy at $z\sim3$

We present the results of combined deep Keck/NIRC2, HST/WFC3 near-infrared and Herschel far infrared observations of an extremely star forming dusty lensed galaxy identified from the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS J133542.9+300401). The galaxy is gravitationally lensed by a massive WISE identified galaxy cluster at $z\sim1$. The lensed galaxy is spectroscopically confirmed at $z=2.685$ from detection of $\rm {CO (1 \rightarrow 0)}$ by GBT and from detection of $\rm {CO (3 \rightarrow 2)}$ obtained with CARMA. We use the combined spectroscopic and imaging observations to construct a detailed lens model of the background dusty star-forming galaxy (DSFG) which allows us to study the source plane properties of the target. The best-fit lens model provide magnification of $μ_{\rm star}=2.10\pm0.11$ and $μ_{\rm dust}=2.02\pm0.06$ for the stellar and dust components respectively. Multi-band data yields a magnification corrected star formation rate of $1900(\pm200)\,M_{\odot}{\rm yr^{-1}}$ and stellar mass of $6.8_{-2.7}^{+0.9}\times10^{11}\,M_{\odot}$ consistent with a main sequence of star formation at $z\sim2.6$. The CO observations yield a molecular gas mass of $8.3(\pm1.0)\times10^{10}\,M_{\odot}$, similar to the most massive star-forming galaxies, which together with the high star-formation efficiency are responsible for the intense observed star formation rates. The lensed DSFG has a very short gas depletion time scale of $\sim40$ Myr. The high stellar mass and small gas fractions observed indicate that the lensed DSFG likely has already formed most of its stellar mass and could be a progenitor of the most massive elliptical galaxies found in the local Universe.

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The SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: final Emission Line Galaxy Target Selection

We describe the algorithm used to select the Emission Line Galaxy (ELG) sample at $z \sim 0.85$ for the extended Baryon Oscillation Spectroscopic Survey of the Sloan Digital Sky Survey IV, using photometric data from the DECam Legacy Survey. Our selection is based on a selection box in the $g-r$ vs. $r-z$ colour-colour space and a cut on the $g$-band magnitude, to favour galaxies in the desired redshift range with strong [OII] emission. It provides a target density of 200 deg$^{-2}$ on the North Galactic Cap (NGC) and of 240 deg$^{-2}$ on the South Galactic Cap (SGC), where we use a larger selection box because of deeper imaging. We demonstrate that this selection passes the eBOSS requirements in terms of homogeneity. About 50,000 ELGs have been observed since the observations have started in 2016, September. These roughly match the expected redshift distribution, though the measured efficiency is slightly lower than expected. The efficiency can be increased by enlarging the redshift range and with incoming pipeline improvement. The cosmological forecast based on these first data predict $σ_{D_V}/D_V = 0.023$, in agreement with previous forecasts. Lastly, we present the stellar population properties of the ELG SGC sample. Once observations are completed, this sample will be suited to provide a cosmological analysis at $z \sim 0.85$, and will pave the way for the next decade of massive spectroscopic cosmological surveys, which heavily rely on ELGs. The target catalogue over the SGC will be released along with DR14.

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The VIMOS Public Extragalactic Redshift Survey (VIPERS). Full spectroscopic data and auxiliary information release (PDR-2)

We present the full public data release (PDR-2) of the VIMOS Public Extragalactic Redshift Survey (VIPERS), performed at the ESO VLT. We release redshifts, spectra, CFHTLS magnitudes and ancillary information (as masks and weights) for a complete sample of 86,775 galaxies (plus 4,732 other objects, including stars and serendipitous galaxies); we also include their full photometrically-selected parent catalogue. The sample is magnitude limited to i_AB < 22.5, with an additional colour-colour pre-selection devised as to exclude galaxies at z<0.5. This practically doubles the effective sampling of the VIMOS spectrograph over the range 0.5 = 2 are shown to have a confidence level of 96% or larger and make up 88% of all measured galaxy redshifts (76,552 out of 86,775), constituting the VIPERS prime catalogue for statistical investigations. For this sample the rms redshift error, estimated using repeated measurements of about 3,000 galaxies, is found to be sigma_z = 0.00054(1+z). All data are available at http://vipers.inaf.it and on the ESO Archive.

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The SDSS-IV eBOSS: emission line galaxy catalogues at z=0.8 and study of systematic errors in the angular clustering

We present two wide-field catalogs of photometrically-selected emission line galaxies (ELGs) at z=0.8 covering about 2800 deg^2 over the south galactic cap. The catalogs were obtained using a Fisher discriminant technique described in a companion paper. The two catalogs differ by the imaging used to define the Fisher discriminant: the first catalog includes imaging from the Sloan Digital Sky Survey and the Wide-Field Infrared Survey Explorer, the second also includes information from the South Galactic Cap U-band Sky Survey (SCUSS). Containing respectively 560,045 and 615,601 objects, they represent the largest ELG catalogs available today and were designed for the ELG programme of the extended Baryon Oscillation Spectroscopic Survey (eBOSS). We study potential sources of systematic variation in the angular distribution of the selected ELGs due to fluctuations of the observational parameters. We model the influence of the observational parameters using a multivariate regression and implement a weighting scheme that allows effective removal of all of the systematic errors induced by the observational parameters. We show that fluctuations in the imaging zero-points of the photometric bands have minor impact on the angular distribution of objects in our catalogs. We compute the angular clustering of both catalogs and show that our weighting procedure effectively removes spurious clustering on large scales. We fit a model to the small scale angular clustering, showing that the selections have similar biases of 1.35/D_a(z) and 1.28/D_a(z). Both catalogs are publicly available.

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The Bullet cluster at its best: weighing stars, gas and dark matter

We present a new strong lensing mass reconstruction of the Bullet cluster (1E 0657-56) at z=0.296, based on WFC3 and ACS HST imaging and VLT/FORS2 spectroscopy. The strong lensing constraints underwent substantial revision compared to previously published analysis, there are now 14 (six new and eight previously known) multiply-imaged systems, of which three have spectroscopically confirmed redshifts (including one newly measured from this work). The reconstructed mass distribution explicitly included the combination of three mass components: i) the intra-cluster gas mass derived from X-ray observation, ii) the cluster galaxies modeled by their fundamental plane scaling relations and iii) dark matter. The model that includes the intra-cluster gas is the one with the best Bayesian evidence. This model has a total RMS value of 0.158" between the predicted and measured image positions for the 14 multiple images considered. The proximity of the total RMS to resolution of HST/WFC3 and ACS (0.07-0.15" FWHM) demonstrates the excellent precision of our mass model. The derived mass model confirms the spatial offset between the X-ray gas and dark matter peaks. The fraction of the galaxy halos mass to total mass is found to be f_s=11+/-5% for a total mass of 2.5+/-0.1 x 10^14 solar mass within a 250 kpc radial aperture.

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Combining Strong Lensing and Dynamics in Galaxy Clusters: integrating MAMPOSSt within LENSTOOL I. Application on SL2S J02140-0535

We present a new framework were we simultaneously fit strong lensing (SL) and dynamical data. The SL analysis is based on LENSTOOL, and the dynamical analysis uses MAMPOSSt code, which we have integrated into LENSTOOL. After describing the implementation of this new tool, we apply it on the galaxy group SL2S\,J02140-0535 ($z_{\rm spec}=0.44$), which we have already studied in the past. We use new VLT/FORS2 spectroscopy of multiple images and group members, as well as shallow X-ray data from \xmm. We confirm that the observed lensing features in SL2S\,J02140-0535 belong to different background sources. One of this sources is located at $z_{\rm spec}$ = 1.017 $\pm$ 0.001, whereas the other source is located at $z_{\rm spec}$ = 1.628 $\pm$ 0.001. With the analysis of our new and our previously reported spectroscopic data, we find 24 secure members for SL2S\,J02140-0535. Both data sets are well reproduced by a single NFW mass profile: the dark matter halo coincides with the peak of the light distribution, with scale radius, concentration, and mass equal to $r_s$ =$82^{+44}_{-17}$ kpc , $c_{200}$ = $10.0^{+1.7}_{-2.5}$, and $M_{200}$ = $1.0^{+0.5}_{-0.2}$ $\times$ 10$^{14}$M$_{\odot}$ respectively. These parameters are better constrained when we fit simultaneously SL and dynamical information. The mass contours of our best model agrees with the direction defined by the luminosity contours and the X-ray emission of SL2S\,J02140-0535. The simultaneous fit lowers the error in the mass estimate by 0.34 dex, when compared to the SL model, and in 0.15 dex when compared to the dynamical method.The combination of SL and dynamics tools yields a more accurate probe of the mass profile of SL2S\,J02140-0535 up to $r_{200}$. However, there is tension between the best elliptical SL model and the best spherical dynamical model.

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