arXiv subjects

A. Amara

Publications and source records attributed to A. Amara.

At least 199 records · Page 11Linked to original sources

arXiv2021

Euclid: Effect of sample covariance on the number counts of galaxy clusters

Aims. We investigate the contribution of shot-noise and sample variance to the uncertainty of cosmological parameter constraints inferred from cluster number counts in the context of the Euclid survey. Methods. By analysing 1000 Euclid-like light-cones, produced with the PINOCCHIO approximate method, we validate the analytical model of Hu & Kravtsov 2003 for the covariance matrix, which takes into account both sources of statistical error. Then, we use such covariance to define the likelihood function that better extracts cosmological information from cluster number counts at the level of precision that will be reached by the future Euclid photometric catalogs of galaxy clusters. We also study the impact of the cosmology dependence of the covariance matrix on the parameter constraints. Results. The analytical covariance matrix reproduces the variance measured from simulations within the 10 per cent level; such difference has no sizeable effect on the error of cosmological parameter constraints at this level of statistics. Also, we find that the Gaussian likelihood with cosmology-dependent covariance is the only model that provides an unbiased inference of cosmological parameters without underestimating the errors.

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arXiv2021

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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arXiv2020

A Deeper Look at DES Dwarf Galaxy Candidates: Grus I and Indus II

We present deep $g$- and $r$-band Magellan/Megacam photometry of two dwarf galaxy candidates discovered in the Dark Energy Survey (DES), Grus I and Indus II (DES J2038-4609). For the case of Grus I, we resolved the main sequence turn-off (MSTO) and $\sim 2$ mags below it. The MSTO can be seen at $g_0\sim 24$ with a photometric uncertainty of $0.03$ mag. We show Grus I to be consistent with an old, metal-poor ($\sim 13.3$ Gyr, [Fe/H]$\sim-1.9$) dwarf galaxy. We derive updated distance and structural parameters for Grus I using this deep, uniform, wide-field data set. We find an azimuthally averaged half-light radius more than two times larger ($\sim 151^{+21}_{-31}$ pc; $\sim 4.^{\prime} 16^{+0.54}_{-0.74}$) and an absolute $V$-band magnitude $\sim-4.1$ that is $\sim 1$ magnitude brighter than previous studies. We obtain updated distance, ellipticity, and centroid parameters which are in agreement with other studies within uncertainties. Although our photometry of Indus II is $\sim 2-3$ magnitudes deeper than the DES Y1 Public release, we find no coherent stellar population at its reported location. The original detection was located in an incomplete region of sky in the DES Y2Q1 data set and was flagged due to potential blue horizontal branch member stars. The best fit isochrone parameters are physically inconsistent with both dwarf galaxies and globular clusters. We conclude that Indus II is likely a false-positive, flagged due to a chance alignment of stars along the line of sight.

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arXiv2020

Predicting Cosmological Observables with PyCosmo

Current and upcoming cosmological experiments open a new era of precision cosmology, thus demanding accurate theoretical predictions for cosmological observables. Because of the complexity of the codes delivering such predictions, reaching a high level of numerical accuracy is challenging. Among the codes already fulfilling this task, $\textsf{PyCosmo}$ is a Python based framework providing solutions to the Einstein-Boltzmann equations and accurate predictions for cosmological observables. In this work, we first describe how the observables are implemented. Then, we check the accuracy of the theoretical predictions for background quantities, power spectra and Limber and beyond-Limber angular power spectra by comparison with other codes: the Core Cosmology Library ($\texttt{CCL}$), $\texttt{CLASS}$, $\texttt{HMCode}$ and $\texttt{iCosmo}$. In our analysis we quantify the agreement of $\textsf{PyCosmo}$ with the other codes, for a range of cosmological models, monitored through a series of $\textit{unit tests}$. $\textsf{PyCosmo}$, conceived as a multi purpose cosmology calculation tool in $\texttt{Python}$, is designed to be interactive and user friendly. A current version of the code (without the Boltzmann Solver) is publicly available and can be used interactively on the platform $\textsf{PyCosmo Hub}$, all accessible from this link: https://cosmology.ethz.ch/research/software-lab/PyCosmo.html . On the hub the users can perform their own computations using $\texttt{Jupyter Notebooks}$ without the need of installing any software, access to the results presented in this work and benefit from tutorial notebooks illustrating the usage of the code. The link above also redirects to the code release and documentation.

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arXiv2020

Noise from Undetected Sources in Dark Energy Survey Images

For ground-based optical imaging with current CCD technology, the Poisson fluctuations in source and sky background photon arrivals dominate the noise budget and are readily estimated. Another component of noise, however, is the signal from the undetected population of stars and galaxies. Using injection of artificial galaxies into images, we demonstrate that the measured variance of galaxy moments (used for weak gravitational lensing measurements) in Dark Energy Survey (DES) images is significantly in excess of the Poisson predictions, by up to 30\%, and that the background sky levels are overestimated by current software. By cross-correlating distinct images of "empty" sky regions, we establish that there is a significant image noise contribution from undetected static sources (US), which on average are mildly resolved at DES resolution. Treating these US as a stationary noise source, we compute a correction to the moment covariance matrix expected from Poisson noise. The corrected covariance matrix matches the moment variances measured on the injected DES images to within 5\%. Thus we have an empirical method to statistically account for US in weak lensing measurements, rather than requiring extremely deep sky simulations. We also find that local sky determinations can remove the bias in flux measurements, at a small penalty in additional, but quantifiable, noise.

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arXiv2020

Modelling the Milky Way. I -- Method and first results fitting the thick disk and halo with DES-Y3 data

We present MWFitting, a method to fit the stellar components of the Galaxy by comparing Hess Diagrams (HDs) from TRILEGAL models to real data. We apply MWFitting to photometric data from the first three years of the Dark Energy Survey (DES). After removing regions containing known resolved stellar systems such as globular clusters, dwarf galaxies, nearby galaxies, the Large Magellanic Cloud and the Sagittarius Stream, our main sample spans a total area of $\sim$2,300 deg$^2$ distributed across the DES footprint. We further explore a smaller subset ($\sim$ 1,300 deg$^2$) that excludes all regions with known stellar streams and stellar overdensities. Validation tests on synthetic data possessing similar properties to the DES data show that the method is able to recover input parameters with a precision better than 3\%. Based on the best-fit models, we create simulated stellar catalogues covering the whole DES footprint down to $g = 24$ magnitude. Comparisons of data and simulations provide evidence for a break in the power law index describing the stellar density of the Milky Way (MW) halo. Several previously discovered stellar over-densities are recovered in the residual stellar density map, showing the reliability of MWFitting in determining the Galactic components. Simulations made with the best-fitting parameters are a promising way to predict MW star counts for surveys such as LSST and Euclid.

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arXiv2019

Observation and Confirmation of Nine Strong Lensing Systems in Dark Energy Survey Year 1 Data

We describe the observation and confirmation of \nbconfirmtext\ new strong gravitational lenses discovered in Year 1 data from the Dark Energy Survey (DES). We created candidate lists based on a) galaxy group and cluster samples and b) photometrically selected galaxy samples. We selected 46 candidates through visual inspection and then used the Gemini Multi-Object Spectrograph (GMOS) at the Gemini South telescope to acquire spectroscopic follow-up of 21 of these candidates. Through analysis of this spectroscopic follow-up data, we confirmed nine new lensing systems and rejected 2 candidates, but the analysis was inconclusive on 10 candidates. For each of the confirmed systems, we report measured spectroscopic properties, estimated \einsteinradiussub, and estimated enclosed masses. The sources that we targeted have an i-band surface brightness range of iSB ~ 22 - 24 mag arcsec^2 and a spectroscopic redshift range of zspec ~0.8 - 2.6. The lens galaxies have a photometric redshift range of zlens ~ 0.3 - 0.7. The lensing systems range in image-lens separation 2 - 9 arcsec and in enclosed mass 10^12 - 10^13 Msol.

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arXiv2019

The PAU Survey: Early demonstration of photometric redshift performance in the COSMOS field

The PAU Survey (PAUS) is an innovative photometric survey with 40 narrow bands at the William Herschel Telescope (WHT). The narrow bands are spaced at 100Å intervals covering the range 4500Å to 8500Å and, in combination with standard broad bands, enable excellent redshift precision. This paper describes the technique, galaxy templates and additional photometric calibration used to determine early photometric redshifts from PAUS. Using BCNz2, a new photometric redshift code developed for this purpose, we characterise the photometric redshift performance using PAUS data on the COSMOS field. Comparison to secure spectra from zCOSMOS DR3 shows that PAUS achieves $σ_{68} /(1+z) = 0.0037$ to $i_{\mathrm{AB}} < 22.5$ when selecting the best 50% of the sources based on a photometric redshift quality cut. Furthermore, a higher photo-z precision ($σ_{68}/(1+z) \sim 0.001$) is obtained for a bright and high quality selection, which is driven by the identification of emission lines. We conclude that PAUS meets its design goals, opening up a hitherto uncharted regime of deep, wide, and dense galaxy survey with precise redshifts that will provide unique insights into the formation, evolution and clustering of galaxies, as well as their intrinsic alignments.

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arXiv2019

Monte Carlo Control Loops for cosmic shear cosmology with DES Year 1

Weak lensing by large-scale structure is a powerful probe of cosmology and of the dark universe. This cosmic shear technique relies on the accurate measurement of the shapes and redshifts of background galaxies and requires precise control of systematic errors. The Monte Carlo Control Loops (MCCL) is a forward modelling method designed to tackle this problem. It relies on the Ultra Fast Image Generator (UFig) to produce simulated images tuned to match the target data statistically, followed by calibrations and tolerance loops. We present the first end-to-end application of this method, on the Dark Energy Survey (DES) Year 1 wide field imaging data. We simultaneously measure the shear power spectrum $C_{\ell}$ and the redshift distribution $n(z)$ of the background galaxy sample. The method includes maps of the systematic sources, Point Spread Function (PSF), an Approximate Bayesian Computation (ABC) inference of the simulation model parameters, a shear calibration scheme, and the fast estimation of the covariance matrix. We find a close statistical agreement between the simulations and the DES Y1 data using an array of diagnostics. In a non-tomographic setting, we derive a set of $C_\ell$ and $n(z)$ curves that encode the cosmic shear measurement, as well as the systematic uncertainty. Following a blinding scheme, we measure the combination of $Ω_m$, $σ_8$, and intrinsic alignment amplitude $A_{\rm{IA}}$, defined as $S_8D_{\rm{IA}} = σ_8(Ω_m/0.3)^{0.5}D_{\rm{IA}}$, where $D_{\rm{IA}}=1-0.11(A_{\rm{IA}}-1)$. We find $S_8D_{\rm{IA}}=0.895^{+0.054}_{-0.039}$, where systematics are at the level of roughly 60\% of the statistical errors. We discuss these results in the context of earlier cosmic shear analyses of the DES Y1 data. Our findings indicate that this method and its fast runtime offer good prospects for cosmic shear measurements with future wide-field surveys.

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arXiv2019

The Dark Energy Survey Data Release 1

We describe the first public data release of the Dark Energy Survey, DES DR1, consisting of reduced single epoch images, coadded images, coadded source catalogs, and associated products and services assembled over the first three years of DES science operations. DES DR1 is based on optical/near-infrared imaging from 345 distinct nights (August 2013 to February 2016) by the Dark Energy Camera mounted on the 4-m Blanco telescope at Cerro Tololo Inter-American Observatory in Chile. We release data from the DES wide-area survey covering ~5,000 sq. deg. of the southern Galactic cap in five broad photometric bands, grizY. DES DR1 has a median delivered point-spread function of g = 1.12, r = 0.96, i = 0.88, z = 0.84, and Y = 0.90 arcsec FWHM, a photometric precision of < 1% in all bands, and an astrometric precision of 151 mas. The median coadded catalog depth for a 1.95" diameter aperture at S/N = 10 is g = 24.33, r = 24.08, i = 23.44, z = 22.69, and Y = 21.44 mag. DES DR1 includes nearly 400M distinct astronomical objects detected in ~10,000 coadd tiles of size 0.534 sq. deg. produced from ~39,000 individual exposures. Benchmark galaxy and stellar samples contain ~310M and ~ 80M objects, respectively, following a basic object quality selection. These data are accessible through a range of interfaces, including query web clients, image cutout servers, jupyter notebooks, and an interactive coadd image visualization tool. DES DR1 constitutes the largest photometric data set to date at the achieved depth and photometric precision.

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arXiv2019

Dark Energy Survey Year 1 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing

We present cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing, using 1321 deg$^2$ of $griz$ imaging data from the first year of the Dark Energy Survey (DES Y1). We combine three two-point functions: (i) the cosmic shear correlation function of 26 million source galaxies in four redshift bins, (ii) the galaxy angular autocorrelation function of 650,000 luminous red galaxies in five redshift bins, and (iii) the galaxy-shear cross-correlation of luminous red galaxy positions and source galaxy shears. To demonstrate the robustness of these results, we use independent pairs of galaxy shape, photometric redshift estimation and validation, and likelihood analysis pipelines. To prevent confirmation bias, the bulk of the analysis was carried out while blind to the true results; we describe an extensive suite of systematics checks performed and passed during this blinded phase. The data are modeled in flat $Λ$CDM and $w$CDM cosmologies, marginalizing over 20 nuisance parameters, varying 6 (for $Λ$CDM) or 7 (for $w$CDM) cosmological parameters including the neutrino mass density and including the 457 $\times$ 457 element analytic covariance matrix. We find consistent cosmological results from these three two-point functions, and from their combination obtain $S_8 \equiv σ_8 (Ω_m/0.3)^{0.5} = 0.783^{+0.021}_{-0.025}$ and $Ω_m = 0.264^{+0.032}_{-0.019}$ for $Λ$CDM for $w$CDM, we find $S_8 = 0.794^{+0.029}_{-0.027}$, $Ω_m = 0.279^{+0.043}_{-0.022}$, and $w=-0.80^{+0.20}_{-0.22}$ at 68% CL. The precision of these DES Y1 results rivals that from the Planck cosmic microwave background measurements, allowing a comparison of structure in the very early and late Universe on equal terms. Although the DES Y1 best-fit values for $S_8$ and $Ω_m$ are lower than the central values from Planck ...

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arXiv2018

A catalogue of structural and morphological measurements for DES Y1

We present a structural and morphological catalogue for 45 million objects selected from the first year of data from the Dark Energy Survey (DES). Single Sersic fits and non-parametric measurements are produced for g, r and i filters. The parameters from the best-fitting Sersic model (total magnitude, half-light radius, Sersic index, axis ratio and position angle) are measured with Galfit; the non-parametric coefficients (concentration, asymmetry, clumpiness, Gini, M20) are provided using the Zurich Estimator of Structural Types (ZEST+). To study the statistical uncertainties, we consider a sample of state-of-the-art image simulations with a realistic distribution in the input parameter space and then process and analyse them as we do with real data: this enables us to quantify the observational biases due to PSF blurring and magnitude effects and correct the measurements as a function of magnitude, galaxy size, Sersic index (concentration for the analysis of the non-parametric measurements) and ellipticity. We present the largest structural catalogue to date: we find that accurate and complete measurements for all the structural parameters are typically obtained for galaxies with SExtractor MAG AUTO I < 21. Indeed, the parameters in the filters i and r can be overall well recovered up to MAG AUTO < 21.5, corresponding to a fitting completeness of ~90% below this threshold, for a total of 25 million galaxies. The combination of parametric and non-parametric structural measurements makes this catalogue an important instrument to explore and understand how galaxies form and evolve. The catalogue described in this paper will be publicly released alongside the Dark Energy Survey collaboration Y1 cosmology data products at the following URL: https://des.ncsa.illinois.edu/releases/y1a1/gold/morphology.

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arXiv2018

The PAU Survey: Spectral features and galaxy clustering using simulated narrow band photometry

We present a mock catalogue for the Physics of the Accelerating Universe Survey (PAUS) and use it to quantify the competitiveness of the narrow band imaging for measuring spectral features and galaxy clustering. The mock agrees with observed number count and redshift distribution data. We demonstrate the importance of including emission lines in the narrow band fluxes. We show that PAUCam has sufficient resolution to measure the strength of the 4000Å break to the nominal PAUS depth. We predict the evolution of a narrow band luminosity function and show how this can be affected by the OII emission line. We introduce new rest frame broad bands (UV and blue) that can be derived directly from the narrow band fluxes. We use these bands along with D4000 and redshift to define galaxy samples and provide predictions for galaxy clustering measurements. We show that systematic errors in the recovery of the projected clustering due to photometric redshift errors in PAUS are significantly smaller than the expected statistical errors. The galaxy clustering on two halo scales can be recovered quantatively without correction, and all qualitative trends seen in the one halo term are recovered. In this analysis mixing between samples reduces the expected contrast between the one halo clustering of red and blue galaxies and demonstrates the importance of a mock catalogue for interpreting galaxy clustering results. The mock catalogue is available on request at https://cosmohub.pic.es/home.

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arXiv2018

Dark Energy Survey Year 1 Results: Cosmological Constraints from Cosmic Shear

We use 26 million galaxies from the Dark Energy Survey (DES) Year 1 shape catalogs over 1321 deg$^2$ of the sky to produce the most significant measurement of cosmic shear in a galaxy survey to date. We constrain cosmological parameters in both the flat $Λ$CDM and $w$CDM models, while also varying the neutrino mass density. These results are shown to be robust using two independent shape catalogs, two independent \photoz\ calibration methods, and two independent analysis pipelines in a blind analysis. We find a 3.5\% fractional uncertainty on $σ_8(Ω_m/0.3)^{0.5} = 0.782^{+0.027}_{-0.027}$ at 68\% CL, which is a factor of 2.5 improvement over the fractional constraining power of our DES Science Verification results. In $w$CDM, we find a 4.8\% fractional uncertainty on $σ_8(Ω_m/0.3)^{0.5} = 0.777^{+0.036}_{-0.038}$ and a dark energy equation-of-state $w=-0.95^{+0.33}_{-0.39}$. We find results that are consistent with previous cosmic shear constraints in $σ_8$ -- $Ω_m$, and see no evidence for disagreement of our weak lensing data with data from the CMB. Finally, we find no evidence preferring a $w$CDM model allowing $w\ne -1$. We expect further significant improvements with subsequent years of DES data, which will more than triple the sky coverage of our shape catalogs and double the effective integrated exposure time per galaxy.

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arXiv2017

DES meets Gaia: discovery of strongly lensed quasars from a multiplet search

We report the discovery, spectroscopic confirmation and first lens models of the first two, strongly lensed quasars from a combined search in WISE and Gaia over the DES footprint. The four-image lensWGD2038-4008 (r.a.=20:38:02.65, dec.=-40:08:14.64) has source- and lens-redshifts $z_{s}=0.777 \pm 0.001$ and $z_l = 0.230 \pm 0.002$ respectively. Its deflector has effective radius $R_{\rm eff} \approx 3.4^{\prime\prime}$, stellar mass $\log(M_{\star}/M_{\odot}) = 11.64^{+0.20}_{-0.43}$, and shows extended isophotal shape variation. Simple lens models yield Einstein radii $R_{\rm E}=(1.30\pm0.04)^{\prime\prime},$ axis ratio $q=0.75\pm0.1$ (compatible with that of the starlight) and considerable shear-ellipticity degeneracies. The two-image lensWGD2021-4115 (r.a.=20:21:39.45, dec.=--41:15:57.11) has $z_{s}=1.390\pm0.001$ and $z_l = 0.335 \pm 0.002$, and Einstein radius $R_{\rm E} = (1.1\pm0.1)^{\prime\prime},$ but higher-resolution imaging is needed to accurately separate the deflector and faint quasar image. We also show high-rank candidate doubles selected this way, some of which have been independently identified with different techniques, and discuss a DES+WISE quasar multiplet selection.

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arXiv2017

Galaxy bias from galaxy-galaxy lensing in the DES Science Verification Data

We present a measurement of galaxy-galaxy lensing around a magnitude-limited ($i_{AB} < 22.5$) sample of galaxies from the Dark Energy Survey Science Verification (DES-SV) data. We split these lenses into three photometric-redshift bins from 0.2 to 0.8, and determine the product of the galaxy bias $b$ and cross-correlation coefficient between the galaxy and dark matter overdensity fields $r$ in each bin, using scales above 4 Mpc/$h$ comoving, where we find the linear bias model to be valid given our current uncertainties. We compare our galaxy bias results from galaxy-galaxy lensing with those obtained from galaxy clustering (Crocce et al. 2016) and CMB lensing (Giannantonio et al. 2016) for the same sample of galaxies, and find our measurements to be in good agreement with those in Crocce et al. (2016), while, in the lowest redshift bin ($z\sim0.3$), they show some tension with the findings in Giannantonio et al. (2016). We measure $b\cdot r$ to be $0.87\pm 0.11$, $1.12 \pm 0.16$ and $1.24\pm 0.23$, respectively for the three redshift bins of width $Δz = 0.2$ in the range $0.2<z <0.8$, defined with the photometric-redshift algorithm BPZ. Using a different code to split the lens sample, TPZ, leads to changes in the measured biases at the 10-20\% level, but it does not alter the main conclusion of this work: when comparing with Crocce et al. (2016) we do not find strong evidence for a cross-correlation parameter significantly below one in this galaxy sample, except possibly at the lowest redshift bin ($z\sim 0.3$), where we find $r = 0.71 \pm 0.11$ when using TPZ, and $0.83 \pm 0.12$ with BPZ.

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arXiv2017

Cosmology from Cosmic Shear with DES Science Verification Data

We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV data, which is less than 3\% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find $σ_8 (Ω_{\rm m}/0.3)^{0.5} = 0.81 \pm 0.06$ (68\% confidence), after marginalising over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable. About $20$\% of our error bar comes from marginalising over shear and photometric redshift calibration uncertainties. The current state-of-the-art cosmic shear measurements from CFHTLenS are mildly discrepant with the cosmological constraints from Planck CMB data; our results are consistent with both datasets. Our uncertainties are $\sim$30\% larger than those from CFHTLenS when we carry out a comparable analysis of the two datasets, which we attribute largely to the lower number density of our shear catalogue. We investigate constraints on dark energy and find that, with this small fraction of the full survey, the DES SV constraints make negligible impact on the Planck constraints. The moderate disagreement between the CFHTLenS and Planck values of $σ_8 (Ω_{\rm m}/0.3)^{0.5}$ is present regardless of the value of $w$.

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arXiv2017

Weak-lensing mass calibration of redMaPPer galaxy clusters in Dark Energy Survey Science Verification data

We use weak-lensing shear measurements to determine the mean mass of optically selected galaxy clusters in Dark Energy Survey Science Verification data. In a blinded analysis, we split the sample of more than 8,000 redMaPPer clusters into 15 subsets, spanning ranges in the richness parameter $5 \leq λ\leq 180$ and redshift $0.2 \leq z \leq 0.8$, and fit the averaged mass density contrast profiles with a model that accounts for seven distinct sources of systematic uncertainty: shear measurement and photometric redshift errors; cluster-member contamination; miscentering; deviations from the NFW halo profile; halo triaxiality; and line-of-sight projections. We combine the inferred cluster masses to estimate the joint scaling relation between mass, richness and redshift, $\mathcal{M}(λ,z) \varpropto M_0 λ^{F} (1+z)^{G}$. We find $M_0 \equiv \langle M_{200\mathrm{m}}\,|\,λ=30,z=0.5\rangle=\left[ 2.35 \pm 0.22\ \rm{(stat)} \pm 0.12\ \rm{(sys)} \right] \cdot 10^{14}\ M_\odot$, with $F = 1.12\,\pm\,0.20\ \rm{(stat)}\, \pm\, 0.06\ \rm{(sys)}$ and $G = 0.18\,\pm\, 0.75\ \rm{(stat)}\, \pm\, 0.24\ \rm{(sys)}$. The amplitude of the mass-richness relation is in excellent agreement with the weak-lensing calibration of redMaPPer clusters in SDSS by Simet et al. (2016) and with the Saro et al. (2015) calibration based on abundance matching of SPT-detected clusters. Our results extend the redshift range over which the mass-richness relation of redMaPPer clusters has been calibrated with weak lensing from $z\leq 0.3$ to $z\leq0.8$. Calibration uncertainties of shear measurements and photometric redshift estimates dominate our systematic error budget and require substantial improvements for forthcoming studies.

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