Engineering topics

Gerdes, D. W.

Publications and source records attributed to Gerdes, D. W..

35 records · Page 2

DOE OSTI2022

The DECam Local Volume Exploration Survey Data Release 2

We present the second public data release (DR2) from the DECam Local Volume Exploration survey (DELVE). DELVE DR2 combines new DECam observations with archival DECam data from the Dark Energy Survey, the DECam Legacy Survey, and other DECam community programs. DELVE DR2 consists of ∼160,000 exposures that cover >21,000 deg$^{2}$ of the high-Galactic-latitude (∣b∣ > 10°) sky in four broadband optical/near-infrared filters (g, r, i, z). DELVE DR2 provides point-source and automatic aperture photometry for ∼2.5 billion astronomical sources with a median 5σ point-source depth of g = 24.3, r = 23.9, i = 23.5, and z = 22.8 mag. A region of ∼17,000 deg$^{2}$ has been imaged in all four filters, providing four-band photometric measurements for ∼618 million astronomical sources. DELVE DR2 covers more than 4 times the area of the previous DELVE data release and contains roughly 5 times as many astronomical objects. DELVE DR2 is publicly available via the NOIRLab Astro Data Lab science platform.

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Cross-correlation of Dark Energy Survey Year 3 lensing data with ACT and Planck thermal Sunyaev-Zel’dovich effect observations. I. Measurements, systematics tests, and feedback model constraints

Here we present a tomographic measurement of the cross-correlation between thermal Sunyaev-Zel’dovich (TSZ) maps from Planck and the Atacama Cosmology Telescope and weak galaxy lensing shears measured during the first three years of observations of the Dark Energy Survey. This correlation is sensitive to the thermal energy in baryons over a wide redshift range and is therefore a powerful probe of astrophysical feedback. We detect the correlation at a statistical significance of 21σ, the highest significance to date. We examine the TSZ maps for potential contaminants, including cosmic infrared background and radio sources, finding that cosmic infrared background has a substantial impact on our measurements and must be taken into account in our analysis. We use the cross-correlation measurements to test different feedback models. In particular, we model the TSZ using several different pressure profile models calibrated against hydrodynamical simulations. Our analysis marginalizes over redshift uncertainties, shear calibration biases, and intrinsic alignment effects. We also marginalize over Ω m and σ 8 using Planck or DES priors. We find that the data prefer the model with a low amplitude of the pressure profile at small scales, compatible with a scenario with strong active galactic nuclei feedback and ejection of gas from the inner part of the halos. When using a more flexible model for the shear profile, constraints are weaker, and the data cannot discriminate between different baryonic prescriptions.

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Cross-correlation of Dark Energy Survey Year 3 lensing data with ACT and P l a n c k thermal Sunyaev-Zel’dovich effect observations. II. Modeling and constraints on halo pressure profiles

Hot, ionized gas leaves an imprint on the cosmic microwave background via the thermal Sunyaev-Zel’dovich (tSZ) effect. The cross-correlation of gravitational lensing (which traces the projected mass) with the tSZ effect (which traces the projected gas pressure) is a powerful probe of the thermal state of ionized baryons throughout the Universe and is sensitive to effects such as baryonic feedback. In a companion paper (Gatti et al. Phys. Rev. D 105, 123525 (2022)), we present tomographic measurements and validation tests of the cross-correlation between Galaxy shear measurements from the first three years of observations of the Dark Energy Survey and tSZ measurements from a combination of Atacama Cosmology Telescope and Planck observations. In this work, we use the same measurements to constrain models for the pressure profiles of halos across a wide range of halo mass and redshift. We find evidence for reduced pressure in low-mass halos, consistent with predictions for the effects of feedback from active Galactic nuclei. We infer the hydrostatic mass bias (B ≡ M 500c /M SZ from our measurements, finding B = 1.8 ± 0.1 when adopting the Planck-preferred cosmological parameters. We additionally find that our measurements are consistent with a nonzero redshift evolution of B, with the correct sign and sufficient magnitude to explain the mass bias necessary to reconcile cluster count measurements with the Planck-preferred cosmology. Our analysis introduces a model for the impact of intrinsic alignments (IAs) of galaxy shapes on the shear-tSZ correlation. We show that IA can have a significant impact on these correlations at current noise levels.

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DOE OSTI2022

The dark energy survey 5-yr photometrically identified type Ia supernovae

ABSTRACT As part of the cosmology analysis using Type Ia Supernovae (SN Ia) in the Dark Energy Survey (DES), we present photometrically identified SN Ia samples using multiband light curves and host galaxy redshifts. For this analysis, we use the photometric classification framework SuperNNovatrained on realistic DES-like simulations. For reliable classification, we process the DES SN programme (DES-SN) data and introduce improvements to the classifier architecture, obtaining classification accuracies of more than 98 per cent on simulations. This is the first SN classification to make use of ensemble methods, resulting in more robust samples. Using photometry, host galaxy redshifts, and a classification probability requirement, we identify 1863 SNe Ia from which we select 1484 cosmology-grade SNe Ia spanning the redshift range of 0.07 < z < 1.14. We find good agreement between the light-curve properties of the photometrically selected sample and simulations. Additionally, we create similar SN Ia samples using two types of Bayesian Neural Network classifiers that provide uncertainties on the classification probabilities. We test the feasibility of using these uncertainties as indicators for out-of-distribution candidates and model confidence. Finally, we discuss the implications of photometric samples and classification methods for future surveys such as Vera C. Rubin Observatory Legacy Survey of Space and Time.

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DOE OSTI2022

The Dark Energy Survey supernova program: cosmological biases from supernova photometric classification

ABSTRACT Cosmological analyses of samples of photometrically identified type Ia supernovae (SNe Ia) depend on understanding the effects of ‘contamination’ from core-collapse and peculiar SN Ia events. We employ a rigorous analysis using the photometric classifier SuperNNova on state-of-the-art simulations of SN samples to determine cosmological biases due to such ‘non-Ia’ contamination in the Dark Energy Survey (DES) 5-yr SN sample. Depending on the non-Ia SN models used in the SuperNNova training and testing samples, contamination ranges from 0.8 to 3.5 per cent, with a classification efficiency of 97.7–99.5 per cent. Using the Bayesian Estimation Applied to Multiple Species (BEAMS) framework and its extension BBC (‘BEAMS with Bias Correction’), we produce a redshift-binned Hubble diagram marginalized over contamination and corrected for selection effects, and use it to constrain the dark energy equation-of-state, w. Assuming a flat universe with Gaussian ΩM prior of 0.311 ± 0.010, we show that biases on w are <0.008 when using SuperNNova, with systematic uncertainties associated with contamination around 10 per cent of the statistical uncertainty on w for the DES-SN sample. An alternative approach of discarding contaminants using outlier rejection techniques (e.g. Chauvenet’s criterion) in place of SuperNNova leads to biases on w that are larger but still modest (0.015–0.03). Finally, we measure biases due to contamination on w0 and wa (assuming a flat universe), and find these to be <0.009 in w0 and <0.108 in wa, 5 to 10 times smaller than the statistical uncertainties for the DES-SN sample.

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DOE OSTI2022

Finding quadruply imaged quasars with machine learning – I. Methods

ABSTRACT Strongly lensed quadruply imaged quasars (quads) are extraordinary objects. They are very rare in the sky and yet they provide unique information about a wide range of topics, including the expansion history and the composition of the Universe, the distribution of stars and dark matter in galaxies, the host galaxies of quasars, and the stellar initial mass function. Finding them in astronomical images is a classic ‘needle in a haystack’ problem, as they are outnumbered by other (contaminant) sources by many orders of magnitude. To solve this problem, we develop state-of-the-art deep learning methods and train them on realistic simulated quads based on real images of galaxies taken from the Dark Energy Survey, with realistic source and deflector models, including the chromatic effects of microlensing. The performance of the best methods on a mixture of simulated and real objects is excellent, yielding area under the receiver operating curve in the range of 0.86–0.89. Recall is close to 100 per cent down to total magnitude i ∼ 21 indicating high completeness, while precision declines from 85 per cent to 70 per cent in the range i ∼ 17–21. The methods are extremely fast: training on 2 million samples takes 20 h on a GPU machine, and 108 multiband cut-outs can be evaluated per GPU-hour. The speed and performance of the method pave the way to apply it to large samples of astronomical sources, bypassing the need for photometric pre-selection that is likely to be a major cause of incompleteness in current samples of known quads.

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DOE OSTI2022

Dark Energy Survey Year 3 results: A 2.7% measurement of baryon acoustic oscillation distance scale at redshift 0.835

We present angular diameter measurements obtained by measuring the position of baryon acoustic oscillations (BAO) in an optimized sample of galaxies from the first three years of Dark Energy Survey data (DES Y3). The sample consists of 7 million galaxies distributed over a footprint of 4100 deg 2 with 0.6 < z photo < 1.1 and a typical redshift uncertainty of 0.03 ( 1 + z ) . The sample selection is the same as in the BAO measurement with the first year of DES data, but the analysis presented here uses three times the area, extends to higher redshift, and makes a number of improvements, including a fully analytical BAO template, the use of covariances from both theory and simulations, and an extensive preunblinding protocol. We used two different statistics; angular correlation function and power spectrum, and validate our pipeline with an ensemble of over 1500 realistic simulations. Both statistics yield compatible results. We combine the likelihoods derived from angular correlations and spherical harmonics to constrain the ratio of comoving angular diameter distance D M at the effective redshift of our sample to the sound horizon scale at the drag epoch. We obtain D M ( z eff = 0.835 ) / r d = 18.92 ± 0.51 , which is consistent with, but smaller than, the Planck prediction assuming flat Λ CDM , at the level of 2.3 σ . The analysis was performed blind and is robust to changes in a number of analysis choices. It represents the most precise BAO distance measurement from imaging data to date, and is competitive with the latest transverse ones from spectroscopic samples at z > 0.75 . When combined with DES 3 x 2 pt + SNIa , they lead to improvements in H 0 and Ω m constraints by ∼ 20 % .

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From the Fire: A Deeper Look at the Phoenix Stream

We use 6 yr of data from the Dark Energy Survey to perform a detailed photometric characterization of the Phoenix stellar stream, a 15° long, thin, dynamically cold, low-metallicity stellar system in the Southern Hemisphere. We use natural splines, a nonparametric modeling technique, to simultaneously fit the stream track, width, and linear density. This updated stream model allows us to improve measurements of the heliocentric distance (17.4 ± 0.1 (stat.) ±0.8 (sys.) kpc) and distance gradient (−0.009 ± 0.006 kpc deg$^{−1}$) of Phoenix, which corresponds to a small change of 0.13 ± 0.09 kpc in heliocentric distance along the length of the stream. We measure linear intensity variations on degree scales, as well as deviations in the stream track on ∼2° scales, suggesting that the stream may have been disturbed during its formation and/or evolution. We recover three peaks and one gap in linear intensity along with fluctuations in the stream track. Compared to other thin streams, the Phoenix stream shows more fluctuations and, consequently, the study of Phoenix offers a unique perspective on gravitational perturbations of stellar streams. We discuss possible sources of perturbations to Phoenix, including baryonic structures in the Galaxy and dark matter subhalos.

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DOE OSTI2022

Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and weak lensing

We present the first cosmology results from large-scale structure using the full 5000 deg 2 of imaging data from the Dark Energy Survey (DES) Data Release 1. We perform an analysis of large-scale structure combining three two-point correlation functions ( 3 × 2 pt ): (i) cosmic shear using 100 million source galaxies, (ii) galaxy clustering, and (iii) the cross-correlation of source galaxy shear with lens galaxy positions, galaxy–galaxy lensing. To achieve the cosmological precision enabled by these measurements has required updates to nearly every part of the analysis from DES Year 1, including the use of two independent galaxy clustering samples, modeling advances, and several novel improvements in the calibration of gravitational shear and photometric redshift inference. The analysis was performed under strict conditions to mitigate confirmation or observer bias; we describe specific changes made to the lens galaxy sample following unblinding of the results and tests of the robustness of our results to this decision. We model the data within the flat Λ CDM and w CDM cosmological models, marginalizing over 25 nuisance parameters. We find consistent cosmological results between the three two-point correlation functions; their combination yields clustering amplitude S 8 = 0.77 6 - 0.017 + 0.017 and matter density Ω m = 0.33 9 - 0.031 + 0.032 in Λ CDM , mean with 68% confidence limits; S 8 = 0.77 5 - 0.024 + 0.026 , Ω m = 0.35 2 - 0.041 + 0.035 , and dark energy equation-of-state parameter w = - 0.9 8 - 0.20 + 0.32 in w CDM . These constraints correspond to an improvement in signal-to-noise of the DES Year 3 3 × 2 pt data relative to DES Year 1 by a factor of 2.1, about 20% more than expected from the increase in observing area alone. This combination of DES data is consistent with the prediction of the model favored by the Planck 2018 cosmic microwave background (CMB) primary anisotropy data, which is quantified with a probability-to-exceed p = 0.13 –0.48. We find better agreement between DES 3 × 2 pt and Planck than in DES Y1, despite the significantly improved precision of both. When combining DES 3 × 2 pt data with available baryon acoustic oscillation, redshift-space distortion, and type Ia supernovae data, we find p = 0.34 . Combining all of these datasets with Planck CMB lensing yields joint parameter constraints of S 8 = 0.81 2 - 0.008 + 0.008 , Ω m = 0.30 6 - 0.005 + 0.004 , h = 0.68 0 - 0.003 + 0.004 , and ∑ m ν < 0.13 eV (95% C.L.) in Λ CDM ; S 8 = 0.81 2 - 0.008 + 0.008 , Ω m = 0.30 2 - 0.006 + 0.006 , h = 0.68 7 - 0.007 + 0.006 , and w = - 1.03 1 - 0.027 + 0.030 in w CDM .

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DOE OSTI2021

Dark Energy Survey Year 3 Results: Galaxy mock catalogs for BAO analysis

The calibration and validation of scientific analysis in simulations is a fundamental tool to ensure unbiased and robust results in observational cosmology. In particular, mock galaxy catalogs are a crucial resource to achieve these goals in the measurement of baryon acoustic oscillation (BAO) in the clustering of galaxies. Here we present a set of 1952 galaxy mock catalogs designed to mimic the Dark Energy Survey Year 3 BAO sample over its full photometric redshift range 0.6 < zphoto < 1.1. The mocks are based upon 488 ICE-COLA fast N-body simulations of full-sky light cones and were created by populating halos with galaxies, using a hybrid halo occupation distribution – halo abundance matching model. This model has ten free parameters, which were determined, for the first time, using an automatic likelihood minimization procedure. We also introduced a novel technique to assign photometric redshift for simulated galaxies, following a two-dimensional probability distribution with VIMOS Public Extragalactic Redshift Survey data. The calibration was designed to match the observed abundance of galaxies as a function of photometric redshift, the distribution of photometric redshift errors, and the clustering amplitude on scales smaller than those used for BAO measurements. An exhaustive analysis was done to ensure that the mocks reproduce the input properties. Finally, mocks were tested by comparing the angular correlation function w(θ), angular power spectrum Cℓ, and projected clustering ξp(r⊥) to theoretical predictions and data. The impact of volume replication in the estimate of the covariance is also investigated. The success in accurately reproducing the photometric redshift uncertainties and the galaxy clustering as a function of redshift render this mock creation pipeline as a benchmark for future analyses of photometric galaxy surveys.Key words: catalogs / large-scale structure of Universe / galaxies: distances and redshifts / Galaxy: halo / methods: numerical

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Synthetic galaxy clusters and observations based on Dark Energy Survey Year 3 Data

ABSTRACT We develop a novel data-driven method for generating synthetic optical observations of galaxy clusters. In cluster weak lensing, the interplay between analysis choices and systematic effects related to source galaxy selection, shape measurement, and photometric redshift estimation can be best characterized in end-to-end tests going from mock observations to recovered cluster masses. To create such test scenarios, we measure and model the photometric properties of galaxy clusters and their sky environments from the Dark Energy Survey Year 3 (DES Y3) data in two bins of cluster richness $\lambda \in [30; 45)$, $\lambda \in [45; 60)$ and three bins in cluster redshift ($z\in [0.3; 0.35)$, $z\in [0.45; 0.5)$ and $z\in [0.6; 0.65)$. Using deep-field imaging data, we extrapolate galaxy populations beyond the limiting magnitude of DES Y3 and calculate the properties of cluster member galaxies via statistical background subtraction. We construct mock galaxy clusters as random draws from a distribution function, and render mock clusters and line-of-sight catalogues into synthetic images in the same format as actual survey observations. Synthetic galaxy clusters are generated from real observational data, and thus are independent from the assumptions inherent to cosmological simulations. The recipe can be straightforwardly modified to incorporate extra information, and correct for survey incompleteness. New realizations of synthetic clusters can be created at minimal cost, which will allow future analyses to generate the large number of images needed to characterize systematic uncertainties in cluster mass measurements.

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DOE OSTI2021

Probing gravity with the DES-CMASS sample and BOSS spectroscopy

ABSTRACT The DES-CMASS sample (DMASS) is designed to optimally combine the weak lensing measurements from the Dark Energy Survey (DES) and redshift-space distortions (RSD) probed by the CMASS galaxy sample from the Baryonic Oscillation Spectroscopic Survey. In this paper, we demonstrate the feasibility of adopting DMASS as the equivalent of CMASS for a joint analysis of DES and BOSS in the framework of modified gravity. We utilize the angular clustering of the DMASS galaxies, cosmic shear of the DES metacalibration sources, and cross-correlation of the two as data vectors. By jointly fitting the combination of the data with the RSD measurements from the CMASS sample and Planck data, we obtain the constraints on modified gravity parameters $\mu _0=-0.37^{+0.47}_{-0.45}$ and $\Sigma _0=0.078^{+0.078}_{-0.082}$. Our constraints of modified gravity with DMASS are tighter than those with the DES Year 1 redMaGiC sample with the same external data sets by 29 per cent for μ0 and 21 per cent for Σ0, and comparable to the published results of the DES Year 1 modified gravity analysis despite this work using fewer external data sets. This improvement is mainly because the galaxy bias parameter is shared and more tightly constrained by both CMASS and DMASS, effectively breaking the degeneracy between the galaxy bias and other cosmological parameters. Such an approach to optimally combine photometric and spectroscopic surveys using a photometric sample equivalent to a spectroscopic sample can be applied to combining future surveys having a limited overlap such as DESI and LSST.

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Galaxy–galaxy lensing with the DES-CMASS catalogue: measurement and constraints on the galaxy-matter cross-correlation

ABSTRACT The DMASS sample is a photometric sample from the DES Year 1 data set designed to replicate the properties of the CMASS sample from BOSS, in support of a joint analysis of DES and BOSS beyond the small overlapping area. In this paper, we present the measurement of galaxy–galaxy lensing using the DMASS sample as gravitational lenses in the DES Y1 imaging data. We test a number of potential systematics that can bias the galaxy–galaxy lensing signal, including those from shear estimation, photometric redshifts, and observing conditions. After careful systematic tests, we obtain a highly significant detection of the galaxy–galaxy lensing signal, with total S/N = 25.7. With the measured signal, we assess the feasibility of using DMASS as gravitational lenses equivalent to CMASS, by estimating the galaxy-matter cross-correlation coefficient rcc. By jointly fitting the galaxy–galaxy lensing measurement with the galaxy clustering measurement from CMASS, we obtain $r_{\rm cc}=1.09^{+0.12}_{-0.11}$ for the scale cut of $4 \, h^{-1}{\rm \,\,Mpc}$ and $r_{\rm cc}=1.06^{+0.13}_{-0.12}$ for $12 \, h^{-1}{\rm \,\,Mpc}$ in fixed cosmology. By adding the angular galaxy clustering of DMASS, we obtain rcc = 1.06 ± 0.10 for the scale cut of $4 \, h^{-1}{\rm \,\,Mpc}$ and rcc = 1.03 ± 0.11 for $12 \, h^{-1}{\rm \,\,Mpc}$. The resulting values of rcc indicate that the lensing signal of DMASS is statistically consistent with the one that would have been measured if CMASS had populated the DES region within the given statistical uncertainty. The measurement of galaxy–galaxy lensing presented in this paper will serve as part of the data vector for the forthcoming cosmology analysis in preparation.

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Dark Energy Survey Year 3 Results: Deep Field optical + near-infrared images and catalogue

ABSTRACT We describe the Dark Energy Survey (DES) Deep Fields, a set of images and associated multiwavelength catalogue (ugrizJHKs) built from Dark Energy Camera (DECam) and Visible and Infrared Survey Telescope for Astronomy (VISTA) data. The DES Deep Fields comprise 11 fields (10 DES supernova fields plus COSMOS), with a total area of ∼30 sq. deg. in ugriz bands and reaching a maximum i-band depth of 26.75 (AB, 10σ, 2 arcsec). We present a catalogue for the DES 3-yr cosmology analysis of those four fields with full 8-band coverage, totalling 5.88 sq. deg. after masking. Numbering 2.8 million objects (1.6 million post-masking), our catalogue is drawn from images coadded to consistent depths of r = 25.7, i = 25, and z = 24.3 mag. We use a new model-fitting code, built upon established methods, to deblend sources and ensure consistent colours across the u-band to Ks-band wavelength range. We further detail the tight control we maintain over the point-spread function modelling required for the model fitting, astrometry and consistency of photometry between the four fields. The catalogue allows us to perform a careful star–galaxy separation and produces excellent photometric redshift performance (NMAD = 0.023 at i < 23). The Deep-Fields catalogue will be made available as part of the cosmology data products release, following the completion of the DES 3-yr weak lensing and galaxy clustering cosmology work.

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OzDES reverberation mapping program: Lag recovery reliability for 6-yr C iv analysis

ABSTRACT We present the statistical methods that have been developed to analyse the OzDES reverberation mapping sample. To perform this statistical analysis we have created a suite of customizable simulations that mimic the characteristics of each source in the OzDES sample. These characteristics include: the variability in the photometric and spectroscopic light curves, the measurement uncertainties, and the observational cadence. By simulating the sources in the OzDES sample that contain the C iv emission line, we developed a set of criteria that rank the reliability of a recovered time-lag depending on the agreement between different recovery methods, the magnitude of the uncertainties, and the rate at which false positives were found in the simulations. These criteria were applied to simulated light curves and these results used to estimate the quality of the resulting Radius–Luminosity relation. We grade the results using three quality levels (gold, silver, and bronze). The input slope of the R–L relation was recovered within 1σ for each of the three quality samples, with the gold standard having the lowest dispersion with a recovered a R–L relation slope of 0.454 ± 0.016 with an input slope of 0.47. Future work will apply these methods to the entire OzDES sample of 771 AGN.

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Dark Energy Survey Y3 results: blending shear and redshift biases in image simulations

ABSTRACT As the statistical power of galaxy weak lensing reaches per cent level precision, large, realistic, and robust simulations are required to calibrate observational systematics, especially given the increased importance of object blending as survey depths increase. To capture the coupled effects of blending in both shear and photometric redshift calibration, we define the effective redshift distribution for lensing, nγ(z), and describe how to estimate it using image simulations. We use an extensive suite of tailored image simulations to characterize the performance of the shear estimation pipeline applied to the Dark Energy Survey (DES) Year 3 data set. We describe the multiband, multi-epoch simulations, and demonstrate their high level of realism through comparisons to the real DES data. We isolate the effects that generate shear calibration biases by running variations on our fiducial simulation, and find that blending-related effects are the dominant contribution to the mean multiplicative bias of approximately $-2{{\ \rm per\ cent}}$. By generating simulations with input shear signals that vary with redshift, we calibrate biases in our estimation of the effective redshift distribution, and demonstrate the importance of this approach when blending is present. We provide corrected effective redshift distributions that incorporate statistical and systematic uncertainties, ready for use in DES Year 3 weak lensing analyses.

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The mass and galaxy distribution around SZ-selected clusters

ABSTRACT We present measurements of the radial profiles of the mass and galaxy number density around Sunyaev–Zel’dovich (SZ)-selected clusters using both weak lensing and galaxy counts. The clusters are selected from the Atacama Cosmology Telescope Data Release 5 and the galaxies from the Dark Energy Survey Year 3 data set. With signal-to-noise ratio of 62 (45) for galaxy (weak lensing) profiles over scales of about 0.2–20 h−1 Mpc, these are the highest precision measurements for SZ-selected clusters to date. Because SZ selection closely approximates mass selection, these measurements enable several tests of theoretical models of the mass and light distribution around clusters. Our main findings are: (1) The splashback feature is detected at a consistent location in both the mass and galaxy profiles and its location is consistent with predictions of cold dark matter N-body simulations. (2) The full mass profile is also consistent with the simulations. (3) The shapes of the galaxy and lensing profiles are remarkably similar for our sample over the entire range of scales, from well inside the cluster halo to the quasilinear regime. We measure the dependence of the profile shapes on the galaxy sample, redshift, and cluster mass. We extend the Diemer & Kravtsov model for the cluster profiles to the linear regime using perturbation theory and show that it provides a good match to the measured profiles. We also compare the measured profiles to predictions of the standard halo model and simulations that include hydrodynamics. Applications of these results to cluster mass estimation, cosmology, and astrophysics are discussed.

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