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Maia, M. A. G.

Publications and source records attributed to Maia, M. A. G..

At least 19 records

Consistent lensing and clustering in a low- S 8 Universe with BOSS, DES Year 3, HSC Year 1, and KiDS-1000

ABSTRACT We evaluate the consistency between lensing and clustering based on measurements from Baryon Oscillation Spectroscopic Survey combined with galaxy–galaxy lensing from Dark Energy Survey (DES) Year 3, Hyper Suprime-Cam Subaru Strategic Program (HSC) Year 1, and Kilo-Degree Survey (KiDS)-1000. We find good agreement between these lensing data sets. We model the observations using the Dark Emulator and fit the data at two fixed cosmologies: Planck (S8 = 0.83), and a Lensing cosmology (S8 = 0.76). For a joint analysis limited to large scales, we find that both cosmologies provide an acceptable fit to the data. Full utilization of the higher signal-to-noise small-scale measurements is hindered by uncertainty in the impact of baryon feedback and assembly bias, which we account for with a reasoned theoretical error budget. We incorporate a systematic inconsistency parameter for each redshift bin, A, that decouples the lensing and clustering. With a wide range of scales, we find different results for the consistency between the two cosmologies. Limiting the analysis to the bins for which the impact of the lens sample selection is expected to be minimal, for the Lensing cosmology, the measurements are consistent with A = 1; A = 0.91 ± 0.04 (A = 0.97 ± 0.06) using DES+KiDS (HSC). For the Planck case, we find a discrepancy: A = 0.79 ± 0.03 (A = 0.84 ± 0.05) using DES+KiDS (HSC). We demonstrate that a kinematic Sunyaev–Zeldovich-based estimate for baryonic effects alleviates some of the discrepancy in the Planck cosmology. This analysis demonstrates the statistical power of small-scale measurements; however, caution is still warranted given modelling uncertainties and foreground sample selection effects.

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Cosmic shear in harmonic space from the Dark Energy Survey Year 1 Data: compatibility with configuration space results

ABSTRACT We perform a cosmic shear analysis in harmonic space using the first year of data collected by the Dark Energy Survey (DES-Y1). We measure the cosmic weak lensing shear power spectra using the metacalibration catalogue and perform a likelihood analysis within the framework of CosmoSIS. We set scale cuts based on baryonic effects contamination and model redshift and shear calibration uncertainties as well as intrinsic alignments. We adopt as fiducial covariance matrix an analytical computation accounting for the mask geometry in the Gaussian term, including non-Gaussian contributions. A suite of 1200 lognormal simulations is used to validate the harmonic space pipeline and the covariance matrix. We perform a series of stress tests to gauge the robustness of the harmonic space analysis. Finally, we use the DES-Y1 pipeline in configuration space to perform a similar likelihood analysis and compare both results, demonstrating their compatibility in estimating the cosmological parameters S8, σ8, and Ωm. We use the DES-Y1 metacalibration shape catalogue, with photometric redshifts estimates in the range of 0.2−1.3, divided in four tomographic bins finding σ8(Ωm/0.3)0.5 = 0.766 ± 0.033 at 68 per cent CL. The methods implemented and validated in this paper will allow us to perform a consistent harmonic space analysis in the upcoming DES data.

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Dwarf AGNs from Optical Variability for the Origins of Seeds (DAVOS): insights from the dark energy survey deep fields

ABSTRACT We present a sample of 706, z < 1.5 active galactic nuclei (AGNs) selected from optical photometric variability in three of the Dark Energy Survey (DES) deep fields (E2, C3, and X3) over an area of 4.64 deg2. We construct light curves using difference imaging aperture photometry for resolved sources and non-difference imaging PSF photometry for unresolved sources, respectively, and characterize the variability significance. Our DES light curves have a mean cadence of 7 d, a 6-yr baseline, and a single-epoch imaging depth of up to g ∼ 24.5. Using spectral energy distribution (SED) fitting, we find 26 out of total 706 variable galaxies are consistent with dwarf galaxies with a reliable stellar mass estimate ($M_{\ast }\lt 10^{9.5}\, {\rm M}_\odot$; median photometric redshift of 0.9). We were able to constrain rapid characteristic variability time-scales (∼ weeks) using the DES light curves in 15 dwarf AGN candidates (a subset of our variable AGN candidates) at a median photometric redshift of 0.4. This rapid variability is consistent with their low black hole (BH) masses. We confirm the low-mass AGN nature of one source with a high S/N optical spectrum. We publish our catalogue, optical light curves, and supplementary data, such as X-ray properties and optical spectra, when available. We measure a variable AGN fraction versus stellar mass and compare to results from a forward model. This work demonstrates the feasibility of optical variability to identify AGNs with lower BH masses in deep fields, which may be more ‘pristine’ analogues of supermassive BH seeds.

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Velocity dispersions of clusters in the Dark Energy Survey Y3 redMaPPer catalogue

ABSTRACT We measure the velocity dispersions of clusters of galaxies selected by the red-sequence Matched-filter Probabilistic Percolation (redMaPPer) algorithm in the first three years of data from the Dark Energy Survey (DES), allowing us to probe cluster selection and richness estimation, λ, in light of cluster dynamics. Our sample consists of 126 clusters with sufficient spectroscopy for individual velocity dispersion estimates. We examine the correlations between cluster velocity dispersion, richness, X-ray temperature, and luminosity, as well as central galaxy velocity offsets. The velocity dispersion–richness relation exhibits a bimodal distribution. The majority of clusters follow scaling relations between velocity dispersion, richness, and X-ray properties similar to those found for previous samples; however, there is a significant population of clusters with velocity dispersions that are high for their richness. These clusters account for roughly 22 per cent of the λ < 70 systems in our sample, but more than half (55 per cent) of λ < 70 clusters at z > 0.5. A couple of these systems are hot and X-ray bright as expected for massive clusters with richnesses that appear to have been underestimated, but most appear to have high velocity dispersions for their X-ray properties likely due to line-of-sight structure. These results suggest that projection effects contribute significantly to redMaPPer selection, particularly at higher redshifts and lower richnesses. The redMaPPer determined richnesses for the velocity dispersion outliers are consistent with their X-ray properties, but several are X-ray undetected and deeper data are needed to understand their nature.

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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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Dark Energy Survey Year 3 results: Cosmology from combined galaxy clustering and lensing validation on cosmological simulations

In this work, we present a validation of the Dark Energy Survey Year 3 (DES Y3) 3×2-point analysis choices by testing them on Buzzard2.0, a new suite of cosmological simulations that is tailored for the testing and validation of combined galaxy clustering and weak-lensing analyses. We show that the buzzard2.0 simulations accurately reproduce many important aspects of the DES Y3 data, including photometric redshift and magnitude distributions, and the relevant set of two-point clustering and weak-lensing statistics. We then show that our model for the 3×2-point data vector is accurate enough to recover the true cosmology in simulated surveys assuming the true redshift distributions for our source and lens samples, demonstrating robustness to uncertainties in the modeling of the nonlinear matter power spectrum, nonlinear galaxy bias, and higher-order lensing corrections. Additionally, we demonstrate for the first time that our photometric redshift calibration methodology, including information from photometry, spectroscopy, clustering cross-correlations, and galaxy–galaxy lensing ratios, is accurate enough to recover the true cosmology in simulated surveys in the presence of realistic photometric redshift uncertainties.

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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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Dark Energy Survey Year 3 results: calibration of lens sample redshift distributions using clustering redshifts with BOSS/eBOSS

ABSTRACT We present clustering redshift measurements for Dark Energy Survey (DES) lens sample galaxies used in weak gravitational lensing and galaxy clustering studies. To perform these measurements, we cross-correlate with spectroscopic galaxies from the Baryon Acoustic Oscillation Survey (BOSS) and its extension, eBOSS. We validate our methodology in simulations, including a new technique to calibrate systematic errors that result from the galaxy clustering bias, and we find that our method is generally unbiased in calibrating the mean redshift. We apply our method to the data, and estimate the redshift distribution for 11 different photometrically selected bins. We find general agreement between clustering redshift and photometric redshift estimates, with differences on the inferred mean redshift found to be below |Δz| = 0.01 in most of the bins. We also test a method to calibrate a width parameter for redshift distributions, which we found necessary to use for some of our samples. Our typical uncertainties on the mean redshift ranged from 0.003 to 0.008, while our uncertainties on the width ranged from 4 to 9 per cent. We discuss how these results calibrate the photometric redshift distributions used in companion papers for DES Year 3 results.

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Optical variability of quasars with 20-yr photometric light curves

ABSTRACT We study the optical gri photometric variability of a sample of 190 quasars within the SDSS Stripe 82 region that have long-term photometric coverage during ∼1998−2020 with SDSS, PanSTARRS-1, the Dark Energy Survey, and dedicated follow-up monitoring with Blanco 4m/DECam. With on average ∼200 nightly epochs per quasar per filter band, we improve the parameter constraints from a Damped Random Walk (DRW) model fit to the light curves over previous studies with 10–15 yr baselines and ≲ 100 epochs. We find that the average damping time-scale τDRW continues to rise with increased baseline, reaching a median value of ∼750 d (g band) in the rest frame of these quasars using the 20-yr light curves. Some quasars may have gradual, long-term trends in their light curves, suggesting that either the DRW fit requires very long baselines to converge, or that the underlying variability is more complex than a single DRW process for these quasars. Using a subset of quasars with better-constrained τDRW (less than 20 per cent of the baseline), we confirm a weak wavelength dependence of τDRW∝λ0.51 ± 0.20. We further quantify optical variability of these quasars over days to decades time-scales using structure function (SF) and power spectrum density (PSD) analyses. The SF and PSD measurements qualitatively confirm the measured (hundreds of days) damping time-scales from the DRW fits. However, the ensemble PSD is steeper than that of a DRW on time-scales less than ∼ a month for these luminous quasars, and this second break point correlates with the longer DRW damping time-scale.

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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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Dark Energy Survey Year 3 results: galaxy clustering and systematics treatment for lens galaxy samples

ABSTRACT In this work, we present the galaxy clustering measurements of the two DES lens galaxy samples: a magnitude-limited sample optimized for the measurement of cosmological parameters, maglim, and a sample of luminous red galaxies selected with the redmagic algorithm. maglim/redmagic sample contains over 10 million/2.5 million galaxies and is divided into six/five photometric redshift bins spanning the range z ∈ [0.20, 1.05]/z ∈ [0.15, 0.90]. Both samples cover 4143 $\deg ^2$ over which we perform our analysis blind, measuring the angular correlation function with an S/N ∼ 63 for both samples. In a companion paper, these measurements of galaxy clustering are combined with the correlation functions of cosmic shear and galaxy–galaxy lensing of each sample to place cosmological constraints with a 3 × 2pt analysis. We conduct a thorough study of the mitigation of systematic effects caused by the spatially varying survey properties and we correct the measurements to remove artificial clustering signals. We employ several decontamination methods with different configurations to ensure the robustness of our corrections and to determine the systematic uncertainty that needs to be considered for the final cosmology analyses. We validate our fiducial methodology using lognormal mocks, showing that our decontamination procedure induces biases no greater than 0.5σ in the (Ωm, b) plane, where b is the galaxy bias.

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Dark Energy Survey Year 3 results: marginalization over redshift distribution uncertainties using ranking of discrete realizations

ABSTRACT Cosmological information from weak lensing surveys is maximized by sorting source galaxies into tomographic redshift subsamples. Any uncertainties on these redshift distributions must be correctly propagated into the cosmological results. We present hyperrank, a new method for marginalizing over redshift distribution uncertainties, using discrete samples from the space of all possible redshift distributions, improving over simple parametrized models. In hyperrank, the set of proposed redshift distributions is ranked according to a small (between one and four) number of summary values, which are then sampled, along with other nuisance parameters and cosmological parameters in the Monte Carlo chain used for inference. This approach can be regarded as a general method for marginalizing over discrete realizations of data vector variation with nuisance parameters, which can consequently be sampled separately from the main parameters of interest, allowing for increased computational efficiency. We focus on the case of weak lensing cosmic shear analyses and demonstrate our method using simulations made for the Dark Energy Survey (DES). We show that the method can correctly and efficiently marginalize over a wide range of models for the redshift distribution uncertainty. Finally, we compare hyperrank to the common mean-shifting method of marginalizing over redshift uncertainty, validating that this simpler model is sufficient for use in the DES Year 3 cosmology results presented in companion papers.

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Dark Energy Survey Year 3 Results: Measuring the Survey Transfer Function with Balrog

Abstract We describe an updated calibration and diagnostic framework, Balrog , used to directly sample the selection and photometric biases of the Dark Energy Survey (DES) Year 3 (Y3) data set. We systematically inject onto the single-epoch images of a random 20% subset of the DES footprint an ensemble of nearly 30 million realistic galaxy models derived from DES Deep Field observations. These augmented images are analyzed in parallel with the original data to automatically inherit measurement systematics that are often too difficult to capture with generative models. The resulting object catalog is a Monte Carlo sampling of the DES transfer function and is used as a powerful diagnostic and calibration tool for a variety of DES Y3 science, particularly for the calibration of the photometric redshifts of distant “source” galaxies and magnification biases of nearer “lens” galaxies. The recovered Balrog injections are shown to closely match the photometric property distributions of the Y3 GOLD catalog, particularly in color, and capture the number density fluctuations from observing conditions of the real data within 1% for a typical galaxy sample. We find that Y3 colors are extremely well calibrated, typically within ∼1–8 mmag, but for a small subset of objects, we detect significant magnitude biases correlated with large overestimates of the injected object size due to proximity effects and blending. We discuss approaches to extend the current methodology to capture more aspects of the transfer function and reach full coverage of the survey footprint for future analyses.

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The DES view of the Eridanus supervoid and the CMB cold spot

ABSTRACT The Cold Spot is a puzzling large-scale feature in the Cosmic Microwave Background temperature maps and its origin has been subject to active debate. As an important foreground structure at low redshift, the Eridanus supervoid was recently detected, but it was subsequently determined that, assuming the standard ΛCDM model, only about 10–20 per cent of the observed temperature depression can be accounted for via its Integrated Sachs–Wolfe imprint. However, R ≳ 100 h−1Mpc supervoids elsewhere in the sky have shown ISW imprints AISW ≈ 5.2 ± 1.6 times stronger than expected from ΛCDM (AISW = 1), which warrants further inspection. Using the Year-3 redMaGiC catalogue of luminous red galaxies from the Dark Energy Survey, here we confirm the detection of the Eridanus supervoid as a significant underdensity in the Cold Spot’s direction at z < 0.2. We also show, with S/N ≳ 5 significance, that the Eridanus supervoid appears as the most prominent large-scale underdensity in the dark matter mass maps that we reconstructed from DES Year-3 gravitational lensing data. While we report no significant anomalies, an interesting aspect is that the amplitude of the lensing signal from the Eridanus supervoid at the Cold Spot centre is about 30 per cent lower than expected from similar peaks found in N-body simulations based on the standard ΛCDM model with parameters Ωm = 0.279 and σ8 = 0.82. Overall, our results confirm the causal relation between these individually rare structures in the cosmic web and in the CMB, motivating more detailed future surveys in the Cold Spot region.

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Lensing without borders – I. A blind comparison of the amplitude of galaxy–galaxy lensing between independent imaging surveys

ABSTRACT Lensing without borders is a cross-survey collaboration created to assess the consistency of galaxy–galaxy lensing signals (ΔΣ) across different data sets and to carry out end-to-end tests of systematic errors. We perform a blind comparison of the amplitude of ΔΣ using lens samples from BOSS and six independent lensing surveys. We find good agreement between empirically estimated and reported systematic errors which agree to better than 2.3σ in four lens bins and three radial ranges. For lenses with zL > 0.43 and considering statistical errors, we detect a 3–4σ correlation between lensing amplitude and survey depth. This correlation could arise from the increasing impact at higher redshift of unrecognized galaxy blends on shear calibration and imperfections in photometric redshift calibration. At zL > 0.54, amplitudes may additionally correlate with foreground stellar density. The amplitude of these trends is within survey-defined systematic error budgets that are designed to include known shear and redshift calibration uncertainty. Using a fully empirical and conservative method, we do not find evidence for large unknown systematics. Systematic errors greater than 15 per cent (25 per cent) ruled out in three lens bins at 68 per cent (95 per cent) confidence at z < 0.54. Differences with respect to predictions based on clustering are observed to be at the 20–30 per cent level. Our results therefore suggest that lensing systematics alone are unlikely to fully explain the ‘lensing is low’ effect at z < 0.54. This analysis demonstrates the power of cross-survey comparisons and provides a promising path for identifying and reducing systematics in future lensing analyses.

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Multiwavelength optical and NIR variability analysis of the Blazar PKS 0027-426

ABSTRACT We present multiwavelength spectral and temporal variability analysis of PKS 0027-426 using optical griz observations from Dark Energy Survey between 2013 and 2018 and VEILS Optical Light curves of Extragalactic TransienT Events (VOILETTE) between 2018 and 2019 and near-infrared (NIR) JKs observations from Visible and Infrared Survey Telescope for Astronomy Extragalactic Infrared Legacy Survey (VEILS) between 2017 and 2019. Multiple methods of cross-correlation of each combination of light curve provides measurements of possible lags between optical–optical, optical–NIR, and NIR–NIR emission, for each observation season and for the entire observational period. Inter-band time lag measurements consistently suggest either simultaneous emission or delays between emission regions on time-scales smaller than the cadences of observations. The colour–magnitude relation between each combination of filters was also studied to determine the spectral behaviour of PKS 0027-426. Our results demonstrate complex colour behaviour that changes between bluer when brighter, stable when brighter, and redder when brighter trends over different time-scales and using different combinations of optical filters. Additional analysis of the optical spectra is performed to provide further understanding of this complex spectral behaviour.

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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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