arXiv subjects

M. Smith

Publications and source records attributed to M. Smith.

At least 181 records · Page 10Linked to original sources

arXiv2022

Optical Variability of Quasars with 20-Year Photometric Light Curves

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 $\sim 1998-2020$ with SDSS, PanSTARRS-1, the Dark Energy Survey, and dedicated follow-up monitoring with Blanco 4m/DECam. With on average $\sim 200$ 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 $\lesssim 100$ epochs. We find that the average damping timescale $τ_{\rm DRW}$ continues to rise with increased baseline, reaching a median value of $\sim 750$ days ($g$ 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 $τ_{\rm DRW}$ (less than 20\% of the baseline), we confirm a weak wavelength dependence of $τ_{\rm DRW}\propto λ^{0.51\pm0.20}$. We further quantify optical variability of these quasars over days to decades timescales using structure function (SF) and power spectrum density (PSD) analyses. The SF and PSD measurements qualitatively confirm the measured (hundreds of days) damping timescales from the DRW fits. However, the ensemble PSD is steeper than that of a DRW on timescales less than $\sim$ a month for these luminous quasars, and this second break point correlates with the longer DRW damping timescale.

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arXiv2022

A DECam Search for Explosive Optical Transients Associated with IceCube Neutrinos

In this work, we investigate the likelihood of association between realtime, TeV-PeV energy neutrino alerts from IceCube and optical counterparts in the form of core-collapse supernovae (CC SNe). The optical follow-up of IceCube alerts requires two main instrumental capabilities: (1) deep imaging, since 73\% of neutrinos would come from CC SNe at redshifts $z > 0.3$, and (2) a large field of view (FoV), since typical IceCube muon neutrino pointing accuracy is on the order of $\sim1$~deg. With Blanco/DECam ($gri$ to 24th magnitude and $2.2$~deg diameter FoV), we performed a triggered optical follow-up observation of two IceCube alerts, IC170922A and IC171106A on $\sim6$~nights during the $\sim3$~weeks following each alert. For the IC170922A (IC171106A) follow-up observations, we expect that 12.1\% (9.5\%) of coincident CC SNe at $z \lesssim 0.3$ are detectable, and that on average, 0.23 (0.07) unassociated SNe in the neutrino 90\% containment regions also pass our selection criteria. We find two candidate CC SNe that are temporally coincident with the neutrino alerts in the FoV, but none in the 90\% containment regions, which is statistically consistent with expected rates of background CC SNe for these observations. If CC SNe are the dominant source of TeV-PeV neutrinos, we would expect an excess of coincident CC SNe to be detectable at the $3σ$ confidence level using DECam observations similar to those of this work for $\sim60$ ($\sim200$) neutrino alerts with (without) redshift information for all candidates.

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arXiv2022

DeepZipper II: Searching for Lensed Supernovae in Dark Energy Survey Data with Deep Learning

Gravitationally lensed supernovae (LSNe) are important probes of cosmic expansion, but they remain rare and difficult to find. Current cosmic surveys likely contain and 5-10 LSNe in total while next-generation experiments are expected to contain several hundreds to a few thousands of these systems. We search for these systems in observed Dark Energy Survey (DES) 5-year SN fields -- 10 3-sq. deg. regions of sky imaged in the $griz$ bands approximately every six nights over five years. To perform the search, we utilize the DeepZipper approach: a multi-branch deep learning architecture trained on image-level simulations of LSNe that simultaneously learns spatial and temporal relationships from time series of images. We find that our method obtains a LSN recall of 61.13% and a false positive rate of 0.02% on the DES SN field data. DeepZipper selected 2,245 candidates from a magnitude-limited ($m_i$ $<$ 22.5) catalog of 3,459,186 systems. We employ human visual inspection to review systems selected by the network and find three candidate LSNe in the DES SN fields.

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arXiv2022

Constraints on the Physical Properties of GW190814 through Simulations based on DECam Follow-up Observations by the Dark Energy Survey

On 14 August 2019, the LIGO and Virgo Collaborations detected gravitational waves from a black hole and a 2.6 solar mass compact object, possibly the first neutron star -- black hole (NSBH) merger. In search of an optical counterpart, the Dark Energy Survey (DES) obtained deep imaging of the entire 90 percent confidence level localization area with Blanco/DECam 0, 1, 2, 3, 6, and 16 nights after the merger. Objects with varying brightness were detected by the DES Pipeline and we systematically reduced the candidate counterparts through catalog matching, light curve properties, host-galaxy photometric redshifts, SOAR spectroscopic follow-up observations, and machine-learning-based photometric classification. All candidates were rejected as counterparts to the merger. To quantify the sensitivity of our search, we applied our selection criteria to full light curve simulations of supernovae and kilonovae as they would appear in the DECam observations. Since the source class of the merger was uncertain, we utilized an agnostic, three-component kilonova model based on tidally-disrupted NS ejecta properties to quantify our detection efficiency of a counterpart if the merger included a NS. We find that if a kilonova occurred during this merger, configurations where the ejected matter is greater than 0.07 solar masses, has lanthanide abundance less than $10^{-8.56}$, and has a velocity between $0.18c$ and $0.21c$ are disfavored at the $2σ$ level. Furthermore, we estimate that our background reduction methods are capable of associating gravitational wave signals with a detected electromagnetic counterpart at the $4σ$ level in $95\%$ of future follow-up observations.

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arXiv2022

DeepZipper: A Novel Deep Learning Architecture for Lensed Supernovae Identification

Large-scale astronomical surveys have the potential to capture data on large numbers of strongly gravitationally lensed supernovae (LSNe). To facilitate timely analysis and spectroscopic follow-up before the supernova fades, an LSN needs to be identified soon after it begins. To quickly identify LSNe in optical survey datasets, we designed ZipperNet, a multi-branch deep neural network that combines convolutional layers (traditionally used for images) with long short-term memory (LSTM) layers (traditionally used for time series). We tested ZipperNet on the task of classifying objects from four categories -- no lens, galaxy-galaxy lens, lensed type Ia supernova, lensed core-collapse supernova -- within high-fidelity simulations of three cosmic survey data sets -- the Dark Energy Survey (DES), Rubin Observatory's Legacy Survey of Space and Time (LSST), and a Dark Energy Spectroscopic Instrument (DESI) imaging survey. Among our results, we find that for the LSST-like dataset, ZipperNet classifies LSNe with a receiver operating characteristic area under the curve of 0.97, predicts the spectroscopic type of the lensed supernovae with 79\% accuracy, and demonstrates similarly high performance for LSNe 1-2 epochs after first detection. We anticipate that a model like ZipperNet, which simultaneously incorporates spatial and temporal information, can play a significant role in the rapid identification of lensed transient systems in cosmic survey experiments.

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arXiv2022

Milliarcsecond astrometry for the Galilean moons using stellar occultations

A stellar occultation occurs when a Solar System object passes in front of a star for an observer. This technique allows the determination of sizes and shapes of the occulting body with kilometer precision. Also, this technique constrains the occulting body's positions, albedos, densities, etc. In the context of the Galilean moons, these events can provide their best ground-based astrometry, with uncertainties in the order of 1 mas ($\sim$ 3 km at Jupiter's distance during opposition). We organized campaigns and successfully observed a stellar occultation by Io (JI) in 2021, one by Ganymede (JIII) in 2020, and one by Europa (JII) in 2019, with stations in North and South America. Also, we re-analyzed two previously published events, one by Europa in 2016 and another by Ganymede in 2017. Then, we fit the known 3D shape of the occulting satellite and determine its center of figure. That resulted in astrometric positions with uncertainties in the milliarcsecond level. The positions obtained from these stellar occultations can be used together with dynamical models to ensure highly accurate orbits of the Galilean moons. These orbits can help plan future space probes aiming at the Jovian system, such as JUICE by ESA and Europa Clipper by NASA, and allow more efficient planning of flyby maneuvers.

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arXiv2022

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 optimised 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 $0.6 < z_{\rm photo} < 1.1$ 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 pre-unblinding 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 $D_M(z_{\rm eff}=0.835)/r_{\rm d} = 18.92 \pm 0.51$, which is consistent with, but smaller than, the Planck prediction assuming flat \lcdm, 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 3x2pt + SNIa, they lead to improvements in $H_0$ and $Ω_m$ constraints by $\sim 20\%$

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arXiv2022

Dark Energy Survey Year 3 Results: Weak Lensing Shape Catalogue

We present and characterise the galaxy shape catalogue from the first 3 years of Dark Energy Survey (DES) observations, over an effective area of ~4143 deg$^2$ of the southern sky. We describe our data analysis process and our self-calibrating shear measurement pipeline METACALIBRATION, which builds and improves upon the pipeline used in the DES Year 1 analysis in several aspects. The DES Year 3 weak-lensing shape catalogue consists of 100,204,026 galaxies, measured in the $riz$ bands, resulting in a weighted source number density of $n_{\rm eff} = 5.59$ gal/arcmin$ ^{2}$ and corresponding shape noise $σ_e = 0.261$. We perform a battery of internal null tests on the catalogue, including tests on systematics related to the point-spread function (PSF) modelling, spurious catalogue B-mode signals, catalogue contamination, and galaxy properties.

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arXiv2022

New Modules for the SEDMachine to Remove Contaminations from Cosmic Rays and Non-target Light: BYECR and CONTSEP

Currently time-domain astronomy can scan the entire sky on a daily basis, discovering thousands of interesting transients every night. Classifying the ever-increasing number of new transients is one of the main challenges for the astronomical community. One solution that addresses this issue is the robotically controlled Spectral Energy Distribution Machine (SEDM) which supports the Zwicky Transient Facility (ZTF). SEDM with its pipeline PYSEDM demonstrates that real-time robotic spectroscopic classification is feasible. In an effort to improve the quality of the current SEDM data, we present here two new modules, BYECR and CONTSEP. The first removes contamination from cosmic rays, and the second removes contamination from non-target light. These new modules are part of the automated PYSEDM pipeline and fully integrated with the whole process. Employing BYECR and CONTSEP modules together automatically extracts more spectra than the current PYSEDM pipeline. Using SNID classification results, the new modules show an improvement in the classification rate and accuracy of 2.8% and 1.7%, respectively, while the strength of the cross-correlation remains the same. Improvements to the SEDM astrometry would further boost the improvement of the CONTSEP module. This kind of robotic follow-up with a fully automated pipeline has the potential to provide the spectroscopic classifications for the transients discovered by ZTF and also by the Rubin Observatory's Legacy Survey of Space and Time.

astro-ph.IM↗

arXiv2022

Constraining Type Ia supernova explosions and early flux excesses with the Zwicky Transient Factory

In the new era of time-domain surveys Type Ia supernovae are being caught sooner after explosion, which has exposed significant variation in their early light curves. Two driving factors for early time evolution are the distribution of nickel in the ejecta and the presence of flux excesses of various causes. We perform an analysis of the largest young SN Ia sample to date. We compare 115 SN Ia light curves from the Zwicky Transient Facility to the turtls model grid containing light curves of Chandrasekhar-mass explosions with a range of nickel masses, nickel distributions and explosion energies. We find that the majority of our observed light curves are well reproduced by Chandrasekhar-mass explosion models with a preference for highly extended nickel distributions. We identify six SNe Ia with an early-time flux excess in our g- and r-band data (four `blue' and two `red' flux excesses). We find an intrinsic rate of 18+/-11 per cent of early flux excesses in SNe Ia at z < 0.07, based on three detected flux excesses out of 30 (10 per cent) observed SNe Ia with a simulated efficiency of 57 per cent. This is comparable to rates of flux excesses in the literature but also accounts for detection efficiencies. Two of these events are mostly consistent with CSM interaction, while the other four have longer lifetimes in agreement with companion interaction and nickel-clump models. We find a higher frequency of flux excesses in 91T/99aa-like events (44+/-13 per cent).

astro-ph.HE↗

arXiv2022

Measuring Cosmological Parameters with Type Ia Supernovae in redMaGiC galaxies

Current and future cosmological analyses with Type Ia Supernovae (SNe Ia) face three critical challenges: i) measuring redshifts from the supernova or its host galaxy; ii) classifying SNe without spectra; and iii) accounting for correlations between the properties of SNe Ia and their host galaxies. We present here a novel approach that addresses each challenge. In the context of the Dark Energy Survey (DES), we analyze a SNIa sample with host galaxies in the redMaGiC galaxy catalog, a selection of Luminous Red Galaxies. Photo-$z$ estimates for these galaxies are expected to be accurate to $σ_{Δz/(1+z)}\sim0.02$. The DES-5YR photometrically classified SNIa sample contains approximately 1600 SNe and 125 of these SNe are in redMaGiC galaxies. We demonstrate that redMaGiC galaxies almost exclusively host SNe Ia, reducing concerns with classification uncertainties. With this subsample, we find similar Hubble scatter (to within $\sim0.01$ mag) using photometric redshifts in place of spectroscopic redshifts. With detailed simulations, we show the bias due to using photo-$z$s from redMaGiC host galaxies on the measurement of the dark energy equation-of-state $w$ is up to $Δw \sim 0.01-0.02$. With real data, we measure a difference in $w$ when using redMaGiC photometric redshifts versus spectroscopic redshifts of $Δw = 0.005$. Finally, we discuss how SNe in redMaGiC galaxies appear to be a more standardizable population due to a weaker relation between color and luminosity ($β$) compared to the DES-3YR population by $\sim5σ$; this finding is consistent with predictions that redMaGiC galaxies exhibit lower reddening ratios ($\textrm{R}_\textrm{V}$) than the general population of SN host galaxies. These results establish the feasibility of performing redMaGiC SN cosmology with photometric survey data in the absence of spectroscopic data.

astro-ph.CO↗

arXiv2022

Dark Energy Survey Year 3 Results: Point-Spread Function Modeling

We introduce a new software package for modeling the point-spread function (PSF) of astronomical images, called Piff (PSFs In the Full FOV), which we apply to the first three years (known as Y3) of the Dark Energy Survey (DES) data. We describe the relevant details about the algorithms used by Piff to model the PSF, including how the PSF model varies across the field of view (FOV). Diagnostic results show that the systematic errors from the PSF modeling are very small over the range of scales that are important for the DES Y3 weak lensing analysis. In particular, the systematic errors from the PSF modeling are significantly smaller than the corresponding results from the DES year one (Y1) analysis. We also briefly describe some planned improvements to Piff that we expect to further reduce the modeling errors in future analyses.

astro-ph.IM↗

arXiv2022

Robust sampling for weak lensing and clustering analyses with the Dark Energy Survey

Recent cosmological analyses rely on the ability to accurately sample from high-dimensional posterior distributions. A variety of algorithms have been applied in the field, but justification of the particular sampler choice and settings is often lacking. Here we investigate three such samplers to motivate and validate the algorithm and settings used for the Dark Energy Survey (DES) analyses of the first 3 years (Y3) of data from combined measurements of weak lensing and galaxy clustering. We employ the full DES Year 1 likelihood alongside a much faster approximate likelihood, which enables us to assess the outcomes from each sampler choice and demonstrate the robustness of our full results. We find that the ellipsoidal nested sampling algorithm $\texttt{MultiNest}$ reports inconsistent estimates of the Bayesian evidence and somewhat narrower parameter credible intervals than the sliced nested sampling implemented in $\texttt{PolyChord}$. We compare the findings from $\texttt{MultiNest}$ and $\texttt{PolyChord}$ with parameter inference from the Metropolis-Hastings algorithm, finding good agreement. We determine that $\texttt{PolyChord}$ provides a good balance of speed and robustness, and recommend different settings for testing purposes and final chains for analyses with DES Y3 data. Our methodology can readily be reproduced to obtain suitable sampler settings for future surveys.

astro-ph.CO↗

arXiv2022

Cosmological Constraints from DES Y1 Cluster Abundances and SPT Multi-wavelength data

We perform a joint analysis of the counts of redMaPPer clusters selected from the Dark Energy Survey (DES) Y1 data and multi-wavelength follow-up data collected within the 2500 deg$^2$ South Pole Telescope (SPT) SZ survey. The SPT follow-up data, calibrating the richness--mass relation of the optically selected redMaPPer catalog, enable the cosmological exploitation of the DES cluster abundance data. To explore possible systematics related to the modeling of projection effects, we consider two calibrations of the observational scatter on richness estimates: a simple Gaussian model which account only for the background contamination (BKG), and a model which further includes contamination and incompleteness due to projection effects (PRJ). Assuming either a $Λ$CDM+$\sum m_ν$ or $w$CDM+$\sum m_ν$ cosmology, and for both scatter models, we derive cosmological constraints consistent with multiple cosmological probes of the low and high redshift Universe, and in particular with the SPT cluster abundance data. This result demonstrates that the DES Y1 and SPT cluster counts provide consistent cosmological constraints, if the same mass calibration data set is adopted. It thus supports the conclusion of the DES Y1 cluster cosmology analysis which interprets the tension observed with other cosmological probes in terms of systematics affecting the stacked weak lensing analysis of optically--selected low--richness clusters. Finally, we analyse the first combined optically-SZ selected cluster catalogue obtained by including the SPT sample above the maximum redshift probed by the DES Y1 redMaPPer sample. Besides providing a mild improvement of the cosmological constraints, this data combination serves as a stricter test of our scatter models: the PRJ model, providing scaling relations consistent between the two abundance and multi-wavelength follow-up data, is favored over the BKG model.

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arXiv2022

From the Fire: A Deeper Look at the Phoenix Stream

We use six years of data from the Dark Energy Survey to perform a detailed photometric characterization of the Phoenix stellar stream, a 15-degree long, thin, dynamically cold, low-metallicity stellar system in the southern hemisphere. We use natural splines, a non-parametric 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 ($17.4 \pm 0.1\,{\rm (stat.)} \pm 0.8\,{\rm (sys.)}$ kpc) and distance gradient ($-0.009 \pm 0.006$ kpc deg$^{-1}$) of Phoenix, which corresponds to a small change of $0.13 \pm 0.09$ 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 $\sim 2$-degree 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.

astro-ph.GA↗

arXiv2022

The Evolution of AGN Activity in Brightest Cluster Galaxies

We present the results of an analysis of Wide-field Infrared Survey Explorer (WISE) observations on the full 2500 deg^2 South Pole Telescope (SPT)-SZ cluster sample. We describe a process for identifying active galactic nuclei (AGN) in brightest cluster galaxies (BCGs) based on WISE mid-infrared color and redshift. Applying this technique to the BCGs of the SPT-SZ sample, we calculate the AGN-hosting BCG fraction, which is defined as the fraction of BCGs hosting bright central AGNs over all possible BCGs. Assuming {\bf an evolving} single-burst stellar population model, we find statistically significant evidence (>99.9%) for a mid-IR excess at high redshift compared to low redshift, suggesting that the fraction of AGN-hosting BCGs increases with redshift over the range of 0 < z < 1.3. The best-fit redshift trend of the AGN-hosting BCG fraction has the form (1+z)^(4.1+/-1.0). These results are consistent with previous studies in galaxy clusters as well as field galaxies. One way to explain this result is that member galaxies at high redshift tend to have more cold gas. While BCGs in nearby galaxy clusters grow mostly by dry mergers with cluster members, leading to no increase in AGN activity, BCGs at high redshift could primarily merge with gas-rich satellites, providing fuel for feeding AGNs. If this observed increase in AGN activity is linked to gas-rich mergers, rather than ICM cooling, we would expect to see an increase in scatter in the P_cav vs L_cool relation at z > 1. Lastly, this work confirms that the runaway cooling phase, as predicted by the classical cooling flow model, in the Phoenix cluster is extremely rare and most BCGs have low (relative to Eddington) black hole accretion rates.

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arXiv2022

Systematic errors on optical-SED stellar mass estimates for galaxies across cosmic time and their impact on cosmology

Studying galaxies at different cosmic epochs entails several observational effects that need to be taken into account to compare populations across a large time span in a consistent manner. We use a sample of 166 nearby galaxies that hosted type Ia supernovae (SNe Ia) and have been observed with the integral field spectrograph MUSE through the AMUSING survey. Here, we present a study of the systematic errors and bias in the host stellar mass with increasing redshifts that are generally overlooked in SNe Ia cosmological analyses. We simulate observations at different redshifts (0.1<z<2.0) using four photometric bands (griz, similar to the Dark Energy Survey-SN program) to then estimate the host galaxy properties across cosmic time. We find that stellar masses are systematically underestimated as we move towards higher redshifts, due mostly to different rest-frame wavelength coverage, with differences reaching 0.3 dex at z~1. We have used the newly derived corrections as a function of redshift to correct the stellar masses of a known sample of SN Ia hosts and derive cosmological parameters. We show that these corrections have a small impact on the derived cosmological parameters. The most affected is the value of the mass step $Δ_M$, which is reduced by $\sim$0.004 (6% lower). The dark energy equation of state parameter $w$ changes by $Δw \sim $0.006 (0.6% higher) and the value of $Ω_m$ increases at most by 0.001 ($\sim$0.3%), all within the derived uncertainties of the model. While the systematic error found in the estimate of the host stellar mass does not significantly affect the derived cosmological parameters, it is an important source of a systematic error that one should correct for as we enter a new era of precision cosmology.

astro-ph.CO↗

arXiv2022

Synthetic Galaxy Clusters and Observations Based on Dark Energy Survey Year 3 Data

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 $λ\in[30;\,45)$, $λ\in[45;\,60)$ 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 catalogs 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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