arXiv subjects

M. A. G. Maia

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

At least 19 recordsLinked to original sources

arXiv2022

Cross-correlation of DES Y3 lensing and ACT/${\it Planck}$ thermal Sunyaev Zel'dovich Effect 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. 2021), 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 ${\it Planck}$ 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 ($B \equiv M_{500c}/M_{\rm SZ}$) from our measurements, finding $B = 1.8\pm0.1$ when adopting the ${\it Planck}$-preferred cosmological parameters. We additionally find that our measurements are consistent with a non-zero redshift evolution of $B$, with the correct sign and sufficient magnitude to explain the mass bias necessary to reconcile cluster count measurements with the ${\it Planck}$-preferred cosmology. Our analysis introduces a model for the impact of intrinsic alignments (IA) 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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arXiv2022

Consistent lensing and clustering in a low-$S_8$ Universe with BOSS, DES Year 3, HSC Year 1 and KiDS-1000

We evaluate the consistency between lensing and clustering probes of large-scale structure based on measurements of projected galaxy clustering from BOSS combined with overlapping galaxy-galaxy lensing from three surveys: DES Y3, HSC Y1, and KiDS-1000. An intra-lensing-survey study finds good agreement between these lensing data. We model the observations using the Dark Emulator and fit the data at two fixed cosmologies: Planck, with $S_8=0.83$, and a Lensing cosmology with $S_8=0.76$. For a joint analysis limited to scales with $R>5.25h^{-1}$Mpc, we find that both cosmologies provide an acceptable fit to the data. Full utilisation of the small-scale clustering and lensing 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 scaling parameter for each redshift bin, $A$, that decouples the lensing and clustering to capture any inconsistency. When a wide range of scales ($0.15<R<60h^{-1}$Mpc) are incorporated, we find different results for the consistency of clustering and lensing between the two cosmologies. Limiting the analysis to the bins for which the impact of the selection of the lens sample is expected to be minimal, for the low-$S_8$ Lensing cosmology, the measurements are consistent with $A$=1; $A=0.91\pm0.04$ using DES+KiDS and $A=0.97\pm0.06$ using HSC. For the Planck cosmology case, we find a discrepancy: $A=0.79\pm0.03$ using DES+KiDS and $A=0.84\pm0.05$ using HSC. We demonstrate that a kSZ-based estimate for baryonic effects alleviates some of the discrepancy in the Planck cosmology. This analysis demonstrates the statistical power of these small-scale measurements, but also indicates that caution is still warranted given current uncertainties in modelling baryonic effects, assembly bias, and selection effects in the foreground sample.

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arXiv2022

Cosmic Shear in Harmonic Space from the Dark Energy Survey Year 1 Data: Compatibility with Configuration Space Results

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 $S_8$, $σ_8$ and $Ω_m$. 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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arXiv2022

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps

We present a cosmological analysis using the second and third moments of the weak lensing mass (convergence) maps from the first three years of data (Y3) data of the Dark Energy Survey (DES). The survey spans an effective area of 4139 square degrees and uses the images of over 100 million galaxies to reconstruct the convergence field. The second moment of the convergence as a function of smoothing scale contains information similar to standard shear 2-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The data is analysed in the context of the $Λ$CDM model, varying 5 cosmological parameters and 19 nuisance parameters modelling astrophysical and measurement systematics. Our modelling of the observables is completely analytical, and has been tested with simulations in our previous methodology study. We obtain a 1.7\% measurement of the amplitude of fluctuations parameter $S_8\equiv σ_8 (Ω_m/0.3)^{0.5} = 0.784\pm 0.013$. The measurements are shown to be internally consistent across redshift bins, angular scales, and between second and third moments. In particular, the measured third moment is consistent with the expectation of gravitational clustering under the $Λ$CDM model. The addition of the third moment improves the constraints on $S_8$ and $Ω_{\rm m}$ by $\sim$15\% and $\sim$25\% compared to an analysis that only uses second moments. We compare our results with {\it Planck} constraints from the Cosmic Microwave Background (CMB), finding a $2.2$ \textendash $2.8σ$ tension in the full parameter space, depending on the combination of moments considered. The third moment independently is in $2.8σ$ tension with {\it Planck}, and thus provides a cross-check on analyses of 2-point correlations.

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arXiv2022

Dwarf AGNs from Optical Variability for the Origins of Seeds (DAVOS): Insights from the Dark Energy Survey Deep Fields

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 deg$^2$. 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 days, a 6 year baseline, and a single-epoch imaging depth of up to $g \sim 24.5$. 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 ($M_{\ast}<10^{9.5}\ M_\odot$; median photometric redshift of 0.9). We were able to constrain rapid characteristic variability timescales ($\sim$ 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 masses. We confirm the low-mass AGN nature of one source with a high S/N optical spectrum. We publish our catalog, 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 black hole masses in deep fields, which may be more "pristine" analogs of supermassive black hole seeds.

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arXiv2022

Superclustering with the Atacama Cosmology Telescope and Dark Energy Survey: I. Evidence for thermal energy anisotropy using oriented stacking

The cosmic web contains filamentary structure on a wide range of scales. On the largest scales, superclustering aligns multiple galaxy clusters along inter-cluster bridges, visible through their thermal Sunyaev-Zel'dovich signal in the Cosmic Microwave Background. We demonstrate a new, flexible method to analyze the hot gas signal from multi-scale extended structures. We use a Compton-$y$ map from the Atacama Cosmology Telescope (ACT) stacked on redMaPPer cluster positions from the optical Dark Energy Survey (DES). Cutout images from the $y$ map are oriented with large-scale structure information from DES galaxy data such that the superclustering signal is aligned before being overlaid. We find evidence for an extended quadrupole moment of the stacked $y$ signal at the 3.5$σ$ level, demonstrating that the large-scale thermal energy surrounding galaxy clusters is anisotropically distributed. We compare our ACT$\times$DES results with the Buzzard simulations, finding broad agreement. Using simulations, we highlight the promise of this novel technique for constraining the evolution of anisotropic, non-Gaussian structure using future combinations of microwave and optical surveys.

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arXiv2022

Dark Energy Survey Year 3 Results: Three-Point Shear Correlations and Mass Aperture Moments

We present high signal-to-noise measurements of three-point shear correlations and the third moment of the mass aperture statistic using the first 3 years of data from the Dark Energy Survey. We additionally obtain the first measurements of the configuration and scale dependence of the four three-point shear correlations which carry cosmological information. With the third-order mass aperture statistic, we present tomographic measurements over angular scales of 4 to 60 arcminutes with a combined statistical significance of 15.0$σ$. Using the tomographic information and measuring also the second-order mass aperture, we additionally obtain a skewness parameter and its redshift evolution. We find that the amplitudes and scale-dependence of these shear 3pt functions are in qualitative agreement with measurements in a mock galaxy catalog based on N-body simulations, indicating promise for including them in future cosmological analyses. We validate our measurements by showing that B-modes, parity-violating contributions and PSF modeling uncertainties are negligible, and determine that the measured signals are likely to be of astrophysical and gravitational origin.

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arXiv2022

Milky Way Satellite Census. IV. Constraints on Decaying Dark Matter from Observations of Milky Way Satellite Galaxies

We use a recent census of the Milky Way (MW) satellite galaxy population to constrain the lifetime of particle dark matter (DM). We consider two-body decaying dark matter (DDM) in which a heavy DM particle decays with lifetime $τ$ comparable to the age of the Universe to a lighter DM particle (with mass splitting $ε$) and to a dark radiation species. These decays impart a characteristic "kick velocity," $V_{\mathrm{kick}}=εc$, on the DM daughter particles, significantly depleting the DM content of low-mass subhalos and making them more susceptible to tidal disruption. We fit the suppression of the present-day DDM subhalo mass function (SHMF) as a function of $τ$ and $V_{\mathrm{kick}}$ using a suite of high-resolution zoom-in simulations of MW-mass halos, and we validate this model on new DDM simulations of systems specifically chosen to resemble the MW. We implement our DDM SHMF predictions in a forward model that incorporates inhomogeneities in the spatial distribution and detectability of MW satellites and uncertainties in the mapping between galaxies and DM halos, the properties of the MW system, and the disruption of subhalos by the MW disk using an empirical model for the galaxy--halo connection. By comparing to the observed MW satellite population, we conservatively exclude DDM models with $τ< 18\ \mathrm{Gyr}$ ($29\ \mathrm{Gyr}$) for $V_{\mathrm{kick}}=20\ \mathrm{km}\, \mathrm{s}^{-1}$ ($40\ \mathrm{km}\, \mathrm{s}^{-1}$) at $95\%$ confidence. These constraints are among the most stringent and robust small-scale structure limits on the DM particle lifetime and strongly disfavor DDM models that have been proposed to alleviate the Hubble and $S_8$ tensions.

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arXiv2022

Velocity Dispersions of Clusters in the Dark Energy Survey Y3 redMaPPer Catalog

We measure the velocity dispersions of clusters of galaxies selected by the 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 which are high for their richness. These clusters account for roughly 22\% of the $λ< 70$ systems in our sample, but more than half (55\%) 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 is needed to understand their nature.

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arXiv2022

Dark Energy Survey Year 3 Results: Calibration of Lens Sample Redshift Distributions using Clustering Redshifts with BOSS/eBOSS

We present clustering redshift measurements for Dark Energy Survey (DES) lens sample galaxies to be used in weak gravitational lensing and galaxy clustering studies. To perform this measurement, 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 due to the galaxy clustering bias, finding our method to be generally unbiased in calibrating the mean redshift. We apply our method to the data, and estimate the redshift distribution for eleven different photometrically-selected bins. We find general agreement between clustering redshift and photometric redshift estimates, with differences on the inferred mean redshift 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\%. We discuss how these results calibrate the photometric redshift distributions used in companion DES Year 3 Results papers.

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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

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

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

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.

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arXiv2022

Dark Energy Survey Year 3 Results: Deep Field Optical + Near-Infrared Images and Catalogue

We describe the Dark Energy Survey (DES) Deep Fields, a set of images and associated multi-wavelength 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 $\sim30~$ square degrees 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-year 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 $r=25.7, i=25, z=24.3$ 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 (${\rm NMAD} = 0.023$ 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-year weak lensing and galaxy clustering cosmology work.

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