arXiv subjects

P. Melchior

Publications and source records attributed to P. Melchior.

At least 19 recordsLinked to original sources

arXiv2023

Designing an Optimal Kilonova Search using DECam for Gravitational Wave Events

We address the problem of optimally identifying all kilonovae detected via gravitational wave emission in the upcoming LIGO/Virgo/KAGRA Collaboration observing run, O4, which is expected to be sensitive to a factor of $\sim 7$ more Binary Neutron Stars alerts than previously. Electromagnetic follow-up of all but the brightest of these new events will require $>1$ meter telescopes, for which limited time is available. We present an optimized observing strategy for the Dark Energy Camera during O4. We base our study on simulations of gravitational wave events expected for O4 and wide-prior kilonova simulations. We derive the detectabilities of events for realistic observing conditions. We optimize our strategy for confirming a kilonova while minimizing telescope time. For a wide range of kilonova parameters, corresponding to a fainter kilonova compared to GW170817/AT2017gfo we find that, with this optimal strategy, the discovery probability for electromagnetic counterparts with the Dark Energy Camera is $\sim 80\%$ at the nominal binary neutron star gravitational wave detection limit for the next LVK observing run (190 Mpc), which corresponds to a $\sim 30\%$ improvement compared to the strategy adopted during the previous observing run. For more distant events ($\sim 330$ Mpc), we reach a $\sim 60\%$ probability of detection, a factor of $\sim 2$ increase. For a brighter kilonova model dominated by the blue component that reproduces the observations of GW170817/AT2017gfo, we find that we can reach $\sim 90\%$ probability of detection out to 330 Mpc, representing an increase of $\sim 20 \%$, while also reducing the total telescope time required to follow-up events by $\sim 20\%$.

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arXiv2023

Constructing Impactful Machine Learning Research for Astronomy: Best Practices for Researchers and Reviewers

Machine learning has rapidly become a tool of choice for the astronomical community. It is being applied across a wide range of wavelengths and problems, from the classification of transients to neural network emulators of cosmological simulations, and is shifting paradigms about how we generate and report scientific results. At the same time, this class of method comes with its own set of best practices, challenges, and drawbacks, which, at present, are often reported on incompletely in the astrophysical literature. With this paper, we aim to provide a primer to the astronomical community, including authors, reviewers, and editors, on how to implement machine learning models and report their results in a way that ensures the accuracy of the results, reproducibility of the findings, and usefulness of the method.

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arXiv2023

Dark Energy Survey Year 3 Results: Redshift Calibration of the MagLim Lens Sample from the combination of SOMPZ and clustering and its impact on Cosmology

We present an alternative calibration of the MagLim lens sample redshift distributions from the Dark Energy Survey (DES) first three years of data (Y3). The new calibration is based on a combination of a Self-Organising Maps based scheme and clustering redshifts to estimate redshift distributions and inherent uncertainties, which is expected to be more accurate than the original DES Y3 redshift calibration of the lens sample. We describe in detail the methodology, we validate it on simulations and discuss the main effects dominating our error budget. The new calibration is in fair agreement with the fiducial DES Y3 redshift distributions calibration, with only mild differences ($<3σ$) in the means and widths of the distributions. We study the impact of this new calibration on cosmological constraints, analysing DES Y3 galaxy clustering and galaxy-galaxy lensing measurements, assuming a $Λ$CDM cosmology. We obtain $Ω_{\rm m} = 0.30\pm 0.04$, $σ_8 = 0.81\pm 0.07 $ and $S_8 = 0.81\pm 0.04$, which implies a $\sim 0.4σ$ shift in the $Ω_{\rm}-S_8$ plane compared to the fiducial DES Y3 results, highlighting the importance of the redshift calibration of the lens sample in multi-probe cosmological analyses.

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arXiv2023

Rates and properties of type Ia supernovae in galaxy clusters within the Dark Energy Survey

We identify 66 photometrically classified type Ia supernovae (SNe Ia) from the Dark Energy Survey (DES) that have occurred within red-sequence selected galaxy clusters. We compare light-curve and host galaxy properties of the cluster SNe to 1024 DES SNe Ia located in field galaxies, the largest comparison of two such samples at high redshift (z > 0.1). We find that cluster SN light curves decline faster than those in the field (97.7 per cent confidence). However, when limiting these samples to host galaxies of similar colour and mass, there is no significant difference in the SN light curve properties. Motivated by previous detections of a higher-normalised SN Ia delay time distribution in galaxy clusters, we measure the intrinsic rate of SNe Ia in cluster and field environments. We find the average ratio of the SN Ia rate per galaxy between high mass ($10\leq\log\mathrm{(M_{*}/M_{\odot})} \leq 11.25$) cluster and field galaxies to be $0.594 \pm0.068$. This difference is mass-dependent, with the ratio declining with increasing mass, which suggests that the stellar populations in cluster hosts are older than those in field hosts. We show that the mass-normalised rate (or SNe per unit mass) in massive-passive galaxies is consistent between cluster and field environments. Additionally, both of these rates are consistent with rates previously measured in clusters at similar redshifts. We conclude that in massive-passive galaxies, which are the dominant hosts of cluster SNe, the cluster DTD is comparable to the field.

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arXiv2023

The Intrinsic Alignment of Red Galaxies in DES Y1 redMaPPer Galaxy Clusters

Clusters of galaxies are sensitive to the most nonlinear peaks in the cosmic density field. The weak gravitational lensing of background galaxies by clusters can allow us to infer their masses. However, galaxies associated with the local environment of the cluster can also be intrinsically aligned due to the local tidal gradient, contaminating any cosmology derived from the lensing signal. We measure this intrinsic alignment in Dark Energy Survey (DES) Year 1 redMaPPer clusters. We find evidence of a non-zero mean radial alignment of galaxies within clusters between redshift 0.1-0.7. We find a significant systematic in the measured ellipticities of cluster satellite galaxies that we attribute to the central galaxy flux and other intracluster light. We attempt to correct this signal, and fit a simple model for intrinsic alignment amplitude ($A_{\textrm{IA}}$) to the measurement, finding $A_{\textrm{IA}}=0.15\pm 0.04$, when excluding data near the edge of the cluster. We find a significantly stronger alignment of the central galaxy with the cluster dark matter halo at low redshift and with higher richness and central galaxy absolute magnitude (proxies for cluster mass). This is an important demonstration of the ability of large photometric data sets like DES to provide direct constraints on the intrinsic alignment of galaxies within clusters. These measurements can inform improvements to small-scale modeling and simulation of the intrinsic alignment of galaxies to help improve the separation of the intrinsic alignment signal in weak lensing studies.

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arXiv2023

The PSZ-MCMF catalogue of Planck clusters over the DES region

We present the first systematic follow-up of Planck Sunyaev-Zeldovich effect (SZE) selected candidates down to signal-to-noise (S/N) of 3 over the 5000 deg$^2$ covered by the Dark Energy Survey. Using the MCMF cluster confirmation algorithm, we identify optical counterparts, determine photometric redshifts and richnesses and assign a parameter, $f_{\rm cont}$, that reflects the probability that each SZE-optical pairing represents a random superposition of physically unassociated systems rather than a real cluster. The new PSZ-MCMF cluster catalogue consists of 853 MCMF confirmed clusters and has a purity of 90%. We present the properties of subsamples of the PSZ-MCMF catalogue that have purities ranging from 90% to 97.5%, depending on the adopted $f_{\rm cont}$ threshold. Halo mass estimates $M_{500}$, redshifts, richnesses, and optical centers are presented for all PSZ-MCMF clusters. The PSZ-MCMF catalogue adds 589 previously unknown Planck identified clusters over the DES footprint and provides redshifts for an additional 50 previously published Planck selected clusters with S/N>4.5. Using the subsample with spectroscopic redshifts, we demonstrate excellent cluster photo-$z$ performance with an RMS scatter in $Δz/(1+z)$ of 0.47%. Our MCMF based analysis allows us to infer the contamination fraction of the initial S/N>3 Planck selected candidate list, which is ~50%. We present a method of estimating the completeness of the PSZ-MCMF cluster sample. In comparison to the previously published Planck cluster catalogues. this new S/N>3 MCMF confirmed cluster catalogue populates the lower mass regime at all redshifts and includes clusters up to z$\sim$1.3.

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arXiv2023

Identification of Galaxy-Galaxy Strong Lens Candidates in the DECam Local Volume Exploration Survey Using Machine Learning

We perform a search for galaxy-galaxy strong lens systems using a convolutional neural network (CNN) applied to imaging data from the first public data release of the DECam Local Volume Exploration Survey (DELVE), which contains $\sim 520$ million astronomical sources covering $\sim 4,000$ $\mathrm{deg}^2$ of the southern sky to a $5σ$ point-source depth of $g=24.3$, $r=23.9$, $i=23.3$, and $z=22.8$ mag. Following the methodology of similar searches using DECam data, we apply color and magnitude cuts to select a catalog of $\sim 11$ million extended astronomical sources. After scoring with our CNN, the highest scoring 50,000 images were visually inspected and assigned a score on a scale from 0 (definitely not a lens) to 3 (very probable lens). We present a list of 581 strong lens candidates, 562 of which are previously unreported. We categorize our candidates using their human-assigned scores, resulting in 55 Grade A candidates, 149 Grade B candidates, and 377 Grade C candidates. We additionally highlight eight potential quadruply lensed quasars from this sample. Due to the location of our search footprint in the northern Galactic cap ($b > 10$ deg) and southern celestial hemisphere (${\rm Dec.}<0$ deg), our candidate list has little overlap with other existing ground-based searches. Where our search footprint does overlap with other searches, we find a significant number of high-quality candidates which were previously unidentified, indicating a degree of orthogonality in our methodology. We report properties of our candidates including apparent magnitude and Einstein radius estimated from the image separation.

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arXiv2023

Cool Cores in Clusters of Galaxies in the Dark Energy Survey

We search for the presence of cool cores in optically-selected galaxy clusters from the Dark Energy Survey (DES) and investigate their prevalence as a function of redshift and cluster richness. Clusters were selected from the redMaPPer analysis of three years of DES observations that have archival Chandra X-ray observations, giving a sample of 99 clusters with a redshift range of $0.11 < z < 0.87$ and a richness range of $25 < λ< 207$. Using the X-ray data, the core temperature was compared to the outer temperature to identify clusters where the core temperature is a factor of 0.7 or less than the outer temperature. We found a cool core fraction of approximately 20% with no significant trend in the cool core fraction with either redshift or richness.

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arXiv2023

Mapping Variations of Redshift Distributions with Probability Integral Transforms

We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the probability integral transformations it relies on, uses a difference in curves between distribution functions in an ensemble as a transformation to apply to another distribution function, thus transferring the variation in the ensemble to the latter distribution function. This procedure is broadly applicable to the problem of uncertainty propagation. In the context of redshift distributions, for example, the uncertainty contribution due to certain effects can be studied effectively only in simulations, thus necessitating a transfer of variation measured in simulations to the redshift distributions measured from data. We illustrate the use of PITPZ by using the method to propagate photometric calibration uncertainty to redshift distributions of the Dark Energy Survey Year 3 weak lensing source galaxies. For this test case, we find that PITPZ yields a lensing amplitude uncertainty estimate due to photometric calibration error within 1 per cent of the truth, compared to as much as a 30 per cent underestimate when using traditional methods.

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arXiv2022

The Dark Energy Survey Year 3 and eBOSS: constraining galaxy intrinsic alignments across luminosity and colour space

We present direct constraints on galaxy intrinsic alignments using the Dark Energy Survey Year 3 (DES Y3), the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) and its precursor, the Baryon Oscillation Spectroscopic Survey (BOSS). Our measurements incorporate photometric red sequence (redMaGiC) galaxies from DES with median redshift $z\sim0.2-1.0$, luminous red galaxies (LRGs) from eBOSS at $z\sim0.8$, and also a SDSS-III BOSS CMASS sample at $z\sim0.5$. We measure two point intrinsic alignment correlations, which we fit using a model that includes lensing, magnification and photometric redshift error. Fitting on scales $6<r_{\rm p} < 70$ Mpc$/h$, we make a detection of intrinsic alignments in each sample, at $5σ-22σ$ (assuming a simple one parameter model for IAs). Using these red samples, we measure the IA-luminosity relation. Our results are statistically consistent with previous results, but offer a significant improvement in constraining power, particularly at low luminosity. With this improved precision, we see detectable dependence on colour between broadly defined red samples. It is likely that a more sophisticated approach than a binary red/blue split, which jointly considers colour and luminosity dependence in the IA signal, will be needed in future. We also compare the various signal components at the best fitting point in parameter space for each sample, and find that magnification and lensing contribute $\sim2-18\%$ of the total signal. As precision continues to improve, it will certainly be necessary to account for these effects in future direct IA measurements. Finally, we make equivalent measurements on a sample of Emission Line Galaxies (ELGs) from eBOSS at $z\sim 0.8$. We report a null detection, constraining the IA amplitude (assuming the nonlinear alignment model) to be $A_1=0.07^{+0.32}_{-0.42}$ ($|A_1|<0.78$ at $95\%$ CL).

astro-ph.CO↗

arXiv2022

A Sample of Dust Attenuation Laws for DES Supernova Host Galaxies

Type Ia supernovae (SNe Ia) are useful distance indicators in cosmology, provided their luminosity is standardized by applying empirical corrections based on light-curve properties. One factor behind these corrections is dust extinction, accounted for in the color-luminosity relation of the standardization. This relation is usually assumed to be universal, which could potentially introduce systematics into the standardization. The ``mass-step'' observed for SNe Ia Hubble residuals has been suggested as one such systematic. We seek to obtain a completer view of dust attenuation properties for a sample of 162 SN Ia host galaxies and to probe their link to the ``mass-step''. We infer attenuation laws towards hosts from both global and local (4 kpc) Dark Energy Survey photometry and Composite Stellar Population model fits. We recover a optical depth/attenuation slope relation, best explained by differing star/dust geometry for different galaxy orientations, which is significantly different from the optical depth/extinction slope relation observed directly for SNe. We obtain a large variation of attenuation slopes and confirm these change with host properties, like stellar mass and age, meaning a universal SN Ia correction should ideally not be assumed. Analyzing the cosmological standardization, we find evidence for a ``mass-step'' and a two dimensional ``dust-step'', both more pronounced for red SNe. Although comparable, the two steps are found no to be completely analogous. We conclude that host galaxy dust data cannot fully account for the ``mass-step'', using either an alternative SN standardization with extinction proxied by host attenuation or a ``dust-step'' approach.

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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

Mapping gas around massive galaxies: cross-correlation of DES Y3 galaxies and Compton-$y$-maps from SPT and Planck

We cross-correlate positions of galaxies measured in data from the first three years of the Dark Energy Survey with Compton-$y$-maps generated using data from the South Pole Telescope (SPT) and the {\it Planck} mission. We model this cross-correlation measurement together with the galaxy auto-correlation to constrain the distribution of gas in the Universe. We measure the hydrostatic mass bias or, equivalently, the mean halo bias-weighted electron pressure $\langle b_{h}P_{e}\rangle$, using large-scale information. We find $\langle b_{h}P_{e}\rangle$ to be $[0.16^{+0.03}_{-0.04},0.28^{+0.04}_{-0.05},0.45^{+0.06}_{-0.10},0.54^{+0.08}_{-0.07},0.61^{+0.08}_{-0.06},0.63^{+0.07}_{-0.08}]$ meV cm$^{-3}$ at redshifts $z \sim [0.30, 0.46, 0.62,0.77, 0.89, 0.97]$. These values are consistent with previous work where measurements exist in the redshift range. We also constrain the mean gas profile using small-scale information, enabled by the high-resolution of the SPT data. We compare our measurements to different parametrized profiles based on the cosmo-OWLS hydrodynamical simulations. We find that our data are consistent with the simulation that assumes an AGN heating temperature of $10^{8.5}$K but are incompatible with the model that assumes an AGN heating temperature of $10^{8.0}$K. These comparisons indicate that the data prefer a higher value of electron pressure than the simulations within $r_{500c}$ of the galaxies' halos.

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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

Characterising the Intracluster Light over the Redshift Range $0.2 < z < 0.8$ in the DES-ACT Overlap

We characterise the properties and evolution of Bright Central Galaxies (BCGs) and the surrounding intracluster light (ICL) in galaxy clusters identified in overlapping regions of the Dark Energy Survey and Atacama Cosmology Telescope Survey (DES-ACT), covering the redshift range $0.20 $14.4. We also measure the stellar mass - halo mass (SMHM) relation for the BCG+ICL system and find that the slope, $β$, which characterises the dependence of $M_{\rm 200m,SZ}$ on the BCG+ICL stellar mass, increases with radius. The outskirts are more strongly correlated with the halo than the core, which supports that the BCG+ICL system follows a two-phase growth, where recent growth ($z<2$) occurs beyond the BCG's core. Additionally, we compare our observed SMHM relation results to the IllustrisTNG 300-1 cosmological hydrodynamic simulations and find moderate qualitative agreement in the amount of diffuse light. However, the SMHM relation's slope is steeper in TNG300-1 and the intrinsic scatter is lower, likely from the absence of projection effects in TNG300-1. Additionally, we find that the ICL exhibits a colour gradient such that the outskirts are bluer than the core. Moreover, for the lower halo mass clusters (log$_{10}(M_{\rm 200m,SZ}$/M$_{\odot})<$14.59 ), we detect a modest change in the colour gradient's slope with lookback time, which combined with the absence of stellar mass growth may suggest that lower mass clusters have been involved in growth via tidal stripping more recently than their higher mass counterparts.

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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

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.

astro-ph.CO↗

arXiv2022

Dark Energy Survey Year 3 results: imprints of cosmic voids and superclusters in the Planck CMB lensing map

The CMB lensing signal from cosmic voids and superclusters probes the growth of structure in the low-redshift cosmic web. In this analysis, we cross-correlated the Planck CMB lensing map with voids detected in the Dark Energy Survey Year 3 (Y3) data set ($\sim$5,000 deg$^{2}$), expanding on previous measurements that used Y1 catalogues ($\sim$1,300 deg$^{2}$). Given the increased statistical power compared to Y1 data, we report a $6.6σ$ detection of negative CMB convergence ($κ$) imprints using approximately 3,600 voids detected from a redMaGiC luminous red galaxy sample. However, the measured signal is lower than expected from the MICE N-body simulation that is based on the $Λ$CDM model (parameters $Ω_{\rm m} = 0.25$, $σ_8 = 0.8$), and the discrepancy is associated mostly with the void centre region. Considering the full void lensing profile, we fit an amplitude $A_κ=κ_{\rm DES}/κ_{\rm MICE}$ to a simulation-based template with fixed shape and found a moderate $2σ$ deviation in the signal with $A_κ\approx0.79\pm0.12$. We also examined the WebSky simulation that is based on a Planck 2018 $Λ$CDM cosmology, but the results were even less consistent given the slightly higher matter density fluctuations than in MICE. We then identified superclusters in the DES and the MICE catalogues, and detected their imprints at the $8.4σ$ level; again with a lower-than-expected $A_κ=0.84\pm0.10$ amplitude. The combination of voids and superclusters yields a $10.3σ$ detection with an $A_κ=0.82\pm0.08$ constraint on the CMB lensing amplitude, thus the overall signal is $2.3σ$ weaker than expected from MICE.

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