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Kuropatkin, N.

Publications and source records attributed to Kuropatkin, N..

At least 19 records

The DECADE cosmic shear project I: A new weak lensing shape catalog of 107 million galaxies

We present the Dark Energy Camera All Data Everywhere (DECADE) weak lensing dataset: a catalog of 107 million galaxies observed by the Dark Energy Camera (DECam) in the northern Galactic cap. This catalog was assembled from public DECam data including survey and standard observing programs. These data were consistently processed with the Dark Energy Survey Data Management pipeline as part of the DECADE campaign and serve as the basis of the DECam Local Volume Exploration survey (DELVE) Early Data Release 3 (EDR3). We apply the Metacalibration measurement algorithm to generate and calibrate galaxy shapes. After cuts, the resulting cosmology-ready galaxy shape catalog covers a region of $5,\!412 \,\,{\rm deg}^2$ with an effective number density of $4.59\,\, {\rm arcmin}^{-2}$. The coadd images used to derive this data have a median limiting magnitude of $r = 23.6$, $i = 23.2$, and $z = 22.6$, estimated at ${\rm S/N} = 10$ in a 2 arcsecond aperture. We present a suite of detailed studies to characterize the catalog, measure any residual systematic biases, and verify that the catalog is suitable for cosmology analyses. In parallel, we build an image simulation pipeline to characterize the remaining multiplicative shear bias in this catalog, which we measure to be $m = (-2.454 \pm 0.124) \times10^{-2}$ for the full sample. Despite the significantly inhomogeneous nature of the data set, due to it being an amalgamation of various observing programs, we find the resulting catalog has sufficient quality to yield competitive cosmological constraints.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The Dark Energy Survey Supernova Program: Cosmological Analysis and Systematic Uncertainties

We present the full Hubble diagram of photometrically classified Type Ia supernovae (SNe Ia) from the Dark Energy Survey supernova program (DES-SN). DES-SN discovered more than 20,000 SN candidates and obtained spectroscopic redshifts of 7000 host galaxies. Based on the light-curve quality, we select 1635 photometrically identified SNe Ia with spectroscopic redshift 0.10 < z < 1.13, which is the largest sample of supernovae from any single survey and increases the number of known z > 0.5 supernovae by a factor of 5. In a companion paper, we present cosmological results of the DES-SN sample combined with 194 spectroscopically classified SNe Ia at low redshift as an anchor for cosmological fits. Here we present extensive modeling of this combined sample and validate the entire analysis pipeline used to derive distances. We show that the statistical and systematic uncertainties on cosmological parameters are ${\sigma }_{{{\rm{\Omega }}}_{M},\mathrm{stat}+\mathrm{sys}}^{{\rm{\Lambda }}\mathrm{CDM}}=$ 0.017 in a flat ΛCDM model, and $({\sigma }_{{{\rm{\Omega }}}_{M}},{\sigma }_{w}{)}_{\mathrm{stat}+\mathrm{sys}}^{w\mathrm{CDM}}$ = (0.082, 0.152) in a flat wCDM model. Combining the DES SN data with the highly complementary cosmic microwave background measurements by Planck Collaboration reduces by a factor of 4 uncertainties on cosmological parameters. In all cases, statistical uncertainties dominate over systematics. We show that uncertainties due to photometric classification make up less than 10% of the total systematic uncertainty budget. This result sets the stage for the next generation of SN cosmology surveys such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time.

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SPT clusters with DES and HST weak lensing. I. Cluster lensing and Bayesian population modeling of multiwavelength cluster datasets

We present a Bayesian population modeling method to analyze the abundance of galaxy clusters identified by the South Pole Telescope (SPT) with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). We discuss and validate the modeling choices with a particular focus on a robust, weak-lensing-based mass calibration using DES data. For the DES Year 3 data, we report a systematic uncertainty in weak-lensing mass calibration that increases from 1% at z = 0.25 to 10% at z = 0.95 , to which we add 2% in quadrature to account for uncertainties in the impact of baryonic effects. We implement an analysis pipeline that joins the cluster abundance likelihood with a multiobservable likelihood for the Sunyaev-Zel’dovich effect, optical richness, and weak-lensing measurements for each individual cluster. We validate that our analysis pipeline can recover unbiased cosmological constraints by analyzing mocks that closely resemble the cluster sample extracted from the SPT-SZ, SPTpol ECS, and SPTpol 500d surveys and the DES Year 3 and HST-39 weak-lensing datasets. This work represents a crucial prerequisite for the subsequent cosmological analysis of the real dataset.

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The SRG/eROSITA All-Sky Survey: Dark Energy Survey year 3 weak gravitational lensing by eRASS1 selected galaxy clusters

Context. Number counts of galaxy clusters across redshift are a powerful cosmological probe if a precise and accurate reconstruction of the underlying mass distribution is performed – a challenge called mass calibration. With the advent of wide and deep photometric surveys, weak gravitational lensing (WL) by clusters has become the method of choice for this measurement. Aims. We measured and validated the WL signature in the shape of galaxies observed in the first three years of the Dark Energy Survey (DES Y3) caused by galaxy clusters and groups selected in the first all-sky survey performed by SRG (Spectrum Roentgen Gamma)/eROSITA (eRASS1). These data were then used to determine the scaling between the X-ray photon count rate of the clusters and their halo mass and redshift. Methods. We empirically determined the degree of cluster member contamination in our background source sample. The individual cluster shear profiles were then analyzed with a Bayesian population model that self-consistently accounts for the lens sample selection and contamination and includes marginalization over a host of instrumental and astrophysical systematics. To quantify the accuracy of the mass extraction of that model, we performed mass measurements on mock cluster catalogs with realistic synthetic shear profiles. This allowed us to establish that hydrodynamical modeling uncertainties at low lens redshifts (z < 0.6) are the dominant systematic limitation. At high lens redshift, the uncertainties of the sources’ photometric redshift calibration dominate. Results. With regard to the X-ray count rate to halo mass relation, we determined its amplitude, its mass trend, the redshift evolution of the mass trend, the deviation from self-similar redshift evolution, and the intrinsic scatter around this relation. Conclusions. The mass calibration analysis performed here sets the stage for a joint analysis with the number counts of eRASS1 clusters to constrain a host of cosmological parameters. We demonstrate that WL mass calibration of galaxy clusters can be performed successfully with source galaxies whose calibration was performed primarily for cosmic shear experiments, opening the way for the cluster cosmological exploitation of future optical and NIR surveys like Euclid and LSST.

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Dark Energy Survey Year 6 results: Intra-cluster light from redshift 0.2 to 0.5

Using the full 6 years of imaging data from the Dark Energy Survey, we study the surface brightness profiles of galaxy cluster central galaxies and intra-cluster light. We apply a ‘stacking’ method to over 4000 galaxy clusters identified by the redMaPPer cluster finder in the redshift range of 0.2−0.5. This yields high-signal-to-noise circularly averaged profile measurements of the central galaxy and intra-cluster light out to 1 Mpc from the cluster centre. Using redMaPPer richness as a cluster mass indicator, we find that the brightness of the intra-cluster light has a strong mass dependence throughout the 0.2−0.5 redshift range, and this dependence grows stronger at a larger radius. In terms of redshift evolution, we find some evidence that the central galaxy, as well as the diffuse light within the transition region between the cluster central galaxy and intra-cluster light within 80 kpc from the centre, may be growing over time. At larger radii, more than 80 kpc away from the cluster centre, we do not detect evidence of additional redshift evolution beyond the cluster mass dependence, consistent with the findings from the IllustrisTNG hydrodynamic simulation. We speculate that the major driver of intra-cluster light growth, especially at large radii, is associated with cluster mass growth. Finally, we find that the colour of the cluster central galaxy and intra-cluster light displays a radial gradient that becomes bluer at a larger radius, which is consistent with a stellar stripping and disruption origin of intra-cluster light as suggested by simulation studies.

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Dark Energy Survey Year 3 results: Simulation-based cosmological inference with wavelet harmonics, scattering transforms, and moments of weak lensing mass maps. Validation on simulations

Beyond-two-point statistics contain additional information on cosmological as well as astrophysical and observational (systematics) parameters. In this methodology paper we provide an end-to-end simulationbased analysis of a set of Gaussian and non-Gaussian weak lensing statistics using detailed mock catalogs of the Dark Energy Survey (DES). Here, we implement: 1) second and third moments; 2) wavelet phase harmonics (WPH); 3) the scattering transform (ST). Our analysis is fully based on simulations, it spans a space of seven $νw$CDM cosmological parameters, and it forward models the most relevant sources of systematics of the data (masks, noise variations, clustering of the sources, intrinsic alignments, and shear and redshift calibration). We implement a neural network compression of the summary statistics, and we estimate the parameter posteriors using a likelihood-free-inference approach. We validate the pipeline extensively, and we find that WPH exhibits the strongest performance when combined with second moments, followed by ST, and then by third moments. The combination of all the different statistics further enhances constraints with respect to second moments, up to 25 percent, 15 percent, and 90 percent for S 8 , Ω m , and the figure-of-merit FoM S8;Ωm , respectively. We further find that non-Gaussian statistics improve constraints on w and on the amplitude of intrinsic alignment with respect to second moments constraints. The methodological advances presented here are suitable for application to Stage IV surveys from Euclid, Rubin-LSST, and Roman with additional validation on mock catalogs for each survey. In a companion paper we present an application to DES Year 3 data.

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A sample of dust attenuation laws for Dark Energy Survey 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, which is accounted for in the color–luminosity relation of the standardization. This relation is usually assumed to be universal, which can potentially introduce systematics into the standardization. The “mass step” observed for SN Ia Hubble residuals has been suggested as one such systematic. We seek to obtain a more complete view of dust attenuation properties for a sample of 162 SN Ia host galaxies and to probe their link to the mass step. We inferred attenuation laws toward hosts from both global and local (4 kpc) Dark Energy Survey photometry and composite stellar population model fits. We recovered a relation between the optical depth and the attenuation slope, best explained by differing star-to-dust geometry for different galaxy orientations, which is significantly different from the optical depth and extinction slope relation observed directly for SNe. We obtain a large variation of attenuation slopes and confirm these change with host properties, such as the 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 not found 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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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-normalized 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 (⁠|$10\le \log \mathrm{(\mathit{ M}_{*}/{\rm \mathit{ M}}_{\odot })} \le 11.25$|⁠) cluster and field galaxies to be 0.594 ± 0.068. 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-normalized 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 delay-time distribution is comparable to the field.

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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

ABSTRACT We present an alternative calibration of the MagLim lens sample redshift distributions from the Dark Energy Survey (DES) first 3 yr of data (Y3). The new calibration is based on a combination of a self-organizing-map-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, and 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 n(z) 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 Lambda cold dark matter cosmology. We obtain Ωm = 0.30 ± 0.04, σ8 = 0.81 ± 0.07, and S8 = 0.81 ± 0.04, which implies a ∼0.4σ shift in the Ω − S8 plane compared to the fiducial DES Y3 results, highlighting the importance of the redshift calibration of the lens sample in multiprobe cosmological analyses.

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Beyond the 3rd moment: a practical study of using lensing convergence CDFs for cosmology with DES Y3

ABSTRACT Widefield surveys probe clustered scalar fields – such as galaxy counts, lensing potential, etc. – which are sensitive to different cosmological and astrophysical processes. Constraining such processes depends on the statistics that summarize the field. We explore the cumulative distribution function (CDF) as a summary of the galaxy lensing convergence field. Using a suite of N-body light-cone simulations, we show the CDFs’ constraining power is modestly better than the second and third moments, as CDFs approximately capture information from all moments. We study the practical aspects of applying CDFs to data, using the Dark Energy Survey (DES Y3) data as an example, and compute the impact of different systematics on the CDFs. The contributions from the point spread function and reduced shear approximation are $\lesssim 1~{{\ \rm per\ cent}}$ of the total signal. Source clustering effects and baryon imprints contribute 1–10 per cent. Enforcing scale cuts to limit systematics-driven biases in parameter constraints degrade these constraints a noticeable amount, and this degradation is similar for the CDFs and the moments. We detect correlations between the observed convergence field and the shape noise field at 13σ. The non-Gaussian correlations in the noise field must be modelled accurately to use the CDFs, or other statistics sensitive to all moments, as a rigorous cosmology tool.

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DES Y3 + KiDS-1000: Consistent cosmology combining cosmic shear surveys

We present a joint cosmic shear analysis of the Dark Energy Survey (DES Y3) and the Kilo-Degree Survey (KiDS-1000) in a collaborative effort between the two survey teams. We find consistent cosmological parameter constraints between DES Y3 and KiDS-1000 which, when combined in a joint-survey analysis, constrain the parameter $S_8 = \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$ with a mean value of $0.790^{+0.018}_{-0.014}$. The mean marginal is lower than the maximum a posteriori estimate, $S_8=0.801$, owing to skewness in the marginal distribution and projection effects in the multi-dimensional parameter space. Our results are consistent with $S_8$ constraints from observations of the cosmic microwave background by Planck, with agreement at the $1.7\sigma$ level. We use a Hybrid analysis pipeline, defined from a mock survey study quantifying the impact of the different analysis choices originally adopted by each survey team. We review intrinsic alignment models, baryon feedback mitigation strategies, priors, samplers and models of the non-linear matter power spectrum.

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The Dark Energy Survey Year 3 high-redshift sample: selection, characterization, and analysis of galaxy clustering

ABSTRACT The fiducial cosmological analyses of imaging surveys like DES typically probe the Universe at redshifts z < 1. We present the selection and characterization of high-redshift galaxy samples using DES Year 3 data, and the analysis of their galaxy clustering measurements. In particular, we use galaxies that are fainter than those used in the previous DES Year 3 analyses and a Bayesian redshift scheme to define three tomographic bins with mean redshifts around z ∼ 0.9, 1.2, and 1.5, which extend the redshift coverage of the fiducial DES Year 3 analysis. These samples contain a total of about 9 million galaxies, and their galaxy density is more than 2 times higher than those in the DES Year 3 fiducial case. We characterize the redshift uncertainties of the samples, including the usage of various spectroscopic and high-quality redshift samples, and we develop a machine-learning method to correct for correlations between galaxy density and survey observing conditions. The analysis of galaxy clustering measurements, with a total signal to noise S/N ∼ 70 after scale cuts, yields robust cosmological constraints on a combination of the fraction of matter in the Universe Ωm and the Hubble parameter h, $\Omega _m h = 0.195^{+0.023}_{-0.018}$, and 2–3 per cent measurements of the amplitude of the galaxy clustering signals, probing galaxy bias and the amplitude of matter fluctuations, bσ8. A companion paper (in preparation) will present the cross-correlations of these high-z samples with cosmic microwave background lensing from Planck and South Pole Telescope, and the cosmological analysis of those measurements in combination with the galaxy clustering presented in this work.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

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

ABSTRACT 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 deg2 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, fcont, 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 per cent. We present the properties of subsamples of the PSZ-MCMF catalogue that have purities ranging from 90 per cent to 97.5 per cent, depending on the adopted fcont threshold. Halo mass estimates M500, redshifts, richnesses, and optical centres 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 per cent. Our MCMF based analysis allows us to infer the contamination fraction of the initial S/N>3 Planck-selected candidate list, which is ∼50 per cent. 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∼1.3.

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

ABSTRACT We present direct constraints on galaxy intrinsic alignments (IAs) 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 ∼ 0.2–1.0, luminous red galaxies from eBOSS at z ∼ 0.8, and also an SDSS-III BOSS CMASS sample at z ∼ 0.5. We measure two-point IA correlations, which we fit using a model that includes lensing, magnification, and photometric redshift error. Fitting on scales 6 Mpc h−1 < rp < 70 Mpc h−1, we make a detection of IAs 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 $\sim 2\!-\!18~{{\ \rm per\ cent}}$ 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 from eBOSS at z ∼ 0.8. We constrain the non-linear alignment amplitude to be $A_1=0.07^{+0.32}_{-0.42}$ (|A1| < 0.78 at 95 per cent CL).

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Dark Energy Survey Year 3 results: magnification modelling and impact on cosmological constraints from galaxy clustering and galaxy–galaxy lensing

We study the effect of magnification in the Dark Energy Survey Year 3 analysis of galaxy clustering and galaxy–galaxy lensing, using two different lens samples: a sample of luminous red galaxies, redMaGiC, and a sample with a redshift-dependent magnitude limit, MagLim. We account for the effect of magnification on both the flux and size selection of galaxies, accounting for systematic effects using the Balrog image simulations. We estimate the impact of magnification on the galaxy clustering and galaxy–galaxy lensing cosmology analysis, finding it to be a significant systematic for the MagLim sample. We show cosmological constraints from the galaxy clustering autocorrelation and galaxy–galaxy lensing signal with different magnifications priors, finding broad consistency in cosmological parameters in ΛCDM and wCDM. However, when magnification bias amplitude is allowed to be free, we find the two-point correlation functions prefer a different amplitude to the fiducial input derived from the image simulations. We validate the magnification analysis by comparing the cross-clustering between lens bins with the prediction from the baseline analysis, which uses only the autocorrelation of the lens bins, indicating that systematics other than magnification may be the cause of the discrepancy. We show that adding the cross-clustering between lens redshift bins to the fit significantly improves the constraints on lens magnification parameters and allows uninformative priors to be used on magnification coefficients, without any loss of constraining power or prior volume concerns.

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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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The XMM cluster survey: exploring scaling relations and completeness of the dark energy survey year 3 redMaPPer cluster catalogue

ABSTRACT We cross-match and compare characteristics of galaxy clusters identified in observations from two sky surveys using two completely different techniques. One sample is optically selected from the analysis of 3 years of Dark Energy Survey observations using the redMaPPer cluster detection algorithm. The second is X-ray selected from XMM observations analysed by the XMM Cluster Survey. The samples comprise a total area of 57.4 deg2, bounded by the area of four contiguous XMM survey regions that overlap the DES footprint. We find that the X-ray-selected sample is fully matched with entries in the redMaPPer catalogue, above λ > 20 and within 0.1 <$z$ <0.9. Conversely, only 38 per cent of the redMaPPer catalogue is matched to an X-ray extended source. Next, using 120 optically clusters and 184 X-ray-selected clusters, we investigate the form of the X-ray luminosity–temperature (LX –TX ), luminosity–richness (LX –λ), and temperature–richness (TX –λ) scaling relations. We find that the fitted forms of the LX –TX relations are consistent between the two selection methods and also with other studies in the literature. However, we find tentative evidence for a steepening of the slope of the relation for low richness systems in the X-ray-selected sample. When considering the scaling of richness with X-ray properties, we again find consistency in the relations (i.e. LX –λ and TX –λ) between the optical and X-ray-selected samples. This is contrary to previous similar works that find a significant increase in the scatter of the luminosity scaling relation for X-ray-selected samples compared to optically selected samples.

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

ABSTRACT 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 Planck mission. We model this cross-correlation measurement together with the galaxy autocorrelation to constrain the distribution of gas in the Universe. We measure the hydrostatic mass bias or, equivalently, the mean halo bias-weighted electron pressure 〈bhPe 〉, using large-scale information. We find 〈bhPe 〉 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 ∼ [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 108.5 K but are incompatible with the model that assumes an AGN heating temperature of 108.0 K. These comparisons indicate that the data prefer a higher value of electron pressure than the simulations within r500c of the galaxies’ haloes.

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