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At least 613 records · Page 34

Cosmological parameter forecasts for a CMB-HD survey

We present forecasts on cosmological parameters for a CMB-HD survey. For a $\Lambda$CDM + $N_{eff}$ + $\sum m_\nu$ model, we find $\sigma(n_s) = 0.0013$ and $\sigma(N_{eff}) = 0.014$ using CMB and CMB lensing multipoles in the range of $\ell \in [30, 20000]$, after adding anticipated residual foregrounds, delensing the acoustic peaks, and adding DESI BAO data. This is about a factor of two improvement in ability to probe inflation via $n_s$ compared to precursor CMB surveys. The $N_{eff}$ constraint can rule out light thermal particles back to the end of inflation with 95% CL; for example, it can rule out the QCD axion in a model-independent way assuming the Universe's reheating temperature was high enough that the axion thermalized. We find that delensing the acoustic peaks and adding DESI BAO tightens parameter constraints. We also find that baryonic effects can bias parameters if not marginalized over, and that uncertainties in baryonic effects can increase parameter error bars; however, the latter can be mitigated by including information about baryonic effects from kinetic and thermal Sunyaev-Zel'dovich measurements by CMB-HD. The CMB-HD likelihood and Fisher estimation codes used here are publicly available; the likelihood is integrated with Cobaya to facilitate parameter forecasting.

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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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Cosmological constraints from the tomographic cross-correlation of DESI Luminous Red Galaxies and Planck CMB lensing

We use luminous red galaxies selected from the imaging surveys that are being used for targeting by the Dark Energy Spectroscopic Instrument (DESI) in combination with CMB lensing maps from the Planck collaboration to probe the amplitude of large-scale structure over 0.4 ≤ z ≤ 1. Our galaxy sample, with an angular number density of approximately 500 deg -2 over 18,000 sq.deg., is divided into 4 tomographic bins by photometric redshift and the redshift distributions are calibrated using spectroscopy from DESI. We fit the galaxy autospectra and galaxy-convergence cross-spectra using models based on cosmological perturbation theory, restricting to large scales that are expected to be well described by such models. Within the context of ΛCDM, combining all 4 samples and using priors on the background cosmology from supernova and baryon acoustic oscillation measurements, we find S 8 = σ 8 (Ωm/0.3) 0.5 = 0.73 ± 0.03. This result is lower than the prediction of the ΛCDM model conditioned on the Planck data. Furthermore, our data prefer a slower growth of structure at low redshift than the model predictions, though at only modest significance.

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The STRong lensing Insights into the Dark Energy Survey (STRIDES) 2017/2018 follow-up campaign: discovery of 10 lensed quasars and 10 quasar pairs

Here, we report the results of the STRong lensing Insights into the Dark Energy Survey (STRIDES) follow-up campaign of the late 2017/early 2018 season. We obtained spectra of 65 lensed quasar candidates with ESO Faint Object Spectrograph and Camera 2 on the NTT and Echellette Spectrograph and Imager on Keck, confirming 10 new lensed quasars and 10 quasar pairs. Eight lensed quasars are doubly imaged with source redshifts between 0.99 and 2.90, one is triply imaged (DESJ0345-2545, z = 1.68), and one is quadruply imaged (quad: DESJ0053-2012, z = 3.8). Singular isothermal ellipsoid models for the doubles, based on high-resolution imaging from SAMI on Southern Astrophysical Research Telescope or Near InfraRed Camera 2 on Keck, give total magnifications between 3.2 and 5.6, and Einstein radii between 0.49 and 1.97 arcsec. After spectroscopic follow-up, we extract multi-epoch grizY photometry of confirmed lensed quasars and contaminant quasar + star pairs from DES data using parametric multiband modelling, and compare variability in each system’s components. By measuring the reduced χ 2 associated with fitting all epochs to the same magnitude, we find a simple cut on the less variable component that retains all confirmed lensed quasars, while removing 94 per cent of contaminant systems. Based on our spectroscopic follow-up, this variability information improves selection of lensed quasars and quasar pairs from 34-45 per cent to 51–70 per cent, with most remaining contaminants being star-forming galaxies. Using mock lensed quasar light curves we demonstrate that selection based only on variability will over-represent the quad fraction by 10 per cent over a complete DES magnitude-limited sample, explained by the magnification bias and hence lower luminosity/more variable sources in quads.

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An empirical approach to model selection: weak lensing and intrinsic alignments

ABSTRACT In cosmology, we routinely choose between models to describe our data, and can incur biases due to insufficient models or lose constraining power with overly complex models. In this paper, we propose an empirical approach to model selection that explicitly balances parameter bias against model complexity. Our method uses synthetic data to calibrate the relation between bias and the χ2 difference between models. This allows us to interpret χ2 values obtained from real data (even if catalogues are blinded) and choose a model accordingly. We apply our method to the problem of intrinsic alignments – one of the most significant weak lensing systematics, and a major contributor to the error budget in modern lensing surveys. Specifically, we consider the example of the Dark Energy Survey Year 3 (DES Y3), and compare the commonly used non-linear alignment (NLA) and tidal alignment and tidal torque (TATT) models. The models are calibrated against bias in the Ωm–S8 plane. Once noise is accounted for, we find that it is possible to set a threshold Δχ2 that guarantees an analysis using NLA is unbiased at some specified level Nσ and confidence level. By contrast, we find that theoretically defined thresholds (based on, e.g. p-values for χ2) tend to be overly optimistic, and do not reliably rule out cosmological biases up to ∼1–2σ. Considering the real DES Y3 cosmic shear results, based on the reported difference in χ2 from NLA and TATT analyses, we find a roughly $30{{\ \rm per\ cent}}$ chance that were NLA to be the fiducial model, the results would be biased (in the Ωm–S8 plane) by more than 0.3σ. More broadly, the method we propose here is simple and general, and requires a relatively low level of resources. We foresee applications to future analyses as a model selection tool in many contexts.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Advances in constraining intrinsic alignment models with hydrodynamic simulations

We use galaxies from the illustristng, massiveblack-ii, and illustris-1 hydrodynamic simulations to investigate the behaviour of large scale galaxy intrinsic alignments. Our analysis spans four redshift slices over the approximate range of contemporary lensing surveys z = 0–1. We construct comparable weighted samples from the three simulations, which we then analyse using an alignment model that includes both linear and quadratic alignment contributions. Our data vector includes galaxy–galaxy, galaxy–shape, and shape–shape projected correlations, with the joint covariance matrix estimated analytically. In all of the simulations, we report non-zero IAs at the level of several σ. For a fixed lower mass threshold, we find a relatively strong redshift dependence in all three simulations, with the linear IA amplitude increasing by a factor of ~2 between redshifts z = 0 and z = 1. We report no significant evidence for non-zero values of the tidal torquing amplitude, A 2 , in TNG, above statistical uncertainties, although MBII favours a moderately negative A 2 ~ –2. Examining the properties of the TATT model as a function of colour, luminosity and galaxy type (satellite or central), our findings are consistent with the most recent measurements on real data. We also outline a novel method for constraining the TATT model parameters directly from the pixelized tidal field, alongside a proof-of-concept exercise using TNG. This technique is shown to be promising, although comparison with previous results obtained via other methods is non-trivial.

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

ABSTRACT 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 (∼5000 deg2), expanding on previous measurements that used Y1 catalogues (∼1300 deg2). Given the increased statistical power compared to Y1 data, we report a 6.6σ detection of negative CMB convergence (κ) imprints using approximately 3600 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 ΛCDM model (parameters Ωm = 0.25, σ8 = 0.8), and the discrepancy is associated mostly with the void centre region. Considering the full void lensing profile, we fit an amplitude $A_{\kappa }=\kappa _{{\rm DES}}/\kappa _{{\rm MICE}}$ to a simulation-based template with fixed shape and found a moderate 2σ deviation in the signal with Aκ ≈ 0.79 ± 0.12. We also examined the WebSky simulation that is based on a Planck 2018 ΛCDM 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 Aκ = 0.84 ± 0.10 amplitude. The combination of voids and superclusters yields a 10.3σ detection with an Aκ = 0.82 ± 0.08 constraint on the CMB lensing amplitude, thus the overall signal is 2.3σ weaker than expected from MICE.

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Optimizing LSST observing strategy for weak lensing systematics

ABSTRACT The Legacy Survey of Space and Time (LSST) survey will provide unprecedented statistical power for measurements of dark energy. Consequently, controlling systematic uncertainties is becoming more important than ever. The LSST observing strategy will affect the statistical uncertainty and systematics control for many science cases; here, we focus on weak lensing (WL) systematics. The fact that the LSST observing strategy involves hundreds of visits to the same sky area provides new opportunities for systematics mitigation. We explore these opportunities by testing how different dithering strategies (pointing offsets and rotational angle of the camera in different exposures) affect additive WL shear systematics on a baseline operational simulation, using the ρ-statistics formalism. Some dithering strategies improve systematics control at the end of the survey by a factor of up to ∼3–4 better than others. We find that a random translational dithering strategy, applied with random rotational dithering at every filter change, is the most effective of those strategies tested in this work at averaging down systematics. Adopting this dithering algorithm, we explore the effect of varying the area of the survey footprint, exposure time, number of exposures in a visit, and exposure to the Galactic plane. We find that any change that increases the average number of exposures (in filters relevant to WL) reduces the additive shear systematics. Some ways to achieve this increase may not be favorable for the WL statistical constraining power or for other probes, and we explore the relative trade-offs between these options given constraints on the overall survey parameters.

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Combining cosmic shear data with correlated photo-z uncertainties: constraints from DESY1 and HSC-DR1

An accurate calibration of the source redshift distribution p(z) is a key aspect in the analysis of cosmic shear data. This, one way or another, requires the use of spectroscopic or high-quality photometric samples. However, the difficulty to obtain colour-complete spectroscopic samples matching the depth of weak lensing catalogs means that the analyses of different cosmic shear datasets often use the same samples for redshift calibration. This introduces a source of statistical and systematic uncertainty that is highly correlated across different weak lensing datasets, and which must be accurately characterised and propagated in order to obtain robust cosmological constraints from their combination. In this paper we introduce a method to quantify and propagate the uncertainties on the source redshift distribution in two different surveys sharing the same calibrating sample. The method is based on an approximate analytical marginalisation of the p(z) statistical uncertainties and the correlated marginalisation of residual systematics. We apply this method to the combined analysis of cosmic shear data from the DESY1 data release and the HSC-DR1 data, using the COSMOS 30-band catalog as a common redshift calibration sample. We find that, although there is significant correlation in the uncertainties on the redshift distributions of both samples, this does not change the final constraints on cosmological parameters significantly. The same is true also for the impact of residual systematic uncertainties from the errors in the COSMOS 30-band photometric redshifts. Additionally, we show that these effects will still be negligible in Stage-IV datasets. Finally, the combination of DESY1 and HSC-DR1 allows us to constrain the "clumpiness" parameter to S 8 = ${0.768}_{-0.017}^{+0.021}$. This corresponds to a ~√(2) improvement in uncertainties with respect to either DES or HSC alone.

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Revisiting MOA 2013-BLG-220L: A Solar-type Star with a Cold Super-Jupiter Companion

We present the analysis of high-resolution images of MOA-2013-BLG-220, taken with the Keck adaptive optics system six years after the initial observation, identifying the lens as a solar-type star hosting a super-Jupiter-mass planet. The masses of planets and host stars discovered by microlensing are often not determined from light-curve data, while the star–planet mass ratio and projected separation in units of Einstein ring radius are well measured. High-resolution follow-up observations after the lensing event is complete can resolve the source and lens. This allows direct measurements of flux, and the amplitude and direction of proper motion, giving strong constraints on the system parameters. Due to the high relative proper motion, μ{sub rel,Geo}=12.62±0.11 mas yr{sup −1}, the source and lens were resolved in 2019, with a separation of 77.1 ± 0.5 mas. Thus, we constrain the lens flux to K{sub Keck,lens}=17.92±0.02. By combining constraints from the model and Keck flux, we find the lens mass to be M{sub L}=0.88±0.05 M{sub ⊙} at D{sub L}=6.72±0.59 kpc. With a mass ratio of q=(3.00±0.03)×10{sup −3} the planet’s mass is determined to be M{sub P}=2.74±0.17 M{sub J} at a separation of r{sub ⊥}=3.03±0.27 au. The lens mass is much higher than the prediction made by Bayesian analysis that assumes all stars have an equal probability to host a planet of the measured mass ratio, and suggests that planets with mass ratios of a few times 10{sup −3} are more common orbiting massive stars. This demonstrates the importance of high-resolution follow-up observations for testing theories like these.

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Transitioning from Stage-III to Stage-IV: cosmology from galaxy×CMB lensing and shear×CMB lensing

ABSTRACT We examine the cosmological constraining power from two cross-correlation probes between galaxy and cosmic microwave background (CMB) surveys: the cross-correlation of lens galaxy density with CMB lensing convergence 〈δgκCMB〉, and source galaxy weak lensing shear with CMB lensing convergence 〈γκCMB〉. These two cross-correlation probes provide an independent cross-check of other large-scale structure constraints and are insensitive to galaxy-only or CMB-only systematic effects. In addition, when combined with other large-scale structure probes, the cross-correlations can break degeneracies in cosmological and nuisance parameters, improving both the precision and robustness of the analysis. In this work, we study how the constraining power of 〈δgκCMB〉 + 〈γκCMB〉 changes from Stage-III (ongoing) to Stage-IV (future) surveys. Given the flexibility in selecting the lens galaxy sample, we also explore systematically the impact on cosmological constraints when we vary the redshift range and magnitude limit of the lens galaxies using mock galaxy catalogs. We find that in our setup, the contribution to cosmological constraints from 〈δgκCMB〉 and 〈γκCMB〉 are comparable in the Stage-III data sets; but in Stage-IV surveys, the noise in 〈δgκCMB〉 becomes subdominant to cosmic variance, preventing 〈δgκCMB〉 to further improve the constraints. This implies that to maximize the cosmological constraints from future 〈δgκCMB〉 + 〈γκCMB〉 analyses, we should focus more on the requirements on 〈γκCMB〉 instead of 〈δgκCMB〉. Furthermore, the selection of the lens sample should be optimized in terms of our ability to characterize its redshift or galaxy bias instead of its number density.

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First measurement of the characteristic depletion radius of dark matter haloes from weak lensing

ABSTRACT We use weak lensing observations to make the first measurement of the characteristic depletion radius, one of the three radii that characterize the region where matter is being depleted by growing haloes. The lenses are taken from the halo catalogue produced by the extended halo-based group/cluster finder applied to DESI Legacy Imaging Surveys DR9, while the sources are extracted from the DECaLS DR8 imaging data with the fourier_quad pipeline. We study halo masses $12 \lt \log (M_{\rm grp} \,[{\rm M_{\odot }}\, h^{-1}]) \le 15.3$ within redshifts 0.2 ≤ z ≤ 0.3. The virial and splashback radii are also measured and used to test the original findings on the depletion region. When binning haloes by mass, we find consistency between most of our measurements and predictions from the cosmicgrowth simulation, with exceptions to the lowest mass bins. The characteristic depletion radius is found to be roughly 2.5 times the virial radius and 1.7–3 times the splashback radius, in line with an approximately universal outer density profile, and the average enclosed density within the characteristic depletion radius is found to be roughly 29 times the mean matter density of the Universe in our sample. When binning haloes by both mass and a proxy for halo concentration, we do not detect a significant variation of the depletion radius with concentration, on which the simulation prediction is also sensitive to the choice of concentration proxy. We also confirm that the measured splashback radius varies with concentration differently from simulation predictions.

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The catalog-to-cosmology framework for weak lensing and galaxy clustering for LSST

We present TXPipe, a modular, automated and reproducible pipeline for ingesting catalog data and performing all the calculations required to obtain quality-assured two-point measurements of lensing and clustering, and their covariances, with the metadata necessary for parameter estimation. The pipeline is developed within the Rubin Observatory Legacy Survey of Space and Time (LSST) Dark Energy Science Collaboration (DESC), and designed for cosmology analyses using LSST data. In this paper, we present the pipeline for the so-called 3x2pt analysis -- a combination of three two-point functions that measure the auto- and cross-correlation between galaxy density and shapes. We perform the analysis both in real and harmonic space using TXPipe and other LSST-DESC tools. We validate the pipeline using Gaussian simulations and show that it accurately measures data vectors and recovers the input cosmology to the accuracy level required for the first year of LSST data under this simplified scenario. We also apply the pipeline to a realistic mock galaxy sample extracted from the CosmoDC2 simulation suite (Korytov et al. 2019). TXPipe establishes a baseline framework that can be built upon as the LSST survey proceeds. Furthermore, the pipeline is designed to be easily extended to science probes beyond the 3x2pt analysis.

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A Comparison of Rest-frame Ultraviolet and Optical Emission-Line Diagnostics in the Lensed Galaxy SDSS J1723+3411 at Redshift z = 1.3293

For the extremely bright lensed galaxy SDSS J1723+3411 at z = 1.3293, we analyze spatially integrated MMT, Keck, and Hubble Space Telescope spectra that fully cover the rest-frame wavelength range of 1400 ̊A to 7200 ̊A. We also analyze near-IR spectra from Gemini that cover Hαfor a portion of the lensed arc. We report fluxes for 42 detected emission lines, and upper limits for an additional22. This galaxy has extreme emission line ratios and high equivalent widths that are characteristic of extreme emission-line galaxies. We compute strong emission line diagnostics from both the rest-frame optical and rest-frame ultraviolet (UV), to constrain physical conditions and test the spectral diagnostics themselves. We tightly determine the nebular physical conditions using the most reliable diagnostics, and then compare to results from other diagnostics. We find disappointing performance from the UV–only diagnostics: they either are unable to measure the metallicity or dramatically under-estimate it; they over-estimate the pressure; and the UV diagnostic of ionization parameter has a strong metallicity dependence in this regime. Based on these results, we suggest that upcoming James Webb Space Telescope(JWST) spectroscopic surveys of galaxies in the reionization epoch should invest the additional integration time to capture the optical [O II] and [O III] emission lines, and not rely solely on the rest-frame UV emission lines. We make available the spectra; they represent one of the highest-quality emission line spectral atlases of star-forming galaxy available beyond the local universe, and will aid planning observations with JWST.

galaxies↗

Non-Gaussianity in the weak lensing correlation function likelihood – implications for cosmological parameter biases

ABSTRACT We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in 1D marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in 1D posteriors of Ωm and σ8 due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data (100 deg2). We also present a systematic approach to constructing approximate multivariate likelihoods with 1D parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the 1D marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions. Modelling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of ∼5.

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Cosmological constraints from the cross-correlation of DESI Luminous Red Galaxies with CMB lensing from Planck PR4 and ACT DR6

Here, we infer the growth of large scale structure over the redshift range 0.4 ≲ z ≲ 1 from the cross-correlation of spectroscopically calibrated Luminous Red Galaxies (LRGs) selected from the Dark Energy Spectroscopic Instrument (DESI) legacy imaging survey with CMB lensing maps reconstructed from the latest Planck and ACT data. We adopt a hybrid effective field theory (HEFT) model that robustly regulates the cosmological information obtainable from smaller scales, such that our cosmological constraints are reliably derived from the (predominantly) linear regime. We perform an extensive set of bandpower- and parameter-level systematics checks to ensure the robustness of our results and to characterize the uniformity of the LRG sample. We demonstrate that our results are stable to a wide range of modeling assumptions, finding excellent agreement with a linear theory analysis performed on a restricted range of scales. From a tomographic analysis of the four LRG photometric redshift bins we find that the rate of structure growth is consistent with ΛCDM with an overall amplitude that is ≃ 5-7% lower than predicted by primary CMB measurements with modest (∼ 2σ) statistical significance. From the combined analysis of all four bins and their cross-correlations with Planck we obtain S 8 = 0.765 ± 0.023, which is less discrepant with primary CMB measurements than previous DESI LRG cross Planck CMB lensing results. From the cross-correlation with ACT we obtain S 8 = 0.790 +0.024 -0.027 , while when jointly analyzing Planck and ACT we find S 8 = 0.775 +0.019 -0.022 from our data alone and σ 8 = 0.772 +0.020 -0.023 with the addition of BAO data. These constraints are consistent with the latest Planck primary CMB analyses at the ≃ 1.6-2.2σ level, and are in excellent agreement with galaxy lensing surveys.

cosmological parameters from LSS↗

Dark Energy Survey year 3 results: point spread function modelling

ABSTRACT We introduce a new software package for modelling 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 modelling 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 modelling 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 modelling errors in future analyses.

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Mass calibration of distant SPT galaxy clusters through expanded weak-lensing follow-up observations with HST, VLT, & Gemini-South

Expanding from previous work, we present weak-lensing (WL) measurements for a total sample of 30 distant (z median = 0.93) massive galaxy clusters from the South Pole Telescope Sunyaev–Zel’dovich (SPT-SZ) Survey, measuring galaxy shapes in Hubble Space Telescope (HST) Advanced Camera for Surveys images. We remove cluster members and preferentially select z ≳ 1.4 background galaxies via V - I colour, employing deep photometry from VLT/FORS2 and Gemini-South/GMOS. We apply revised calibrations for the WL shape measurements and the source redshift distribution to estimate the cluster masses. In combination with earlier Magellan/Megacam results for lower-redshifts clusters, we infer refined constraints on the scaling relation between the SZ detection significance and the cluster mass, in particular regarding its redshift evolution. The mass scale inferred from the WL data is lower by a factor $0.76^{+0.10}_{-0.14}$ (at our pivot redshift z = 0.6) compared to what would be needed to reconcile a flat Planck νΛCDM cosmology (in which the sum of the neutrino masses is a free parameter) with the observed SPT-SZ cluster counts. In order to sensitively test the level of (dis-)agreement between SPT clusters and Planck, further expanded WL follow-up samples are needed.

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