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Galaxy Cluster Mass Reconstruction Project - II. Quantifying scatter and bias using contrasting mock catalogues

Our paper is the second in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilize the positions, velocities and colours of galaxies. Our aim is to quantify the scatter, systematic bias and completeness of cluster masses derived from a diverse set of 25 galaxy-based methods using two contrasting mock galaxy catalogues based on a sophisticated halo occupation model and a semi-analytic model. Analysing 968 clusters, we find a wide range in the rms errors in log M200c delivered by the different methods (0.18–1.08 dex, i.e. a factor of ~1.5–12), with abundance-matching and richness methods providing the best results, irrespective of the input model assumptions. In addition, certain methods produce a significant number of catastrophic cases where the mass is under- or overestimated by a factor greater than 10. Given the steeply falling high-mass end of the cluster mass function, we recommend that richness- or abundance-matching-based methods are used in conjunction with these methods as a sanity check for studies selecting high-mass clusters. We also see a stronger correlation of the recovered to input number of galaxies for both catalogues in comparison with the group/cluster mass, however, this does not guarantee that the correct member galaxies are being selected. Finally, we did not observe significantly higher scatter for either mock galaxy catalogues. These results have implications for cosmological analyses that utilize the masses, richnesses, or abundances of clusters, which have different uncertainties when different methods are used.

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Physical properties of star clusters in the outer LMC as observed by the DES

The Large Magellanic Cloud (LMC) harbors a rich and diverse system of star clusters, whose ages, chemical abundances, and positions provide information about the LMC history of star formation. We use Science Verification imaging data from the Dark Energy Survey to increase the census of known star clusters in the outer LMC and to derive physical parameters for a large sample of such objects using a spatially and photometrically homogeneous data set. Our sample contains 255 visually identified cluster candidates, of which 109 were not listed in any previous catalog. We quantify the crowding effect for the stellar sample produced by the DES Data Management pipeline and conclude that the stellar completeness is < 10% inside typical LMC cluster cores. We therefore develop a pipeline to sample and measure stellar magnitudes and positions around the cluster candidates using DAOPHOT. We also implement a maximum-likelihood method to fit individual density profiles and colour-magnitude diagrams. For 117 (from a total of 255) of the cluster candidates (28 uncatalogued clusters), we obtain reliable ages, metallicities, distance moduli and structural parameters, confirming their nature as physical systems. The distribution of cluster metallicities shows a radial dependence, with no clusters more metal-rich than [Fe/H] ~ -0.7 beyond 8 kpc from the LMC center. Furthermore, the age distribution has two peaks at ≃ 1.2 Gyr and ≃ 2.7 Gyr.

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redMaGiC: Selecting luminous red galaxies from the DES Science Verification data

Here, we introduce redMaGiC, an automated algorithm for selecting luminous red galaxies (LRGs). The algorithm was specifically developed to minimize photometric redshift uncertainties in photometric large-scale structure studies. redMaGiC achieves this by self-training the colour cuts necessary to produce a luminosity-thresholded LRG sample of constant comoving density. We demonstrate that redMaGiC photo-zs are very nearly as accurate as the best machine learning-based methods, yet they require minimal spectroscopic training, do not suffer from extrapolation biases, and are very nearly Gaussian. We apply our algorithm to Dark Energy Survey (DES) Science Verification (SV) data to produce a redMaGiC catalogue sampling the redshift range z ϵ [0.2, 0.8]. Our fiducial sample has a comoving space density of 10 –3 (h –1 Mpc) –3 , and a median photo-z bias (zspec – zphoto) and scatter (σz/(1 + z)) of 0.005 and 0.017, respectively. The corresponding 5σ outlier fraction is 1.4 per cent. We also test our algorithm with Sloan Digital Sky Survey Data Release 8 and Stripe 82 data, and discuss how spectroscopic training can be used to control photo-z biases at the 0.1 per cent level.

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Unbiased contaminant removal for 3D galaxy power spectrum measurements

In this work, we assess and develop techniques to remove contaminants when calculating the 3D galaxy power spectrum. We separate the process into three separate stages: (i) removing the contaminant signal, (ii) estimating the uncontaminated cosmological power spectrum and (iii) debiasing the resulting estimates. For (i), we show that removing the best-fitting contaminant (mode subtraction) and setting the contaminated components of the covariance to be infinite (mode deprojection) are mathematically equivalent. For (ii), performing a quadratic maximum likelihood (QML) estimate after mode deprojection gives an optimal unbiased solution, although it requires the manipulation of large $N^2_{\text{mode}}$ matrices ($N_{\text{mode}}$ being the total number of modes), which is unfeasible for recent 3D galaxy surveys. Measuring a binned average of the modes for (ii) as proposed by Feldman, Kaiser & Peacock (FKP) is faster and simpler, but is sub-optimal and gives rise to a biased solution. We present a method to debias the resulting FKP measurements that does not require any large matrix calculations. We argue that the sub-optimality of the FKP estimator compared with the QML estimator, caused by contaminants, is less severe than that commonly ignored due to the survey window.

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The weirdest SDSS galaxies: results from an outlier detection algorithm

How can we discover objects we did not know existed within the large data sets that now abound in astronomy? In this paper, we present an outlier detection algorithm that we developed, based on an unsupervised Random Forest. We test the algorithm on more than two million galaxy spectra from the Sloan Digital Sky Survey and examine the 400 galaxies with the highest outlier score. We find objects which have extreme emission line ratios and abnormally strong absorption lines, objects with unusual continua, including extremely reddened galaxies. We find galaxy–galaxy gravitational lenses, double-peaked emission line galaxies and close galaxy pairs. We find galaxies with high ionization lines, galaxies that host supernovae and galaxies with unusual gas kinematics. Only a fraction of the outliers we find were reported by previous studies that used specific and tailored algorithms to find a single class of unusual objects. Our algorithm is general and detects all of these classes, and many more, regardless of what makes them peculiar. Lastly, it can be executed on imaging, time series and other spectroscopic data, operates well with thousands of features, is not sensitive to missing values and is easily parallelizable.

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Constraining the dark energy equation of state using Bayes theorem and the Kullback–Leibler divergence

Data-driven model-independent reconstructions of the dark energy equation of state w(z) are presented using Planck 2015 era CMB, BAO, SNIa and Lyman-α data. These reconstructions identify the w(z) behaviour supported by the data and show a bifurcation of the equation of state posterior in the range 1.5 < z < 3. Although the concordance ΛCDM model is consistent with the data at all redshifts in one of the bifurcated spaces, in the other a supernegative equation of state (also known as ‘phantom dark energy’) is identified within the 1.5σ confidence intervals of the posterior distribution. In order to identify the power of different datasets in constraining the dark energy equation of state, we use a novel formulation of the Kullback–Leibler divergence. Moreover, this formalism quantifies the information the data add when moving from priors to posteriors for each possible dataset combination. The SNIa and BAO datasets are shown to provide much more constraining power in comparison to the Lyman-α datasets. Furthermore, SNIa and BAO constrain most strongly around redshift range 0.1 - 0.5, whilst the Lyman-α data constrains weakly over a broader range. We do not attribute the supernegative favouring to any particular dataset, and note that the ΛCDM model was favoured at more than 2 log-units in Bayes factors over all the models tested despite the weakly preferred w(z) structure in the data.

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Galaxy clustering with photometric surveys using PDF redshift information

Here, photometric surveys produce large-area maps of the galaxy distribution, but with less accurate redshift information than is obtained from spectroscopic methods. Modern photometric redshift (photo-z) algorithms use galaxy magnitudes, or colors, that are obtained through multi-band imaging to produce a probability density function (PDF) for each galaxy in the map. We used simulated data to study the effect of using different photo-z estimators to assign galaxies to redshift bins in order to compare their effects on angular clustering and galaxy bias measurements. We found that if we use the entire PDF, rather than a single-point (mean or mode) estimate, the deviations are less biased, especially when using narrow redshift bins. When the redshift bin widths are $\Delta z=0.1$, the use of the entire PDF reduces the typical measurement bias from 5%, when using single point estimates, to 3%.

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Redshift remapping and cosmic acceleration in dark-matter-dominated cosmological models

The standard relation between the cosmological redshift and cosmic scale factor underlies cosmological inference from virtually all kinds of cosmological observations, leading to the emergence of the LambdaCDM cosmological model. This relation is not a fundamental theory and thus observational determination of this function (redshift remapping) should be regarded as an insightful alternative to holding its standard form in analyses of cosmological data. We present non-parametric reconstructions of redshift remapping in dark-matter-dominated models and constraints on cosmological parameters from a joint analysis of all primary cosmological probes including the local measurement of the Hubble constant, Type Ia supernovae, baryonic acoustic oscillations (BAO), Planck observations of the cosmic microwave background (CMB) radiation (temperature power spectrum) and cosmic chronometers. The reconstructed redshift remapping points to an additional boost of redshift operating in late epoch of cosmic evolution, but affecting both low-redshift observations and the CMB. The model then predicts a significant difference between the actual Hubble constant, h=0.48±0.02, and its local determination, h obs =0.73±0.02. The ratio of these two values coincides closely with the maximum expansion rate inside voids formed in the corresponding open cosmological model with Ω m =0.87±0.03, whereas the actual value of the Hubble constant implies the age of the Universe that is compatible with the Planck LambdaCDM cosmology. The new dark-matter-dominated model with redshift remapping provides excellent fits to all data and eliminates recently reported tensions between the Planck LambdaCDM cosmology, the local determination of the Hubble constant and the BAO measurements from the Ly α forest of high-redshift quasars.

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CMU DeepLens: deep learning for automatic image-based galaxy–galaxy strong lens finding

Galaxy-scale strong gravitational lensing can not only provide a valuable probe of the dark matter distribution of massive galaxies, but also provide valuable cosmological constraints, either by studying the population of strong lenses or by measuring time delays in lensed quasars. Due to the rarity of galaxy-scale strongly lensed systems, fast and reliable automated lens finding methods will be essential in the era of large surveys such as Large Synoptic Survey Telescope, Euclid and Wide-Field Infrared Survey Telescope. To tackle this challenge, we introduce CMU DeepLens, a new fully automated galaxy-galaxy lens finding method based on deep learning. This supervised machine learning approach does not require any tuning after the training step which only requires realistic image simulations of strongly lensed systems. We train and validate our model on a set of 20 000 LSST-like mock observations including a range of lensed systems of various sizes and signal-to-noise ratios (S/N). We find on our simulated data set that for a rejection rate of non-lenses of 99 per cent, a completeness of 90 per cent can be achieved for lenses with Einstein radii larger than 1.4 arcsec and S/N larger than 20 on individual g-band LSST exposures. Finally, we emphasize the importance of realistically complex simulations for training such machine learning methods by demonstrating that the performance of models of significantly different complexities cannot be distinguished on simpler simulations. We make our code publicly available at https://github.com/McWilliamsCenter/CMUDeepLens.

gravitational lensing: strong↗

Models of the strongly lensed quasar DES J0408-5354

We present gravitational lens models of the multiply imaged quasar DES J0408-5354, recently discovered in the Dark Energy Survey (DES) footprint, with the aim of interpreting its remarkable quad-like configuration. We first model the DES single-epoch $grizY$ images as a superposition of a lens galaxy and four point-like objects, obtaining spectral energy distributions (SEDs) and relative positions for the objects. Three of the point sources (A,B,D) have SEDs compatible with the discovery quasar spectra, while the faintest point-like image (G2/C) shows significant reddening and a `grey' dimming of $\approx0.8$mag. In order to understand the lens configuration, we fit different models to the relative positions of A,B,D. Models with just a single deflector predict a fourth image at the location of G2/C but considerably brighter and bluer. The addition of a small satellite galaxy ($R_{\rm E}\approx0.2$") in the lens plane near the position of G2/C suppresses the flux of the fourth image and can explain both the reddening and grey dimming. All models predict a main deflector with Einstein radius between $1.7"$ and $2.0",$ velocity dispersion $267-280$km/s and enclosed mass $\approx 6\times10^{11}M_{\odot},$ even though higher resolution imaging data are needed to break residual degeneracies in model parameters. The longest time-delay (B-A) is estimated as $\approx 85$ (resp. $\approx125$) days by models with (resp. without) a perturber near G2/C. The configuration and predicted time-delays of J0408-5354 make it an excellent target for follow-up aimed at understanding the source quasar host galaxy and substructure in the lens, and measuring cosmological parameters. We also discuss some lessons learnt from J0408-5354 on lensed quasar finding strategies, due to its chromaticity and morphology.

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Brightest galaxies as halo centre tracers in SDSS DR7

Determining the positions of halo centres in large-scale structure surveys is crucial for many cosmological studies. A common assumption is that halo centres correspond to the location of their brightest member galaxies. In this paper, we study the dynamics of brightest galaxies with respect to other halo members in the Sloan Digital Sky Survey DR7. Specifically, we look at the line-of-sight velocity and spatial offsets between brightest galaxies and their neighbours. We compare those to detailed mock catalogues, constructed from high-resolution, dark-matter-only N-body simulations, in which it is assumed that satellite galaxies trace dark matter subhaloes. This allows us to place constraints on the fraction f(BNC) of haloes in which the brightest galaxy is not the central. Compared to previous studies, we explicitly take into account the unrelaxed state of the host haloes, velocity offsets of halo cores and correlations between f(BNC) and the satellite occupation. We find that f(BNC) strongly decreases with the luminosity of the brightest galaxy and increases with the mass of the host halo. Overall, in the halo mass range 10(13-)10(14.5) h(-1) M-circle dot we find f(BNC) similar to 30 per cent, in good agreement with a previous study by Skibba et al. We discuss the implications of these findings for studies inferring the galaxy-halo connection from satellite kinematics, models of the conditional luminosity function and galaxy formation in general

cosmology: dark matter↗

Optical–SZE scaling relations for DES optically selected clusters within the SPT-SZ Survey

We study the Sunyaev-Zel'dovich effect (SZE) signature in South Pole Telescope (SPT) data for an ensemble of 719 optically identified galaxy clusters selected from 124.6 deg$^2$ of the Dark Energy Survey (DES) science verification data, detecting a stacked SZE signal down to richness $\lambda\sim20$. The SZE signature is measured using matched-filtered maps of the 2500 deg$^2$ SPT-SZ survey at the positions of the DES clusters, and the degeneracy between SZE observable and matched-filter size is broken by adopting as priors SZE and optical mass-observable relations that are either calibrated using SPT selected clusters or through the Arnaud et al. (2010, A10) X-ray analysis. We measure the SPT signal to noise $\zeta$-$\lambda$, relation and two integrated Compton-$y$ $Y_\textrm{500}$-$\lambda$ relations for the DES-selected clusters and compare these to model expectations accounting for the SZE-optical center offset distribution. For clusters with $\lambda > 80$, the two SPT calibrated scaling relations are consistent with the measurements, while for the A10-calibrated relation the measured SZE signal is smaller by a factor of $0.61 \pm 0.12$ compared to the prediction. For clusters at $20 < \lambda < 80$, the measured SZE signal is smaller by a factor of $\sim$0.20-0.80 (between 2.3 and 10~$\sigma$ significance) compared to the prediction, with the SPT calibrated scaling relations and larger $\lambda$ clusters showing generally better agreement. We quantify the required corrections to achieve consistency, showing that there is a richness dependent bias that can be explained by some combination of contamination of the observables and biases in the estimated masses. We discuss possible physical effects, as contamination from line-of-sight projections or from point sources, larger offsets in the SZE-optical centering or larger scatter in the $\lambda$-mass relation at lower richnesses.

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DES meets Gaia: discovery of strongly lensed quasars from a multiplet search

We report the discovery, spectroscopic confirmation and first lens models of the first two, strongly lensed quasars from a combined search in WISE and Gaia over the DES footprint. Their Einstein radii span a range between ≈2.0 arcsec and ≈0.4 arcsec. Two of these (WGD2038-4008, RA = 20:38:02.65, Dec. = -40:08:14.64; WGD2021-4115, RA = 20:21:39.45, Dec. = -41:15:57.11) also have confirmed deflector redshifts. The four-image lens WGD2038-4008, with source and deflector redshifts s = 0.777 ± 0.001 and zl = 0.230 ± 0.002, respectively, has a deflector with radius R eff ≈ 3.4 arcsec, stellar mass $\log(M_{\star}/M_{\odot}) = 11.64^{+0.20}_{-0.43}$, and shows extended isophotal shape variation. Simple lens models yield Einstein radii $R_{\rm E}=(1.30\pm0.04)^{\prime\prime},$ axis ratio $q=0.75\pm0.1$ (compatible with that of the starlight) and considerable shear-ellipticity degeneracies. The two-image lens WGD2021-4115 (r.a.=20:21:39.45, dec.=--41:15:57.11) has $z_{s}=1.390\pm0.001$ and $z_l = 0.335 \pm 0.002$, and Einstein radius $R_{\rm E} = (1.1\pm0.1)^{\prime\prime},$ but higher-resolution imaging is needed to accurately separate the deflector and faint quasar image. Finally, we also show high-rank candidate doubles selected this way, some of which have been independently identified with different techniques, and discuss a DES+WISE quasar multiplet selection.

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Survey geometry and the internal consistency of recent cosmic shear measurements

We explore the impact of an update to the typical approximation for the shape noise term in the analytic covariance matrix for cosmic shear experiments that assumes the absence of survey boundary and mask effects. We present an exact expression for the number of galaxy pairs in this term based on the survey mask, which leads to more than a factor of three increase in the shape noise on the largest measured scales for the Kilo-Degree Survey (KiDS-450) real-space cosmic shear data. We compare the result of this analytic expression to several alternative methods for measuring the shape noise from the data and find excellent agreement. This update to the covariance resolves any internal model tension evidenced by the previously large cosmological best-fitting χ 2 for the KiDS-450 cosmic shear data. The best-fitting χ 2 is reduced from 161 to 121 for 118 degrees of freedom. We also apply a correction to how the multiplicative shear calibration uncertainty is included in the covariance. This change shifts the inferred amplitude of the correlation function to higher values. In conclusion, we find that this improves agreement of the KiDS-450 cosmic shear results with Dark Energy Survey Year 1 and Planck results.

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Galaxy Cluster Mass Reconstruction Project – IV. Understanding the effects of imperfect membership on cluster mass estimation

Here, the primary difficulty in measuring dynamical masses of galaxy clusters from galaxy data lies in the separation between true cluster members from interloping galaxies along the line of sight. We study the impact of membership contamination and incompleteness on cluster mass estimates obtained with 25 commonly used techniques applied to nearly 1000 mock clusters with precise spectroscopic redshifts. We show that all methods overestimate or underestimate cluster masses when applied to contaminated or incomplete galaxy samples, respectively. This appears to be the main source of the intrinsic scatter in the mass scaling relation. Applying corrections based on a prior knowledge of contamination and incompleteness can reduce the scatter to the level of shot noise expected for poorly sampled clusters. We establish an empirical model quantifying the effect of imperfect membership on cluster mass estimation and discuss its universal and method-dependent features. We find that both imperfect membership and the response of the mass estimators depend on cluster mass, effectively causing a flattening of the estimated–true mass relation. Imperfect membership thus alters cluster counts determined from spectroscopic surveys, hence the cosmological parameters that depend on such counts.

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Large covariance matrices: accurate models without mocks

Abstract Covariance matrix estimation is a persistent challenge for cosmology. We focus on a class of model covariance matrices that can be generated with high accuracy and precision, using a tiny fraction of the computational resources that would be required to achieve comparably precise covariance matrices using mock catalogues. In previous work, the free parameters in these models were determined using sample covariance matrices computed using a large number of mocks, but we demonstrate that those parameters can be estimated consistently and with good precision by applying jackknife methods to a single survey volume. This enables model covariance matrices that are calibrated from data alone, with no reference to mocks.

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