KiDS+VIKING-450: Cosmic shear tomography with optical+infrared data

We present a tomographic cosmic shear analysis of the Kilo-Degree Survey (KiDS) combined with the VISTA Kilo-Degree Infrared Galaxy Survey. This is the first time that a full optical to near-infrared data set has been used for a wide-field cosmological weak lensing experiment. This unprecedented data, spanning 450 deg2, allows us to significantly improve the estimation of photometric redshifts, such that we are able to include robustly higher-redshift sources for the lensing measurement, and – most importantly – to solidify our knowledge of the redshift distributions of the sources. Based on a flat ΛCDM model we find S8 ≡ σ8 Ωm/0.3 = 0.737+0.040−0.036 in a blind analysis from cosmic shear alone. The tension between KiDS cosmic shear and the Planck-Legacy CMB measurements remains in this systematically more robust analysis, with S8 differing by 2.3σ. This result is insensitive to changes in the priors on nuisance parameters for intrinsic alignment, baryon feedback, and neutrino mass. KiDS shear measurements are calibrated with a new, more realistic set of image simulations and no significant B-modes are detected in the survey, indicating that systematic errors are under control. When calibrating our redshift distributions by assuming the 30-band COSMOS-2015 photometric redshifts are correct (following the Dark Energy Survey and the Hyper Suprime-Cam Survey), we find the tension with Planck is alleviated. The robust determination of source redshift distributions remains one of the most challenging aspects for future cosmic shear surveys

Photometric Redshift Calibration with Self Organising Maps

Accurate photometric redshift calibration is central to the robustness of all cosmology constraints from cosmic shear surveys. Analyses of the KiDS re-weighted training samples from all overlapping spectroscopic surveys to provide a direct redshift calibration. Using self-organising maps (SOMs) we demonstrate that this spectroscopic compilation is sufficiently complete for KiDS, representing $99\%$ of the effective 2D cosmic shear sample. We use the SOM to define a $100\%$ represented `gold' cosmic shear sample, per tomographic bin. Using mock simulations of KiDS and the spectroscopic training set, we estimate the uncertainty on the SOM redshift calibration, and find that photometric noise, sample variance, and spectroscopic selection effects (including redshift and magnitude incompleteness) induce a combined maximal scatter on the bias of the redshift distribution reconstruction ($\Delta \langle z \rangle=\langle z \rangle_{\rm est}-\langle z \rangle_{\rm true}$) of $\sigma_{\Delta \langle z \rangle} \leq 0.006$ in all tomographic bins. We show that the SOM calibration is unbiased in the cases of noiseless photometry and perfectly representative spectroscopic datasets, as expected from theory. The inclusion of both photometric noise and spectroscopic selection effects in our mock data introduces a maximal bias of $\Delta \langle z \rangle =0.013\pm0.006$, or $\Delta \langle z \rangle \leq 0.025$ at $97.5\%$ confidence, once quality flags have been applied to the SOM. The method presented here represents a significant improvement over the previously adopted direct redshift calibration implementation for KiDS, owing to its diagnostic and quality assurance capabilities. The implementation of this method in future cosmic shear studies will allow better diagnosis, examination, and mitigation of systematic biases in photometric redshift calibration.Comment: 22 pages, 10 figures, 4 appendices, accepted for publication in A&

KiDS-1000 catalogue: Redshift distributions and their calibration

We present redshift distribution estimates of galaxies selected from the fourth data release of the Kilo-Degree Survey over an area of ∼1000 deg2 (KiDS-1000). These redshift distributions represent one of the crucial ingredients for weak gravitational lensing measurements with the KiDS-1000 data. The primary estimate is based on deep spectroscopic reference catalogues that are re-weighted with the help of a self-organising map (SOM) to closely resemble the KiDS-1000 sources, split into five tomographic redshift bins in the photometric redshift range 0.1 < zB ≤ 1.2. Sources are selected such that they only occupy that volume of nine-dimensional magnitude-space that is also covered by the reference samples (‘gold’ selection). Residual biases in the mean redshifts determined from this calibration are estimated from mock catalogues to be ≲0.01 for all five bins with uncertainties of ∼0.01. This primary SOM estimate of the KiDS-1000 redshift distributions is complemented with an independent clustering redshift approach. After validation of the clustering-z on the same mock catalogues and a careful assessment of systematic errors, we find no significant bias of the SOM redshift distributions with respect to the clustering-z measurements. The SOM redshift distributions re-calibrated by the clustering-z represent an alternative calibration of the redshift distributions with only slightly larger uncertainties in the mean redshifts of ∼0.01 − 0.02 to be used in KiDS-1000 cosmological weak lensing analyses. As this includes the SOM uncertainty, clustering-z are shown to be fully competitive on KiDS-1000 data

KiDS+VIKING-450:Improved cosmological parameter constraints from redshift calibration with self-organising maps

We present updated cosmological constraints for the KiDS+VIKING-450 cosmic shear data set (KV450), estimated using redshift distributions and photometric samples defined using self-organising maps (SOMs). Our fiducial analysis finds marginal posterior constraints of $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}=0.716^{+0.043}_{-0.038}$; smaller than, but otherwise consistent with, previous work using this data set ($|\Delta S_8| = 0.023$). We analyse additional samples and redshift distributions constructed in three ways: excluding certain spectroscopic surveys during redshift calibration, excluding lower-confidence spectroscopic redshifts in redshift calibration, and considering only photometric sources which are jointly calibrated by at least three spectroscopic surveys. In all cases, the method utilised here proves robust: we find a maximal deviation from our fiducial analysis of $|\Delta S_8| \leq 0.011$ for all samples defined and analysed using our SOM. To demonstrate the reduction in systematic biases found within our analysis, we highlight our results when performing redshift calibration without the DEEP2 spectroscopic data set. In this case we find marginal posterior constraints of $S_8=0.707_{-0.042}^{+0.046}$; a difference with respect to the fiducial that is both significantly smaller than, and in the opposite direction to, the equivalent shift from previous work. These results suggest that our improved cosmological parameter estimates are insensitive to pathological misrepresentation of photometric sources by the spectroscopy used for direct redshift calibration, and therefore that this systematic effect cannot be responsible for the observed difference between $S_8$ estimates made with KV450 and Planck CMB probes.Comment: 10 pages, 3 figures, 4 appendices, accepted for publication in A&A Letter

Testing KiDS cross-correlation redshifts with simulations

Measuring cosmic shear in wide-field imaging surveys requires accurate knowledge of the redshift distribution of all sources. The clustering-redshift technique exploits the angular cross-correlation of a target galaxy sample with unknown redshifts and a reference sample with known redshifts. It represents an attractive alternative to colour-based methods of redshift calibration. Here we test the performance of such clustering redshift measurements using mock catalogues that resemble the Kilo-Degree Survey (KiDS). These mocks are created from the MICE simulation and closely mimic the properties of the KiDS source sample and the overlapping spectroscopic reference samples. We quantify the performance of the clustering redshifts by comparing the cross-correlation results with the true redshift distributions in each of the five KiDS photometric redshift bins. Such a comparison to an informative model is necessary due to the incompleteness of the reference samples at high redshifts. Clustering mean redshifts are unbiased at |Δz|< 0.006 under these conditions. The redshift evolution of the galaxy bias of the reference and target samples represents one of the most important systematic errors when estimating clustering redshifts. It can be reliably mitigated at this level of precision using auto-correlation measurements and self-consistency relations, and will not become a dominant source of systematic error until the arrival of Stage-IV cosmic shear surveys. Using redshift distributions from a direct colour-based estimate instead of the true redshift distributions as a model for comparison with the clustering redshifts increases the biases in the mean to up to |Δz|∼0.04. This indicates that the interpretation of clustering redshifts in real-world applications will require more sophisticated (parameterised) models of the redshift distribution in the future. If such better models are available, the clustering-redshift technique promises to be a highly complementary alternative to other methods of redshift calibration

KiDS-1000: cosmic shear with enhanced redshift calibration

We present a cosmic shear analysis with an improved redshift calibration for the fourth data release of the Kilo-Degree Survey (KiDS-1000) using self-organising maps (SOMs). Compared to the previous analysis of the KiDS-1000 data, we expand the redshift calibration sample to more than twice its size, now consisting of data of 17 spectroscopic redshift campaigns, and significantly extending the fraction of KiDS galaxies we are able to calibrate with our SOM redshift methodology. We then enhance the calibration sample with precision photometric redshifts from COSMOS2015 and the Physics of the Accelerated Universe Survey (PAUS), allowing us to fill gaps in the spectroscopic coverage of the KiDS data. Finally we perform a Complete Orthogonal Sets of E/B-Integrals (COSEBIs) cosmic shear analysis of the newly calibrated KiDS sample. We find $S_8 = 0.748_{-0.025}^{+0.021}$, which is in good agreement with previous KiDS studies and increases the tension with measurements of the cosmic microwave background to 3.4{\sigma}. We repeat the redshift calibration with different subsets of the full calibration sample and obtain, in all cases, agreement within at most 0.5{\sigma} in $S_8$ compared to our fiducial analysis. Including additional photometric redshifts allows us to calibrate an additional 6 % of the source galaxy sample. Even though further systematic testing with simulated data is necessary to quantify the impact of redshift outliers, precision photometric redshifts can be beneficial at high redshifts and to mitigate selection effects commonly found in spectroscopically selected calibration samples.Comment: 18 pages, 15 figures, 6 table

Testing KiDS cross-correlation redshifts with simulations

Measuring cosmic shear in wide-field imaging surveys requires accurate knowledge of the redshift distribution of all sources. The clustering-redshift technique exploits the angular cross-correlation of a target galaxy sample with unknown redshifts and a reference sample with known redshifts, and is an attractive alternative to colour-based methods of redshift calibration. We test the performance of such clustering redshift measurements using mock catalogues that resemble the Kilo-Degree Survey (KiDS). These mocks are created from the MICE simulation and closely mimic the properties of the KiDS source sample and the overlapping spectroscopic reference samples. We quantify the performance of the clustering redshifts by comparing the cross-correlation results with the true redshift distributions in each of the five KiDS photometric redshift bins. Such a comparison to an informative model is necessary due to the incompleteness of the reference samples at high redshifts. Clustering mean redshifts are unbiased at $|\Delta z|<0.006$ under these conditions. The redshift evolution of the galaxy bias can be reliably mitigated at this level of precision using auto-correlation measurements and self-consistency relations, and will not become a dominant source of systematic error until the arrival of Stage-IV cosmic shear surveys. Using redshift distributions from a direct colour-based estimate instead of the true redshift distributions as a model for comparison with the clustering redshifts increases the biases in the mean to up to $|\Delta z|\sim0.04$. This indicates that the interpretation of clustering redshifts in real-world applications will require more sophisticated (parameterised) models of the redshift distribution in the future. If such better models are available, the clustering-redshift technique promises to be a highly complementary alternative to other methods of redshift calibration.Comment: 21 pages, 18 figures, 10 tables, submitted to A&

Magnification bias in galaxy surveys with complex sample selection functions

Gravitational lensing magnification modifies the observed spatial distribution of galaxies and can severely bias cosmological probes of large-scale structure if not accurately modelled. Standard approaches to modelling this magnification bias may not be applicable in practice as many galaxy samples have complex, often implicit, selection functions. We propose and test a procedure to quantify the magnification bias induced in clustering and galaxy-galaxy lensing (GGL) signals in galaxy samples subject to a selection function beyond a simple flux limit. The method employs realistic mock data to calibrate an effective luminosity function slope, $\alpha_{\rm{obs}}$, from observed galaxy counts, which can then be used with the standard formalism. We demonstrate this method for two galaxy samples derived from the Baryon Oscillation Spectroscopic Survey (BOSS) in the redshift ranges $0.2 < z \leq 0.5$ and $0.5 < z \leq 0.75$, complemented by mock data built from the MICE2 simulation. We obtain $\alpha_{\rm{obs}} = 1.93 \pm 0.05$ and $\alpha_{\rm{obs}} = 2.62 \pm 0.28$ for the two BOSS samples. For BOSS-like lenses, we forecast a contribution of the magnification bias to the GGL signal between the angular scales of $100$ and $4600$ with a cumulative signal-to-noise ratio between $0.1$ and $1.1$ for sources from the Kilo-Degree Survey (KiDS), between $0.4$ and $2.0$ for sources from the Hyper Suprime-Cam survey (HSC), and between $0.3$ and $2.8$ for ESA Euclid-like source samples. These contributions are significant enough to require explicit modelling in future analyses of these and similar surveys.Comment: 15 pages, 13 figure

KiDS-1000: Cross-correlation with Planck cosmic microwave background lensing and intrinsic alignment removal with self-calibration

CONTEXT: Galaxy shear and cosmic microwave background (CMB) lensing convergence cross-correlations contain additional information on cosmology with respect to auto-correlations. While remaining immune to certain systemic effects, these cross-correlations are nonetheless affected by the galaxy's intrinsic alignments (IA). These effects may, in fact, be responsible for the reported low lensing amplitude of the galaxy shear × CMB convergence cross-correlations, compared to the standard Planck ACDM (cosmological constant and cold dark matter) cosmology predictions. AIMS: In this work, we investigate how IA affects the Kilo-Degree Survey (KiDS) galaxy lensing shear and Planck CMB lensing convergence cross-correlation and we compare it to previous treatments, both with and without IA taken into consideration. METHODS: We compared the marginalization over IA parameters and the IA self-calibration (SC) method (with additional observables defined only from the source galaxies) to demonstrate that SC can efficiently break the degeneracy between the CMB lensing amplitude, Alens, and the IA amplitude, AIA. We further investigated how different systematics affect the resulting AIA and Alens and we validated our results with the MICE2 simulation. RESULTS: We find that by including the SC method to constrain IA, the information loss due to the degeneracy between CMB lensing and IA is strongly reduced. The best-fit values are Alens = 0.84-0.22+0.22 and AIA = 0.60-1.03+1.03, while different angular scale cuts can affect Alens by ~10%. We show that an appropriate treatment of the boost factor, cosmic magnification, and photometric redshift modeling is important for obtaining the correct IA and cosmological results

KiDS+VIKING-450 and DES-Y1 combined:Cosmology with cosmic shear

We present a combined tomographic weak gravitational lensing analysis of the Kilo Degree Survey (KV450) and the Dark Energy Survey (DES-Y1). We homogenize the analysis of these two public cosmic shear datasets by adopting consistent priors and modeling of nonlinear scales, and determine new redshift distributions for DES-Y1 based on deep public spectroscopic surveys. Adopting these revised redshifts results in a $0.8\sigma$ reduction in the DES-inferred value for $S_8$, which decreases to a $0.5\sigma$ reduction when including a systematic redshift calibration error model from mock DES data based on the MICE2 simulation. The combined KV450 + DES-Y1 constraint on $S_8 = 0.762^{+0.025}_{-0.024}$ is in tension with the Planck 2018 constraint from the cosmic microwave background at the level of $2.5\sigma$. This result highlights the importance of developing methods to provide accurate redshift calibration for current and future weak lensing surveys.Comment: 8 pages, 4 figures, new appendix added including a simulated analysis, version accepted for publication by A&A Letters, chains can be found at https://github.com/sjoudaki/kidsde