Relations between three-point configuration space shear and convergence statistics

With the growing interest in and ability of using weak lensing studies to probe the non-Gaussian properties of the matter density field, there is an increasing need for the study of suitable statistical measures, e.g. shear three-point statistics. In this paper we establish the relations between the three-point configuration space shear and convergence statistics, which are an important missing link between different weak lensing three-point statistics and provide an alternative way of relating observation and theory. The method we use also allows us to derive the relations between other two- and three-point correlation functions. We show the consistency of the relations obtained with already established results and demonstrate how they can be evaluated numerically. As a direct application, we use these relations to formulate the condition for E/B-mode decomposition of lensing three-point statistics, which is the basis for constructing new three-point statistics which allow for exact E/B-mode separation. Our work applies also to other two-dimensional polarization fields such as that of the Cosmic Microwave Background.Comment: 17 pages, 5 figures, submitted to A&

Non-linear shrinkage estimation of large-scale structure covariance

In many astrophysical settings, covariance matrices of large data sets have to be determined empirically from a finite number of mock realizations. The resulting noise degrades inference and precludes it completely if there are fewer realizations than data points. This work applies a recently proposed non-linear shrinkage estimator of covariance to a realistic example from large-scale structure cosmology. After optimizing its performance for the usage in likelihood expressions, the shrinkage estimator yields subdominant bias and variance comparable to that of the standard estimator with a factor of ∼50 less realizations. This is achieved without any prior information on the properties of the data or the structure of the covariance matrix, at a negligible computational cost

Euclid - an ESA Medium Class Mission

Euclid is an ESA Medium Class mission in the Cosmic Visions program to be launched in 2020. With its 1.2 m telescope, Euclid is going to survey 15, 000 deg2 of extragalactic sky in a broad optical band with outstanding image quality fit for weak gravitational lensing measurements. It will also provide near-infrared slitless spectroscopy of more than 107 emission-line galaxies with the main goal of measuring galaxy clustering. Imaging in three near-infrared bands by Euclid will be complemented by ground-based follow-up in optical bands to supply high-quality photometric redshift estimates out to z = 2. In combination, its primary cosmological science drivers, weak gravitational lensing and galaxy clustering, will yield unprecedented constraints on the properties of dark matter and dark energy, as well as the validity of Einstein gravity on large scales. Euclid’s rich datasets will facilitate further cosmological probes such as statistics of galaxy clusters or the study of galactic dark matter haloes, and a vast array of legacy science. In the following a brief overview on the Euclid mission and its key science is provided

Characterising improvements in photometric redshift probability density functions with galaxy morphology

In this work, we studied the impact of galaxy morphology on photometric redshift (photo-z) probability density functions (PDFs). By including galaxy morphological parameters like the radius, axis-ratio, surface brightness and the Sérsic index in addition to the ugriz broadbands as input parameters, we used the machine learning photo-z algorithm ANNZ2 to train and test on galaxies from the Canada-France-Hawaii Telescope Stripe-82 (CS82) Survey. Metrics like the continuous ranked probability score (CRPS), probability integral transform (PIT), Bayesian odds parameter, and even the width and height of the PDFs were evaluated, and the results were compared when different number of input parameters were used during the training process. We find improvements in the CRPS and width of the PDFs when galaxy morphology has been added to the training, and the improvement is larger especially when the number of broadband magnitudes are lacking

Self-calibration of weak lensing systematic effects using combined two- and three-point statistics

We investigate the prospects for using the weak lensing bispectrum alongside the power spectrum to control systematic uncertainties in a Euclid-like survey. Three systematic effects are considered: the intrinsic alignment of galaxies, uncertainties in the means of tomographic redshift distributions, and multiplicative bias in the measurement of the shear signal. We find that the bispectrum is very effective in mitigating these systematic errors. Varying all three systematics simultaneously, a joint power spectrum and bispectrum analysis reduces the area of credible regions for the cosmological parameters Ω_{m} and σ_{8} by a factor of 90 and for the two parameters of a time-varying dark energy equation of state by a factor of almost 20, compared with the baseline approach of using the power spectrum alone and of imposing priors consistent with the accuracy requirements specified for Euclid. We also demonstrate that including the bispectrum self-calibrates all three systematic effects to the stringent levels required by the forthcoming generation of weak lensing surveys, thereby reducing the need for external calibration data

Intrinsic alignment of redMaPPer clusters: cluster shape-matter density correlation

We measure the alignment of the shapes of galaxy clusters, as traced by their satellite distributions, with the matter density field using the public redMaPPer catalogue based on Sloan Digital Sky Survey–Data Release 8 (SDSS-DR8), which contains 26 111 clusters up to z ∼ 0.6. The clusters are split into nine redshift and richness samples; in each of them, we detect a positive alignment, showing that clusters point towards density peaks. We interpret the measurements within the tidal alignment paradigm, allowing for a richness and redshift dependence. The intrinsic alignment (IA) amplitude at the pivot redshift z = 0.3 and pivot richness λ = 30 is AgenIA=12.6+1.5−1.2 AIAgen=12.6−1.2+1.5 . We obtain tentative evidence that the signal increases towards higher richness and lower redshift. Our measurements agree well with results of maxBCG clusters and with dark-matter-only simulations. Comparing our results to the IA measurements of luminous red galaxies, we find that the IA amplitude of galaxy clusters forms a smooth extension towards higher mass. This suggests that these systems share a common alignment mechanism, which can be exploited to improve our physical understanding of IA

Cosmic shear covariance matrix in wCDM: Cosmology matters

We present here the cosmo-SLICS, a new suite of simulations specially designed for the analysis of current and upcoming weak lensing data beyond the standard two-point cosmic shear. We sampled the [Ωm, σ8, h, w0] parameter space at 25 points organised in a Latin hyper-cube, spanning a range that contains most of the 2σ posterior distribution from ongoing lensing surveys. At each of these nodes we evolved a pair of N-body simulations in which the sampling variance is highly suppressed, and ray-traced the volumes 800 times to further increase the effective sky coverage. We extracted a lensing covariance matrix from these pseudo-independent light-cones and show that it closely matches a brute-force construction based on an ensemble of 800 truly independent N-body runs. More precisely, a Fisher analysis reveals that both methods yield marginalized two-dimensional constraints that vary by less than 6% in area, a result that holds under different survey specifications and that matches to within 15% the area obtained from an analytical covariance calculation. Extending this comparison with our 25 wCDM models, we probed the cosmology dependence of the lensing covariance directly from numerical simulations, reproducing remarkably well the Fisher results from the analytical models at most cosmologies. We demonstrate that varying the cosmology at which the covariance matrix is evaluated in the first place might have an order of magnitude greater impact on the parameter constraints than varying the choice of covariance estimation technique. We present a test case in which we generate fast predictions for both the lensing signal and its associated variance with a flexible Gaussian process regression emulator, achieving an accuracy of a few percent on the former and 10% on the latter