Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFast Generation of Covariance Matrices for Weak Lensing
100
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Upcoming weak lensing surveys will probe large fractions of the sky with unprecedented accuracy. To infer cosmological constraints, a large ensemble of survey simulations are required to accurately model cosmological observables and their covariances. We develop a parallelized multi-lens-plane pipeline called UFalcon, designed to generate full-sky weak lensing maps from lightcones within a minimal runtime. It makes use of L-PICOLA, an approximate numerical code, which provides a fast and accurate alternative to cosmological $N$-Body simulations. The UFalcon maps are constructed by nesting 2 simulations covering a redshift-range from $z=0.1$ to $1.5$ without replicating the simulation volume. We compute the convergence and projected overdensity maps for L-PICOLA in the lightcone or snapshot mode. The generation of such a map, including the L-PICOLA simulation, takes about 3 hours walltime on 220 cores. We use the maps to calculate the spherical harmonic power spectra, which we compare to theoretical predictions and to UFalcon results generated using the full $N$-Body code GADGET-2. We then compute the covariance matrix of the full-sky spherical harmonic power spectra using 150 UFalcon maps based on L-PICOLA in lightcone mode. We consider the PDF, the higher-order moments and the variance of the smoothed field variance to quantify the accuracy of the covariance matrix, which we find to be a few percent for scales $ell sim 10^2$ to $10^3$. We test the impact of this level of accuracy on cosmological constraints using an optimistic survey configuration, and find that the final results are robust to this level of uncertainty. The speed and accuracy of our developed pipeline provides a basis to also include further important features such as masking, varying noise and will allow us to compute covariance matrices for models beyond $Lambda$CDM. [abridged]
rate research
Read More
Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate and numerically stable computation of non-Gaussian real space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatorys Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real space covariances with or without the flat sky approximation is released along with this paper.
(Abridged) We investigate and quantify the impact of finite simulation volume on weak lensing two- and four-point statistics. These {it finite support} (FS) effects are modelled for several estimators, simulation box sizes and source redshifts, and validated against a new large suite of 500 $N$-body simulations. The comparison reveals that our theoretical model is accurate to better than 5 per cent for the shear correlation function $xi_{+}(theta)$ and its error. We find that the most important quantities for FS modelling is the ratio between the measured angle $theta$ and the angular size of the simulation box at the source redshift, $theta_{box}(z_s)$, or the multipole equivalent $ell / ell_{box}(z_s)$. When this ratio reaches 0.1, independently of the source redshift, the shear correlation function $xi_+$ is suppressed by 5, 10, 20 and 25 percent for $L_{box}= 1000$, $500$, $250$ and $147mbox{Mpc}/h$ respectively. When it reaches 0.2, the suppression exceeds 25 percent even for the largest box. The same effect is observed in $xi_{-}(theta)$, but at much larger angles. This has important consequences for cosmological analyses using $N$-body simulations to calibrate the impact of non-linear gravitational clustering or to estimate errors and systematics effects, and should not be overlooked. We propose simple semi-analytic solutions to correct for these finite box effects with and without the presence of survey masks, and the method can be generalized to any weak lensing estimator. This offers a graceful solution to the important problem of estimating accurate covariance matrices for weak lensing studies: there is no need to run extra large simulation volumes, as long as the box effects are corrected.
Gravitational lensing surveys have now become large and precise enough that the interpretation of the lensing signal has to take into account an increasing number of theoretical limitations and observational biases. Since the lensing signal is the strongest at small angular scales, only numerical simulations can reproduce faithfully the non-linear dynamics and secondary effects at play. This work is the first of a series in which all gravitational lensing corrections known so far will be implemented in the same set of simulations, using realistic mock catalogues and non-Gaussian statistics. In this first paper, we present the TCS simulation suite and compute basic statistics such as the second and third order convergence and shear correlation functions. These simple tests set the range of validity of our simulations, which are resolving most of the signals at the sub-arc minute level (or $ell sim 10^4$). We also compute the non-Gaussian covariance matrix of several statistical estimators, including many that are used in the Canada France Hawaii Telescope Lensing Survey (CFHTLenS). From the same realizations, we construct halo catalogues, computing a series of properties that are required by most galaxy population algorithms. These simulation products are publicly available for download.
Full ray-tracing maps of gravitational lensing, constructed from N-Body simulations, represent a fundamental tool to interpret present and future weak lensing data. However the limitation of computational resources and storage capabilities severely restrict the number of realizations that can be performed in order to accurately sample both the cosmic shear models and covariance matrices. In this paper we present a halo model formalism for weak gravitational lensing that alleviates these issues by producing weak-lensing mocks at a reduced computational cost. Our model takes as input the halo population within a desired light-cone and the linear power spectrum of the underlined cosmological model. We examine the contribution given by the presence of substructures within haloes to the cosmic shear power spectrum and quantify it to the percent level. Our method allows us to reconstruct high-resolution convergence maps, for any desired source redshifts, of light-cones that realistically trace the matter density distribution in the universe, account for masked area and sample selections. We compare our analysis on the same large scale structures constructed using ray-tracing techniques and find very good agreements both in the linear and non-linear regimes up to few percent levels. The accuracy and speed of our method demonstrate the potential of our halo model for weak lensing statistics and the possibility to generate a large sample of convergence maps for different cosmological models as needed for the analysis of large galaxy redshift surveys.
87 -
Jan Niklas Grieb (Universitatssternwarte Munchen
, n Ludwig-Maximilians-Universitat Munchen
, Max-Planck-Institut furn extraterrestrische Physik
2015
Measurements of the redshift-space galaxy clustering have been a prolific source of cosmological information in recent years. Accurate covariance estimates are an essential step for the validation of galaxy clustering models of the redshift-space two-point statistics. Usually, only a limited set of accurate N-body simulations is available. Thus, assessing the data covariance is not possible or only leads to a noisy estimate. Further, relying on simulated realisations of the survey data means that tests of the cosmology dependence of the covariance are expensive. With these points in mind, this work presents a simple theoretical model for the linear covariance of anisotropic galaxy clustering observations with synthetic catalogues. Considering the Legendre moments (`multipoles) of the two-point statistics and projections into wide bins of the line-of-sight parameter (`clustering wedges), we describe the modelling of the covariance for these anisotropic clustering measurements for galaxy samples with a trivial geometry in the case of a Gaussian approximation of the clustering likelihood. As main result of this paper, we give the explicit formulae for Fourier and configuration space covariance matrices. To validate our model, we create synthetic HOD galaxy catalogues by populating the haloes of an ensemble of large-volume N-body simulations. Using linear and non-linear input power spectra, we find very good agreement between the model predictions and the measurements on the synthetic catalogues in the quasi-linear regime.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
