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Register a new userGravitational Lensing Simulations I : Covariance Matrices and Halo Catalogues
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Added by
Joachim Harnois-Deraps
Publication date
2012
fields
Physics
and research's language is
English
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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.
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This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic two-point correlation function measurements. Our comparison includes seven approximate methods, which can be divided into three categories: predictive methods that follow the evolution of the linear density field deterministically (ICE-COLA, Peak Patch, and Pinocchio), methods that require a calibration with N-body simulations (Patchy and Halogen), and simpler recipes based on assumptions regarding the shape of the probability distribution function (PDF) of density fluctuations (log-normal and Gaussian density fields). We analyse the impact of using covariance estimates obtained from these approximate methods on cosmological analyses of galaxy clustering measurements, using as a reference the covariances inferred from a set of full N-body simulations. We find that all approximate methods can accurately recover the mean parameter values inferred using the N-body covariances. The obtained parameter uncertainties typically agree with the corresponding N-body results within 5% for our lower mass threshold, and 10% for our higher mass threshold. Furthermore, we find that the constraints for some methods can differ by up to 20% depending on whether the halo samples used to define the covariance matrices are defined by matching the mass, number density, or clustering amplitude of the parent N-body samples. The results of our configuration-space analysis indicate that most approximate methods provide similar results, with no single method clearly outperforming the others.
(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.
We compare the measurements of the bispectrum and the estimate of its covariance obtained from a set of different methods for the efficient generation of approximate dark matter halo catalogs to the same quantities obtained from full N-body simulations. To this purpose we employ a large set of three-hundred realisations of the same cosmology for each method, run with matching initial conditions in order to reduce the contribution of cosmic variance to the comparison. In addition, we compare how the error on cosmological parameters such as linear and nonlinear bias parameters depends on the approximate method used for the determination of the bispectrum variance. As general result, most methods provide errors within 10% of the errors estimated from N-body simulations. Exceptions are those methods requiring calibration of the clustering amplitude but restrict this to two-point statistics. Finally we test how our results are affected by being limited to a few hundreds measurements from N-body simulation, and therefore to the bispectrum variance, by comparing with a larger set of several thousands realisations performed with one approximate method.
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]
We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constrains related to growth rate of structure, Alcock-Paczynski distortions and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE-COLA, Pinocchio and PeakPatch), methods that rely on halo assignment schemes onto dark-matter overdensities calibrated with a target N-body run (Halogen, Patchy) and two standard assumptions about the full density PDF (Gaussian and Lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within $5%$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10%$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10%$ of those from the N-body based covariance.
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