A new cosmic shear function: Optimised E-/B-mode decomposition on a finite interval

The decomposition of the cosmic shear field into E- and B-mode is an important diagnostic in weak gravitational lensing. However, commonly used techniques to perform this separation suffer from mode-mixing on very small or very large scales. We introduce a new E-/B-mode decomposition of the cosmic shear two-point correlation on a finite interval. This new statistic is optimised for cosmological applications, by maximising the signal-to-noise ratio (S/N) and a figure of merit (FoM) based on the Fisher matrix of the cosmological parameters Omega_m and sigma_8. We improve both S/N and FoM results substantially with respect to the recently introduced ring statistic, which also provides E-/B-mode separation on a finite angular range. The S/N (FoM) is larger by a factor of three (two) on angular scales between 1 and 220 arc minutes. In addition, it yields better results than for the aperture-mass dispersion ^2, with improvements of 20% (10%) for S/N (FoM). Our results depend on the survey parameters, most importantly on the covariance of the two-point shear correlation function. Although we assume parameters according to the CFHTLS-Wide survey, our method and optimisation scheme can be applied easily to any given survey settings and observing parameters. Arbitrary quantities, with respect to which the E-/B-mode filter is optimised, can be defined, therefore generalising the aim and context of the new shear statistic.Comment: 11 pages, 7 figures, 2 tables. MNRAS accepted. C-program freely available at http://www2.iap.fr/users/kilbinge/decomp_eb

A new model to predict weak-lensing peak counts II. Parameter constraint strategies

Peak counts have been shown to be an excellent tool to extract the non-Gaussian part of the weak lensing signal. Recently, we developped a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analyses. In this work, we explore and compare various strategies for constraining parameter using our model, focusing on the matter density $\Omega_\mathrm{m}$ and the density fluctuation amplitude $\sigma_8$. First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique which makes a weaker assumption compared to the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. We find that neglecting the CDC effect enlarges parameter contours by 22%, and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in an excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution.Comment: 15 pages, 11 figures. Accepted versio

Cosmological Parameters from Second- and Third-Order Cosmic Shear Statistics

The weak gravitational lensing effect caused by the large-scale structure of the matter in the Universe (cosmic shear) is a powerful tool to study the matter distribution on very large scales. Cosmic shear surveys provide high-precision measurements of the large-scale distribution of matter in the Universe and yield valuable information about cosmology. In this thesis I study the efficacy of cosmic shear statistics to constrain cosmological parameters. In the first part of this work, different strategies of shear surveys are considered and their influence on the measurement accuracy of cosmological parameters is investigated. From Monte-Carlo simulations, the covariance of second-order shear statistics, in particular the aperture mass dispersion Map2>, is obtained. The covariance encodes the measurement errors and correlations between different angular scales which depend on the survey design. Using the Fisher information matrix, Karhunen-Loève eigenmodes and likelihood techniques, various survey settings are compared with the result that a rigorous sampling on medium and large angular scales is more important than a small cosmic variance. By appropriately choosing the survey geometry a 25 percent improvement on the 1s-errors on cosmological parameters is possible. The second part of this thesis presents predictions of the improvement of constraints on cosmological parameters by combining second- and third-order aperture mass statistics of cosmic shear. The three-point correlation function and the third-order aperture mass statistics are calculated from theoretical non-linear models of structure formation. These predictions are tested and compared with ray-tracing simulations. The dependence of the third-order aperture mass statistics with respect to cosmological parameters is discussed and a two-dimensional visualization of the shear three-point correlation function is presented. After this preparatory work, the second- and third-order aperture mass statistics, Map2> and Map3>, are combined to reduce near-degeneracies between cosmological parameters and to improve the resulting error bars. From ?CDM ray-tracing simulations, the covariance and the cross-correlation of Map2> and Map3> are estimated. A Fisher matrix analysis shows that the combination of second- and third-order statistics can partially lift the parameter degeneracies, e.g. between Ωm and σ8. The resulting error bars on all considered cosmological parameters are reduced by a factor of 10

Photometric redshifts: estimating their contamination and distribution using clustering information

We present a new technique to estimate the level of contamination between photometric redshift bins. If the true angular cross-correlation between redshift bins can be safely assumed to be zero, any measured cross-correlation is a result of contamination between the bins. We present the theory for an arbitrary number of redshift bins, and discuss in detail the case of two and three bins which can be easily solved analytically. We use mock catalogues constructed from the Millennium Simulation to test the method, showing that artificial contamination can be successfully recovered with our method. We find that degeneracies in the parameter space prohibit us from determining a unique solution for the contamination, though constraints are made which can be improved with larger data sets. We then apply the method to an observational galaxy survey: the deep component of the Canada-France-Hawaii Telescope Legacy Survey. We estimate the level of contamination between photometric redshift bins and demonstrate our ability to reconstruct both the true redshift distribution and the true average redshift of galaxies in each photometric bin.Comment: 14 pages, 12 figures, accepted for publication in MNRAS V2: Section 4.4 added. Significant additions to analysis in section 5.

Measurement of the halo bias from stacked shear profiles of galaxy clusters

We present the observational evidence of the 2-halo term in the stacked shear profile of a sample of about 1200 optically selected galaxy clusters based on imaging data and the public shear catalog from the CFHTLenS. We find that the halo bias, a measure of the correlated distribution of matter around galaxy clusters, has amplitude and correlation with galaxy cluster mass in very good agreement with the predictions based on the LCDM standard cosmological model. The mass-concentration relation is flat but higher than theoretical predictions. We also confirm the close scaling relation between the optical richness of galaxy clusters and their mass.Comment: 5 pages, 4 figures. In press on ApJ Letter

The ring statistics - how to separate E- and B-modes of cosmic shear correlation functions on a finite interval

Aims. One of the main probes for systematic errors in the cosmic shear signal are the division of the shear field into E- and B-mode shear, where gravitational lensing only produces the former. As shown in a recent note, all currently used E-/B-mode separation methods for the shear correlation functions xi_pm require them to be measured to arbitrarily small and/or large separations which is of course not feasible in practice. Methods. We derive second-order shear statistics which provide a clean separation into E- and B-modes from measurements of xi_pm(theta) over a finite interval only. We call these new statistics the circle and ring statistics, respectively; the latter is obtained by an integral over the former. The mathematical properties of these new shear statistics are obtained, as well as specific expressions for applying them to observed data. Results. It is shown that an E-/B-mode separation can be performed on measurements of xi_pm over a finite interval in angular separation, using the ring statistics. We furthermore generalize this result to derive the most general class of second-order shear statistics which provide a separation of E- and B-mode shear on a given angular interval theta_min <= theta <= theta_max. Our results will be of practical use particularly for future cosmic shear surveys where highly precise measurements of the shear will become available and where control of systematics will be mandatory.Comment: 10 pages, 5 figues, minor changes, matches the published version (A&A in press

A new model to predict weak-lensing peak counts: I. Comparison with N-body simulations

International audienceContext. Weak-lensing peak counts have been shown to be a powerful tool for cosmology. They provide non-Gaussian information of large scale structures and are complementary to second-order statistics.Aims. We propose a new flexible method for predicting weak-lensing peak counts, which can be adapted to realistic scenarios, such as a real source distribution, intrinsic galaxy alignment, mask effects, and photo-z errors from surveys. The new model is also suitable for applying the tomography technique and nonlinear filters.Methods. A probabilistic approach to modeling peak counts is presented. First, we sample halos from a mass function. Second, we assign them density profiles. Third, we place those halos randomly on the field of view. The creation of these “fast simulations” requires much less computing time than do N-body runs. Then, we perform ray-tracing through these fast simulation boxes and select peaks from weak-lensing maps to predict peak number counts. The computation is achieved by our Camelus algorithm.Results. We compare our results to N-body simulations to validate our model. We find that our approach is in good agreement with full N-body runs. We show that the lensing signal dominates shape noise and Poisson noise for peaks with S/N between 4 and 6. Also, counts from the same S/N range are sensitive to Ωm and σ8. We show how our model can distinguish between various combinations of those two parameters.Conclusions. In this paper, we offer a powerful tool for studying weak-lensing peaks. The potential of our forward model is its high flexibility, which makes the using peak counts under realistic survey conditions feasible

A new model to predict weak-lensing peak counts III. Filtering technique comparisons

This is the third in a series of papers that develop a new and flexible model to predict weak-lensing (WL) peak counts, which have been shown to be a very valuable non-Gaussian probe of cosmology. In this paper, we compare the cosmological information extracted from WL peak counts using different filtering techniques of the galaxy shear data, including linear filtering with a Gaussian and two compensated filters (the starlet wavelet and the aperture mass), and the nonlinear filtering method MRLens. We present improvements to our model that account for realistic survey conditions, which are masks, shear-to-convergence transformations, and non-constant noise. We create simulated peak counts from our stochastic model, from which we obtain constraints on the matter density $\Omega_\mathrm{m}$, the power spectrum normalisation $\sigma_8$, and the dark-energy parameter $w_0$. We use two methods for parameter inference, a copula likelihood, and approximate Bayesian computation (ABC). We measure the contour width in the $\Omega_\mathrm{m}$-$\sigma_8$ degeneracy direction and the figure of merit to compare parameter constraints from different filtering techniques. We find that starlet filtering outperforms the Gaussian kernel, and that including peak counts from different smoothing scales helps to lift parameter degeneracies. Peak counts from different smoothing scales with a compensated filter show very little cross-correlation, and adding information from different scales can therefore strongly enhance the available information. Measuring peak counts separately from different scales yields tighter constraints than using a combined peak histogram from a single map that includes multiscale information. Our results suggest that a compensated filter function with counts included separately from different smoothing scales yields the tightest constraints on cosmological parameters from WL peaks.Comment: 14 pages, 12 figures, published versio