1,150 research outputs found
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 and the
density fluctuation amplitude . 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
Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation
In cosmic shear likelihood analyses the covariance is most commonly assumed
to be constant in parameter space. Therefore, when calculating the covariance
matrix (analytically or from simulations), its underlying cosmology should not
influence the likelihood contours. We examine whether the aforementioned
assumption holds and quantify how strong cosmic shear covariances vary within a
reasonable parameter range. Furthermore, we examine the impact on likelihood
contours when assuming different cosmologies in the covariance. We find that
covariances vary significantly within the considered parameter range
(Omega_m=[0.2;0.4], sigma_8=[0.6;1.0]) and that this has a non-negligible
impact on the size of likelihood contours. This impact increases with
increasing survey size, increasing number density of source galaxies,
decreasing ellipticity noise, and when using non-Gaussian covariances. To
improve on the assumption of a constant covariance we present two methods. The
adaptive covariance is the most accurate method, but it is computationally
expensive. To reduce the computational costs we give a scaling relation for
covariances. As a second method we outline the concept of an iterative
likelihood analysis. Here, we additionally account for non-Gaussianity using a
ray-tracing covariance derived from the Millennium simulation.Comment: 11 pages, 8 figure
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
Principal Component Analysis of Weak Lensing Surveys
We study degeneracies between cosmological parameters and measurement errors
from cosmic shear surveys using a principal component analysis of the Fisher
matrix. We simulate realistic survey topologies with non-uniform sky coverage,
and quantify the effect of survey geometry, depth and noise from intrinsic
galaxy ellipticities on the parameter errors. This analysis allows us to
optimise the survey geometry. Using the shear two-point correlation functions
and the aperture mass dispersion, we study various degeneracy directions in a
multi-dimensional parameter space spanned by Omega_m, Omega_Lambda, sigma_8,
the shape parameter Gamma, the spectral index n_s, along with parameters that
specify the distribution of source galaxies. If only three parameters are to be
obtained from weak lensing data, a single principal component is dominant and
contains all information about the main parameter degeneracies and their
errors. The variance of the dominant principal component of the Fisher matrix
shows a minimum for survey strategies which have small cosmic variance and
measure the shear correlation up to several degrees [abridged].Comment: 13 pages, 17 figures. A&A in press, matches the version to be
publishe
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
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
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