Comparing cosmic shear measures

Free access article

Issue		A&A Volume 482, Number 1, April IV 2008


Page(s)		9 - 19
Section		Cosmology (including clusters of galaxies)
DOI		http://dx.doi.org/10.1051/0004-6361:20078573
Published online		14 February 2008

A&A 482, 9-19 (2008)
DOI: 10.1051/0004-6361:20078573

Optimizing the information content of cosmic shear data vectors

T. Eifler¹, M. Kilbinger^{1, 2}, and P. Schneider¹

¹ Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
e-mail: tim.eifler@astro.uni-bonn.de
² Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France

(Received 29 August 2007 / Accepted 12 January 2008)

Abstract
Aims. We introduce an optimized data vector of cosmic shear measures $(\vec{\mathcal N})$ . This data vector has high information content, is not sensitive to B-mode contamination, and only shows small correlation between data points of different angular scales.
Methods. We show that a data vector of the two-point correlation function (2PCF), hereafter denoted as $\vec \xi$ , in general contains more information on cosmological parameters compared to a data vector of the aperture mass dispersion, hereafter referred to as $\langle \vec{M}_{\rm ap}^2 \rangle$ . The reason for this is the fact that $\langle \vec{M}_{\rm ap}^2 \rangle$ lacks the information of the convergence power spectrum $(\mathcal P_\kappa)$ on large angular scales, which is contained in $\vec \xi$ . Nevertheless, $\langle \vec{M}_{\rm ap}^2 \rangle$ has valuable properties (small correlation between data points of different angular scales, not sensitive to B-mode contamination) that one wants to preserve in an optimized data vector. Therefore we combine $\vec \xi$ and $\langle \vec{M}_{\rm ap}^2 \rangle$ to a new data vector $\vec{\mathcal N}=\left( \langle \vec{M}_{\rm ap}^2\rangle (\theta_1), ..., \langle \vec{M}_{\rm ap}^2\rangle (\theta_n), \xi_+(\theta_0) \right)$ , which retains the advantages of $\langle \vec{M}_{\rm ap}^2 \rangle$ and is also sensitive to the large-scale information of $\mathcal P_\kappa$ . We compare the information content of the three data vectors by performing a detailed likelihood analysis and use ray-tracing simulations to derive the covariance matrices. In the last part of the paper we contaminate all data vectors with B-modes on small angular scales and examine their robustness against this contamination.
Results. The combined data vector $\vec{\mathcal N}$ strongly improves constraints on cosmological parameters compared to $\langle \vec{M}_{\rm ap}^2 \rangle$ . Although, the information content of $\vec \xi$ is higher in the case of a pure E-mode signal, in the more realistic case where B-modes are present the 2PCF data vector is strongly contaminated and yields biased cosmological parameter estimates. The new data vector $\vec{\mathcal N}$ shows to be robust against this contamination. Furthermore the individual data points of $\vec{\mathcal N}$ show a much smaller correlation compared to $\vec \xi$ , leading to an almost diagonal covariance matrix.

Key words: cosmology: theory -- gravitational lensing -- large-scale structure of Universe -- methods: statistical

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