Issue |
A&A
Volume 520, September-October 2010
|
|
---|---|---|
Article Number | A116 | |
Number of page(s) | 16 | |
Section | Cosmology (including clusters of galaxies) | |
DOI | https://doi.org/10.1051/0004-6361/201014235 | |
Published online | 13 October 2010 |
COSEBIs: Extracting the full E-/B-mode information from cosmic shear correlation functions
1
Argelander-Institut für Astronomie,
Universität Bonn, Auf dem Hügel 71,
53121 Bonn, Germany e-mail: peter@astro.uni-bonn.de
2
Center for Cosmology and Astro-Particle Physics, The Ohio State University,
191 W. Woodruff Ave., Columbus, OH 43210, USA e-mail: teifler@mps.ohio-state.edu
3
California Institute of Technology, Dept. of Astronomy,
MC 105-24, Pasadena CA 91125, USA e-mail: ekrause@astro.caltech.edu
Received:
10
February
2010
Accepted:
29
June
2010
Context. Cosmic shear is considered one of the most powerful
methods for studying the properties of dark energy in the
Universe. As a standard method, the two-point correlation
functions (ϑ) of the cosmic shear field are used as
statistical measures for the shear field.
Aims. In order to separate
the observed shear into E- and B-modes, the latter being most
likely produced by remaining systematics in the data set and/or
intrinsic alignment effects, several statistics have been defined
before. Here we aim at a complete E-/B-mode decomposition of the
cosmic shear information contained in the on a finite
angular interval.
Methods. We construct two sets of such E-/B-mode
measures, namely Complete Orthogonal Sets of E-/B-mode Integrals
(COSEBIs), characterized by weight functions between the
and the COSEBIs which are polynomials in ϑ or
polynomials in
ϑ, respectively. Considering the likelihood
in cosmological parameter space, constructed from the COSEBIs, we
study their information content.
Results. We show that the information
grows with the number of COSEBI modes taken into account, and
that an asymptotic limit is reached which defines the maximum
available information in the E-mode component of the
. We show that this limit is reached the earlier (i.e.,
for a smaller number of modes considered) the narrower the
angular range is over which
are measured, and it is
reached much earlier for logarithmic weight functions. For
example, for
on the interval 1' ≤ ϑ ≤ 400', the
asymptotic limit for the parameter pair (
,
) is reached for ~25 modes in the linear
case, but already for 5 modes in the logarithmic case. The
COSEBIs form a natural discrete set of quantities, which we
suggest as method of choice in future cosmic shear likelihood
analyses.
Key words: large-scale structure of Universe / gravitational lensing: weak / cosmological parameters / methods: statistical
© ESO, 2010
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