Issue |
A&A
Volume 462, Number 3, February II 2007
|
|
---|---|---|
Page(s) | 841 - 849 | |
Section | Cosmology (including clusters of galaxies) | |
DOI | https://doi.org/10.1051/0004-6361:20065532 | |
Published online | 09 October 2006 |
The ring statistics – how to separate E- and B-modes of cosmic shear correlation functions on a finite interval
Argelander-Institut für Astronomie (Founded by merging of the Sternwarte, Radioastronomisches Institut and Institut für Astrophysik und Extraterrestrische Forschung der Universität Bonn.) , Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany e-mail: [peter;kilbinge]@astro.uni-bonn.de
Received:
2
May
2006
Accepted:
29
September
2006
Aims.Cosmic shear, the distortion of images of distant
sources by the tidal gravitational field of the large-scale matter
distribution in the Universe, is one of the most powerful
cosmological probes. The measured shear field may be due not only
to the gravitational lensing effect, but may contain systematic
effects from the measurement process or intrinsic alignment of
galaxy shapes. One of the main probes for these systematics is the
division of the shear field into E- and B-mode shear, where lensing
only produces the former. As shown in a recent note, all currently
used E-/B-mode separation methods for the shear correlation
functions 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
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 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
. In
view of these generalization, we discuss the aperture dispersion
and the shear dispersion and their relation to the shear
correlation functions. 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.
Key words: methods: statistical / gravitational lensing / cosmology: large-scale structure of the Universe / cosmology: dark matter
© ESO, 2007
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