


ID:
10388.0,
MPI für Astrophysik / Cosmology 
The threepoint correlation function of cosmic shear  I. The natural components 
Authors:  Schneider, P.; Lombardi, M.  Language:  English  Date of Publication (YYYYMMDD):  200301  Title of Journal:  Astronomy & Astrophysics  Journal Abbrev.:  Astron. Astrophys.  Volume:  397  Issue / Number:  3  Start Page:  809  End Page:  818  Review Status:  Peerreview  Audience:  Experts Only  Abstract / Description:  The threepoint correlation function of cosmic shear, the weak distortion of the images of distant galaxies by the gravitational field of the inhomogeneous matter distribution in the Universe, is studied here. Previous work on threepoint statistics of cosmic shear has mainly concentrated on the convergence, or on aperture measures of the shear. However, as has become clear recently for the twopoint statistics of cosmic shear, the basic quantity that should be used is the correlation function: first, it is much easier to measure from observational data, since it is immune against complicated geometries of data fields (which contain gaps and holes, e. g. due to masking); second, all other (linear) twopoint statistics can be expressed as integrals over the correlation function. The situation is the same for the threepoint statistics. However, in contrast to the twopoint correlation function, the invariants (with respect to rotations) of the shear threepoint correlation function have not been employed yet. Here we consider the transformation properties of the shear threepoint correlation function under rotations. We show that there are four complex linear combinations of components of the threepoint correlation function, which we shall call "natural components", since they are multiplied just by a phase factor for arbitrary rotations, but do not mix. In particular, their moduli are invariant under rotations and thus (non linear) invariants of the threepoint correlation function. In terms of these natural components, the invariance of the statistical properties of the shear field under parity transformations are easily obtained. Our results do not apply only to cosmic shear, but also to other quantities with the same mathematical properties that of a polar. For example, practically every relation derived here applies also to the polarization of the cosmic microwave background radiation.  Free Keywords:  cosmology : theory; gravitational lensing; largescale structure of the Universe; cosmic microwave background  External Publication Status:  published  Document Type:  Article 
Communicated by:  N. N.  Affiliations:  MPI für Astrophysik/Gravitational Lensing
 External Affiliations:  Univ Bonn, Inst Astrophys & Extraterr Forsch, Hugel 71, D53121; Bonn, Germany; Univ Bonn, Inst Astrophys & Extraterr Forsch, D53121 Bonn, Germany; Max Planck Inst Astrophys, D85741 Garching, Germany
 Identifiers:  ISI:000180249800008 ISSN:00046361 URL:http://www.edpsciences.org/articles/aa/abs/2003/03...  


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