Volume 519, September 2010
|Number of page(s)||7|
|Section||Cosmology (including clusters of galaxies)|
|Published online||07 September 2010|
Fitting formulae of the reduced-shear power spectrum for weak lensing*
Excellence Cluster Universe, Technische Universität München,
Boltzmannstr. 2, 85748 Garching, Germany e-mail: email@example.com
2 Universitäts-Sternwarte München, Scheinerstr. 1, 81679 München, Germany
3 Shanghai Key Lab for Astrophysics, Shanghai Normal University, Shanghai 200234, PR China
Accepted: 9 June 2010
Context. Weak gravitational lensing is a powerful probe of large-scale structure and cosmology. Most commonly, second-order correlations of observed galaxy ellipticities are expressed as a projection of the matter power spectrum, corresponding to the lowest-order approximation between the projected and the three-dimensional power spectrum.
Aims. The dominant lensing-only contribution beyond the zero-order approximation is the reduced shear, which takes into account not only lensing-induced distortions but also the isotropic magnification of galaxy images. This involves an integral over the matter bispectrum. We provide a fast and general way to calculate this correction term.
Methods. Using a model for the matter bispectrum, we fit elementary functions to the reduced-shear contribution and its derivatives with respect to cosmological parameters. The dependence on cosmology is encompassed in a Taylor-expansion around a fiducial model.
Results. Within a region in parameter space comprising the WMAP7 68% error ellipsoid, the total reduced-shear power spectrum (shear plus fitted reduced-shear correction) is accurate to 1% (2%) for < 104 ( < 2 × 105). This corresponds to a factor of four reduction in the bias compared to the case where no correction is used. This precision is necessary to match the accuracy of current non-linear power spectrum predictions from numerical simulations.
Key words: gravitational lensing: weak / large-scale structure of Universe
Appendix A is only available in electronic form at http://www.aanda.org
© ESO, 2010
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