Research Note

Fitting formulae of the reduced-shear power spectrum for weak lensing^*

¹ Excellence Cluster Universe, Technische Universität München, Boltzmannstr. 2, 85748 Garching, Germany e-mail: martin.kilbinger@universe-cluster.de
² Universitäts-Sternwarte München, Scheinerstr. 1, 81679 München, Germany
³ Shanghai Key Lab for Astrophysics, Shanghai Normal University, Shanghai 200234, PR China

Received: 20 April 2010
Accepted: 9 June 2010

Abstract

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.

Conclusions.