A direct measurement of tomographic lensing power spectra from CFHTLenS

Abstract

We measure the weak gravitational lensing shear power spectra and their cross-power in two photometric redshift bins from the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS). The measurements are performed directly in multipole space in terms of adjustable band powers. For the extraction of the band powers from the data we have implemented and extended a quadratic estimator, a maximum likelihood method that allows us to readily take into account irregular survey geometries, masks, and varying sampling densities. We find the 68 per cent credible intervals in the σ<inf>8</inf>–Ω<inf>m</inf> plane to be marginally consistent with results from <it>Planck</it> for a simple five-parameter Λ cold dark matter (ΛCDM) model. For the projected parameter <it>S</it><inf>8</inf> ≡ σ<inf>8</inf>(Ω<inf>m</inf>/0.3)0.5 we obtain a best-fitting value of <f>$S_8 = 0.768_{-0.039}^{+0.045}$</f>. This constraint is consistent with results from other CFHTLenS studies as well as the Dark Energy Survey. Our most conservative model, including modifications to the power spectrum due to baryon feedback and marginalization over photometric redshift errors, yields an upper limit on the total mass of three degenerate massive neutrinos of Σ<it>m</it><inf>ν</inf> < 4.53 eV at 95 per cent credibility, while a Bayesian model comparison does not favour any model extension beyond a simple five-parameter ΛCDM model. Combining the shear likelihood with <it>Planck</it> breaks the σ<inf>8</inf>–Ω<inf>m</inf> degeneracy and yields σ<inf>8</inf> = 0.818 ± 0.013 and Ω<inf>m</inf> = 0.300 ± 0.011 which is fully consistent with results from <it>Planck</it> alone.