Measuring cosmic shear with the ring statistics

Context. Commonly used methods to decompose Eand B-modes in cosmic shear, namely the aperture mass dispersion and the E/B-mode shear correlation function, suffer from incomplete knowledge of the two-point correlation function (2PCF) on very small and/or very large scales. The ring statistics, the most recently developed cosmic shear measure, improves on this issue and is able to decompose Eand B-modes using a 2PCF measured on a finite interval. Aims. First, we improve on the ring statistics’ filter function with respect to the signal-to-noise ratio. Second, we examine the ability of the ring statistics to constrain cosmology and compare the results to cosmological constraints obtained with the aperture mass dispersion. Third, we use the ring statistics to measure a cosmic shear signal from CFHTLS (Canada-France-Hawaii Telescope Legacy Survey) data. Methods. We consider a scale-dependent filter function for the ring statistics which improves its signal-to-noise ratio. To examine the information content of the ring statistics we employ ray-tracing simulations and develop an expression of the ring statistics’ covariance in terms of a 2PCF covariance. We perform a likelihood analysis with simulated data for the ring statistics in the Ωm-σ8 parameter space and compare the information content of ring statistics and aperture mass dispersion. Regarding our third aim, we use the 2PCF of the latest CFHTLS analysis to calculate the ring statistics and its error bars. Results. Although the scale-dependent filter function improves the S/N ratio of the ring statistics, the S/N ratio of the aperture mass dispersion is higher. In addition, we show that there exist filter functions which decompose Eand B-modes using a finite range of 2PCFs (EB-statistics) and have higher S/N ratio than the ring statistics. However, we find that data points of the latter are significantly less correlated than data points of the aperture mass dispersion and the EB-statistics. As a consequence the ring statistics is an ideal tool to identify remaining systematics accurately as a function of angular scale. We use the ring statistics to measure a Eand B-mode shear signal from CFHTLS data.