## Measuring cosmic shear with the ring statistics

^{1}
Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany e-mail: tim.eifler@astro.uni-bonn.de

^{2}
California Institute of Technology, M/C 350-17, Pasadena, California 91125, USA

Received:
14
July
2009

Accepted:
10
November
2009

*Context. *Commonly used methods of decomposing E- and 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 E- and B-modes using a 2PCF measured on a finite interval.

*Aims. *First, we improve on the ring statistics' filter function over the signal-to-noise ratio (*S*/*N*). 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 *S*/*N*. To examine the information content of the ring statistics, we employed ray-tracing simulations and developed an expression of the ring statistics' covariance in terms of a 2PCF covariance. We performed a likelihood analysis with simulated data for the ring statistics in the Ω_{m}-σ_{8} parameter space and compared the information content of ring statistics and aperture mass dispersion. Regarding our third aim, we used 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* of the ring statistics, the *S*/*N* of the aperture mass dispersion is higher. In addition, we show that filter functions exist that decompose E- and B-modes using a finite range of 2PCFs (*EB*-statistics) and have higher *S*/*N* 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 for identifying remaining systematics accurately as a function of angular scale. We use the ring statistics to measure a E- and B-mode shear signal from CFHTLS data.

Key words: gravitational lensing: weak / large-scale structure of Universe / methods: data analysis

*© ESO, 2010*