1 Introduction

Cosmological gravitational lensing produced by large-scale structure (or cosmic shear) has been advocated as a powerful tool to probe the mass distribution in the universe (see the reviews from Mellier 1999; Bartelmann & Schneider 2001 and references therein). The first detections reported over the past year (Van Waerbeke et al. 2000; Bacon et al. 2000; Kaiser et al. 2000; Wittman et al. 2000; Maoli et al. 2001; Rhodes et al. 2001) confirmed that the amplitude and the shape of the signal are compatible with theoretical expectations, although the data sets were not large enough to place strong constraints on cosmological models. Maoli et al. (2001) combined the results from different groups to obtain constraints on the power spectrum normalization $\sigma_8$ and the mean density of the universe $\Omega_0$: Their result is in agreement with the cluster abundance constraints, but they were not yet able to break the degeneracy between $\sigma_8$ and $\Omega_0$.

The physical interpretation of the weak lensing signal can be made more securely using detections of cosmic shear from different statistics and angular scales on the same data set (as in Van Waerbeke et al. 2000). Unfortunately, their joint detection of the variance and the correlation function using the same data was not fully conclusive: the sample was too small to enable a significant detection of the cosmic shear from variances with different weighting schemes and 2-point statistics over a wide range of scales. The use of independent approaches is nevertheless necessary and it is an important step to validate the reliability of cosmic shear, to check the consistency of the measurements against theoretical predictions and to understand the residual systematics. A relevant example is the aperture mass statistic (defined in Schneider et al. 1998). It is a direct probe of the projected mass power spectrum, and it is not sensitive to certain type of systematics (like a uniform PSF anisotropy) which may corrupt the top-hat smoothed variance, or the shear correlation function. Even the shear correlation function can be measured in several ways, by splitting for instance the tangential and radial modes.

In this paper we report the measurement of the top-hat smoothed variance, the aperture mass, the shear correlation function, and the tangential and radial shear correlation functions on a new homogeneous data set covering an effective area of 6.5 deg². The depth and the field of view are well suited for a comprehensive analysis using various statistics. We show that the amplitude of residual systematics is very low compared to the signal and discuss the consistency of these measurements against the predictions of cosmological models.

We also discuss alternative interpretations. It has been suggested recently that intrinsic alignments of galaxies caused by tidal fields could contribute to the lensing signal (Pen et al. 2000; Croft & Metzler 2000; Heavens et al. 2000; Catelan et al. 2000; Crittenden et al. 2000a; Crittenden et al. 2000b). This type of systematic is problematic because its signature on different 2-points statistics mimics the lensing effect. A mode decomposition in electric and magnetic types (or E and B modes), similar to what is performed for the polarization analysis in the Cosmic Microwave Background, can separate lensing from intrinsic alignment (see Crittenden et al. 2000a; Crittenden et al. 2000b). The E and B mode analysis is the subject of a forthcoming paper; the aperture mass statistic presented in this paper is a similar analysis to the E and B mode decomposition, and allows us to put an upper limit on the contamination of our survey by the intrinsic alignments.

This paper is organized as follow: Sect. 2 describes our data set, and highlights the differences in the data preprocessing from our previous analysis (Van Waerbeke et al. 2000). The measurement of the shear from this imaging data is discussed in Sect. 3. Section 4 summarizes the theoretical aspects of the different quantities we measure, and lists the statistical estimators used. The results and comparison to a few standard cosmological models are shown in Sect. 5. In Sect. 6 we perform a maximum likelihood analysis of cosmological models in the $(\Omega_0, \sigma_8)$ parameter space. The results on very small scales are shown separately in Sect. 7, and we conclude in Sect. 8.