2008MNRAS.385..695B

We present a joint weak lensing and X-ray analysis of 4 deg² from the CFHTLS and XMM-LSS surveys. Our weak lensing analysis is the first analysis of a real survey using shapelets, a new generation weak lensing analysis method. We create projected mass maps of the images, and extract six weak-lensing-detected clusters of galaxies. We show that their counts can be used to constrain the power-spectrum normalization σ₈= 0.92^+0.26_–0.30 for Ω_m= 0.24. We show that despite the large scatter generally observed in the mass-temperature (M-T) relation derived from lensing masses, tight constraints on both its slope and normalization M_* can be obtained with a moderate number of sources provided that the covered mass range is large enough. Adding clusters given by Bardeau et al. to our sample, we measure M_*= 2.71^+0.79_–0.61x10¹⁴h^–1M_solar. Although they are dominated by shot noise and sample variance, our measurements are consistent with currently favoured values, and set the stage for future surveys. We thus investigate the dependence of those estimates on survey size, depth and integration time, for joint weak lensing and X-ray surveys. We show that deep surveys should be dedicated to the study of the physics of clusters and groups of galaxies. For a given exposure time, wide surveys provide a larger number of detected clusters and are therefore preferred for the measurement of cosmological parameters, such as σ₈ and M_*. We show that a wide survey of a few hundred square degrees is needed to improve upon current measurements of these parameters. More ambitious surveys covering 7000 deg² will provide the 1 per cent accuracy in the estimation of the power-spectrum and the M-T relation normalizations.