New constraints on σ8 from a joint analysis of stacked gravitational lensing and clustering of galaxy clusters

The joint analysis of clustering and stacked gravitational lensing of galaxy clusters in large surveys can constrain the formation and evolution of structures and the cosmological parameters. On scales outside a few virial radii, the halo bias, b, is linear and the lensing signal is dominated by the correlated distribution of matter around galaxy clusters. We discuss a method to measure the power spectrum amplitude σ8 and b based on a minimal modelling.We considered a sample of ~120 000 clusters photometrically selected from the Sloan Digital Sky Survey in the redshift range 0.1 < z < 0.6. The autocorrelation was studied through the twopoint function of a subsample of ~70 000 clusters; the matter-halo correlation was derived from the weak lensing signal of the subsample of ~1200 clusters with Canada-France-Hawaii Telescope Lensing Survey data.We obtained a direct measurement of b, which increases with mass in agreement with predictions of the Λ cold dark matter paradigm. Assuming Ω<inf>M</inf> = 0.3, we found σ8 = 0.79 ± 0.16. We used the same clusters for measuring both lensing and clustering and the estimate of σ8 did require neither the mass-richness relation, nor the knowledge of the selection function, nor the modelling of b. With an additional theoretical prior on the bias, we obtained σ8 = 0.75 ± 0.08.