Intrinsic correlation of halo ellipticity and its implications for large‐scale weak lensing surveys

We use a large set of state‐of‐the‐art cosmological N ‐body simulations [512 3 particles] to study the intrinsic ellipticity correlation functions of haloes. With the simulations of different resolutions, we find that the ellipticity correlations converge once the haloes have more than 160 members. For haloes with fewer members, the correlations are underestimated, and the underestimation amounts to a factor of 2 when the haloes have only 20 particles. After correcting for the resolution effects, we show that the ellipticity correlations of haloes in the bigger box L = 300 h −1 Mpc) agree very well with those obtained in the smaller box ( L = 100 h −1 Mpc) . Combining these results from the different simulation boxes, we present accurate fitting formulae for the ellipticity correlation function c 11 ( r ) and for the projected correlation functions Σ 11 ( r p ) and Σ 22 ( r p ) over three orders of magnitude in halo mass. The latter two functions are useful for predicting the contribution of the intrinsic correlations to deep lensing surveys. With reasonable assumptions for the redshift distribution of galaxies and for the mass of galaxies, we find that the intrinsic ellipticity correlation can contribute significantly not only to shallow surveys but also to deep surveys. Our results indicate that previous similar studies significantly underestimated this contribution for their limited simulation resolutions.