Measuring the scatter of the mass-richness relation in galaxy clusters in photometric imaging surveys by means of their correlation function

Knowledge of the scatter in the mass-observable relation is a key ingredient for a cosmological analysis based on galaxy clusters in a photometric survey. In this paper we aim to quantify the capability of the correlation function of galaxy cluster to constrain the intrinsic scatter $\sigma_{\ln M}$. We demonstrate how the linear bias measured in the correlation function of clusters can be used to determine the value of this parameter. The new method is tested in simulations of a $5, 000 deg^2$ optical survey up to $z \sim 1$, similar to the ongoing Dark Energy Survey (DES). Our results show that our method works better at lower scatter values. We can measured the intrinsic scatter $\sigma_{ln M} = 0.1$ with a standard deviation of $\sigma(\sigma_{ln M}) \sim 0.03$ using this technique. However, the expected intrinsic scatter of the DES RedMaPPer cluster catalog $\sigma_{ln M} \sim 0.2$ cannot be recovered with this method at suitable accuracy and precision because the area coverage is insufficient. For future photometric surveys with a larger area such as LSST and Euclid, the statistical errors will be reduced. Therefore, we forecast higher precision to measure the intrinsic scatter including the value mention before. We conclude that this method can be used as an internal consistency check method on their simplifying assumptions and complementary to cross-calibration techniques in multi-wavelength cluster observations