Mass variance and cluster abundance in the context of a Gaussian + lognormal distribution model

Abstract

Context. We investigate the behavior of the mass variance and the mass function of galaxy clusters in a mixed distribution model. Aims. Our aim is to find a relation between the mass variance at a 8 h -1 Mpc scale, $\sigma_8$, and the parameter controlling the Gaussian deviation in the model, $\alpha_0$, and to constrain the non-Gaussianity using observational data at cluster scales. Methods. By assuming that the statistics of the density field is built as a weighted mixture of two components, a Gaussian + Lognormal distribution, we rewrite the mass variance expression and the mass function for galaxy clusters. Results. We find a relation between the mass variance at a 8 h -1 Mpc scale, $\sigma_8$, and the scale parameter controlling the Gaussian deviation in the model, $\alpha_0$. This result, in conjunction with observational constraints on the mass variance and high- z galaxy clustering, suggests a scenario where structures develop earlier in comparison to strictly Gaussian models, even for $\alpha_0\lesssim 0.003$ Mpc. Our model also indicates that only well selected galaxy cluster samples at $z\gtrsim 1$ can discriminate between Gaussian and non-Gaussian (mixed) distribution models.