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

¹ Laboratório de Astrofísica Teórica e Observacional, Departamento de Ciências Exatas e Tecnológicas, Universidade Estadual de Santa Cruz – 45650-000, Ilhéus, Brazil e-mail: [albr;apaula]@uesc.br
² Instituto Nacional de Pesquisas Espaciais, Divisão de Astrofísica – CP 515, 12245-970, São José dos Campos, SP, Brazil e-mail: carla@das.inpe.br
³ Instituto Nacional de Pesquisas Espaciais, Laboratório Associado de Computação e Matemática Aplicada – CP 515, 12245-970, São José dos Campos, SP, Brazil e-mail: msdantas@lac.inpe.br

Received: 5 January 2006
Accepted: 5 February 2007

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, , and the parameter controlling the Gaussian deviation in the model, , 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, , and the scale parameter controlling the Gaussian deviation in the model, . 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  Mpc. Our model also indicates that only well selected galaxy cluster samples at can discriminate between Gaussian and non-Gaussian (mixed) distribution models.