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, σ 8 , and the parameter controlling the Gaussian deviation in the model, α 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, σ 8 , and the scale parameter controlling the Gaussian deviation in the model, α 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 α 0 0.003 Mpc. Our model also indicates that only well selected galaxy cluster samples at z 1 can discriminate between Gaussian and non-Gaussian (mixed) distribution models.

Evolution of massive haloes in non-Gaussian scenarios

“…So far, the investigation of the effects of NG models in the LSS has been carried out primarily by analytic means (Lucchin & Matarrese 1988; Chiu, Ostriker & Strauss 1998; Koyama, Soda & Taruya 1999; Avelino & Viana 2000; Matarrese, Verde & Jimenez 2000; Robinson, Gawiser & Silk 2000; Robinson & Baker 2000; Verde et al 2000, 2001; Inoue & Nagashima 2002; Komatsu et al 2003; Chen et al 2003; Amara & Refregier 2004; Avelino & Liddle 2004, 2006; Scoccimarro, Sefusatti & Zaldarriaga 2004; Ribeiro et al 2007; Sadeh, Rephaeli & Silk 2007; Sefusatti et al 2007; Sefusatti & Komatsu 2007). N ‐body simulations with NG initial conditions were performed in the early 1990s (Messina et al 1990; Moscardini et al 1991; Weinberg & Cole 1992), but the considered NG models were rather simplistic, being based on fairly arbitrary distributions for the primordial density fluctuations (see also Mathis, Diego & Silk 2004).…”

“…anisotropies in the 21cm background (Pillepich et al 2007, see also Cooray (2006)), or studying the statistics of rare events, such as massive clusters, which are sensitive to the tails of the distribution of primordial fluctuations. So far, the investigation of the effects of NG models in the LSS has been carried out primarily by analytic means (Lucchin & Matarrese 1988;Koyama et al 1999;Matarrese et al 2000;Robinson & Baker 2000;Verde et al 2000Verde et al , 2001Komatsu et al 2003;Scoccimarro et al 2004;Amara & Refregier 2004;Ribeiro et al 2007;Sefusatti & Komatsu 2007;Sadeh et al 2007). N-body simulations with NG initial conditions were performed in the early nineties (Messina et al 1990;Moscardini et al 1991;Weinberg & Cole 1992), but the considered NG models were rather simplistic, being based on fairly arbitrary distributions for the primordial density fluctuations (see also Mathis et al 2004).…”