The Extended Zel'dovich Mass Functions of Clusters and Isolated Clusters in the Presence of Primordial Non-Gaussianity

TL;DR

This paper introduces new analytic formulas for the mass functions of clusters and isolated clusters under primordial non-Gaussianity, validated against N-body simulations, and useful for constraining non-Gaussianity parameters.

Contribution

It extends the EZL model to accurately describe mass functions with primordial non-Gaussianity, requiring only a few fitting parameters.

Findings

EZL formula with fixed parameters matches N-body results well.

Modified EZL formula for isolated clusters fits various $f_{nl}$ values.

Formulas are simple, accurate, and useful for constraining non-Gaussianity.

Abstract

We present new formulae for the mass functions of the clusters and the isolated clusters with non Gaussian initial conditions. For this study, we adopt the Extended Zel'dovich (EZL) model as a basic framework, focusing on the case of primordial non-Gaussianity of the local type whose degree is quantified by a single parameter $f_{nl}$. By making a quantitative comparison with the N-body results, we first demonstrate that the EZL formula with the constant values of three fitting parameters still works remarkably well for the local $f_{nl}$ case. We also modify the EZL formula to find an analytic expression for the mass function of isolated clusters which turns out to have only one fitting parameter other than the overall normalization factor and showed that the modified EZL formula with a constant value of the fitting parameter matches excellently the N-body results with various values of $f_{nl}$ at various redshifts. Given the simplicity of the generalized EZL formulae and their good agreements with the numerical results, we finally conclude that the EZL mass functions of the massive clusters and isolated clusters should be useful as an analytic guideline to constrain the scale dependence of the primordial non-Gaussianity of the local type.