An Extended Zel'dovich Model for the Halo Mass Function

TL;DR

This paper introduces an extended Zel'dovich model that provides a highly accurate, scale- and redshift-independent fitting formula for the halo mass function, validated against high-resolution N-body simulations.

Contribution

It presents a novel fitting formula based on a modified Jedamzik matrix equation that automatically satisfies normalization and fits simulation data across various scales and cosmologies.

Findings

Achieves less than 10% deviation from N-body results over a wide mass range.

Works effectively across different redshifts (z=0, 0.5, 1).

Independent of scale, redshift, and background cosmology.

Abstract

A new way to construct a fitting formula for the halo mass function is presented. Our formula is expressed as a solution to the modified Jedamzik matrix equation that automatically satisfies the normalization constraint. The characteristic parameters expressed in terms of the linear shear eigenvalues are empirically determined by fitting the analytic formula to the numerical results from the high-resolution N-body simulation and found to be independent of scale, redshift and background cosmology. Our fitting formula with the best-fit parameters is shown to work excellently in the wide mass-range at various redshifts: The ratio of the analytic formula to the N-body results departs from unity by up to 10% and 5% over 10^{11}<= M/(M_sun/h)<= 5x10^{15} at z=0,\ 0.5 and 1 for the FoF-halo and SO-halo cases, respectively.