An Extended Zel'dovich Model for the Halo Mass Function

Understand

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.