A Cosmological Mass Function with Broken Hierarchy

Abstract

We construct an analytic formalism for the mass function of cold dark matter halos, assuming that there is a break in the hierarchical merging process. According to this {\it broken-hierarchy} scenario, due to the inherent nature of the gravitational tidal field the formation of massive pancakes precedes that of dark halos of low-mass. In the framework of the Zel&#39;dovich approximation which generically predicts the presence of pancakes, we first derive analytically the conditional probability that a low-mass halo observed at present epoch was embedded in an isolated pancake at some earlier epoch. Then, we follow the standard Press-Schechter approach to count analytically the number density of low-mass halos that formed through anti-hierarchical fragmentation of the massive pancakes. Our mass function is well approximated by a power-law dN/dM = M^{-l} in the mass range 10^{6}M_{sun}/h < M < 10^{10}M_{sun}/h with the slope l=1.86 shallower than that of the currently popular Sheth-Tormen mass function l = 2.1. It is expected that our mass function will provide a useful analytic tool for investigating the effect of broken hierarchy on the structure formation.