A Cosmological Mass Function with Broken Hierarchy

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 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’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 PressSchechter 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 in the mass range 106h−1M⊙ ≤ M ≤ 1010h−1M⊙ 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. Subject headings: cosmology:theory — large-scale structure of universe