  Our heuristic understanding of the abundance of dark matter halos centers
around the concept of a density threshold, or "barrier", for gravitational
collapse. If one adopts the ansatz that regions of the linearly evolved density
field smoothed on mass scale M with an overdensity that exceeds the barrier
will undergo gravitational collapse into halos of mass M, the corresponding
abundance of such halos can be estimated simply as a fraction of the mass
density satisfying the collapse criterion divided by the mass M. The key
ingredient of this ansatz is therefore the functional form of the collapse
barrier as a function of mass M or, equivalently, of the variance sigma^2(M).
Several such barriers based on the spherical, Zel'dovich, and ellipsoidal
collapse models have been extensively discussed. Using large scale cosmological
simulations, we show that the relation between the linear overdensity and the
mass variance for regions that collapse to form halos by the present epoch
resembles expectations from dynamical models of ellipsoidal collapse. However,
we also show that using such a collapse barrier with the excursion set ansatz
predicts a halo mass function inconsistent with that measured directly in
cosmological simulations. This inconsistency demonstrates a failure of the
excursion set ansatz as a physical model for halo collapse. We discuss
implications of our results for understanding the collapse epoch for halos as a
function of mass, and avenues for improving consistency between analytical
models for the collapse epoch and the results of cosmological simulations.
