Seunghwan Lim, Jounghun Lee
A non-stochastic scale-independent multi-dimensional barrier model of ellipsoidal collapse for the excursion set halo mass function is presented. The key concept of our model is that a bound halo forms at the moment when the initial shear eigenvalues hit a multi-dimensional absorbing barrier of constant height in their random walking process. The multi-dimensional barrier height that characterizes the analytic halo mass function is empirically determined by fitting the numerical results from the high-resolution N-body simulation to our model. It is found that the best-fit value of the barrier height is independent of redshift and key cosmological parameters. Our analytic model with empirically determined barrier-height is shown to work excellently in the wide mass-range at various redshifts: The ratio of the model to the N-body results departs from unity by up to 5% over $10^{11}\le M/(h^{-1}M_{\odot})\le 5\times 10^{15}$ at $z=0,\ 0.5$ and 1 for both of the FoF-halo and SO-halo cases. It is also shown that our analytic model naturally explains the stochastic behaviors of the density threshold value and its log-normal distribution.
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http://arxiv.org/abs/1206.5351
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