The halo mass functions at redshift z = 0, for halos defined by a nonlinear density contrast δ_∗ = 200,400,800, and 1600. The solid line is our model (35), the dashed line is the fit from Sheth & Tormen (1999), which does not change with δ_∗, and the points are the results from numerical simulations in Tinker et al. (2008). The value of the parameter α in Eq. (31) is set to α = 2.2. Here M = M_δ∗ is the halo mass enclosed within the radius defined by the density threshold δ_∗.