Abstract
We study the differential energy distribution of dark matter halos by carrying out a cosmological N-body simulation. We give an analytical formula for the differential energy distribution of dark matter in the halos obtained by the numerical simulation. From the analytical formula we reconstruct the density profile described by the Navarro, Frenk, & White (NFW) profile. The NFW profile is consistent with the analytical formula of our fractional mass distribution. We find a parameter in our analytical formula for the differential energy distribution that is related to the slope of the inner cusp of the dark halo. We obtain the distribution function for the NFW profile, which has a sharp cutoff at the high binding energy. We discuss physical reasons for the form of the analytical formula.
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