We discuss the evolved mass profile near the center of an
initial spherical density perturbation, δ ∝ M–ε, of collision-less particles with non-radial
motions. W consider a scheme in
which a particle moves on a radial orbit until it reaches its
turnaround radius, r*. At turnaround the particle acquires an
angular momentum $L={\cal L} \sqrt{GM_* r_*}$ per unit mass, where
M* is the mass interior to r*. In this scheme, the mass profile
is M ∝ r3/(1+3ε) for all ε > 0, in the region r/rt ≪ ${\cal L}$, where rt is the current turnaround radius.
If ${\cal L}$ ≪ 1 then the profile in the region ${\cal L}$ ≪ r/rt ≪ is M ∝ r for ε <2/3.
We also present a model for the growth of dark matter halos and
use it to study their evolved density profiles.
In this model, halos are spherical and form by
quiescent accretion of matter in clumps, called satellites.
The halo mass as a function of redshift is given by the mass of
the most massive progenitor, and is determined from Monte-Carlo
realizations of the merger-history tree.
Inside the halo, satellites move under the action of the
gravitational force of the halo and a dynamical friction drag force.
The associated equation of motion is solved numerically.
The energy lost to dynamical friction is transferred to the halo
in the form of kinetic energy.
As they sink into the halo, satellites continually lose matter as
a result of tidal stripping. The stripped matter moves inside the
for mass scales where the effective spectral index of the initial
density field is less than –1, the model predicts a profile which
can only approximately be matched by the NFW one parameter family of curves. For scale-free
power-spectra with initial slope n, the density
profile within about 1% of the virial radius is
ρ ∝ r–β, with 3(3+n)/(5+n) ≤ β ≤ 3(3+n)/(4+n).