Self-similar collapse with non-radial motions

Abstract

We discuss the evolved mass profile near the center of aninitial spherical density perturbation, δ ∝ M^–ε, of collision-less particles with non-radialmotions. W consider a scheme inwhich a particle moves on a radial orbit until it reaches itsturnaround radius, r_*. At turnaround the particle acquires anangular momentum $L={\cal L} \sqrt{GM_* r_*}$ per unit mass, whereM_* is the mass interior to r_*. In this scheme, the mass profileis M ∝ r^3/(1+3ε) for all ε > 0, in the region r/r_t ≪ ${\cal L}$, where r_t is the current turnaround radius.If ${\cal L}$ ≪ 1 then the profile in the region ${\cal L}$ ≪ r/r_t ≪ 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 byquiescent 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).