The Structure of Dark Matter Halos in Hierarchical Clustering Theories

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Abstract
During hierarchical clustering, smaller masses generally collapse earlier than larger masses and so are denser on the average. The core of a small-mass halo could be dense enough to resist disruption and survive undigested when it is incorporated into a larger object. We explore the possibility that a nested sequence of undigested cores in the center of the halo that have survived the hierarchical, inhomogeneous collapse to form larger and larger objects determines the halo structure in the inner regions. For a flat universe with P(k) ∝ kn, scaling arguments then suggest that the core density profile is ρ ∝ r-α, with α = (9 + 3n)/(5 + n). For any n < 1, the signature of undigested cores is a core density profile shallower than ρ ∝ 1/r2 and dependent on the power spectrum. For typical objects formed from a cold dark matter (CDM)-like power spectrum, the effective value of n is close to -2, and thus α could typically be near 1, the Navarro, Frenk, & White (NFW) value. Velocity dispersions should also decrease with decreasing radius within the core. However, whether such behavior holds depends on detailed dynamics. We first examine the dynamics using a fluid approach to the self-similar collapse solutions for the dark matter phase-space density, including the effect of velocity dispersions. We highlight the importance of tangential velocity dispersions to obtain density profiles shallower than 1/r2 in the core regions. If tangential velocity dispersions in the core are constrained to be less than the radial dispersion, a cuspy core density profile shallower than 1/r cannot hold in self-similar collapse. We then look at the profiles of the outer halos in low-density cosmological models in which the total halo mass is convergent. We find a limiting r-4 outer profile for the open case and a limiting outer profile for the Λ-dominated case, which approaches the form [1 - (r/λ)-3]1/2, where 3 is the logarithmic slope of the initial density profile. Finally, we analyze a suite of dark halo density and velocity dispersion profiles obtained in cosmological N-body simulations of models with n = 0, -1, and -2. The core-density profiles show considerable scatter in their properties, but nevertheless do appear to reflect a memory of the initial power spectrum, with steeper initial spectra producing flatter core profiles. These results apply as well for low-density cosmological models (Ωmatter = 0.2-0.3), since high-density cores were formed early, where Ωmatter ≈ 1.
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