The structure of dark matter halos in hierarchical clustering theories

During hierarchical clustering, smaller masses generally collapse earlier t han larger masses and so are denser on the average. The core of a small-mas s halo could be dense enough to resist disruption and survive undigested wh en 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 uni verse with P(k) proportional to k(n), scaling arguments then suggest that t he core density profile is rho proportional to r(-alpha), with alpha = (9 3n)/(5 + n). For any n < 1, the signature of undigested cores is a core de nsity profile shallower than rho proportional to 1/r(2) and dependent on th e 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 cl c ould typically be near 1, the Navarro, Frenk, & White (NFW) value. Velocity dispersions should also decrease with decreasing radius within the core. H owever, whether such behavior holds depends on detailed dynamics. We first examine the dynamics using a fluid approach to the self-similar collapse so lutions for the dark matter phase-space density, including the effect of ve locity dispersions. We highlight the importance of tangential velocity disp ersions to obtain density profiles shallower than 1/r(2) in the core region s. If tangential velocity dispersions in the core are constrained to be les s 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 th e outer halos in low-density cosmological models in which the total halo ma ss is convergent. We find a limiting r(-4) outer profile for the open case and a limiting outer profile for the A-dominated case, which approaches the form [1- (r/(r) over bar(lambda))(-3 epsilon)](1/2), where 3 epsilon is th e logarithmic slope of the initial density profile. Finally, we analyze a s uite of dark halo density and velocity dispersion profiles obtained in cosm ological N-body simulations of models with n = 0, -1, and -2. The core-dens ity profiles show considerable scatter in their properties, but nevertheles s do appear to reflect a memory of the initial power spectrum, with steeper initial spectra producing flatter core profiles. These results apply as we ll for low-density cosmological models (Q(matter) = 0.2-0.3), since high-de nsity cores were formed early, where Omega(matter) approximate to 1.