Investigating the origins of dark matter halo density profiles

Although high-resolution N-body simulations make robust empirical predictions of the density distribution within cold dark matter halos, these studies have yielded little physical insight into the origins of the distribution. We therefore attempt to investigate the problem using analytic and semianalytic approaches. Simple analytic considerations suggest that the inner slope of the central cusps in dark matter halos cannot be steeper than alpha = 2 (where rho proportional to r(-alpha)), with alpha = 1.5-1.7 being a more realistic upper limit. Moreover, our analysis suggests that any number of effects, whether real (e.g., angular momentum imparted by tidal torques and secondary perturbations) or artificial (e.g., two-body interactions, the accuracy of the numerical integrator, round-off errors) will result in shallower slopes. We also find that the halos should exhibit a well-defined relationship between r(peri)/r(apo) and j(theta)/j(r). We derive this relationship analytically and speculate that it may be "universal." Using a semianalytic scheme based on Ryden & Gunn, we further explore the relationship between the specific angular momentum distribution in a halo and its density profile. For present purposes, we restrict ourselves to halos that form primarily via the nearly smooth accretion of matter, and consider only the specific angular momentum generated by secondary perturbations associated with the cold dark matter spectrum of density fluctuations. Compared to those formed in N-body simulations, our "semianalytic" halos are more extended, have flatter rotation curves, and have a higher specific angular momentum, even though we have not yet taken into account the effects of tidal torques. Whether the density profile of numerical halos is indeed the result of loss in angular momentum outside the central region, and whether this loss is a feature of hierarchical merging and major mergers in particular, is under investigation.