  Although high-resolution N-body simulations make robust empirical predictions
for the density distribution within cold dark matter halos, these studies have
yielded little physical insight into the origins of the distribution. We
investigate the problem using analytic and semi-analytic approaches. Simple
analytic considerations suggest that the inner slope of dark matter halos
cannot be steeper than alpha=2 (rho ~ r^-alpha), with alpha=1.5-1.7 being a
more realistic upper limit. Our analysis suggests that any number of effects,
both real (angular momentum from tidal torques, secondary perturbations) and
artificial (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 relation between r_peri/r_apo and j_theta/j_r. We
derive this relation analytically and speculate that it may be "universal".
Using a semi-analytic scheme based on Ryden & Gunn (1987), we further explore
the relationship between the specific angular momentum distribution in a halo
and its density profile. For now we restrict ourselves to halos that form
primarily via nearly-smooth accretion of matter, and only consider 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 ``semi-analytic'' halos are more extended, have flatter
rotation curves and have higher specific angular momentum, even though we have
not yet taken into account the effects of tidal torques. Whether the density
profiles 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.
