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 therefore attempt to investigate the problem using analytic and semi-analytic approaches .
Simple analytic considerations suggest that the inner slope of the central cusps in dark matter halos can not be steeper than \alpha = 2 ( where \rho \propto 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 ( eg .
angular momentum imparted by tidal torques and secondary perturbations ) or artificial ( eg .
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 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 present purposes , 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 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 .