N-body simulations of structure formation in the universe are reaching the point at which galaxy scale objects can be resolved. These structures have proven to have remarkably similar characteristics. Their density profiles appear to be well described by an analytical function that has become known as the NFW profile, after the work of Navarro, Frenk, & White. Halos with this profile have densities which are inversely proportional to radial distance close to the center (logarithmic slope=-1), a transition region where the logarithmic slope changes, and an outer region where the density is inversely proportional to the cube of the radial distance (logarithmic slope=-3).
What we are interested in answering is, why do N-body simulations produce this kind of profile? Is there some underlying physical mechanism governing collisionless systems that drives the halos to have this form? Are these halos the result of hierarchical structure formation? Or, is is simply the result of cosmological initial conditions?
Since N-body simulations are, by definition, complicated procedures, it is difficult to untangle different causes and effects within them. So, we are taking a step back and utilizing a simpler, more controllable technique to create halos. Ryden & Gunn laid out a method of determining the structure of a halo based on analytical expressions. We are utilizing a slightly modified form of this method which gives us a great deal of control over specific changes to conditions. This control will hopefully allow us to dissect root causes of the prevalence of NFW halos.
We are also investigating a "thermodynamic" approach to this problem; are there global quantities that determine the structure of self-gravitating equilibria? We have begun to make our own N-body models that we can compare to analytical models derived from, for example, nonextensive thermodynamic considerations.