Dark Matters

If gravitationally bound structures grew from small uctuations in the initial distribution, then the statistics of the initial uctuation eld may be used to estimate many properties of the evolved dark halo distribution. I only consider hierarchical clustering. That is, I assume that mergers are common and fragmentation is not; objects present at any given time were made by mergers of smaller objects that had formed still earlier. I describe current models of the evolved halo density prooles, the forest of merger history trees associated with dark halos, and how knowledge of this forest allows one to quantify the extent to which halos are biased tracers of the dark matter distribution. 1 Density prooles of dark matter halos Numerical simulations of hierarchical gravitational clustering show that, when expressed in units of the virial density and radius, the ensemble averaged density prooles of virialized dark matter halos show the following trends: on average, for a given initial uctuation eld, more massive halos are less centrally concentrated, and halos that form from initial conditions with more large scale power have shallower prooles (e.g. Navarro, Frenk & White 1996). The rst of these trends is sometimes called the mass{density relation. The smooth spherical collapse of a single object has been relatively well studied. The secondary infall model allows one to compute the nal density proole of the object if the initial proole is known (Gunn & Gott 1972; Fillmore & Goldreich 1984; Bertschinger 1985). Roughly speaking, in these models the mass associated with a shell that is initially a certain distance from the 1