  We investigate the collapse and internal structure of dark matter halos. We
consider halo formation from initially scale-free perturbations, for which
gravitational collapse is self-similar. Fillmore and Goldreich (1984) and
Bertschinger (1985) solved the one dimensional (i.e. spherically symmetric)
case. We generalize their results by formulating the three dimensional
self-similar equations. We solve the equations numerically and analyze the
similarity solutions in detail, focusing on the internal density profiles of
the collapsed halos. By decomposing the total density into subprofiles of
particles that collapse coevally, we identify two effects as the main
determinants of the internal density structure of halos: adiabatic contraction
and the shape of a subprofile shortly after collapse; the latter largely
reflects the triaxiality of the subprofile. We develop a simple model that
describes the results of our 3D simulations. In a companion paper, we apply
this model to more realistic cosmological fluctuations, and thereby explain the
origin of the nearly universal (NFW-like) density profiles found in N-body
simulations.
