Self-Similar Spherical Collapse with Tidal Torque
  N-body simulations have revealed a wealth of information about dark matter
halos however their results are largely empirical. Using analytic means, we
attempt to shed light on simulation results by generalizing the self-similar
secondary infall model to include tidal torque. In this first of two papers, we
describe our halo formation model and compare our results to empirical mass
profiles inspired by N-body simulations. Each halo is determined by four
parameters. One parameter sets the mass scale and the other three define how
particles within a mass shell are torqued throughout evolution. We choose
torque parameters motivated by tidal torque theory and N-body simulations and
analytically calculate the structure of the halo in different radial regimes.
We find that angular momentum plays an important role in determining the
density profile at small radii. For cosmological initial conditions, the
density profile on small scales is set by the time rate of change of the
angular momentum of particles as well as the halo mass. On intermediate scales,
however, $\rho\propto r^{-2}$, while $\rho\propto r^{-3}$ close to the virial
radius.
