Relaxing and Virializing a Dark Matter Halo

Navarro, Frenk, and White have suggested that the density profiles of simulated dark matter halos have a ``universal'' shape so that a given halo can be characterized by a single free parameter which fixes its mass. In this paper, we revisit the spherical infall model in the hope of recognizing in detail the existence and origin of any such universality. A system of particles is followed from linear perturbation, through first shell crossing, then through an accretion or infall phase, and finally to virialization. During the accretion phase, the system relaxes through a combination of phase mixing, phase space instability, and moderate violent relation. It is driven quickly, by the flow of mass through its surface, toward self-similar evolution. The self-similar solution plays its usual role of intermediate attractor and can be recognized from a virial-type theorem in scaled variables and from our numerical simulations. The transition to final equilibrium state once infall has ceased is relatively gentle, an observation which leads to an approximate form for the distribution function of the final system. The infall phase fixes the density profile in intermediate regions of the halo to be close to r^{-2}. We make contact with the standard hierarchical clustering scenario and explain how modifications of the self-similar infall model might lead to density profiles in agreement with those found in numerical simulations.Comment: 26 pages, Latex, plus 11 figure

On Stationary, Self-Similar Distributions of a Collisionless, Self-Gravitating, Gas

We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution functions where the mass density and gravitational potential are strict power laws in $r$, the distance from the symmetry point. We treat as special cases, systems built from purely radial orbits and systems that are isotropic in velocity space. We then discuss systems with arbitrary velocity space anisotropy finding a new and very general class of distribution functions. These distributions may prove useful in modelling galaxies. Distribution functions in cylindrical and planar geometries are also discussed. Finally, we study spatially spheroidal systems that again exhibit strict power-law behaviour for the density and potential and find results in agreement with results published recently.Comment: 23 pages, regular Tex, figures in separate .uu file to follo

Microlensing By a Prolate All-Macho Halo

It is widely believed that dark matter halos are flattened, that is closer to oblate than prolate. The evidence cited is based largely on observations of galaxies which do not look anything like our own and on numerical simulations which use ad hoc initial conditions. Given what we believe to be a ``reasonable doubt'' concerning the shape of dark Galactic halo we calculate the optical depth and event rate for microlensing of stars in the LMC assuming a wide range of models that include both prolate and oblate halos. We find, in agreement with previous analysis, that the optical depth for a spherical (E0) halo and for an oblate (E6) halo are roughly the same, essentially because two competing effects cancel approximately. However the optical depth for an E6 prolate halo is reduced by ~35%. This means that an all-Macho prolate halo with reasonable parameters for the Galaxy is consistent with the published microlensing event rate.Comment: 7 pages (24K), LaTeX; 2 Postscript figure