Observational and Theoretical Constraints on Singular Dark Matter Halos

The distribution of dark matter around galactic or cluster halos has usually been assumed to be approximately isothermal with a non-zero core radius, which is expected to be of the order of the size of the visible matter distribution. Recently, the possibility has been raised that dark matter halos might be singular in the sense that the dark matter density $\rho$ could increase monotonically with radius $r$ down to a very small distance from the center of galaxies or clusters. Such central cusps in the dark matter density could lead to a high flux of gamma rays from WIMP dark matter annihilation. Here we analyze two possibilities that have been discussed in the literature, $\rho \propto r^{-n}$ with $n \approx 1\ {\rm or}\ 2$, and point out that such density profiles are excluded by gravitional lensing analyses on cluster scales and by the rotation curves of gas-rich, halo-dominated dwarf spirals on small scales. We also point out that if spiral galaxies form by gas infall inside dark matter halos, as they are expected to do in any hierarchical clustering model, such profiles almost always lead to falling rotation curves after infall, contrary to observations.