Cold collapse and the core catastrophe

We show that a universe dominated by cold dark matter fails to reproduce th e rotation curves of dark matter dominated galaxies, one of the key problem s that it was designed to resolve. We perform numerical simulations of the formation of dark matter haloes, each containing greater than or similar to 10(6) particles and resolved to 0.003 times the virial radius, allowing an accurate comparison with rotation curve data. A good fit to both Galactic and cluster-sized haloes can be achieved using the density profile rho(r) p roportional to [(rr(s))(1.5)(1 + (rr(s))(1.5))](-1), where r(s) is a scale radius. This profile has a steeper asymptotic slope, rho(r) proportional to r(-1.5), and a sharper turn-over than found by lower resolution studies. T he central structure of relaxed haloes that form within a hierarchical univ erse has a remarkably small scatter. We compare the results with a sample o f dark matter dominated, low surface brightness (LSB) galaxies with circula r velocities in the range 100-300 km s(-1). The rotation curves of discs wi thin cold dark matter haloes rise too steeply to match these data, which re quire a constant mass density in the central regions. The effects of Omega( mass) and Lambda cannot reconcile the cold dark matter (CDM) model with dat a - even if we leave the concentration as a free parameter, we are unable t o reproduce the observations with such a steep central density profile. It is important to confirm these results using stellar rather than H I rotatio n curves for LSB galaxies. We test the effects of introducing a cut-off in the power spectrum that may occur in a universe dominated by warm dark matt er. In this case, haloes form by a monolithic collapse but the final densit y profile barely changes, demonstrating that the merger history does not pl ay a role in determining the halo structure.