Cold collapse and the core catastrophe

We show that a universe dominated by cold dark matter fails to reproduce the rotation curves of dark matter dominated galaxies, one of the key problems 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) proportional 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. The central structure of relaxed haloes that form within a hierarchical universe has a remarkably small scatter. We compare the results with a sample of dark matter dominated, low surface brightness (LSB) galaxies with circular velocities in the range 100-300 km s(-1). The rotation curves of discs within cold dark matter haloes rise too steeply to match these data, which require a constant mass density in the central regions. The effects of Omega(mass) and Lambda cannot reconcile the cold dark matter (CDM) model with data - even if we leave the concentration as a free parameter, we are unable to reproduce the observations with such a steep central density profile. It is important to confirm these results using stellar rather than H I rotation 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 matter. In this case, haloes form by a monolithic collapse but the final density profile barely changes, demonstrating that the merger history does not play a role in determining the halo structure.