The paper by Moore et al. (1998) addresses the issue of how cold dark matter (CDM) models fail to reproduce the rotation curves of dark matter-dominated galaxies, a key problem in cosmology. They perform high-resolution numerical simulations of CDM halo formation, using a large number of particles and resolving the halos to a significant fraction of their virial radii. The simulations reveal that the density profiles of these halos are steeper and have a sharper turnover than previously observed in lower-resolution studies. Specifically, the density profile is given by \(\rho(r) \propto [(r/r_s)^{1.5}(1+(r/r_s)^{1.5})^{-1}]^{-1}\), where \(r_s\) is the scale radius. This profile has a steeper asymptotic slope of \(\rho(r) \propto r^{-1.5}\) compared to the NFW profile, which is often used in CDM models. The authors compare the rotation curves of their high-resolution halos with those of low surface brightness (LSB) galaxies, which have circular velocities in the range 100-300 km s\(^{-1}\). They find that the rotation curves of the simulated halos rise too steeply to match the data, which require a constant mass density in the central regions. This discrepancy is also observed when comparing the scale-free shape of observed rotation curves with simulation data. The authors suggest that stellar rather than HI rotation curves should be used for LSB galaxies to confirm these results. To test the effects of a cut-off in the power spectrum, which may occur in a universe dominated by warm dark matter, the authors perform additional simulations where halos form through monolithic collapse. Despite this, the final density profiles remain similar, indicating that the merger history does not significantly affect the halo structure. The authors conclude that the standard CDM model, as currently formulated, cannot explain the observed rotation curves of dark matter-dominated galaxies and suggest that additional physical processes, such as a dark matter particle with a large cross-section for annihilation, may be necessary to resolve the core-halo structure observed in LSB galaxies.The paper by Moore et al. (1998) addresses the issue of how cold dark matter (CDM) models fail to reproduce the rotation curves of dark matter-dominated galaxies, a key problem in cosmology. They perform high-resolution numerical simulations of CDM halo formation, using a large number of particles and resolving the halos to a significant fraction of their virial radii. The simulations reveal that the density profiles of these halos are steeper and have a sharper turnover than previously observed in lower-resolution studies. Specifically, the density profile is given by \(\rho(r) \propto [(r/r_s)^{1.5}(1+(r/r_s)^{1.5})^{-1}]^{-1}\), where \(r_s\) is the scale radius. This profile has a steeper asymptotic slope of \(\rho(r) \propto r^{-1.5}\) compared to the NFW profile, which is often used in CDM models. The authors compare the rotation curves of their high-resolution halos with those of low surface brightness (LSB) galaxies, which have circular velocities in the range 100-300 km s\(^{-1}\). They find that the rotation curves of the simulated halos rise too steeply to match the data, which require a constant mass density in the central regions. This discrepancy is also observed when comparing the scale-free shape of observed rotation curves with simulation data. The authors suggest that stellar rather than HI rotation curves should be used for LSB galaxies to confirm these results. To test the effects of a cut-off in the power spectrum, which may occur in a universe dominated by warm dark matter, the authors perform additional simulations where halos form through monolithic collapse. Despite this, the final density profiles remain similar, indicating that the merger history does not significantly affect the halo structure. The authors conclude that the standard CDM model, as currently formulated, cannot explain the observed rotation curves of dark matter-dominated galaxies and suggest that additional physical processes, such as a dark matter particle with a large cross-section for annihilation, may be necessary to resolve the core-halo structure observed in LSB galaxies.