We use numerical simulations to examine the substructure within galactic and cluster mass halos that form within a hierarchical universe. Clusters are easily reproduced with a steep mass spectrum of thousands of substructure clumps that closely matches the observations. However, the survival of dark matter substructure also occurs on galactic scales, leading to the remarkable result that galaxy halos appear as scaled versions of galaxy clusters. The model predicts that the virialized extent of the Milky Way's halo should contain about 500 satellites with circular velocities larger than the Draco and Ursa Minor systems, i.e., bound masses տ10 8 M , and tidally limited sizes տ1 kpc. The substructure clumps are on orbits that take a large fraction of them through the stellar disk, leading to significant resonant and impulsive heating. Their abundance and singular density profiles have important implications for the existence of old thin disks, cold stellar streams, gravitational lensing, and indirect/ direct detection experiments.

Disturbed spiral galaxies with high rates of star formation pervaded clusters of galaxies just a few billion years ago, but nearby clusters exclude spirals in favor of ellipticals. "Galaxy harassment" (frequent high speed galaxy encounters) drives the morphological transformation of galaxies in clusters, provides fuel for quasars in subluminous hosts and leaves detectable debris arcs. Simulated images of harassed galaxies are strikingly similar to the distorted spirals in clusters at z ∼ 0.4 observed by the Hubble Space Telescope.Clusters of galaxies are unique cosmological laboratories. There are several hundred galaxies moving at relative velocities up to several thousand km s −1 in regions no larger than the distance between the Milky Way and its nearest neighbor, the Andromeda galaxy (M31). Clusters of galaxies have been observed at redshifts up to 2 1 . By understanding their evolution over cosmic times, we probe the geometry of the Universe and the development of its largest structures.Nearby rich galaxy clusters are dominated by elliptical "E" and lenticular "S0" galaxies 2 , mostly low luminosity dwarfs. Twenty years ago Butcher and Oemler 3,4 discovered that clusters at z ∼ > 0.4 have a substantial population of "blue galaxies" seen only as fuzzy blobs in their ground based images. Recent Hubble Space Telescope (HST) images revealed that the "fuzzy blue blobs" are low luminosity, often disturbed, spiral galaxies "Sp" 5−8 . The HST imaging teams stress that the disturbed blue galaxies are ubiquitous, but few have other galaxies nearby 5 and there were multiple bursts of star formation spanning up to 2 Gyr 8 . The dramatic transformation of clusters (shown in Figure 1) occured during a "look-back time" of just 4-5 billion years, only a few cluster orbital times. In contrast, the morphological fraction in the field shows far less evolution 9 . Given a mechanism for distorting galaxies and promoting star formation that operates when a spiral first enters a cluster, hierarchical clustering models will naturally enhance the number of "Butcher-Oemler clusters" at z ∼ 0.4 13 . Proposed mechanisms include: mergers 14,15 , compression of gas in the high pressure cluster environment 16,17 and tidal compression by the cluster 18,19 . Each of these scenarios can produce star-bursts, but none address morphological evolution or identify the remnants of these distorted blue galaxies in present day clusters. By analyzing their HST images, Oemler et al 20 conclude that merging is implausible as the blue galaxy fraction is large and the merging probability is low. They observe disturbed spirals throughout the cluster, whereas both ram pressure stripping and global tides will only operate efficiently near the cluster's center.What mechanism drives star-bursts and rapid morphological evolution throughout a cluster of galaxies? Although direct mergers are extremely rare, every galaxy experiences a high speed close encounter with a bright galaxy once per Gyr. Here, "close" means within 50 kiloparsecs (several optical radii) ...

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 halos, each containing \gsim 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 halos can be achieved using the density profile rho(r) \propto [(r/r_s)^1.5(1+(r/r_s)^1.5)]^-1, where r_s is a scale radius. This profile has a steeper asymptotic slope, rho(r) \propto r^-1.5, and a sharper turnover than found by lower resolution studies. The central structure of relaxed halos that form within a hierarchical universe has a remarkably small scatter (unrelaxed halos would not host disks). 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. The rotation curves of disks within cold dark matter halos rise too steeply to match these data which require a constant mass density in the central regions. The same conclusion is reached if we compare the scale free shape of observed rotation curves with the simulation data. It is important to confirm these results using stellar rather than HI 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 halos form by a monolithic collapse but the final density profile hardly changes, demonstrating that the merger history does not play a role in determining the halo structure.Comment: Latex 13 pages, 4 figures. Submitted to MNRAS. High resolution colour version of figure 4 and other N-body images here: http://star-www.dur.ac.uk:80/~moore/images

We examine the effects of mass resolution and force softening on the density profiles of cold dark matter halos that form within cosmological N-body simulations. As we increase the mass and force resolution, we resolve progenitor halos that collapse at higher redshifts and have very high densities. At our highest resolution we have nearly particles within the virial radius, which is several orders of magnitude more than previously used, 63 # 10 and we can resolve more than 1000 surviving dark matter halos within this single virialized system. The halo profiles become steeper in the central regions, and we may not have achieved convergence to a unique slope within the inner 10% of the virialized region. Results from two very high resolution halo simulations yield steep inner density profiles, . The abundance and properties of arcs formed within this potential will be Ϫ1.4r(r) ∼ r different from calculations based on lower resolution simulations. The kinematics of disks within such a steep potential may prove problematic for the cold dark matter model when compared with the observed properties of halos on galactic scales.