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.

Can dissipationless N-body simulations be used to reliably determine the structural and substructure properties of dark matter halos? A large simulation of a galaxy cluster in a cold dark matter universe is used to increase the force and mass resolution of current "high resolution simulations" by almost an order of magnitude to examine the convergence of the important physical quantities. The cluster contains ∼ 5 million particles within the final virial radius, R vir ≃ 2 Mpc (with H 0 = 50 Km s −1 Mpc −1 ), and is simulated using a force resolution of 1.0 kpc (≡ 0.05% of R vir ); the final virial mass is 4.3 10 14 M ⊙ , equivalent to a circular velocity v circ ≡ (GM/R) 1/2 ≃ 1000 km s −1 at the virial radius. The central density profile has a logarithmic slope of -1.5, identical to lower resolution studies of the same halo, indicating that the profiles measured from simulations of this resolution have converged to the "physical" limit down to scales of a few kpc (∼ 0.2% of R vir ). Also the abundance and properties of substructure are consistent with those derived from lower resolution runs; from small to large galaxy scales (v circ > 100 km s −1 , m > 10 11 M ⊙ ), the circular velocity function and the mass function of substructures can be approximated by power laws with slopes ∼ −4 and ∼ −2 respectively. At the current resolution, overmerging -a numerical effect that leads to structureless virialized halos in low-resolution N -body simulations -seems to be globally unimportant for substructure halos with circular velocities v circ > 100 km s −1 (∼ 10% of the cluster's v circ ). We can identify subhalos orbiting in the very central region of the cluster (R ∼ < 100 kpc) and we can trace most of the cluster progenitors from high redshift to the present. The object at the cluster center (the dark matter analog of a cD galaxy) is assembled between z = 3 and z = 1 from the merging of a dozen halos with v circ ∼ > 300 km s −1 . Tidal stripping and halo-halo collisions decrease the mean circular velocity of the substructure halos by ≈ 20% over a 5 billion year period. We use the sample of 2000 substructure halos to explore the possibility of biases using galactic tracers in clusters: the velocity dispersions of the halos globally agree with the dark matter within ∼ < 10%, but the halos are spatially anti-biased, and in the very central region of the cluster (R/R vir < 0.3), they show positive velocity bias (b v ≡ σ v3D,halos /σ v3D,DM ≃ 1.2-1.3); however, this effect appears to depend on numerical resolution.

We examine the properties of dark matter haloes within a rich galaxy cluster using a high‐resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 haloes with circular velocities larger than 80 km s−1 within the cluster virial radius of 2 Mpc (with Hubble constant H0 = 50 km s−1 Mpc−1). This enables an unprecedented study of the statistical properties of a large sample of dark matter haloes evolving in a dense environment. The cumulative fraction of mass attached to these haloes varies from close to zero per cent at 200 kpc to 13 per cent at the virial radius. Even at this resolution the overmerging problem persists; haloes that pass within 100–200 kpc of the cluster centre are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor haloes. The median ratio of apocentric to pericentric radii is 6:1, so that the orbital distribution is close to isotropic, circular orbits are rare and radial orbits are common. The orbits of haloes are unbiased with respect to both position within the cluster and the orbits of the smooth dark matter background, and no velocity bias is detected. The tidal radii of surviving haloes are generally well‐fitted using the simple analytic prediction applied to their orbital pericentres. Haloes within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other haloes that cause significant mass loss —‘galaxy harassment’. Mergers between haloes do not occur inside the cluster virial radius.

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We use a cosmological simulation of the Local Group to make quantitative and speculative predictions for direct detection experiments. Cold dark matter (CDM) halos form via a complex series of mergers, accretion events and violent relaxation which precludes the formation of significant caustic features predicted by axially symmetric collapse. The halo density profiles are combined with observational constraints on the galactic mass distribution to constrain the local density of cold dark matter to lie in the range 0.18 ∼ < ρ CDM (R⊙)/(GeV cm −3 ) ∼ < 0.30. In velocity space, coherent streams of dark matter from tidally disrupted halos fill the halo and provide a tracer of the merging hierarchy. The particle velocities within triaxial CDM halos cannot be approximated by a simple Maxwellian distribution and is radially biased at the solar position. The detailed phase space structure within the solar system will depend on the early merger history of the progenitor halos and the importance of major mergers over accretion dominated growth. We follow the formation of a "Draco" sized dSph halo of mass 10 8 M⊙ with several million particles and high force accuracy. Its internal structure and substructure resembles that of galactic or cluster mass halos: the density profile has a singular central cusp and it contains thousands of sub-halos orbiting within its virial radius demonstrating a self-similar nature to collisionless dark matter sub-clustering. The singular cores of substructure halos always survive complete tidal disruption although mass loss is continuous and rapid. Extrapolating wildly to earth mass halos with velocity dispersion of 1 m s −1 (roughly equal to the free streaming scale for neutralinos) we find that most of the dark matter may remain attached to bound subhalos. Further numerical and analytic work is required to confirm the existence of a detectable smooth component. PACS number(s): 95.35.+d, 98.35.Gi, 98.35.Df, 98.35.Mp, 95.75.Pq