We use the Fourth Data Release of the Sloan Digital Sky Survey to test the ubiquity of infall patterns around galaxy clusters and measure cluster mass profiles to large radii. We match X-ray cluster catalogs with SDSS, search for infall patterns, and compute mass profiles for a complete sample of X-ray selected clusters. Very clean infall patterns are apparent in most of the clusters, with the fraction decreasing with increasing redshift due to shallower sampling. All 72 clusters in a well-defined sample limited by redshift (ensuring good sampling) and X-ray flux (excluding superpositions) show infall patterns sufficient to apply the caustic technique. This sample is by far the largest sample of cluster mass profiles extending to large radii to date. Similar to CAIRNS, cluster infall patterns are better defined in observations than in simulations. Further work is needed to determine the source of this difference. We use the infall patterns to compute mass profiles for 72 clusters and compare them to model profiles. Cluster scaling relations using caustic masses agree well with those using X-ray or virial mass estimates, confirming the reliability of the caustic technique. We confirm the conclusion of CAIRNS that cluster infall regions are well fit by NFW and Hernquist profiles and poorly fit by singular isothermal spheres. This much larger sample enables new comparisons of cluster properties with those in simulations. The shapes (specifically, NFW concentrations) of the mass profiles agree well with the predictions of simulations. The mass inside the turnaround radius is on average 2.19$\pm$0.18 times that within the virial radius. This ratio agrees well with recent predictions from simulations of the final masses of dark matter haloes.Comment: 34 pages, 24 figures, accepted for publication in AJ, full resolution version available at http://www.astro.yale.edu/krines

We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both non-linear and linear theory ter

We write the correlation function of dark matter particles, ξ(r), as the sum of two terms — one which accounts for non-linear evolution, and dominate

The cold dark-matter model successfully explains both the emergence and evolution of cosmic structures on large scales and, when we include a cosmological constant, the properties of the homogeneous and isotropic Universe. However, the cold dark-matter model faces persistent challenges on the scales of galaxies. Indeed, N-body simulations predict some galaxy properties that are at odds with the observations. These discrepancies are primarily related to the dark-matter distribution in the innermost regions of the halos of galaxies and to the dynamical properties of dwarf galaxies. They may have three different origins: (1) the baryonic physics affecting galaxy formation is still poorly understood and it is thus not properly included in the model; (2) the actual properties of dark matter differs from those of the conventional cold dark matter; (3) the theory of gravity departs from General Relativity. Solving these discrepancies is a rapidly evolving research field. We illustrate some of the solutions proposed within the cold dark-matter model, and solutions when including warm dark matter, self-interacting dark matter, axion-like particles, or fuzzy dark matter. We also illustrate some modifications of the theory of gravity: Modified Newtonian Dynamics (MOND), MOdified Gravity (MOG), and $f\left(R\right)$ gravity.

Modern cosmological observations allow us to study in great detail the evolution and history of the large scale structure hierarchy. The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological model, requires precise modelling of the observed structure. In this paper we briefly review the current most effective techniques of large scale structure simulations, emphasising both their advantages and shortcomings. Starting with basics of the direct N-body simulations appropriate to modelling cold dark matter evolution, we then discuss the direct-sum technique GRAPE, particle-mesh (PM) and hybrid methods, combining the PM and the tree algorithms. Simulations of baryonic matter in the Universe often use hydrodynamic codes based on both particle methods that discretise mass, and grid-based methods. We briefly describe Eulerian grid methods, and also some variants of Lagrangian smoothed particle hydrodynamics (SPH) methods.

We present a spectroscopic sample of 910 distant halo stars from the Hypervelocity Star survey from which we derive the velocity dispersion profile of the Milky Way halo. The sample is a mix of 74% evolved horizontal branch stars and 26% blue stragglers. We estimate distances to the stars using observed colors, metallicities, and stellar evolution tracks. Our sample contains twice as many objects with R > 50 kpc as previous surveys. We compute the velocity dispersion profile in two ways: with a parametric method based on a Milky Way potential model and with a non-parametric method based on the caustic technique originally developed to measure galaxy cluster mass profiles. The resulting velocity dispersion profiles are remarkably consistent with those found by two independent surveys based on other stellar populations: the Milky Way halo exhibits a mean decline in radial velocity dispersion of –0.38 ± 0.12 km s^–1 kpc^–1 over 15 < R < 75 kpc. This measurement is a useful basis for calculating the total mass and mass distribution of the Milky Way halo.