We study the evolution of phase-space density during the hierarchical structure formation of LCDM halos. We compute both a spherically-averaged surrogate for phase-space density (Q) and the coarse-grained distribution function f(x,v) for dark matter
particles that lie within~2 virial radii of four Milky-Way-sized dark matter halos. The estimated f(x,v) spans over four decades at any radius. Dark matter particles that end up within two virial radii of a Milky-Way-sized DM halo at $z=0$ have an approximately Gaussian distribution in log(f) at early redshifts, but the distribution becomes increasingly skewed at lower redshifts. The value corresponding to the peak of the Gaussian decreases as the evolution progresses and is well described by a power-law in (1+z). The highest values of f are found at the centers of dark matter halos and subhalos, where f can be an order of magnitude higher than in the center of the main halo. The power-law Q(r) profile likely reflects the distribution of entropy (K = sigma^2/rho^{2/3} propto r^{1.2}), which dark matter acquires as it is accreted onto a growing halo. The estimated f(x, v), on the other hand, exhibits a more complicated behavior. Although the median coarse-grained phase-space density profile F(r) can be approximated by a power-law in the inner regions of halos and at larger radii the profile flattens significantly. This is because phase-space density averaged on small scales is sensitive to the high-f material associated with surviving subhalos, as well as relatively unmixed material (probably in streams) resulting from disrupted subhalos, which contribute a sizable fraction of matter at large radii. (ABRIDGED)
We review recent progress in the description of the formation and evolution of galaxy clusters in a cosmological context by using numerical simulations. We focus our presentation on the comparison between simulated and observed X-ray properties, whil
e we will also discuss numerical predictions on properties of the galaxy population in clusters. Many of the salient observed properties of clusters, such as X-ray scaling relations, radial profiles of entropy and density of the intracluster gas, and radial distribution of galaxies are reproduced quite well. In particular, the outer regions of cluster at radii beyond about 10 per cent of the virial radius are quite regular and exhibit scaling with mass remarkably close to that expected in the simplest case in which only the action of gravity determines the evolution of the intra-cluster gas. However, simulations generally fail at reproducing the observed cool-core structure of clusters: simulated clusters generally exhibit a significant excess of gas cooling in their central regions, which causes an overestimate of the star formation and incorrect temperature and entropy profiles. The total baryon fraction in clusters is below the mean universal value, by an amount which depends on the cluster-centric distance and the physics included in the simulations, with interesting tensions between observed stellar and gas fractions in clusters and predictions of simulations. Besides their important implications for the cosmological application of clusters, these puzzles also point towards the important role played by additional physical processes, beyond those already included in the simulations. We review the role played by these processes, along with the difficulty for their implementation, and discuss the outlook for the future progress in numerical modeling of clusters.
Our heuristic understanding of the abundance of dark matter halos centers around the concept of a density threshold, or barrier, for gravitational collapse. If one adopts the ansatz that regions of the linearly evolved density field smoothed on mass
scale M with an overdensity that exceeds the barrier will undergo gravitational collapse into halos of mass M, the corresponding abundance of such halos can be estimated simply as a fraction of the mass density satisfying the collapse criterion divided by the mass M. The key ingredient of this ansatz is therefore the functional form of the collapse barrier as a function of mass M or, equivalently, of the variance sigma^2(M). Several such barriers based on the spherical, Zeldovich, and ellipsoidal collapse models have been extensively discussed. Using large scale cosmological simulations, we show that the relation between the linear overdensity and the mass variance for regions that collapse to form halos by the present epoch resembles expectations from dynamical models of ellipsoidal collapse. However, we also show that using such a collapse barrier with the excursion set ansatz predicts a halo mass function inconsistent with that measured directly in cosmological simulations. This inconsistency demonstrates a failure of the excursion set ansatz as a physical model for halo collapse. We discuss implications of our results for understanding the collapse epoch for halos as a function of mass, and avenues for improving consistency between analytical models for the collapse epoch and the results of cosmological simulations.
