We present gas and total mass profiles for 13 low-redshift, relaxed clusters spanning a temperature range 0.7-9 keV, derived from all available Chandra data of sufficient quality. In all clusters, gas-temperature profiles are measured to large radii (Vikhlinin et al.) so that direct hydrostatic mass estimates are possible to nearly r 500 or beyond. The gas density was accurately traced to larger radii; its profile is not described well by a beta model, showing continuous steepening with radius. The derived tot profiles and their scaling with mass generally follow the Navarro-Frenk-White model with concentration expected for dark matter halos in ÃCDM cosmology. However, in three cool clusters, we detect a central mass component in excess of the Navarro-Frenk-White profile, apparently associated with their cD galaxies. In the inner region (r < 0:1r 500 ), the gas density and temperature profiles exhibit significant scatter and trends with mass, but they become nearly self-similar at larger radii. Correspondingly, we find that the slope of the masstemperature relation for these relaxed clusters is in good agreement with the simple self-similar behavior, M 500 / T , where ¼ (1:5 1:6) AE 0:1, if the gas temperatures are measured excluding the central cool cores. The normalization of this M-T relation is significantly, by %30%, higher than most previous X-ray determinations. We derive accurate gas mass fraction profiles, which show an increase with both radius and cluster mass. The enclosed f gas profiles within r 2500 ' 0:4r 500 have not yet reached any asymptotic value and are still far (by a factor of 1.5À2) from the universal baryon fraction according to the cosmic microwave background (CMB) observations. The f gas trends become weaker and its values closer to universal at larger radii, in particular, in spherical shells r 2500 < r < r 500 .

Chandra observations of large samples of galaxy clusters detected in X-rays by ROSAT provide a new, robust determination of the cluster mass functions at low and high redshifts. Statistical and systematic errors are now sufficiently small, and the redshift leverage sufficiently large for the mass function evolution to be used as a useful growth of a structure-based dark energy probe. In this paper, we present cosmological parameter constraints obtained from Chandra observations of 37 clusters with z = 0.55 derived from 400 deg 2 ROSAT serendipitous survey and 49 brightest z ≈ 0.05 clusters detected in the All-Sky Survey. Evolution of the mass function between these redshifts requires Ω Λ > 0 with a ∼ 5σ significance, and constrains the dark energy equationof-state parameter to w 0 = −1.14 ± 0.21, assuming a constant w and a flat universe. Cluster information also significantly improves constraints when combined with other methods. Fitting our cluster data jointly with the latest supernovae, Wilkinson Microwave Anisotropy Probe, and baryonic acoustic oscillation measurements, we obtain w 0 = −0.991 ± 0.045 (stat) ±0.039 (sys), a factor of 1.5 reduction in statistical uncertainties, and nearly a factor of 2 improvement in systematics compared with constraints that can be obtained without clusters. The joint analysis of these four data sets puts a conservative upper limit on the masses of light neutrinos m ν < 0.33 eV at 95% CL. We also present updated measurements of Ω M h and σ 8 from the low-redshift cluster mass function.

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We present a systematic analysis of 43 nearby galaxy groups (kT 500 = 0.7 − 2.7 keV or M 500 = 10 13 − 10 14 h −1 M ⊙ , 0.012 < z < 0.12), based on Chandra archival data. With robust background subtraction and modeling, we trace gas properties to at least r 2500 for all 43 groups. For 11 groups, gas properties can be robustly derived to r 500 . For an additional 12 groups, we derive gas properties to at least r 1000 and estimate properties at r 500 from extrapolation. We show that in spite of the large variation in temperature profiles inside 0.15 r 500 , the temperature profiles of these groups are similar at > 0.15 r 500 and are consistent with a "universal temperature profile." We present the K − T relations at six characteristic radii (30 kpc, 0.15 r 500 , r 2500 , r 1500 , r 1000 and r 500 ), for 43 groups from this work and 14 clusters from the Vikhlinin et al. (2008) sample. Despite large scatter in the entropy values at 30 kpc and 0.15 r 500 , the intrinsic scatter at r 2500 is much smaller and remains the same (∼ 10%) to r 500 . The entropy excess at r 500 is confirmed, in both groups and clusters, but the magnitude is smaller than previous ROSAT and ASCA results. We also present scaling relations for the gas fraction. It appears that the average gas fraction between r 2500 and r 500 has no temperature dependence, ∼ 0.12 for 1 -10 keV systems. The group gas fractions within r 2500 are generally low and have large scatter. This work shows that the difference of groups from hotter clusters stems from the difficulty of compressing group gas inside of r 2500 . The large scatter of the group gas fraction within r 2500 causes large scatter in the group entropy around the center and may be responsible for the large scatter of the group luminosities. Nevertheless, the groups appear more regular and more like clusters beyond r 2500 , from the results on gas fraction and entropy. Therefore, mass proxies can be extended into low mass systems. The M 500 − T 500 and M 500 − Y X,500 relations derived in this work are indeed well behaved down to at least 2 ×10 13 h −1 M ⊙ .

We compare new maps of the hot gas, dark matter, and galaxies for 1E 0657À56, a cluster with a rare highvelocity merger occurring nearly in the plane of the sky. The X-ray observations reveal a bullet-like gas subcluster just exiting the collision site. A prominent bow shock gives an estimate of the subcluster velocity, 4500 km s À1 , which lies mostly in the plane of the sky. The optical image shows that the gas lags behind the subcluster galaxies. The weak-lensing mass map reveals a dark matter clump lying ahead of the collisional gas bullet but coincident with the effectively collisionless galaxies. From these observations, one can directly estimate the cross section of the dark matter self-interaction. That the dark matter is not fluid-like is seen directly in the X-ray-lensing mass overlay; more quantitative limits can be derived from three simple independent arguments. The most sensitive constraint, =m < 1 cm 2 g À1 , comes from the consistency of the subcluster mass-to-light ratio with the main cluster (and universal) value, which rules out a significant mass loss due to dark matter particle collisions. This limit excludes most of the 0.5-5 cm 2 g À1 interval proposed to explain the flat mass profiles in galaxies. Our result is only an orderof-magnitude estimate that involves a number of simplifying, but always conservative, assumptions; stronger constraints may be derived using hydrodynamic simulations of this cluster.

We present detailed comparisons of the intracluster medium (ICM) in cosmological Eulerian cluster simulations with deep Chandra observations of nearby relaxed clusters. To assess the impact of galaxy formation, we compare two sets of simulations, one performed in the nonradiative regime and another with radiative cooling and several physical processes critical to various aspects of galaxy formation: star formation, metal enrichment, and stellar feedback. We show that the observed ICM properties outside cluster cores are well reproduced in the simulations that include cooling and star formation, while the nonradiative simulations predict an overall shape of the ICM profiles inconsistent with observations. In particular, we find that the ICM entropy in our runs with cooling is enhanced to the observed levels at radii as large as half of the virial radius. We also find that outside cluster cores entropy scaling with the mean ICM temperature in both simulations and Chandra observations is consistent with being self-similar within current error bars. We find that the pressure profiles of simulated clusters are also close to self-similar and exhibit little cluster-to-cluster scatter. We provide analytic fitting formulae for the pressure profiles of the simulated and observed clusters. The X-ray observable mass relations for our simulated sample agree with the Chandra measurements to %10%Y20% in normalization. We show that this systematic difference could be caused by the subsonic gas motions, unaccounted for in X-ray hydrostatic mass estimates. The much improved agreement of simulations and observations in the ICM profiles and scaling relations is encouraging, and the existence of tight relations of X-ray observables, such as Y X , and total cluster mass and the simple redshift evolution of these relations hold promise for the use of clusters as cosmological probes. However, the disagreement between the predicted and observed fractions of cluster baryons in stars remains a major puzzle.

Table of contents (abridged): COLD FRONTS Origin and evolution of merger cold fronts Cold fronts in cluster cool cores . . . Simulations of gas sloshing. Origin of density discontinuity. . . . Effect of sloshing on cluster mass estimates and cooling flows. Zoology of cold fronts COLD FRONTS AS EXPERIMENTAL TOOL Velocities of gas flows Thermal conduction and diffusion across cold fronts Stability of cold fronts . . . Rayleigh-Taylor instability. Kelvin-Helmholtz instability. Possible future measurements using cold fronts . . . Plasma depletion layer and magnetic field. Effective viscosity of ICM. SHOCK FRONTS AS EXPERIMENTAL TOOL Cluster merger shocks Mach number determination Front width Mach cone and reverse shock? Test of electron-ion equilibrium . . . Comparison with other astrophysical plasmas Shocks and cluster cosmic ray population . . . Shock acceleration. Compression of fossil electrons. . . . Yet another method to measure intracluster magnetic field.Comment: 67 pages, 38 figures. v2: minor corrections. An updated version of a review article to appear in Physics Report

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