While in the hierarchical model of structure formation, groups of galaxies are believed to be the scaled-down version of clusters of galaxies, a similarity breaking in the fundamental laws may occur on the group scale, reflecting a transition between galaxy-dominated and intracluster medium dominated properties. In this paper, we present an extensive study of the relations between the X-ray luminosity (L x ), the temperature (T ) of hot diffuse gas and the velocity dispersion (σ) of galaxies for groups and clusters of galaxies, based on the largest sample of 66 groups and 274 clusters drawn from literature. Our best fit L x -T and L x -σ relations for groups read L x ∝ T 5.57±1.79 ∝ σ 2.35±0.21 , which deviates remarkably from those for clusters: L x ∝ T 2.79±0.08 ∝ σ 5.30±0.21 . The significance of these correlations have been justified by both the co-consistency test and the Kendall's τ statistics. We have thus confirmed the existence of similarity breaking in the L x -T and L x -σ relations between groups and clusters as claimed in previous work, although the best fit σ-T relations remain roughly the same in both systems: σ ∝ T 0.64 . Alternatively, the significant disagreement between the observationally fitted L x -T and L x -σ relations for groups and those expected from a perfect hydrostatic equilibrium hypothesis indicates that the X-ray emission of individual galaxies and the non-gravitational heating must play a potentially important role in the dynamical evolution of groups. Therefore, reasonable caution should be exercised in the cosmological applications of the dynamical properties of groups.
The relationships between the X-ray determined bolometric luminosity L x , the temperature T of the intracluster gas, and the optical measured velocity dispersion σ of the cluster galaxies are updated for galaxy clusters using the largest sample of 256 clusters drawn from literature. The newly established relationships, based on the doubly weighted orthogonal distance regression (ODR) method, are justified by both their self-consistency and co-consistency, which can then be used to test the theoretical models of cluster formation and evolution. The observationally determined L x -T and L x -σ relationships, L x ∝ T 2.72±0.05 ∝ σ 5.24±0.29 , are marginally consistent with those predicted in the scenario that both intracluster gas and galaxies are in isothermal and hydrostatic equilibrium with the underlying gravitational potential of clusters. A comparison between these observed and predicted L x -T relationships also suggests that the mean cluster baryon fraction f b remains approximately constant among different clusters, f b ≈ 0.17, which gives rise to a low-mass density universe of Ω m ≈ 0.3.
The masses of clusters of galaxies estimated by gravitational lensing exceed in many cases the mass estimates based on hydrostatic equilibrium. This may suggest the existence of nonthermal pressure. We ask if radio galaxies can heat and support the cluster gas with injected cosmic ray protons and magnetic field densities, which are permitted by Faraday rotation and gamma ray observations of clusters of galaxies. We conclude that they are powerful enough to do this within a cluster radius of roughly 1 Mpc . If present, nonthermal pressures could lead to a revised estimate of the ratio of baryonic mass to total mass, and the apparent baryonic overdensity in clusters would disappear. In consequence, Ω cold , the clumping part of the cosmological density Ω o , would be larger than 0.4 h −1/2 50 . Subject headings: cosmic rays -cosmology: observations -dark matter -galaxies: clusters: general -intergalactic medium -magnetic fields IntroductionClusters of galaxies, being the most massive coherent objects in the universe, are important probes of the cosmological density. X-ray observations allow a measurement of the density profile of the hot intracluster gas, which dominates the visible, baryonic mass M b of a cluster. Estimates of the total mass M tot can be made from a virial analysis of the galaxy velocities, by integration of the hydrostatic equilibrium between gravitational forces and thermal pressure, or by analyzing background objects that are gravitationally lensed by the cluster. Calibrating Ω b from the standard Big Bang nucleosynthesis with the value Ω b /Ω cold ≈ M b /M tot given by clusters should give then a lower limit to Ω o , if Ω cold is the part of the matter which clumps on the scale of clusters. Unfortunately, the mass derived from velocity dispersion and from hydrostatic equilibrium appears to be often much lower than the mass derived by lensing methods.Miralda-Escudé & Babul (1995) derived the mass of Abell 2218 and Abell 1689 from gravitationally lensed arcs and from X-ray observations and found a mass shortfall of a factor 2.5 ± 0.5. Similar work done by Wu (1994) gave a factor of 3 -6 within a central radius of 300 kpc h −1 50 for four different clusters. Even in the rich, early cluster RXJ1347.5-1145 at z = 0.451 a mass discrepancy of a factor 2 -3 is reported by Schindler et al. (1996). Conversely, Squires et al. (1995) have re-examined Abell 2218 with HST images and found accordance between the different mass determinations at a radius of 800 h −1 50 kpc, applying a weak lensing method that reconstructs the mass distribution by using the distortion of background galaxies. However, they note that their lensing mass could be too low, since it depends on assumptions about the 1/2 50 J Gpc −3 and E th (1.5 Mpc) ≈ 3 · 10 58 h 1/2 50 J Gpc −3 then, as we have argued, the total accumulated energy content should be of the order of 10 58 h 1/2 50 J Gpc −3 within the central region, after allowing for cosmic rays and magnetic fields.Evidence has been found for evolution of the cluster luminosity fun...
The Brownian web can be roughly described as a family of coalescing one-dimensional Brownian motions starting at all times in $\R$ and at all points of $\R$. It was introduced by Arratia; a variant was then studied by Toth and Werner; another variant was analyzed recently by Fontes, Isopi, Newman and Ravishankar. The two-dimensional \emph{Poisson tree} is a family of continuous time one-dimensional random walks with uniform jumps in a bounded interval. The walks start at the space-time points of a homogeneous Poisson process in $\R^2$ and are in fact constructed as a function of the point process. This tree was introduced by Ferrari, Landim and Thorisson. By verifying criteria derived by Fontes, Isopi, Newman and Ravishankar, we show that, when properly rescaled, and under the topology introduced by those authors, Poisson trees converge weakly to the Brownian web.Comment: 22 pages, 1 figure. This version corrects an error in the previous proof. The results are the sam
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