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.

We investigate the vorticity of the IGM velocity field on large scales with cosmological hydrodynamic simulation of the concordance model of ΛCDM. We show that the vorticity field is significantly increasing with time as it can effectively be generated by shocks and complex structures in the IGM. Therefore, the vorticity field is an effective tool to reveal the nonlinear behavior of the IGM, especially the formation and evolution of turbulence in the IGM. We find that the vorticity field does not follow the filaments and sheets structures of underlying dark matter density field and shows highly non-Gaussian and intermittent features. The power spectrum of the vorticity field is then used to measure the development of turbulence in Fourier space. We show that the relation between the power spectra of vorticity and velocity fields is perfectly in agreement with the prediction of a fully developed homogeneous and isotropic turbulence in the scale range from 0.2 to about 3h −1 Mpc at z ∼ 0. This indicates that cosmic baryonic field is in the state of fully developed turbulence on scales less than about 3 h −1 Mpc. The random field of the turbulent fluid yields turbulent pressure to prevent the gravitational collapsing of the IGM. The vorticity and turbulent pressure are strong inside and even outside of high density regions. In IGM regions with 10 times mean overdensity, the turbulent pressure can be on an average equivalent to the thermal pressure of the baryonic gas with a temperature of 1.0 × 10 5 K. Thus, the fully developed turbulence would prevent the baryons in the IGM from falling into the gravitational well of dark matter halos. Moreover, turbulent pressure essentially is dynamical and non-thermal, which makes it different from pre-heating mechanism as it does not affect the thermal state and ionizing process of hydrogen in the IGM.Subject headings: cosmology: theory -intergalactic medium -large-scale structure of the universe -methods: numerical

We perform a discrete wavelet analysis of the COBE-DMR 4yr sky maps and find a significant scale-scale correlation on angular scales from about 11 to 22 degrees, only in the DMR face centered on the North Galactic Pole. This non-Gaussian signature does not arise either from the known foregrounds or the correlated noise maps, nor is it consistent with upper limits on the residual systematic errors in the DMR maps. Either the scale-scale correlations are caused by an unknown foreground contaminate or systematic errors on angular scales as large as 22 degrees, or the standard inflation plus cold dark matter paradigm is ruled out at the > 99% confidence level.Most attempts at quantifying the non-Gaussianity in the cosmic microwave background radiation are motivated by the belief that non-Gaussianity can distinguish inflationary models of structure formation from topological models. While standard inflation predicts a Gaussian distribution of anisotropies [1], spontaneous symmetry breaking produces topological defects whose networks create non-Gaussian patterns on the microwave background radiation on small scales [2]. Minute non-Gaussian features can however be generated by gravitational waves [3] or by the Rees-Sciama [4] and Sunyaev-Zeldovich effects.It is generally held that cosmic gravitational clustering can be roughly described by three régimes: linear, quasilinear, and fully developed nonlinear clustering. Whilst quasi-linear and non-linear clustering induce non-Gaussian distribution functions, if the initial density perturbations are Gaussian, scale-scale correlations and other non-Gaussian features of the density field can not be generated during the linear régime. Hence the linear régime is best suited to study the primordial non-Gaussian fluctuations. Since the amplitudes of the cosmic temperature fluctuations revealed by COBE are as small as ∆T /T 10 −5 , the gravitational clustering should remain in the linear régime on scales larger than about 30 h −1 Mpc and at redshifts higher than 2. Current limits on non-Gaussianity from galaxy surveys probe redshifts smaller than about 1 [5]. Interestingly, at redshifts between 2 and 3, and scales on the order of 40 to 80 h −1 Mpc, there are positive detections of scale-scale correlations in the distribution of Lyα absorption lines in quasar spectra [6]. These clouds are likely to be pre-collapsed and continuously distributed intergalactic gas clouds, and are therefore fair tracers of the cosmic density field, especially on large scales [7]. This may indicate that the primordial fluctuations are scale-scale correlated.While on small angular scales ( 150) there may be some indications of non-Gaussianity [8], studies by traditional non-Gaussian detectors have concluded that there is no evidence of non-Gaussianity in the cosmic temperature fluctuations on large scales [9]. (See however [10].) This does not rule out the existence of scale-scale correlations. Because each non-Gaussian feature is non-Gaussian in its own way, there is no single statistical indicator for ...

In this paper we investigate, using high resolution N-body simulations, the density pro les and the morphologies of galaxy clusters in seven models of structure formation. We show that these properties of clusters are closely related to the occurrence of a signi cant merging event in the recent past. The seven models are: (1) the standard CDM model (SCDM) with 0 = 1, 0 = 0 and h = 0:5; (2) a low-density at model (FL03) with 0 = 0:3, 0 = 0:7 and h = 0:75; (3) an open model (OP03) with 0 = 0:3, 0 = 0 and h = 0:75; (4) a low-density at model (FL02) with 0 = 0:2, 0 = 0:8 and h = 1; (5) an open model (OP02) with 0 = 0:2, 0 = 0 and h = 1; (6) a low-density at model (FL01) with 0 = 0:1 and 0 = 0:9; ( 7) an open model (OP01) with 0 = 0:1 and 0 = 0. We nd that the density pro les and morphologies of clusters depend both on 0 and on 0 . For 0 = 0, these properties are a monotonic function of 0 . Clusters in OP01 have the steepest density pro les, their density contours are the roundest and show the smallest center shifts. The other extreme case is SCDM, where clusters show the least steep density pro les and the most elongated contours. For a given 0 (< 1), clusters in the at model (i.e. with 0 = 1 0 ) have atter density pro les and less substructures than in the corresponding open model. Clusters in FL03 have density pro les and center shifts close to those in SCDM, although their density contours are rounder. Our results show that, although cluster density pro les and morphologies are useful cosmological tests, low-density at models with 0 0:3, which are currently considered as a successful alternative to SCDM, can produce a substantial fraction of clusters with substructures. This is in contrast to the conception that this kind of models may have serious problem in this aspect.

Using a set of P 3 M simulation which accurately treats the density evolution of two components of dark matter, we study the evolution of clusters in the Cold + Hot dark matter (CHDM) model. The mass function, the velocity dispersion function and the temperature function of clusters are calculated for four di erent epochs of z 0:5. We also use the simulation data to test the Press-Schechter expression of the halo abundance as a function of the velocity dispersion v . The model predictions are in good agreement with the observational data of local cluster abundances (z = 0). We also tentatively compare the model with the Gunn and his collaborators' observation of rich clusters at z 0:8 and with the x-ray luminous clusters at z 0:5 of the Einstein Extended Medium Sensitivity Survey. The important feature of the model is the rapid formation of clusters in the near past: the abundances of clusters of v 700 kms 1 and of v 1200 kms 1 at z = 0:5 are only 1/4 and 1/10 respectively of the present values (z = 0). Ongoing ROSAT and AXAF surveys of distant clusters will provide sensitive tests to the model. The abundance of clusters at z 0:5 would also be a good discriminator between the CHDM model and a low-density at CDM model both of which show very similar clustering properties at z = 0.Key words: Clusters: of galaxies {Cosmology {Dark matter {Universe (the): structure of