Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The most common measurement is the correlation in alignments of background galaxies which can be used to infer the variance of the projected surface density of matter. This measurement of the fluctuations is insensitive to the total mass content and is analogous to using waves on the ocean to measure its depths. However, when the depth is shallow as happens near a beach waves become skewed. Similarly, a measurement of skewness in the projected matter distribution directly measures the total matter content of the universe. While skewness has already been convincingly detected, its constraint on cosmology is still weak. We address optimal analyses for the CFHT Legacy Survey in the presence of noise. We show that a compensated Gaussian filter with a width of 2.5 arc minutes optimizes the cosmological constraint, yielding m/m 10%. This is significantly better than other filters which have been considered in the literature. This can be further improved with tomography and other sophisticated analyses.

Weak gravitational lensing provides a direct statistical measure of the dark matter distribution. The variance is easiest to measure, which constrains the degenerate product 8 0.6 0. The degeneracy is broken by measuring the skewness arising from the fact that densities must remain positive, which is not possible when the initially symmetric perturbations become non-linear. Skewness measures the non-linear mass scale, which in combination with the variance measures 0 directly. We present the first detection of dark matter skewness from the Virmos-Decart survey. We have measured the full three point function, and its projections onto windowed skewness. We separate the lensing mode and the B mode. The lensing skewness is detected for a compensated Gaussian on scales of 5.37 arc minutes to be k-3=1.06±0.06×10−6. The B-modes are consistent with zero at this scale. The variance for the same window function is k-2=5.32±0.62±0.98×10−5, resulting in S3=375+342−124. Comparing to N-body simulations, we find 0<0.5 at 90% confidence. The Canada-France-Hawaii-Telescope legacy survey and newer simulations should be able to improve significantly on the constraint.

The statistics of gravitational lensing can provide us with a very powerful probe of the mass distribution of matter in the universe. By comparing predicted strong lensing probabilities with observations, we can test the mass distribution of dark matter halos, in particular, the inner density slope. In this letter, unlike previous work that directly models the density profiles of dark matter halos semi-analytically, we generalize the density profiles of dark matter halos from high-resolution N-body simulations by means of generalized Navarro-Frenk-White (GNFW) models of three populations with slopes, α, of about -1.5, -1.3 and -1.1 for galaxies, groups and clusters, respectively. This approach is an alternative and independent way to examine the slopes of mass density profiles of halos. We present calculations of lensing probabilities using these GNFW profiles for three populations in various spatially flat cosmological models with a cosmological constant. It is shown that the compound model of density profiles does not match well with the observed lensing probabilities derived from the Jodrell-Bank VLA Astrometric Survey data in combination with the Cosmic Lens All-Sky Survey data. Together with the previous work on lensing probability, our results suggest that a singular isothermal sphere mass model of less than about 1013h−1M⊙ can predict strong lensing probabilities that are consistent with observations of small splitting angles.

We study the X-ray emission of baryon fluid in the universe using the WIGEON cosmological hydrodynamic simulations. It has been revealed that cosmic baryon fluid in the nonlinear regime behaves like Burgers turbulence, i.e. the fluid field consists of shocks. Like turbulence in incompressible fluid, the Burgers turbulence plays an important role in converting the kinetic energy of the fluid to thermal energy and heats the gas. We show that the simulation sample of the CDM model without adding extra heating sources can fit well the observed distributions of X-ray luminosity versus temperature (Lx vs. T) of galaxy groups and is also consistent with the distributions of X-ray luminosity versus velocity dispersion (Lx vs. σ). Because the baryonic gas is multiphase, the Lx−T and Lx−σ distributions are significantly scattered. If we describe the relationships by power laws Lx ∝ T LT and Lx ∝ σLV, we find αLT>2.5 and αLV>2.1. The X-ray background in the soft 0.5−2 keV band emitted by the baryonic gas in the temperature range 105<T<107K has also been calculated. We show that of the total background, (1) no more than 2% comes from the region with temperature less than 106.5 K, and (2) no more than 7% is from the region of dark matter with mass density ρdm<50 ρdm. The region of ρdm>50 ρdm is generally clustered and discretely distributed. Therefore, almost all of the soft X-ray background comes from clustered sources, and the contribution from truly diffuse gas is probably negligible. This point agrees with current X-ray observations.

It has been revealed recently that, in the scale free range, i.e. from the scale of the onset of nonlinear evolution to the scale of dissipation, the velocity and mass density fields of cosmic baryon fluid are extremely well described by the self-similar log-Poisson hierarchy. As a consequence of this evolution, the relations among various physical quantities of cosmic baryon fluid should be scale invariant, if the physical quantities are measured in cells on scales larger than the dissipation scale, regardless the baryon fluid is in virialized dark halo, or in pre-virialized state. We examine this property with the relation between the Compton parameter of the thermal Sunyaev-Zel'dovich effect, y(r), and X-ray luminosity, Lx(r), where r being the scale of regions in which y and Lx are measured. According to the self-similar hierarchical scenario of nonlinear evolution, one should expect that 1.) in the y(r)-Lx(r) relation, y(r)=10A(r)[Lx(r)](r), the coefficients A(r) and (r) are scale-invariant; 2.) The relation y(r)=10A(r)[Lx(r)] (r) given by cells containing collapsed objects is also available for cells without collapsed objects, only if r is larger than the dissipation scale. These two predictions are well established with a scale decomposition analysis of observed data, and a comparison of observed y(r)-Lx(r) relation with hydrodynamic simulation samples. The implication of this result on the characteristic scales of non-gravitational heating is also addressed.