Statistical Cluster-QSO Weak Lensing in the Sloan Digital Sky Survey

We investigate the cross-correlation between galaxy clusters and QSOs using Sloan Digital Sky Survey (SDSS) DR4 - 5000 deg2 data. With photometric redshifts of galaxies, we select galaxy clusters based on the local projected densities of LRGs brighter than Mr' = -22. The QSOs are from the main sample of SDSS QSO spectroscopic survey to i' - 19. A significant positive correlation is found between the clusters and QSOs. Under the assumption that the signal is caused by gravitational leasing, we fit the signal with singular isothermal sphere (SIS) model and NFW profile halo model. The velocity dispersionσv = 766 km s-1 is derived for the best-fit of SIS model. Best-fit for the NFW model requires the dark matter halo mass within 1.5 h-1 Mpc to be 4.6×1014 h-1 M⊙. The mass parameterΩcl of the cluster sample is deduced as 0.077 with the SIS model and 0.083 with the NFW model. Our results ofΩcl are smaller than those given by Croom & Shanks and by Myers et al.     

The Amplitude of Mass Fluctuations and Mass Density of the Universe Constrained by Strong Gravitational Lensing

We investigate the linear amplitude of mass fluctuations in the universe, σ8, and the present mass density parameter of the Universe, Ωm, from statistical strong gravitational lensing. We use the two population model of lens halos with fixed cooling mass scale Mc = 3×1013h-1M⊙ to match the observed lensing probabilities, and leave σ8 orΩm as a free parameter to be constrained by the data. Another varying parameter, the equation of state of dark energy ω, and its typical values of -1, -2/3, -1/2 and -1/3 are investigated. We find that σ8 is degenerate with Ωm in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: σ8Ω0.6m≈0.33. However, both σ8≤0.7 and Ωm≤0.2 can be safely ruled out, the best fit is when σ8 = 1.0, Ωm = 0.3 and ω= - 1. This result is different from that obtained by Bahcall & Bode, who gave σ8 = 0.98±0.1 and Ωm = 0.17 ±0.05. For σ8 = 1.0, the higher value ofΩm = 0.35 requires ω = -2/3 and Ωm = 0.40 require     

Constraining the Mass Distribution of Cluster Galaxies by Weak Lensing

Analysing the weak lensing distortions of the images of faint background galaxies provides a means to constrain the average mass distribution of cluster galaxies and potentially to test the extent of their dark matter haloes as a function of the density of their environment. The observable image distortions are a consequence of the interplay between the effects of a global cluster mass distribution and the perturbations resulting from individual cluster galaxies. Starting from a reconstruction of the cluster mass distribution with conventional techniques, we apply a maximum likelihood method to infer the average properties of an ensemble of cluster galaxies. From simulations this approach is found to be reliable as long as the galaxies including their dark matter haloes only contribute a small fraction to the total mass of the system. If their haloes are extended, the galaxies contain a substantial mass fraction. In this case our method is still applicable in the outer regions of clusters, where the surface mass density is low, but yields biased estimates of the parameters describing the mass profiles of the cluster galaxies in the central part of the cluster. In that case it will be necessary to resort to more sophisticated strategies by modelling cluster galaxies and an underlying global mass distribution simultaneously. We conclude that galaxy–galaxy lensing in clusters provides a unique means to probe the presence and extent of dark haloes of cluster galaxies.     

The Effect of Central Baryonic Cores in Dark Halos on the Evaluation of Strong Lensing Probabilities

We present an estimate of the strong lensing probability by dark halos, with emphasis on the role of the baryonic matter arising purely from radiative cooling. We treat the contribution of the cooled baryons optimistically with all the cooled baryons confined within a central core, and including no feedback process from stellar evolution. Our two-component model provides a strong lensing probability that is in good agreement with the observed distribution of multiple images of quasars, provided that the cooled baryons are deposited within a spherical region of radius of 0.1 times the virial radius and follow an isothermal profile. It is pointed out that strong lensing may be used as an additional probe‘of baryon physics in dark halos though this may meanwhile complicate the test of the inner density profiles of dark matter in halos using the observed strong lensing probability.     

基于Shapelets基函数的引力透镜质量重构方法

引力透镜效应是探测星系团物质分布的有效方法之一.目前,利用引力透镜数据重构星系团质量分布的主流方法可以分为两大类,即参数法和非参数法.在实际研究工作中,受限于质量模型假设和计算分辨率等方面的影响,现有的重构算法仍有诸多亟需解决的问题.基于Shapelets基函数的引力透镜质量重构方法通过基函数来实现引力透镜质量重构,使用Shapelets基函数分解引力透镜势,以引力透镜中多重像的位置和背景星系椭率畸变为限制条件来迭代求解基函数系数从而得到透镜体的质量分布.通过拟合一个模拟的NFW (Navarro,Frenk and White)透镜系统测试了新方法的可行性,结果表明新方法可以在整体上重构出透镜体的质量分布,并拟合出接近真实的源位置,能够为星系团质量测量提供一套灵活且高效的重构算法.     

Weak gravitational lensing by voids

We consider the prospects for detecting weak gravitational lensing by underdensities (voids) in the large-scale matter distribution. We derive the basic expressions for magnification and distortion by spherical voids. Clustering of the background sources and cosmic variance are the main factors that limit in principle the detection of lensing by voids. We conclude that only voids with radii larger than ∼100  h ⁻¹ Mpc have lensing signal-to-noise ratio larger than unity.     

A Remark on Using Gravitational Lensing Probability as a Probe of the Central Regions of CDM Halos

We calculate the gravitational lensing probabilities by cold dark matter (CDM) halos with different density profiles, and compare them with current observations from the Cosmic Lens All-Sky Survey (CLASS) and the Jodrell-Bank VLA Astrometric Survey (JVAS). We find that the lensing probability is dramatically sensitive to the clumping of the dark matter, or quantitatively, the concentration parameter. We also find that our predicted lensing probabilities in most cases show inconsistency with the observations. It is argued that high lensing probability may not be an effective tool for probing the statistical properties of inner structures of dark matter halos.     

Lensing magnification effects on the cosmic shear statistics

Gravitational lensing causes a correlation between a population of foreground large-scale structures and the observed number density of the background distant galaxies as a consequence of the flux magnification and the lensing area distortion. This correlation has not been taken into account in calculations of the theoretical predictions of the cosmic shear statistics but may cause a systematic error in a cosmic shear measurement. We examine its impact on the cosmic shear statistics using the semi-analytic approach. We find that the lensing magnification has no practical influence on the cosmic shear variance. Exploring the possible shapes of the redshift distribution of source galaxies, we find that the relative amplitude of the effect on the convergence skewness is 3 per cent at most.     

利用弱引力透镜效应的尖峰和尺度-尺度相关统计区分暗能量模型

为了研究不同宇宙学模型下弱引力透镜效应的性质,利用N-体模拟产生的数据,通过光线追踪技术,生成二维的κ样本.对应于不同的暗能量状态方程参数的模型,即w=-0.8,w=-1.0,w=-1.2,生成了3组样本.对于这些模型所生成的样本视场均为3°×3°,并假设所有作为背景源的星系都分布在z=1处的平面上.对这些κ场的样本均进行了尖峰统计和尺度-尺度相关的统计.对尖峰的统计结果显示,包含噪声的κ场中尖峰分布在不同模型下的差别还是存在的.噪声改变了中等幅值和小幅值的尖峰分布,而对高幅值的尖峰分布影响不大.同时降噪后κ场中高幅值尖峰分布的结果表明,降噪后不同模型间高幅值尖峰分布的差别还是非常明显的.对于尺度-尺度相关统计,分析了不同模型的尺度-尺度相关系数的累积概率分布函数,w=-1.2的模型与w=-0.8和w=-1.0的模型的差别能达到20%和30%.因此尺度-尺度相关的统计结合尖峰数目的统计,可以做为确定暗能量状态参数的一种新的手段.     

Weak gravitational lensing in the standard cold dark matter model, using an algorithm for three-dimensional shear

We investigate the effects of weak gravitational lensing in the standard cold dark matter cosmology, using an algorithm that evaluates the shear in three dimensions. The algorithm has the advantage of variable softening for the particles, and our method allows the appropriate angular diameter distances to be applied to every evaluation location within each three-dimensional simulation box. We investigate the importance of shear in the distance–redshift relation, and find it to be very small. We also establish clearly defined values for the smoothness parameter in the relation, finding its value to be at least 0.83 at all redshifts in our simulations. From our results, obtained by linking the simulation boxes back to source redshifts of 4, we are able to observe the formation of structure in terms of the computed shear, and also note that the major contributions to the shear come from a very broad range of redshifts. We show the probability distributions for the magnification, source ellipticity and convergence, and also describe the relationships amongst these quantities for a range of source redshifts. We find a broad range of magnifications and ellipticities; for sources at a redshift of 4, 97.5 per cent of all lines of sight show magnifications up to 1.39 and ellipticities up to 0.23. There is clear evidence that the magnification is not linear in the convergence, as might be expected for weak lensing, but contains contributions from higher order terms in both the convergence and the shear. Our results for the one-point distribution functions are generally different from those obtained by other authors using two-dimensional (planar) approaches, and we suggest reasons for the differences. Our magnification distributions for sources at redshifts of 1 and 0.5 are also very different from the results used by other authors to assess the effect on the perceived value of the deceleration parameter, and we briefly address this question.     

Weak gravitational lensing in different cosmologies, using an algorithm for shear in three dimensions

We present the results of weak gravitational lensing statistics in four different cosmological N -body simulations. The data have been generated using an algorithm for the three-dimensional shear, which makes use of a variable softening facility for the N -body particle masses, and enables a physical interpretation for the large-scale structure to be made. Working in three dimensions also allows the correct use of the appropriate angular diameter distances.
Our results are presented on the basis of the filled-beam approximation in view of the variable particle softening scheme in our algorithm. The importance of the smoothness of matter in the Universe for the weak lensing results is discussed in some detail.
The low-density cosmology with a cosmological constant appears to give the broadest distributions for all the statistics computed for sources at high redshifts. In particular, the range in magnification values for this cosmology has implications for the determination of the cosmological parameters from high-redshift type Ia supernovae. The possibility of determining the density parameter from the non-Gaussianity in the probability distribution for the convergence is discussed.