引力透镜的基本原理及最新研究进展

介绍了引力透镜的基本原理，并针对不同情况，结合目前的观测结果对强透镜、弱透镜和微透镜分别作了系统的说明；特别阐述了近年来正在兴起的宇宙剪切的观测和理论研究，总结了引力透镜在宇宙学研究中的重要意义。     

Galaxy density profiles and shapes – I. Simulation pipeline for lensing by realistic galaxy models

Studies of strong gravitational lensing in current and upcoming wide and deep photometric surveys, and of stellar kinematics from (integral-field) spectroscopy at increasing redshifts, promise to provide valuable constraints on galaxy density profiles and shapes. However, both methods are affected by various selection and modelling biases, which we aim to investigate in a consistent way. In this first paper in a series, we develop a flexible but efficient pipeline to simulate lensing by realistic galaxy models. These galaxy models have separate stellar and dark matter components, each with a range of density profiles and shapes representative of early-type, central galaxies without significant contributions from other nearby galaxies. We use Fourier methods to calculate the lensing properties of galaxies with arbitrary surface density distributions, and Monte Carlo methods to compute lensing statistics such as point-source lensing cross-sections. Incorporating a variety of magnification bias modes lets us examine different survey limitations in image resolution and flux. We rigorously test the numerical methods for systematic errors and sensitivity to basic assumptions. We also determine the minimum number of viewing angles that must be sampled in order to recover accurate orientation-averaged lensing quantities. We find that for a range of non-isothermal stellar and dark matter density profiles typical of elliptical galaxies, the combined density profile and corresponding lensing properties are surprisingly close to isothermal around the Einstein radius. The converse implication is that constraints from strong lensing and/or stellar kinematics, which are indeed consistent with isothermal models near the Einstein radius, cannot trivially be extrapolated to smaller and larger radii.     

Resolving the Mass Discrepancy between Strong and Weak Lensing Methods

We readdress the outstanding cluster mass discrepancy between strong and weak gravitational lensing techniques utilizing updated data of both giant arcs and weak lensing measurements from the literature.We find that the systematically higher values of cluster masses revealed by strong lensing can be attributed to the oversimplification of the lensing model when estimating the cluster mass enclosed within the giant arcs.This arises because inhomogeneities and substructures in the central cores of clusters may invalidate the spherical symmetry assumption used widely in previous applications.When a more realistic modeling of the arcs is used,then the masses by strong lensing agree fairly well with those given by weak lensing when both are extrapolated to the same cluster regions.We conclude that as of now no significant discrepancy has been found among different cluster mass estimators including optical galaxies,X-ray gas and lensing.     

The statistics of multiple gravitational lensing and the application of a single lensing approximation

The statistics of multiple gravitational lensing in a locally inhomogeneous universe is taken into account, based on the expansion of the mean amplification into the summation of various lenses and the pointlike models for both background sources and lensing objects. By comparing the deviation of the effects of various lenses from mean amplification, the redshift ranges over which different lenses dominate are investigated. In particular, the accuracy of a single lensing approximation, which has been widely used in previous statistical lensing, is demonstrated. As the application of a single lensing approximation, the lowest correction to the Mattig's relation due to the inhomogeneities in universe and the lowest effect on the number counts of background sources due to amplification bias are reconsidered. It is emphasized the fact that the effect of statistical lensing, even in a single lensing approximation, is of significance for modern observational cosmology.     

Analytic relations between the observed gravitational microlensing parameters with and without the effect of blending

When a microlensing light curve is contaminated by blended light from unresolved stars near the line of sight to the lensed star, the light curve shape and corresponding parametrization for the event will differ from the values expected when the event is not affected by blending. As a result, blending makes it difficult to identify the major lens population and to estimate the amount of lensing matter. In order to estimate the effect of blending on the result of lensing experiments, it is, therefore, essential to know how the observed lensing parameters change depending on the fraction of blended light. Previously, the changed lensing parameters were obtained with a statistical method that not only required a large amount of computation time but also was prone to uncertainty. In this paper, we derive analytic relations between the lensing parameters with and without the effect of blending. By using these relations, we investigate the dependence of the observed lensing parameters on the amount of blended light, the impact parameter and the threshold amplification for event detection.     

On the astrometric behaviour of binary microlensing events

Despite the suspected binarity for a significant fraction of Galactic lenses, the current photometric surveys detected binary microlensing events only for a small fraction of the total events. The detection efficiency is especially low for non-caustic crossing events, which comprise the majority of the binary lensing events, as a result of the absence of distinctive features in their light curves combined with small deviations from the standard light curve of a single point-mass event. In addition, even if they are detected, it will be difficult to determine the solution of the binary lens parameters owing to the severe degeneracy problem. In this paper, we investigate the properties of binary lensing event expected when they are astrometrically observed by using high-precision interferometers. For this, we construct vector field maps of excess centroid shifts, which represent the deviations of the binary lensing centroid shifts from those of a single lensing event as a function of source position. From the analysis of the maps, we find that the excess centroid shifts are substantial in a considerably large area around caustics. In addition, they have characteristic sizes and directions depending strongly on the source positions with respect to the caustics and the resulting trajectories of the light centroid (astrometric trajectories) have distinctive features, which can be distinguished from the deviations caused by other reasons. We classify the types of the deviations and investigate where they occur. Because of the strong dependence of the centroid shifts on the lens system geometry combined with the distinctive features in the observed astrometric trajectories, astrometric binary lensing observations will provide an important tool that can probe the properties of the Galactic binary lens population.     

Weak lensing of the CMB: extraction of lensing information from the trispectrum

We discuss the four-point correlation function, or the trispectrum in Fourier space, of CMB temperature and polarization anisotropies due to the weak gravitational lensing effect by intervening large scale structure. We discuss the squared temperature power spectrum as a probe of this trispectrum and, more importantly, as an observational approach to extracting the power spectrum of the deflection angle associated with the weak gravitational lensing effect on the CMB. We extend previous discussions on the trispectrum and associated weak lensing reconstruction from CMB data by calculating non-Gaussian noise contributions, beyond the previously discussed dominant Gaussian noise. Non-Gaussian noise contributions are generated by lensing itself and by the correlation between the lensing effect and other foreground secondary anisotropies in the CMB such as the Sunyaev–Zel’dovich (SZ) effect. When the SZ effect is removed from temperature maps using its spectral dependence, we find these additional non-Gaussian noise contributions to be an order of magnitude lower than the dominant Gaussian noise. If the noise-bias due to the dominant Gaussian part of the temperature squared power spectrum is removed, then these additional non-Gaussian contributions provide the limiting noise level for the lensing reconstruction. The temperature squared power spectrum allows a high signal-to-noise extraction of the lensing deflections and a confusion-free separation of the curl (or B-mode) polarization due to inflationary gravitational waves from that due to lensed gradient (or E-mode) polarization. The small angular scale temperature and polarization anisotropy measurements provide a novel approach to weak lensing studies, complementing the approach based on galaxy ellipticities.     

引力透镜与类星体─星系(星系团)成协

综述了背景光源（类星体）与前方天体（星系、星系团等）成协的观测和统计事例．详尽叙述了与成协问题相关的引力透镜理论．全面介绍了对各种成协事例进行引力透镜理论解释的方法、研究现状及存在的问题．还给出了一种计算成协样品中面密度超出因子的改进方法．     

Statistics of weak lensing at small angular scales: analytical predictions for lower order moments

Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasi-linear scales as they relied on perturbative calculations. On the other hand, observational surveys are likely to probe angular scales less than 10 arcmin, for which the relevant physical length-scales are in the non-linear regime of gravitational clustering. We use the hierarchical ansatz to compute the multipoint statistics of the weak lensing convergence for these small smoothing angles. We predict the multipoint cumulants and cumulant correlators up to fourth order and compare our results with high-resolution ray-tracing simulations. Averaging over a large number of simulation realizations for four different cosmological models, we find close agreement with the analytical calculations. In combination with our work on the probability distribution function, these results provide accurate analytical models for the full range of weak lensing statistics. The models allow for a detailed exploration of cosmological parameter space and of the dependence on angular scale and the redshift distribution of source galaxies. We compute the dependence of the higher moments of the convergence on the parameters Ω and Λ.     

Gravitational lensing in quasar samples

The first cosmic mirage was discovered approximately 20 years ago as the double optical counterpart of a radio source. This phenomenon had been predicted some 70 years earlier as a consequence of General Relativity. We present here a summary of what we have learnt since. The applications are so numerous that we had to concentrate on a few selected aspects of this new field of research. This review is focused on strong gravitational lensing, i.e. the formation of multiple images, in QSO samples. It is intended to give the reader an up-to-date status of the observations and to present an overview of its most interesting potential applications in cosmology and astrophysics, as well as numerous important results achieved so far. The first section follows an intuitive approach to the basics of gravitational lensing and is developed in view of our interest in multiply imaged quasars. The astrophysical and cosmological applications of gravitational lensing are outlined in Sect. 2 and the most important results are presented in Sect. 5. Sections 3 and 4 are devoted to the observations. Finally, conclusions are summarized in the last section. We have tried to avoid duplication with existing (and excellent) introductions to the field of gravitational lensing. For this reason, we did not concentrate on the individual properties of specific lens models, as these are already well presented in Narayan and Bartelmann (1996) and on a more intuitive ground in Refsdal and Surdej (1994). Wambsganss (1998) proposes a broad view on gravitational lensing in astronomy; the reviews by Fort and Mellier (1994) and Hattori et al. (1999) deal with lensing by galaxy clusters; microlensing in the Galaxy and the local group is reviewed by Paczyński (1996) and a general panorama on weak lensing is given by Bartelmann and Schneider (1999) and Mellier (1999). The monograph on the theory of gravitational lensing by Schneider, Ehlers and Falco (1992) also remains a reference in the field. Received 4 April 2000 / Published online 9 August 2000     

Weak lensing magnification reconstruction with the modified internal linear combination method

Measuring weak lensing cosmic magnification signal is very challenging due to the overwhelming intrinsic clustering in the observed galaxy distribution.In this paper,we modify the Internal Linear Combination (ILC) method to reconstruct the lensing signal with an extra constraint to suppress the intrinsic clustering.To quantify the performance,we construct a realistic galaxy catalogue for the LSST-like photometric survey,covering 20 000 deg~2 with mean source redshift at z_s~1.We find that the reconstruction performance depends on the width of the photo-z bin we choose.Due to the correlation between the lensing signal and the source galaxy distribution,the derived signal has smaller systematic bias but larger statistical uncertainty for a narrower photo-z bin.We conclude that the lensing signal reconstruction with the Modified ILC method is unbiased with a statistical uncertainty5%for bin width?z~P=0.2.     

Full-sky maps for gravitational lensing of the cosmic microwave background

We use the large cosmological Millennium Simulation (MS) to construct the first all-sky maps of the lensing potential and the angle, aiming at gravitational lensing of the cosmic microwave background (CMB), with the goal of properly including small-scale non-linearities and non-Gaussianity. Exploiting the Born approximation, we implement a map-making procedure based on direct ray tracing through the gravitational potential of the MS. We stack the simulation box in redshift shells up to z ∼ 11, producing continuous all-sky maps with arcmin angular resolution. A randomization scheme avoids the repetition of structures along the line of sight, and structures larger than the MS box size are added to supply the missing contribution of large-scale (LS) structures to the lensing signal. The angular power spectra of the projected lensing potential and the deflection-angle modulus agree quite well with semi-analytic estimates on scales down to a few arcmin, while we find a slight excess of power on small scales, which we interpret as being due to non-linear clustering in the MS. Our map-making procedure, combined with the LS adding technique, is ideally suited for studying lensing of CMB anisotropies, for analysing cross-correlations with foreground structures, or other secondary CMB anisotropies such as the Rees–Sciama effect.     

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.     

Intrinsic correlation of galaxy shapes: implications for weak lensing measurements

Weak gravitational lensing is now established as a powerful method to measure mass fluctuations in the universe. It relies on the measurement of small coherent distortions of the images of background galaxies. Even low-level correlations in the intrinsic shapes of galaxies could however produce a significant spurious lensing signal. These correlations are also interesting in their own right, since their detection would constrain models of galaxy formation. Using     haloes found in N -body simulations, we compute the correlation functions of the intrinsic ellipticity of spiral galaxies assuming that the disc is perpendicular to the angular momentum of the dark matter halo. We also consider a simple model for elliptical galaxies, in which the shape of the dark matter halo is assumed to be the same as that of the light. For deep lensing surveys with median redshifts ∼1, we find that intrinsic correlations of ∼10⁻⁴ on angular scales     are generally below the expected lensing signal, and contribute only a small fraction of the excess signals reported on these scales. On larger scales we find limits to the intrinsic correlation function at a level ∼10⁻⁵, which gives a (model-dependent) range of separations for which the intrinsic signal is about an order of magnitude below the ellipticity correlation function expected from weak lensing. Intrinsic correlations are thus negligible on these scales for dedicated weak lensing surveys. For wider but shallower surveys such as SuperCOSMOS, APM and SDSS, we cannot exclude the possibility that intrinsic correlations could dominate the lensing signal. We discuss how such surveys could be used to calibrate the importance of this effect, as well as study spin–spin correlations of spiral galaxies.     

Revisiting the magnification of type Ia supernovae with SDSS

We cross-correlate the sample of type Ia supernovae from Riess A. G. et al. with the SDSS DR2 photometric galaxy catalogue. In contrast to recent work, we find no detectable correlation between supernova magnitude and galaxy overdensity on scales ranging between 1 and 10 arcmin. Our results are in accord with theoretical expectations for gravitational lensing of supernovae by large-scale structure. Future supernova surveys such as SNAP will be capable of detecting unambiguously the predicted lensing signal.     

Angular cross-correlation of galaxies: a probe of gravitational lensing by large-scale structure

The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise as a result of spatial clustering of the galaxies as well as gravitational lensing by dark matter along the line of sight. The lensing contribution to the two-point autocorrelation function is typically small compared with the gravitational clustering. However, the cross-correlation between two galaxy samples is almost unaffected by gravitational clustering provided that their redshift distributions do not overlap. The cross-correlation is then induced by magnification bias resulting from lensing by large-scale structure. We compute the expected amplitude of the cross-correlation for popular theoretical models of structure formation. For two populations with mean redshifts of ≃0.3 and 1, we find a cross-correlation signal of ≃1 per cent on arcmin scales and ≃3 per cent on scales of a few arcsec. The dependence on the cosmological parameters Ω and Λ, the dark matter power spectrum and the bias factor of the foreground galaxy population is explored.     

Lensing clusters of galaxies in the SDSS-Ⅲ

We identify new strong lensing clusters of galaxies from the Sloan Digital Sky Survey III (SDSS DR8) by visually inspecting color images of a large sample of clusters of galaxies. We find 68 new clusters showing giant arcs in addition to 30 known lensing systems. Among 68 cases, 13 clusters are almost certain lensing systems with tangential giant arcs, 22 clusters are probable and 31 clusters are possible lensing systems. We also find two exotic systems with blue rings. The giant arcs have angular separatio...     

Cosmic statistics through weak lenses

Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical ansatz, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small angular scales (i.e. at high resolution), where the usual perturbative calculations of matter clustering no longer apply. We build on these studies in order to develop a complete picture of weak lensing at small smoothing angles. In particular, we study the full probability distribution function, bias and other multipoint statistics for the 'hot spots' of the convergence field induced by weak lensing, and relate these to the statistics of overdense regions in the underlying mass distribution. It is already known that weak lensing can constrain the background geometry of the Universe, but we further show that it can also provide valuable information about the statistics of collapsed objects and the physics of collisionless clustering. Our results are particularly important for future observations which will, at least initially, focus on small smoothing angles.     

Gravitational Lensing Effect on the Two-Point Correlation of Hot Spots in the Cosmic Microwave Background

We investigate the weak gravitational lensing effect that is due to the large-scale structure of the universe on two-point correlations of local maxima (hot spots) in the two-dimensional sky map of the cosmic microwave background (CMB) anisotropy. According to the Gaussian random statistics, as most inflationary scenarios predict, the hot spots are discretely distributed, with some characteristic angular separations on the last scattering surface that are due to oscillations of the CMB angular power spectrum. The weak lensing then causes pairs of hot spots, which are separated with the characteristic scale, to be observed with various separations. We found that the lensing fairly smooths out the oscillatory features of the two-point correlation function of hot spots. This indicates that the hot spot correlations can be a new statistical tool for measuring the shape and normalization of the power spectrum of matter fluctuations from the lensing signatures.