Intrinsic and extrinsic galaxy alignment

We show with analytic models that the assumption of uncorrelated intrinsic ellipticities of target sources that is usually made in searches for weak gravitational lensing arising from large-scale mass inhomogeneities ('field lensing') is unwarranted. If the orientation of the galaxy image is determined either by the angular momentum or by the shape of the halo in which it forms, then the image should be aligned preferentially with the component of the tidal gravitational field perpendicular to the line of sight. Long-range correlations in the tidal field will thus lead to long-range ellipticity–ellipticity correlations that mimic the shear correlations arising from weak gravitational lensing. We calculate the ellipticity–ellipticity correlation expected if halo shapes determine the observed galaxy shape, and we discuss uncertainties (which are still considerable) in the predicted amplitude of this correlation. The ellipticity–ellipticity correlation induced by angular momenta should be smaller. We consider several methods for discriminating between the weak-lensing (extrinsic) and intrinsic correlations, including the use of redshift information. An ellipticity–tidal-field correlation also implies the existence of an alignment of images of galaxies near clusters. Although the intrinsic alignment may complicate the interpretation of field-lensing results, it is inherently interesting as it may shed light on galaxy formation as well as on structure formation.     

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.     

Sources of contamination to weak lensing three-point statistics: constraints from N-body simulations

We investigate the impact of the observed correlation between a galaxy's shape and its surrounding density field on the measurement of third-order weak lensing shear statistics. Using numerical simulations, we estimate the systematic error contribution to a measurement of the third-order moment of the aperture mass statistic (GGG) from three-point intrinsic ellipticity correlations (III), and the three-point coupling between the weak lensing shear experienced by distant galaxies and the shape of foreground galaxies (GGI and GII). We find that third-order weak lensing statistics are typically more strongly contaminated by these physical systematics compared to second-order shear measurements, contaminating the measured three-point signal for moderately deep surveys with a median redshift   z _m∼ 0.7  by ∼15 per cent. It has been shown that accurate photometric redshifts will be crucial to correct for this effect, once a model and the redshift dependence of the effect can be accurately constrained. To this end we provide redshift-dependent fitting functions to our results and propose a new tool for the observational study of intrinsic galaxy alignments. For a shallow survey with   z _m∼ 0.4  we find III to be an order of magnitude larger than the expected cosmological GGG shear signal. Compared to the two-point intrinsic ellipticity correlation which is similar in amplitude to the two-point shear signal at these survey depths, third-order statistics therefore offer a promising new way to constrain models of intrinsic galaxy alignments. Early shallow data from the next generation of very wide weak lensing surveys will be optimal for this type of study.     

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.     

QSO lensing magnification associated with galaxy groups

We simulated both the matter and light (galaxy) distributions in a wedge of the Universe and calculated the gravitational lensing magnification caused by the mass along the line-of-sight of galaxies and galaxy groups identified in sky surveys. A large volume redshift cone containing cold dark matter particles mimics the expected cosmological matter distribution in a flat universe with low matter density and a cosmological constant. We generate a mock galaxy catalogue from the matter distribution and identify thousands of galaxy groups in the luminous sky projection. We calculate the expected magnification around galaxies and galaxy groups and then the induced quasi-stellar object (QSO)–lens angular correlation due to magnification bias. This correlation is observable and can be used both to estimate the average mass of the lens population and to make cosmological inferences. We also use analytical calculations and various analyses to compare the observational results with theoretical expectations for the cross-correlation between faint QSOs from the 2dF Survey and nearby galaxies and groups from the Automated Plate Measurement and Sloan Digital Sky Survey Early Data Release. The observed QSO–lens anticorrelations are stronger than the predictions for the cosmological model used. This suggests that there could be unknown systematic errors in the observations and data reduction, or that the model used is not adequate. If the observed signal is assumed to be solely due to gravitational lensing, then the lensing is stronger than expected, due to more massive galactic structures or more efficient lensing than simulated.     

Weak lensing from strong clustering

We investigate the effect of weak gravitational lensing in the limit of small angular scales where projected galaxy clustering is strongly non-linear. This is the regime likely to be probed by future weak lensing surveys. We use well-motivated hierarchical scaling arguments and the plane-parallel approximation to study multi-point statistical properties of the convergence field. These statistics can be used to compute the vertex amplitudes in tree models of hierarchical clustering; these can be compared with similar measurements from galaxy surveys, leading to a powerful probe of galaxy bias.     

Angular correlations between LBQS and APM: weak lensing by the large-scale structure

We detect a positive angular correlation between bright, high-redshift QSOs and foreground galaxies. The QSOs are taken from the optically selected LBQS Catalogue, while the galaxies are from the APM Survey. The correlation amplitude is about a few per cent on angular scales of over a degree. It is a function of QSO redshift and apparent magnitude, in a way expected from weak lensing, and inconsistent with QSO–galaxy correlations being caused by physical associations, or uneven obscuration by Galactic dust. The correlations are ascribed to the weak lensing effect of the foreground dark matter, which is traced by the APM galaxies. The amplitude of the effect found here is compared to the analytical predictions from the literature, and to the predictions of a phenomenological model, which is based on the observed counts-in-cells distribution of APM galaxies. While the latter agree reasonably well with the analytical predictions (namely those of Dolag &38; Bartelmann and Sanz et al.), both underpredict the observed correlation amplitude on degree angular scales. We consider the possible ways to reconcile these observations with theory, and discuss the implications that these observations have on some aspects of extragalactic astronomy.     

Galaxy–QSO correlation induced by weak gravitational lensing arising from large-scale structure

Observational evidence shows that gravitational lensing induces an angular correlation between the distribution of galaxies and much more distant QSOs. We use weak gravitational lensing theory to calculate this angular correlation, updating previous calculations and presenting new results exploring the dependence of the correlation on the large-scale structure. We study the dependence of the predictions on a variety of cosmological models, such as cold dark matter models, mixed dark matter models and models based on quintessence. We also study the dependence on the assumptions made about the nature of the primordial fluctuation spectrum: adiabatic, isocurvature and power spectra motivated by the cosmic string scenario are investigated. Special attention is paid to the issue of galaxy biasing, which is fully incorporated. We show that different mass power spectra imply distinct predictions for the angular correlation, and therefore the angular correlation provides an extra source of information about cosmological parameters and mechanisms of structure formation. We compare our results with observational data and discuss their potential uses. In particular, it is suggested that the observational determination of the galaxy–QSO correlation may be used to give an independent measurement of the mass power spectrum.     

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 flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy–galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy–galaxy lensing, examining isothermal sphere and Navarro–Frenk–White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in two-dimensional projection on the sky, and in three dimensions in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence–flexion cross-correlations, and we find that the signal is an effective probe of structure on non-linear scales.     

B0712+472: a new radio four-image gravitational lens

A new four-image gravitational lens system, B0712+472, has been discovered during the Cosmic Lens All-Sky Survey. This system consists of four flat-spectrum radio images that are also seen on a Hubble Space Telescope ( HST ) image, together with the lensing galaxy. We present MERLIN, VLA and VLBA maps and WHT spectra of the system as well as the HST images. The light distribution of the lensing galaxy is highly elongated and so too is the mass distribution deduced from modelling. We suggest a redshift of ∼1.33 for the lensed object; the lens redshift will require further investigation. The discovery of this new system further increases the ratio of four-image to two-image lens systems currently known, exacerbating problems of required ellipticity of matter distributions in lensing galaxies.     

Discovery of four gravitational lensing systems by clusters in the SDSS DR6

We report the discovery of 4 strong gravitational lensing systems by visual inspections of the Sloan Digital Sky Survey images of galaxy clusters in Data Release 6 (SDSS DR6). Two of the four systems show Einstein rings while the others show tangen-tial giant arcs. These arcs or rings have large angular separations ( 8") from the bright central galaxies and show bluer color compared with the red cluster galaxies. In addition,we found 5 probable and 4 possible lenses by galaxy clusters.     

Correlations of cosmic tidal fields

We study correlations amongst tidal fields originated by the large-scale distribution of matter in the Universe. The two-point tidal correlation is described as a rank-4 tensor, the elements of which can be written in terms of four fundamental scalar functions ranging, with respect to the spatial separation, from purely transversal to purely longitudinal correlations. Tidal fields, on both galaxy and cluster scales, are revealed to be correlated over distances larger than the mass–density correlation length, although traceless tidal fields show anti-correlation between diagonal terms along orthogonal directions. The cross-correlation between mass and tidal field is also analysed. These results are relevant for galaxy formation and the interpretation of large-scale weak lensing phenomena.     

Moment-based ellipticity measurement as a statistical parameter estimation problem

We show that galaxy ellipticity estimation for weak gravitational lensing with unweighted image moments reduces to the problem of measuring a combination of the means of three independent normal random variables. Under very general assumptions, the intrinsic image moments of sources can be recovered from observations including effects such as the point-spread function and pixellation. Gaussian pixel noise turns these into three jointly normal random variables, the means of which are algebraically related to the ellipticity. We show that the random variables are approximately independent with known variances, and provide an algorithm for making them exactly independent. Once the framework is developed, we derive general properties of the ellipticity estimation problem, such as the signal-to-noise ratio, a generic form of an ellipticity estimator, and Cramér-Rao lower bounds for an unbiased estimator. We then derive the unbiased ellipticity estimator using unweighted image moments. We find that this unbiased estimator has a poorly behaved distribution and does not converge in practical applications, but demonstrates how to derive and understand the behaviour of new moment-based ellipticity estimators.     

Effects of cluster galaxies on arc statistics

We present the results of a set of numerical simulations evaluating the effect of cluster galaxies on arc statistics.
We perform a first set of gravitational lensing simulations using three independent projections for each of nine different galaxy clusters obtained from N -body simulations. The simulated clusters consist of dark matter only. We add a population of galaxies to each cluster, mimicking the observed luminosity function and the spatial galaxy distribution, and repeat the lensing simulations including the effects of cluster galaxies, which themselves act as individual lenses. Each galaxy is represented by a spherical Navarro, Frenk & White density profile.
We consider the statistical distributions of the properties of the gravitational arcs produced by our clusters with and without galaxies. We find that the cluster galaxies do not introduce perturbations strong enough to significantly change the number of arcs and the distributions of lengths, widths, curvature radii and length-to-width ratios of long arcs. We find some changes to the distribution of short-arc properties in the presence of cluster galaxies. The differences appear in the distribution of curvature radii for arc lengths smaller than 12 arcsec, while the distributions of lengths, widths and length-to-width ratios are significantly changed only for arcs shorter than 4 arcsec.     

A comparison of different cluster mass estimates: consistency or discrepancy?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and its dynamical evolution. Using the hitherto largest sample of lensing clusters drawn from the literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is excellent agreement between the weak lensing, X-ray and isothermal sphere model-determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2–4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters, as well as from assuming an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.     

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.     

CLASS B2108+213: a new wide-separation gravitational lens system

We present observations of CLASS B2108+213, the widest separation gravitational lens system discovered by the Cosmic Lens All-Sky Survey. Radio imaging using the VLA at 8.46 GHz and MERLIN at 5 GHz shows two compact components separated by 4.56 arcsec with a faint third component in between which we believe is emission from a lensing galaxy. 5-GHz VLBA observations reveal milliarcsecond-scale structure in the two lensed images that is consistent with gravitational lensing. Optical emission from the two lensed images and two lensing galaxies within the Einstein radius is detected in Hubble Space Telescope imaging. Furthermore, an optical gravitational arc, associated with the strongest lensed component, has been detected. Surrounding the system is a number of faint galaxies which may help explain the wide image separation. A plausible mass distribution model for CLASS B2108+213 is also presented.