arXiv subjects

Liliya L. R. Williams

Publications and source records attributed to Liliya L. R. Williams.

104 records · Page 6Linked to original sources

arXiv2001

Beware the Non-uniqueness of Einstein Rings

We explain how an approximation to the rings formed by the host galaxies in lensed QSOs can be inferred from the QSO data alone. A simple ring image can be made from any lens model by a simple piece of computer graphics: just plot a contour map of the arrival-time surface with closely-spaced contours. We go on to explain that rings should be (a) sensitive to time-delay ratios between different pairs of images, but (b) very insensitive to H_0. We illustrate this for the well-known quads 1115+080 and 1608+656.

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arXiv1999

Large-Scale QSO-Galaxy Correlations and Weak Lensing

Several recent studies show that bright, intermediate and high redshift optically and radio selected QSOs are positively correlated with nearby galaxies on a range of angular scales up to a degree. Obscuration by unevenly distributed Galactic dust can be ruled out as the cause, leaving weak statistical lensing as the physical process responsible. However the amplitude of correlations on < 1 degree scales is at least a factor of a few larger than lensing model predictions. A possible way to reconcile the observations and theory is to revise the weak lensing formalism. We extend the standard lensing formulation to include the next higher order term (second order) in the geodesic equation of motion for photons. We derive relevant equations applicable in the weak lensing regime, and discuss qualitative properties of the updated formulation. We then perform numerical integrations of the revised equation and study the effect of the extra term using two different types of cosmic mass density fluctuations. We find that nearby large-scale coherent structures increase the amplitude of the predicted lensing-induced correlations between QSOs and foreground galaxies by ~ 10% (not a factor of several required by observations), while the redshift of the optimal, i.e. `most correlated' structures is moved closer to the observer compared to what is predicted using the standard lensing equation.

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arXiv1999

Pixelated Lenses and H_0 from Time-delay QSOs

Observed time delays between images of a lensed QSO lead to the determination of the Hubble constant by Refsdal's method, provided the mass distribution in the lensing galaxy is reasonably well known. Since the two or four QSO images usually observed are woefully inadequate by themselves to provide a unique reconstruction of the galaxy mass, most previous reconstructions have been limited to simple parameterized models, which may lead to large systematic errors in the derived H_0 by failing to consider enough possibilities for the mass distribution of the lens. We use non-parametric modeling of galaxy lenses to better explore physically plausible but not overly constrained galaxy mass maps, all of which reproduce the lensing observables exactly, and derive the corresponding distribution of H_0's. Blind tests - where one of us simulated galaxy lenses, lensing observables, and a value for H_0, and the other applied our modeling technique to estimate H_0 indicate that our procedure is reliable. For four simulated lensed QSOs the distribution of inferred H_0 have an uncertainty of \simeq 10% at 90% confidence. Application to published observations of the two best constrained time-delay lenses, PG1115+080 and B1608+656, yields H_0=61 +/- 11 km/s/Mpc at 68% confidence and 61 +/- 18 km/s/Mpc at 90% confidence.

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arXiv1999

Pixellated Lenses and Estimates of H_0 from Time-delay Quasars

The largest source of uncertainty in the determination of H_0 from a multiply-imaged QSO system is the unknown mass distribution in the lensing galaxy. Parametric models severely restrict the shape of the galaxy thereby underestimating errors and biasing the best estimate of H_0. We present a method that explores the whole of the model space allowed by the image observables and a few general properties of galaxies. We describe blind test of the method and then apply it to PG1115+080 and B1608+656 which yield H_0 between 45 and 80 km/s/Mpc at 90% confidence level, with the best estimate of 60 km/s/Mpc.

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arXiv1999

Cluster Reconstruction from Combined Strong and Weak Lensing

The lensing information provided by multiple images, arclets, and statistical distortions can all be formulated as linear constraints on the arrival-time surface, and hence on the mass distribution. This reduces cluster lens reconstruction from combined strong and weak lensing to a standard type of inversion problem. Moreover, the mass sheet degeneracy is broken if there are sources at different redshifts.

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arXiv1999

Weak Lensing Induced Correlations Between 1 Jy QSOs and APM Galaxies on Angular Scales of a Degree

We find angular correlations between high redshift radio selected QSOs from the 1 Jy Catalog and APM galaxies on ~1 degree scales. We demonstrate that observed correlations are qualitatively consistant with a gravitational lensing explanation and are inconsistant with a Galactic dust obscuration model. Comparing our results with those of Benitez and Martinez-Gonzalez, who also use 1 Jy sources and APM galaxies we come to the conclusion that galaxy selection criteria can have a major effect on the angular scale and amplitude of detected correlations.

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arXiv1999

The Core Structure of Galaxy Clusters from Gravitational Lensing

We examine gravitational lensing constraints on the structure of galaxy clusters and compare them with the results of cosmological N-body simulations of cluster formation in cold dark matter (CDM) dominated universes. We find that cluster core masses, as measured by the observed location of giant tangential arcs, generally exceed those of dark matter halos of similar velocity dispersion. The magnitude of the discrepancy is a strong function of cluster mass. Arc properties in the most massive clusters in the sample (i.e. those with velocity dispersion, σ\sim 1500-2000 km/s) are essentially consistent with the N-body predictions. On the other hand, giant arcs in σ\sim 1000 km/s clusters can only be reconciled with CDM cluster halos if their lensing power has been increased substantially by the presence of a massive (\sim 3 \times 10^{12} h^{-1} M_{\odot}) central galaxy and of significant substructure. Best agreement is found if the mass of the central galaxy and the effects of substructure are approximately independent of cluster mass. Massive central galaxies with steep inner density profiles are also needed to explain a clear trend observed in our dataset between the radial thickness of giant tangential arcs and the velocity dispersion of the cluster lens. The position and redshift of radial arcs may be used as independent tests of these results, but at present the dataset available is too limited to have a significant impact on these conclusions. Our results depend only weakly on the cosmological model adopted, and suggest that structural parameters of clusters derived from strong lensing studies cannot usefully constrain the values of cosmological parameters.

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arXiv1998

Non-parametric Reconstruction of Abell 2218 from Combined Weak and Strong Lensing

We apply a new non-parametric technique to reconstruct, with uncertainties, the projected mass distribution of the inner region of Abell 2218, using combined strong and weak lensing constraints from multiple-image systems and arclets with known redshifts. The reconstructed mass map broadly resembles previous, less detailed, parametric models, but when examined in detail shows several sub-structures, not necessarily associated with light but strongly required by the lensing data. In particular, the highest mass peak is offset by about 30 kpc/h50 from the main light peak, and projected mass-to-light in the directions of different cluster galaxies varies by at least a factor of 10. On comparing with mass estimates from models of the X-ray emitting gas, we find that the X-ray models under-predict the enclosed mass profile by, at least a factor of 2.5; the discrepancy gets worse if we assume that mass traces light to the extent allowed by the lensing constraints.

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arXiv1998

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 percent 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 & Bartelmann 1997, and Sanz et al. 1997), both under-predict the observed correlation amplitude on degree angular scales. We consider the possible ways to reconcile these observations with theory, and discuss the implications these observations have on some aspects of extragalactic astronomy.

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arXiv1997

Cluster Mass Profile from Lensing

We propose a new technique to reconstruct non-parametrically the projected mass distribution of galaxy clusters from their gravitational lens effect on background galaxies. The beauty of our technique, is that it combines information from multiple imaging (strong lensing) and shear (weak lensing) as linear constraints on the projected mass distribution. Moreover, our technique overcomes all the drawbacks of non-linear methods. The method is applied to the first cluster-lens A370 and to the cluster-lens A2218 which is exceptionally rich in multiple images and arc(let)s. The reconstructed maps for both cases revealed unprecedented levels of detail.

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arXiv1997

Undistorted Lensed Images in Galaxy Clusters

To date, the study of high-magnification gravitational lensing effects of galaxy clusters has focused upon the grossly distorted, luminous arc-like features formed in massive, centrally condensed clusters. We investigate the formation of a different type of image, highly magnified yet undistorted, in two widely employed cluster mass density profiles; an isothermal sphere with a core, and a universal dark matter halo profile derived from numerical simulations of Navarro et al. We examine the properties of images of extended sources produced by these two cluster profiles, paying particular attention to the undistorted images. Using simple assumptions about the source and lens population, we estimate the relative frequency of occurrence of highly magnified, undistorted images and the more commonly known giant arcs.

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arXiv1997

Image Separation vs. Redshift of Lensed QSOs: Implications for Galaxy Mass Profiles

Recently, Park and Gott reported an interesting observation: image separation of lensed QSOs declines with QSO redshift more precipitously than expected in any realistic world model, if the lenses are taken to be either singular isothermal spheres or point masses. In this Letter I propose that the observed trend arises naturally if the lensing galaxies have logarithmic surface mass density profiles that gradually change with radius. If the observed lack of central (odd) images is also taken into account, the data favor a universal dark matter density profile over an isothermal sphere with a core. Since the trend of image separation vs. source redshift is mostly a reflection of galaxy properties, it cannot be straightforwardly used as a test of cosmological models. Furthermore, the current upper limits on the cosmological constant may have to be revised.

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arXiv1997

Measurement of the Hubble Constant Via Gravitational Lensing--- A Review of the Jodrell Bank ``Golden Lenses'' Workshop

Gravitational lensing is now widely and successfully used to study a range of astronomical phenomena, from individual objects, like galaxies and clusters, to the mass distribution on various scales, to the overall geometry of the Universe. Here we describe and assess the use of gravitational lensing as ``gold standards'' in addressing one of the fundamental problems in astronomy, the determination of the absolute distance scale to extragalactic objects. This is commonly parameterized by the Hubble constant, $H_0$, the current expansion rate of the Universe. The elegance of the underlying geometrical principle of the gravitational lensing method combined with the recent advances in observations and modelling makes it a very promising technique for measuring $H_0$.

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arXiv1997

Non-parametric reconstruction of the galaxy-lens in PG1115+080

We describe a new, non-parametric, method for reconstructing lensing mass distributions in multiple-image systems, and apply it to PG1115, for which time delays have recently been measured. It turns out that the image positions and the ratio of time delays between different pairs of images constrain the mass distribution in a linear fashion. Since observational errors on image positions and time delay ratios are constantly improving, we use these data as a rigid constraint in our modelling. In addition, we require the projected mass distributions to be inversion-symmetric and to have inward-pointing density gradients. With these realistic yet non-restrictive conditions it is very easy to produce mass distributions that fit the data precisely. We then present models, for $H_0=42$, 63 and 84 \kmsmpc, that in each case minimize mass-to-light variations while strictly obeying the lensing constraints. (Only a very rough light distribution is available at present.) All three values of $H_0$ are consistent with the lensing data, but require quite different morphologies for the lensing galaxy. If $H_0$ is low, the main lensing galaxy could be an early type. If $H_0$ is high, the galaxy is reconstructed as a late elliptical or nearly edge-on disc; a binary or merging system is also plausible.

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