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.     

Gravitational lensing of anisotropic sources

In strong gravitational lensing, the multiple images we see correspond to light rays that leave the source in slightly different directions. If the source emission is anisotropic, the images may differ from conventional lensing predictions (which assume isotropy). To identify scales on which source anisotropy may be important, we study the angle δ between the light rays emerging from the source, for different lensing configurations. If the lens has a power-law profile   M ∝ R ^γ  , the angle δ initially increases with lens redshift and then either diverges (for a steep profile  γ < 1  ), remains constant (for an isothermal profile  γ= 1  ), or vanishes (for a shallow profile  γ > 1  ) as   z _l→ z _s  . The scaling with lens mass is roughly  δ∝ M ^1/(2−γ)  . The results for an Navarro–Frenk–White (NFW) profile are qualitatively similar to those for a shallow power law, with δ peaking at about half the redshift of the source (not half the distance). In practice, beaming could modify the statistics of beamed sources lensed by massive clusters: for an opening angle  θ_jet  , there is a probability as high as   P ∼ 0.02–0.07(θ_jet/0.5°)⁻¹  that one of the lensed images may be missed (for  2 ≲ z _s≲ 6  ). Differential absorption within active galactic nuclei (AGNs) could modify the flux ratios of AGNs lensed by clusters; a sample of AGNs lensed by clusters could provide further constraints on the sizes of absorbing regions. Source anisotropy is not likely to be a significant effect in galaxy-scale strong lensing.     

SDSS J120923.7+264047: a new massive galaxy cluster with a bright giant arc

Highly magnified lensed galaxies allow us to probe the morphological and spectroscopic properties of high-redshift stellar systems in great detail. However, such objects are rare, and there are only a handful of lensed galaxies that are bright enough for a high-resolution spectroscopic study with current instrumentation. We report the discovery of a new massive lensing cluster, SDSS J120923.7+264047, at z = 0.558. Present around the cluster core, at angular distances of up to ∼40 arcsec, are many arcs and arc candidates, presumably due to lensing of background galaxies by the cluster gravitational potential. One of the arcs, 21 arcsec long, has an r -band magnitude of 20, making it one of the brightest known lensed galaxies. We obtained a low-resolution spectrum of this galaxy, using the Keck-I telescope, and found it is at redshift of z = 1.018.     

On the streaming motions of haloes and galaxies

Little is known about the statistics of gravitationally lensed quasars at large (7–30 arcsec) image separations, which probe masses on the scale of galaxy clusters. We have carried out a survey for gravitationally lensed objects, among sources in the FIRST 20-cm radio survey that have unresolved optical counterparts in the digitizations of the Palomar Observatory Sky Survey. From the statistics of ongoing surveys that search for quasars among FIRST sources, we estimate that there are about 9100 quasars in this source sample, making this one of the largest lensing surveys to date. Using broad-band imaging, we have isolated all objects with double radio components separated by 5–30 arcsec that have unresolved optical counterparts with similar BVI colours. Our criteria for similar colours conservatively allow for observational error and for colour variations due to time delays between lensed images. Spectroscopy of these candidates shows that none of the pairs are lensed quasars. This sets an upper limit (95 per cent confidence) on the lensing fraction in this survey of 3.3×10⁻⁴, assuming 9100 quasars. Although the source redshift distribution is poorly known, a rough calculation of the expected lensing frequency and the detection efficiencies and biases suggests that simple theoretical expectations are of the same order of magnitude as our observational upper limit. Our procedure is novel in that our exhaustive search for lensed objects does not require prior identification of the quasars in the sample as such. Characterization of the FIRST-selected quasar population will enable use of our result to constrain quantitatively the mass properties of clusters.     

Spectroscopic confirmation of redshifts predicted by gravitational lensing

We present deep spectroscopic measurements of 18 distant field galaxies identified as gravitationally lensed arcs in a Hubble Space Telescope image of the cluster Abell 2218. Redshifts of these objects were predicted by Kneib et al. using a lensing analysis constrained by the properties of two bright arcs of known redshift and other multiply imaged sources. The new spectroscopic identifications were obtained using long exposures with the LDSS-2 spectrograph on the William Herschel Telescope, and demonstrate the capability of that instrument to reach new limits, R ≃24; the lensing magnification implies true source magnitudes as faint as R ≃25. Statistically, our measured redshifts are in excellent agreement with those predicted from Kneib et al.'s lensing analysis, and this gives considerable support to the redshift distribution derived by the lensing inversion method for the more numerous and fainter arclets extending to R ≃25.5. We explore the remaining uncertainties arising from both the mass distribution in the central regions of Abell 2218 and the inversion method itself, and conclude that the mean redshift of the faint field population at R ≃25.5 ( B ∼26–27) is low, 〈 z 〉=0.8–1. We discuss this result in the context of redshift distributions estimated from multicolour photometry. Although such comparisons are not straightforward, we suggest that photometric techniques may achieve a reasonable level of agreement, particularly when they include near-infrared photometry with discriminatory capabilities in the 1< z <2 range.     

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.     

Modelling the first probable two-plane lens system B2114+022: reproducing two compact radio cores A and D

We test possible lensing scenarios of the JVAS system B2114+022, in which two galaxies at different redshifts ('G1' at z ₁=0.3157 and 'G2' at z ₂=0.5883) are found within 2 arcsec of quadruple radio sources. For our investigation, we use possible lensing constraints derived from a wealth of data on the radio sources obtained with VLA, MERLIN, VLBA and EVN as well as HST imaging data on the two galaxies, which were presented recently in Augusto et al. In the present study, we focus on reproducing the widest separated, observationally similar radio components A and D as lensed images. We first treat G2 (which is the more distant one from the geometric centre) as a shear term, and then consider two-plane lensing explicitly including G2's potential at the z ₂ plane as the first case of two-plane lens modelling. Our modelling results not only support the hypothesis that the system includes gravitationally lensed images of a higher-redshift extragalactic object, but they also show that the explicit inclusion of G2's potential at the second lens plane is necessary in order to fit the data with astrophysically plausible galaxy parameters. Finally, we illustrate a natural consequence of a two-plane lens system, namely the prediction of distortion as well as shift and stretching of G2's isophotes by G1's potential, which can in principle be measured by subtracting out G1's light distribution in an image of high signal-to-noise ratio and good angular resolution, especially a multicolour one.     

Strong lensing of submillimetre galaxies: a tracer of foreground structure?

The steep source counts and negative K -corrections of bright submillimetre galaxies (SMGs) suggest that a significant fraction of those observed at high flux densities may be gravitationally lensed, and that the lensing objects may often lie at redshifts above 1, where clusters of galaxies are difficult to detect through other means. In this case, follow-up of bright SMGs may be used to identify dense structures along the line-of-sight. Here, we investigate the probability for SMGs to experience strong lensing, using the latest N -body simulations and observed source flux and redshift distributions. We find that almost all high-redshift sources with a flux density above 100 mJy will be lensed if they are not relatively local galaxies. We also give estimates of the fraction of sources experiencing strong lensing as a function of observed flux density. This has implications for planning follow-up observations for bright SMGs discovered in future surveys with the Submillimetre Common-User Bolometer Array 2 and other instruments. The largest uncertainty in these calculations is the maximum allowed lensing amplification, which is dominated by the presently unknown spatial extent of SMGs.     

Modelling the 10-image lensed system B1933+503

A gravitational lens model is presented for the newly discovered 10-image system B1933+503. The underlying object, revealed by modelling, is a triple radio source on the scale of a couple of hundred mas that is well-aligned along the line of sight with a foreground and somewhat flattened lensing galaxy, the orientation and location of which match those of an observed galaxy, known to be at a redshift of 0.755. Uncertainties in the modelling are obtained by a Monte Carlo exercise. Observational tests of the lens model are proposed, and the time delays between various pairs of images are determined, as the core of the source is known to be significantly variable. Future observations of the lens hold the key to using B1933+503 to constrain Hubble's constant. Despite the absence of a source redshift, the utility of the system as a probe of the structure of the lens galaxy is unparalleled as it provides a surfeit of easily identifiable constraints for modelling the system.     

The role of luminous substructure in the gravitational lens system MG 2016+112

MG 2016+112 is a quadruply imaged lens system with two complete images A and B and a pair of merging partial images in region C as seen in the radio. The merging images are found to violate the expected mirror symmetry. This indicates an astrometric anomaly which could only be of gravitational origin and could arise due to substructure in the environment or line of sight of the lens galaxy. We present new high-resolution multifrequency very long baseline interferometry (VLBI) observations at 1.7, 5 and 8.4 GHz. Three new components are detected in the new VLBI imaging of both the lensed images A and B. The expected opposite parity of the lensed images A and B was confirmed due to the detection of non-collinear components. Furthermore, the observed properties of the newly detected components are inconsistent with the predictions of previous mass models. We present new scenarios for the background quasar which are consistent with the new observations. We also investigate the role of the satellite galaxy situated at the same redshift as the main lensing galaxy. Our new mass models demonstrate quantitatively that the satellite galaxy is the primary cause of the astrometric anomaly found in region C. The detected satellite is consistent with the abundance of subhaloes expected in the halo from cold dark matter (CDM) simulations. However, the fraction of the total halo mass in the satellite as computed from lens modelling is found to be higher than that predicted by CDM simulations.     

Non-parametric strong lens inversion of SDSS J1004+4112

In this article, we study the well-known strong lensing system SDSS J1004+4112. Not only does it host a large-separation lensed quasar with measured time-delay information, but several other lensed galaxies have been identified as well. A previously developed strong lens inversion procedure that is designed to handle a wide variety of constraints is applied to this lensing system and compared to results reported in other works. Without the inclusion of a tentative central image of one of the galaxies as a constraint, we find that the model recovered by the other constraints indeed predicts an image at that location. An inversion which includes the central image provides tighter constraints on the shape of the central part of the mass map. The resulting model also predicts a central image of a second galaxy where indeed an object is visible in the available Advanced Camera for Surveys images. We find masses of  2.5 × 10¹³  and  6.1 × 10¹³ M_⊙  within a radius of 60 and 110 kpc, respectively, confirming the results from other authors. The resulting mass map is compatible with an elliptical generalization of a projected NFW profile, with   r _s= 58⁺²¹₋₁₃  arcsec and   c _vir= 3.91 ± 0.74  . The orientation of the elliptical NFW profile closely follows the orientation of the central cluster galaxy and the overall distribution of cluster members.     

A strategy for finding gravitationally lensed distant supernovae

Distant Type Ia and II supernovae (SNe) can serve as valuable probes of the history of the cosmic expansion and star formation, and provide important information on their progenitor models. At present, however, there are few observational constraints on the abundance of SNe at high redshifts. A major science driver for the Next Generation Space Telescope is the study of such very distant SNe. In this paper we discuss strategies for finding and counting distant SNe by using repeat imaging of supercritical intermediate redshift clusters whose mass distributions are well constrained via modelling of strongly lensed features. For a variety of different models for the star formation history and supernova progenitors, we estimate the likelihood of detecting lensed SNe as a function of their redshift. In the case of a survey conducted with Hubble Space Telescope ( HST ), we predict a high probability of seeing a supernova in a single return visit with either Wide Field Planetary Camera 2 or Advanced Camera for Surveys, and a much higher probability of detecting examples with     in the lensed case. Most events would represent magnified SNe II at     and a fraction will be more distant examples. We discuss various ways to classify such events using ground-based infrared photometry. We demonstrate an application of the method using the HST archival data and discuss the case of a possible event found in the rich cluster AC 114     .     

The new gravitational lens system B1030 + 074

We report the discovery of a new double-image gravitational lens system, B1030 + 074, which was found during the Jodrell Bank–VLA Astrometric Survey (JVAS). We have collected extensive radio data on the system using the VLA, MERLIN, the EVN and the VLBA, and optical observations using WFPC2 on the HST . The lensed images are separated by 1.56 arcsec and their flux density ratio at centimetric wavelengths is approximately 14:1, although the ratio is slightly frequency-dependent and the images appear to be time-variable. The HST pictures show both the lensed images and the lensing galaxy close to the weaker image. The lensing galaxy has substructure which could be a spiral arm or an interacting galaxy. We have modelled B1030 + 074 using a singular isothermal ellipsoid which yields a time delay of 156/ h ₅₀ d. This lens is likely to be suitable for the measurement of the Hubble constant.     

Infrared constraints on the dark mass concentration observed in the cluster Abell 1942

We present a deep H -band image of the region in the vicinity of the cluster Abell 1942 containing the puzzling dark matter concentration detected in an optical weak lensing study by Erben et al. We demonstrate that our limiting magnitude, H =22 , would be sufficient to detect clusters of appropriate mass out to redshifts comparable with the mean redshift of the background sources. Despite this, our infrared image reveals no obvious overdensity of sources at the location of the lensing mass peak, nor an excess of sources in the I − H versus H colour–magnitude diagram. We use this to constrain further the luminosity and mass-to-light ratio of the putative dark clump as a function of its redshift. We find that for spatially flat cosmologies, background lensing clusters with reasonable mass-to-light ratios lying in the redshift range 0< z <1 are strongly excluded, leaving open the possibility that the mass concentration is a new type of truly dark object.     

ULAS J234311.93-005034.0: a gravitational lens system selected from UKIDSS and SDSS

We report the discovery of a new gravitational lens system. This object, ULAS J234311.93-005034.0, is the first to be selected by using the new UKIRT Infrared Deep Sky Survey (UKIDSS), together with the Sloan Digital Sky Survey (SDSS). The ULAS J234311.93-005034.0 system contains a quasar at redshift 0.788 which is doubly imaged, with separation 1.4 arcsec. The two quasar images have the same redshift and similar, though not identical, spectra. The lensing galaxy is detected by subtracting point spread functions from R -band images taken with the Keck telescope. The lensing galaxy can also be detected by subtracting the spectra of the A and B images, since more of the galaxy light is likely to be present in the latter. No redshift is determined from the galaxy, although the shape of its spectrum suggests a redshift of about 0.3. The object's lens status is secure, due to the identification of two objects with the same redshift together with a lensing galaxy. Our imaging suggests that the lens is found in a cluster environment, in which candidate arc-like structures, that require confirmation, are visible in the vicinity. Further discoveries of lenses from the UKIDSS survey are likely as part of this programme, due to the depth of UKIDSS and its generally good seeing conditions.     

Gravitational lensing of extended high-redshift sources by dark matter haloes

High-redshift galaxies and quasi-stellar objects (QSOs) are most likely to be strongly lensed by intervening haloes between the source and the observer. In addition, a large fraction of lensed sources is expected to be seen in the submillimetre region, as a result of the enhanced magnification bias on the steep intrinsic number counts. We extend in three directions Blain's earlier study of this effect.
First, we use a modification of the Press–Schechter mass function and detailed lens models to compute the magnification probability distribution. We compare the magnification cross-sections of populations of singular isothermal spheres and Navarro, Frenk & White (NFW) haloes and find that they are very similar, in contrast to the image-splitting statistics which were recently investigated in other studies. The distinction between the two types of density profile is therefore irrelevant for our purposes.
Secondly, we discuss quantitatively the maximum magnification, μ _max, that can be achieved for extended sources (galaxies) with realistic luminosity profiles, taking into account the possible ellipticity of the lensing potential. We find that μ _max plausibly falls into the range     for sources of     effective radius at redshifts within     .
Thirdly, we apply our model for the lensing magnification to a class of sources following the luminosity evolution typical for a unified scheme of QSO formation. As a result of the peculiar steepness of their intrinsic number counts, we find that the lensed source counts at a fiducial wave length of 850 μm can exceed the unlensed counts by several orders of magnitude at flux densities ≳100 mJy, even with a conservative choice of the maximum magnification.     

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.     

lemomaf: Lensed Mock Map Facility

We present the Lensed Mock Map Facility ( lemomaf ), a tool designed to perform mock weak-lensing measurements on numerically simulated chunks of the Universe. Coupling N -body simulations to a semi-analytical model of galaxy formation, lemomaf can create realistic lensed images and mock catalogues of galaxies, at wavelengths ranging from the ultraviolet to the submillimetre. To demonstrate the power of such a tool, we compute predictions of the source–lens clustering (SLC) effect on the convergence statistics, and quantify the impact of weak lensing on galaxy counts in two different filters. We find that the SLC effect skews the probability density function of the convergence towards low values, with an intensity which strongly depends on the redshift distribution of galaxies. On the other hand, the degree of enhancement or depletion in galaxy counts due to weak lensing is independent of the SLC effect. We discuss the impact on the two-point shear statistics to be measured by future missions like SNAP and LSST . The SLC effect would bias the estimation of σ₈ from two-point statistics up to 5 per cent for a narrow redshift distribution of mean   z ∼ 0.5  , and up to 2 per cent in small angular scales for a redshift distribution of mean   z ∼ 1.5  . We conclude that accurate photometric redshifts for individual galaxies are necessary in order to quantify and isolate the SLC effect.     

Strong lensing optical depths in a ΛCDM universe

We investigate strong gravitational lensing in the concordance ΛCDM cosmology by carrying out ray tracing along past light cones through the Millennium Simulation, the largest simulation of cosmic structure formation ever carried out. We extend previous ray-tracing methods in order to take full advantage of the large volume and the excellent spatial and mass resolution of the simulation. As a function of source redshift we evaluate the probability that an image will be highly magnified, will be highly elongated or will be one of a set of multiple images. We show that such strong lensing events can almost always be traced to a single dominant lensing object and we study the mass and redshift distribution of these primary lenses. We fit analytic models to the simulated dark haloes in order to study how our optical depth measurements are affected by the limited resolution of the simulation and of the lensing planes that we construct from it. We conclude that such effects lead us to underestimate total strong lensing cross-sections by about 15 per cent. This is smaller than the effects expected from our neglect of the baryonic components of galaxies. Finally we investigate whether strong lensing is enhanced by material in front of or behind the primary lens. Although strong lensing lines of sight are indeed biased towards higher than average mean densities, this additional matter typically contributes only a few per cent of the total surface density.     

Gravitational lens magnification by Abell 1689: distortion of the background galaxy luminosity function

Gravitational lensing magnifies the observed flux of galaxies behind the lens. We use this effect to constrain the total mass in the cluster Abell 1689 by comparing the lensed luminosities of background galaxies with the luminosity function of an undistorted field. Under the assumption that these galaxies are a random sample of luminosity space, this method is not limited by clustering noise. We use photometric redshift information to estimate galaxy distance and intrinsic luminosity. Knowing the redshift distribution of the background population allows us to lift the mass/background degeneracy common to lensing analysis. In this paper we use nine filters observed over 12 h with the Calar Alto 3.5-m telescope to determine the redshifts of 1000 galaxies in the field of Abell 1689. Using a complete sample of 146 background galaxies we measure the cluster mass profile. We find that the total projected mass interior to 0.25  h ⁻¹ Mpc is M _2D(<0.25  h ⁻¹ Mpc)=(0.48±0.16)×10¹⁵  h ⁻¹ M_⊙, where our error budget includes uncertainties from the photometric redshift determination, the uncertainty in the offset calibration and finite sampling. This result is in good agreement with that found by number-count and shear-based methods and provides a new and independent method to determine cluster masses.