Analytic relations for magnifications and time delays in gravitational lenses with fold and cusp configurations

Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton, Gaudi & Petters, this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies.     

The starburst-AGN connection: the role of stellar clusters in AGNs

Nuclear stellar clusters are a common phenomenon in spirals and in starburst galaxies, and they may be a natural consequence of the star formation processes in the central regions of galaxies. HST UV imaging of a few Seyfert 2 galaxies have resolved nuclear starbursts in Seyfert 2 revealing stellar clusters as the main components of the extended emission. However, we do not know whether stellar clusters are always associated with all types of nuclear activity. We present HST NUV and optical images to study the role that stellar clusters play in different types of AGNs. Also with these images, we study the circumnuclear dust morphology as a probe of the circumnuclear environment of AGNs.     

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.     

Using galaxy redshift surveys to detect gravitationally lensed quasars

Gravitationally lensed quasars can be discovered as a by-product of galaxy redshift surveys. Lenses discovered spectroscopically in this way should require less observational effort per event than those found in dedicated lens surveys. Further, the lens galaxies should be relatively nearby, facilitating a number of detailed observations that are impossible for the more common high-redshift lenses. This is epitomized by the wide range of results that have been obtained from Q 2237+0305, which was discovered as part of the Center for Astrophysics redshift survey, and remains the only quasar lens discovered in this way. The likelihood of this survey yielding a lens is calculated to be ∼0.03, which is an order of magnitude larger than previous estimates due to two effects. First, the quasar images themselves increase the observed flux of the lens, so that lens galaxies up to a magnitude fainter than the nominal survey limit must be included in the calculation. Secondly, it is possible for lensed quasars with extremely faint deflectors to enter the survey due to the extended morphology of the multiple images. Extrapolating these results to future surveys, the 2 degree Field galaxy redshift survey should contain between 10 and 50 lenses and the Sloan Digital Sky Survey should yield between 50 and 300 lenses, depending on the cosmological model and the observing conditions.     

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.     

Cluster lenses

Clusters of galaxies are the most recently assembled, massive, bound structures in the Universe. As predicted by General Relativity, given their masses, clusters strongly deform space-time in their vicinity. Clusters act as some of the most powerful gravitational lenses in the Universe. Light rays traversing through clusters from distant sources are hence deflected, and the resulting images of these distant objects therefore appear distorted and magnified. Lensing by clusters occurs in two regimes, each with unique observational signatures. The strong lensing regime is characterized by effects readily seen by eye, namely, the production of giant arcs, multiple images, and arclets. The weak lensing regime is characterized by small deformations in the shapes of background galaxies only detectable statistically. Cluster lenses have been exploited successfully to address several important current questions in cosmology: (i) the study of the lens(es)—understanding cluster mass distributions and issues pertaining to cluster formation and evolution, as well as constraining the nature of dark matter; (ii) the study of the lensed objects—probing the properties of the background lensed galaxy population—which is statistically at higher redshifts and of lower intrinsic luminosity thus enabling the probing of galaxy formation at the earliest times right up to the Dark Ages; and (iii) the study of the geometry of the Universe—as the strength of lensing depends on the ratios of angular diameter distances between the lens, source and observer, lens deflections are sensitive to the value of cosmological parameters and offer a powerful geometric tool to probe Dark Energy. In this review, we present the basics of cluster lensing and provide a current status report of the field.     

The influence of central black holes on gravitational lenses

Recent observations indicate that many if not all galaxies host massive central black holes. In this paper we explore the influence of black holes on the lensing properties. We model the lens as an isothermal ellipsoid with a finite core radius plus a central black hole. We show that the presence of the black hole substantially changes the critical curves and caustics. If the black hole mass is above a critical value, then it will completely suppress the central images for all source positions. Realistic central black holes are likely to have masses below this critical value. Even in such subcritical cases, the black hole can suppress the central image when the source is inside a zone of influence, which depends on the core radius and black hole mass. In the subcritical cases, an additional image may be created by the black hole in some regions, which for some radio lenses may be detectable with high-resolution and large dynamic range VLBI maps. The presence of central black holes should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.     

Dynamical evolution in clusters of galaxies with low-frequency radio emission

Clusters of galaxies in which radio emission at low frequencies (178 MHz) has been detected were classified on the Bautz-Morgan (BM) system according to the dominance of the brightest galaxy. Radio sources with steep low-frequency spectra occur in clusters of all BM types but more often in rich clusters; the distributions of BM types for clusters with high and low spectral indices between 38 and 178 MHz are similar. Glass copies of Mount Palomar Sky Survey plates were measured to determine the distribution of the ten brightest galaxies in clusters without dominant galaxies. Some clusters were found to have central cores of bright galaxies which may reflect mass segregation of galaxies due to dynamical friction. The bright galaxies in such cores may later merge to form dominant cD galaxies. The positions of the cD galaxies and cores of bright galaxies are often at projected distances <200 kpc from the low-frequency radio emission. The low-frequency spectrum of radio emission associated with a cD galaxy may be either steep or normal, but the low-frequency spectrum from a core of bright galaxies is usually steep. A steep spectrum may develop when a radio source is confined by hot gas in a cluster over a long period (10⁹ yr). Confinement would probably occur for radio sources associated with bright galaxies in the cores of clusters and cD galaxies in clusters. However, cD galaxies may have recurrent radio outbursts so that steep spectra are not always observed.     

CLASS B 1359 + 154: Modelling lensing by a group of galaxies

The recently discovered gravitationally lensed system CLASS B1359 +154 appears to have six detectable images of a single background source at a redshift of 3.235. A group of galaxies acts as the lens, at a redshift of ∼ 1. The present work identifies two distinct, physically plausible image configurations, a 7-image one and a 9-image one. Mass models are constructed corresponding to realizations of these two configurations. Both models call for, in addition to non-singular galaxy-type lenses, a larger scale mass component that resembles the extended dark matter distributions seen in relatively low-redshift galaxy groups. It is presently observationally impossible to study the extended X-ray emission from a group at such a high redshift, hence lensing studies are of some interest. A lensed system with a high image multiplicity does not necessarily admit of a unique lensing interpretation; discrimination is possible with additional observable details (e.g., the image parities, which are uncommon among even the simpler systems).     

Discs in early-type lensing galaxies: effects on magnification ratios and measurements of H0

Observations of early-type galaxies, both in the local Universe and in clusters at medium redshifts, suggest that these galaxies often contain discs or disc-like structures. Using the results of Kelson et al. for the incidence of disc-components among the galaxies in the redshift   z = 0.33  cluster CL 1358+62, we investigate the effect of disc structures on the lensing properties of early-type galaxies. Statistical properties, like magnification cross-sections and the expected number of quad (four-image) lens systems, are not affected greatly by the inclusion of discs that contain less than ∼10 per cent of the total stellar mass. However, the properties of individual lens systems are affected. We estimate that 10–30 per cent of all quad-lens systems, with early-type deflector galaxies, would be affected measurably by the presence of disc components. Intriguingly, the image magnification ratios are altered significantly. The amplitude of the predicted change is sufficient to explain the observed magnification ratios in systems like B1422+231 without requiring compact substructure. Furthermore, time-delays between images also change; fitting a bulge-only model to early-type lenses that in fact contain a disc would yield a value of the Hubble constant H ₀ that is systematically too low by ∼25 per cent.     

The structure of spiral galaxies — II. Near-infrared properties of spiral arms

We have imaged a sample of 45 face-on spiral galaxies in the K band, to determine the morphology of the old stellar population, which dominates the mass in the disc. The K -band images of the spiral galaxies have been used to calculate different characteristics of the underlying density perturbation such as arm strengths, profiles and cross-sections, and spiral pitch angles. Contrary to expectations, no correlation was found between arm pitch angle and Hubble type, and combined with previous results this leads us to conclude that the morphology of the old stellar population bears little resemblance to the optical morphology used to classify galaxies. The arm properties of our galaxies seem inconsistent with predictions from the simplest density wave theories, and some observations, such as variations in pitch angle within galaxies, seem hard to reconcile even with more complex modal theories. Bars have no detectable effect on arm strengths for the present sample. We have also obtained B -band images of three of the galaxies. For these galaxies we have measured arm cross-sections and strengths, to investigate the effects of disc density perturbations on star formation in spiral discs. We find that B -band arms lead K -band arms and are narrower than K -band arms, apparently supporting predictions made by the large-scale shock scenario, although the effects of dust on B -band images may contribute towards these results.     

NICMOS images of JVAS/CLASS gravitational lens systems

We present Hubble Space Telescope ( HST ) infrared images of four gravitational lens systems from the JVAS/CLASS gravitational lens survey and compare the new infrared HST pictures with previously published WFPC2 HST optical images and radio maps. Apart from the wealth of information that we get from the flux ratios and accurate positions and separations of the components of the lens systems, which we can use as inputs for better constraints on the lens models, we are able to discriminate between reddening and optical/radio microlensing as the possible cause of differences observed in the flux ratios of the components across the three wavelength bands. Substantial reddening has been known to be present in the lens system B1600+434 and has been further confirmed by the present infrared data. In the two systems B0712+472 and B1030+074 microlensing has been pinpointed as the main cause of the flux ratio discrepancy both in the optical/infrared and in the radio, the radio possibly caused by the substructure revealed in the lensing galaxies. In B0218+357, however, the results are still not conclusive. If we are actually seeing the two 'true' components of the lens system then the flux ratio differences are attributed to a combination of microlensing and reddening or are alternatively the result of some variability in at least one of the images. Otherwise the second 'true' component of B0218+357 may be completely absorbed by a molecular cloud and the anomalous flux density ratios and large difference in separation between the optical/infrared and radio that we see can be explained by emission either from a foreground object or from part of the lensing galaxy.     

Structure through colour: a pixel approach towards understanding galaxies

We present a study of pixel colour–magnitude diagrams (pCMDs) for a sample of 69 nearby galaxies chosen to span a wide range of Hubble types. Our goal is to determine how useful a pixel approach is for studying galaxies according to their stellar light distributions and content. The galaxy images were analysed on a pixel-by-pixel basis to reveal the structure of the individual pCMDs. We find that the average surface brightness (or projected mass density) in each pixel varies according to galaxy type. Early-type galaxies exhibit a clear 'prime sequence' and some pCMDs of face-on spirals reveal 'inverse-L' structures. We find that the colour dispersion at a given magnitude is found to be approximately constant in early-type galaxies but this quantity varies in the mid and late types. We investigate individual galaxies and find that the pCMDs can be used to pick out morphological features. We discuss the discovery of 'Red Hooks' in the pCMDs of six early-type galaxies and two spirals and postulate their origins. We develop quantitative methods to characterize the pCMDs, including measures of the blue-to-red light ratio and colour distributions of each galaxy and we organize these by morphological type. We compare the colours of the pixels in each galaxy with the stellar population models of Bruzual & Charlot to calculate star formation histories for each galaxy type and compare these to the stellar mass within each pixel. Maps of pixel stellar mass and mass-to-light ratio are compared to galaxy images. We apply the pCMD technique to three galaxies in the Hubble Ultra Deep Field to test the usefulness of the analysis at high redshift. We propose that these results can be used as part of a new system of automated classification of galaxies that can be applied at high redshift.     

The European Large Area ISO Survey – III. 90-μm extragalactic source counts

We present results and source counts at 90 μm extracted from the preliminary analysis of the European Large Area ISO Survey (ELAIS). The survey covered about 12 deg² of the sky in four main areas and was carried out with the ISOPHOT instrument onboard the Infrared Space Observatory ( ISO ). The survey is at least an order of magnitude deeper than the IRAS 100-μm survey and is expected to provide constraints on the formation and evolution of galaxies. The majority of the detected sources are associated with galaxies on optical images. In some cases the optical associations are interacting pairs or small groups of galaxies, suggesting that the sample may include a significant fraction of luminous infrared galaxies. The source counts extracted from a reliable subset of the detected sources are in agreement with strongly evolving models of the starburst galaxy population.     

Automated morphological classification of galaxies based on projection gradient nonnegative matrix factorization algorithm

The development of automated morphological classification schemes can successfully distinguish between morphological types of galaxies and can be used for studies of the formation and subsequent evolution of galaxies in our universe. In this paper, we present a new automated machine supervised learning astronomical classification scheme based on the Nonnegative Matrix Factorization algorithm. This scheme is making distinctions between all types roughly corresponding to Hubble types such as elliptical, lenticulars, spiral, and irregular galaxies. The proposed algorithm is performed on two examples with different number of image (small dataset contains 110 image and large dataset contains 700 images). The experimental results show that galaxy images from EFIGI catalog can be classified automatically with an accuracy of ～93% for small and ～92% for large number. These results are in good agreement when compared with the visual classifications.     

Old stellar subsystems in dwarf galaxies

Based on archival Hubble Space Telescope ACS/WFC images, we have performed stellar photometry for eight dwarf galaxies of different types (Irr, S0, E) with a populated horizontal branch on their Hertzsprung-Russell diagrams. We have identified probable RR Lyr stars in these galaxies and constructed the distribution of their number density along the minor axes of the galaxies. For comparison, similar distributions have also been constructed for red giants in the same galaxies. In all cases, the size of the subsystem of RR Lyr stars exceeds that of the subsystem of, on average, younger stars, red giants. Our results are consistent with the hypothesis about expansion of the stellar subsystems in dwarf galaxies that we suggested previously.     

Far-Ultraviolet Emission from Elliptical Galaxies at z = 0.55

The rest-frame UV-to-optical flux ratio, which characterizes the "UV upturn" phenomenon, is potentially the most sensitive tracer of age in elliptical galaxies; models predict that it may change by orders of magnitude over the course of a few gigayears. In order to trace the evolution of the UV upturn as a function of redshift, we have used the far-UV camera on the Space Telescope Imaging Spectrograph to image the galaxy cluster CL 0016+16 at z=0.55. Our 25"x25" field includes four bright elliptical galaxies, spectroscopically confirmed to be passively evolving cluster members. The weak UV emission from the galaxies in our image demonstrates that the UV upturn is weaker at a look-back time approximately 5.6 Gyr earlier than our own, as compared to measurements of the UV upturn in cluster E and S0 galaxies at z=0 and z=0.375. These images are the first with sufficient depth to demonstrate the fading of the UV upturn expected at moderate redshifts. We discuss these observations and the implications for the formation history of galaxies.     

On structures and number-density distributions in clusters of galaxies

The structures of compact groups of galaxies are compared with the structures of rich clusters of galaxies. It was established that there are structural similarities between these two types of clusters of galaxies. It is imaginable that these structures are typical for all such complexes of galaxies and that the different structures are due to different initial conditions at the beginning of their evolution. For a final answer on this question it is necessary to accumulate more observational material with respect to the distribution of galaxies in such clusters. As part of a larger programme the present paper contains the derived number-density distributions and core radii for ten clusters.     

Rotation in gravitational lenses

Gravitational lensing deflects light. A single lens deflector can only shear images, but cannot induce rotations. Multiple lens planes can induce rotations. Such rotations can be observed in quadruply imaged sources, and can be used to distinguish between two proposed solutions of the flux anomaly problem: substructures in lensing galaxies versus large-scale structure. We predict the expected amount of rotation due to large-scale structure in strong lensing systems, and show how this effect can be measured using ∼mas very long baseline interferometry astrometry of quadruple lenses with extended source structures. The magnitude of rotation is around 1°. The biggest theoretical uncertainty is the power spectrum of dark matter on very small scales. This procedure can potentially be turned around to measure the dark matter power spectrum on very small scales. We list the predicted rms rotation angles for several quadruple lenses with known lens and source redshifts.     

Straight Arc in abell 2390

The straight arc in the galaxy-cluster Abell 2390 is investigated in the framework of a gravitational lens model that invokes a single background source galaxy. An extended source galaxy at a redshift of 0.913 is being marginally lensed by the foreground X-ray cluster of galaxies at a redshift of 0.231. It is demonstrated that a single lensed galaxy lying on or very near to the lip caustic of the cluster lens is capable of reproducing the linear morphology with the observed breaks.