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.     

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.     

Submillimetre-wave gravitational lenses and cosmology

One of the most direct routes for investigating the geometry of the Universe is provided by the numbers of strongly magnified gravitationally lensed galaxies as compared with those that are either weakly magnified or de-magnified. In the submillimetre waveband the relative abundance of strongly lensed galaxies is expected to be larger as compared with the optical or radio wavebands, both in the field and in clusters of galaxies. The predicted numbers depend on the properties of the population of faint galaxies in the submillimetre waveband, which was formerly very uncertain; however, recent observations of lensing clusters have reduced this uncertainty significantly and confirm that a large sample of galaxy–galaxy lenses could be detected and investigated using forthcoming facilities, including the FIRST and Planck Surveyor space missions and a large ground-based millimetre/submillimetre-wave interferometer array (MIA). We discuss how this sample could be used to impose limits on the values of cosmological parameters and the total density and form of evolution of the mass distribution of bound structures, even in the absence of detailed lens modelling for individual members of the sample. The effects of different world models on the form of the magnification bias expected in sensitive submillimetre-wave observations of clusters are also discussed, because an MIA could resolve and investigate images in clusters in detail.     

Scalar field haloes as gravitational lenses

A non-topological soliton model with a repulsive scalar self-interaction of the Emden type provides a constant-density core, similarly as the empirical Burkert profile of dark matter (DM) haloes. As a further test, we derive the gravitational lens properties of our model, in particular, the demarcation curves between 'weak' and 'strong' lensing. Accordingly, strong lensing with typically three images is almost three times more probable for our solitonic model than for the Burkert fit. Moreover, some prospective consequences of a possible flattening of DM haloes are indicated.     

Two new large-separation gravitational lenses from SDSS

We present discovery images, together with follow-up imaging and spectroscopy, of two large-separation gravitational lenses found by our survey for wide arcs [the CAmbridge Sloan Survey Of Wide ARcs in the skY (CASSOWARY)]. The survey exploits the multicolour photometry of the Sloan Digital Sky Survey to find multiple blue components around red galaxies. CASSOWARY 2 (or 'the Cheshire Cat') is composed of two massive early-type galaxies at   z = 0.426  and 0.432, respectively, lensing two background sources, the first a star-forming galaxy at   z = 0.97  and the second a high -redshift galaxy  ( z > 1.4)  . There are at least three images of the former source and probably four or more of the latter, arranged in two giant arcs. The mass enclosed within the larger arc of radius ∼11 arcsec is  ∼33 × 10¹² M_⊙  . CASSOWARY 3 comprises an arc of three bright images of a   z = 0.725  source, lensed by a foreground elliptical at   z = 0.274  . The radius of the arc is ∼4 arcsec and the enclosed mass is  ∼2.5 × 10¹² M_⊙  . Together with earlier discoveries like the Cosmic Horseshoe and the 8 o'clock Arc, these new systems, with separations intermediate between the arcsecond-separation lenses of typical strong galaxy lensing and arcminute-separation cluster lenses, probe the very high end of the galaxy mass function.     

A maximum-entropy method for reconstructing the projected mass distribution of gravitational lenses

The maximum-entropy method is applied to the problem of reconstructing the projected mass density of a galaxy cluster using its gravitational lensing effects on background galaxies. We demonstrate the method by reconstructing the mass distribution in a model cluster using simulated shear and magnification data to which Gaussian noise is added. The mass distribution is reconstructed directly and the inversion is regularized using the entropic prior for this positive additive distribution. For realistic noise levels, we find that the method faithfully reproduces the main features of the cluster mass distribution not only within the observed field but also slightly beyond it. We estimate the uncertainties in the reconstruction by calculating an analytic approximation to the covariance matrix of the reconstruction values of each pixel. This result is compared with error estimates derived from Monte Carlo simulations for different noise realizations and found to be in good agreement.     

An analytic model for non-spherical lenses in covariant MOdified Newtonian Dynamics

Strong gravitational lensing by galaxies in MOdified Newtonian Dynamics (MOND) has until now been restricted to spherically symmetric models. These models were able to account for the size of the Einstein ring of observed lenses, but were unable to account for double-imaged systems with collinear images, as well as four-image lenses. Non-spherical models are generally cumbersome to compute numerically in MOND, but we present here a class of analytic non-spherical models that can be applied to fit double-imaged and quadruple-imaged systems. We use them to obtain a reasonable MOND fit to 10 double-imaged systems, as well as to the quadruple-imaged system Q2237+030 which is an isolated bulge-disc lens producing an Einstein cross. However, we also find five double-imaged systems and three quadruple-imaged systems for which no reasonable MOND fit can be obtained with our models. We argue that this is mostly due to the intrinsic limitation of the analytic models, even though the presence of small amounts of additional dark mass on galaxy scales in MOND is also plausible.     

Perturbative signature of substructures in strong gravitational lenses

In the perturbative approach, substructures in the lens can be reduced to their effect on the two perturbative fields f ₁ and  d f ₀/dθ  . A simple generic model of an elliptical lens with a substructure situated near the critical radius is investigated in detail. Analytical expressions are derived for each perturbative field, and basic properties are analysed. The power spectrum of the fields is well approximated by a power law, resulting in significant tails at high frequencies. Another feature of the perturbation by a substructure is that the ratio of the power spectrum at order n of the two fields   R _n   is almost one. The ratio   R _n ≃ 1  is specific to substructures, for instance a higher order distortion  ( n > 2)  but with autosimilar isophotes will result in   R _n ∝ 1/ n ²  . Finally, the problem of reconstructing the perturbative field is investigated. Local field models are implemented and fitted to maximize image similarity in the source plane. The non-linear optimization is greatly facilitated, since in the perturbative approach the circular source solution is always known. Examples of image distortions in the subcritical regime due to substructures are presented, and analysed for different source shapes. Provided enough images and signal are available, the substructure field can be identified confidently. These results suggest that the perturbative method is an efficient tool to estimate the contribution of substructures to the mass distribution of lenses.     

Detecting mass substructure in galaxy clusters: an aperture mass statistic for gravitational flexion

Gravitational flexion has been introduced as a technique by which one can map out and study substructure in clusters of galaxies. Previous analyses involving flexion have measured the individual galaxy–galaxy flexion signal, or used either parametric techniques or a Kaiser, Squires and Broadhurst (KSB)-type inversion to reconstruct the mass distribution in Abell 1689. In this paper, we present an aperture mass statistic for flexion, and apply it to the lensed images of background galaxies obtained by ray-tracing simulations through a simple analytic mass distribution and through a galaxy cluster from the Millennium Simulation. We show that this method is effective at detecting and accurately tracing structure within clusters of galaxies on subarcminute scales with high signal to noise even using a moderate background source number density and image resolution. In addition, the method provides much more information about both the overall shape and the small-scale structure of a cluster of galaxies than can be achieved through a weak lensing mass reconstruction using gravitational shear data. Lastly, we discuss how the zero-points of the aperture mass might be used to infer the masses of structures identified using this method.     

The Planck Surveyor mission and gravitational lenses

An extremely sensitive all-sky survey will be carried out in the millimetre/submillimetre waveband by the forthcoming ESA mission Planck Surveyor . The main scientific goal of the mission is to make very accurate measurements of the spatial power spectrum of primordial anisotropies in the cosmic microwave background radiation; however, hundreds of thousands of distant dusty galaxies and quasars will also be detected. These sources are much more likely to be gravitationally lensed by intervening galaxies compared with sources discovered in surveys in other wavebands. Here the number of lenses expected in the survey is estimated, and techniques for discriminating between lensed and unlensed sources are discussed. A practical strategy for this discrimination is presented, based on exploiting the remarkable sensitivity and resolving power of large ground-based millimetre/submillimetre-wave interferometer arrays. More than a thousand gravitational lenses could be detected: a sample that would be an extremely valuable resource in observational cosmology.     

A Remark on Using Gravitational Lensing Probability as a Probe of the Central Regions of CDM Halos

We calculate the gravitational lensing probabilities by cold dark matter (CDM) halos with different density profiles, and compare them with current observations from the Cosmic Lens All-Sky Survey (CLASS) and the Jodrell-Bank VLA Astrometric Survey (JVAS). We find that the lensing probability is dramatically sensitive to the clumping of the dark matter, or quantitatively, the concentration parameter. We also find that our predicted lensing probabilities in most cases show inconsistency with the observations. It is argued that high lensing probability may not be an effective tool for probing the statistical properties of inner structures of dark matter halos.     

IRAM observations of JVAS/CLASS gravitational lenses

We have searched for molecular absorption lines at millimetre wavelengths in 11 gravitational lens systems discovered in the JVAS/CLASS surveys of flat spectrum radio sources. Spectra of only one source 1030+074 were obtained in the 3-, 2- and 1.3-mm bands at the frequencies corresponding to common molecular transitions of CO and HCO⁺ as continuum emission was not found in any of the other sources. We calculated upper limits to the column density in molecular absorption for 1030+074, using an excitation temperature of 15 K, to be N _CO<6.3×10¹³ cm⁻² and N _HCO+<1.3×10¹¹ cm⁻² , equivalent to hydrogen column density of the order N _H<10¹⁸ cm⁻² , assuming standard molecular abundances. We also present the best upper limits of the continuum at the lower frequency for the other 10 gravitational lenses.     

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.     

The Hubble constant from galaxy lenses: impacts of triaxiality and model degeneracies

The Hubble constant can be constrained using the time delays between multiple images of gravitationally lensed sources. In some notable cases, typical lensing analyses assuming isothermal galaxy density profiles produce low values for the Hubble constant, inconsistent with the result of the HST Key Project  (72 ± 8 km s⁻¹ Mpc⁻¹)  . Possible systematics in the values of the Hubble constant derived from galaxy lensing systems can result from a number of factors, for example, neglect of environmental effects, assumption of isothermality, or contamination by line-of-sight structures. One additional potentially important factor is the triaxial structure of the lensing galaxy halo; most lens models account for halo shape simply by perturbing the projected spherical lensing potential, an approximation that is often necessary but that is inadequate at the levels of triaxiality predicted in the cold dark matter paradigm. To quantify the potential error introduced by this assumption in estimates of the Hubble parameter, we strongly lens a distant galaxy through a sample of triaxial softened isothermal haloes and use an Markov Chain Monte Carlo method to constrain the lensing halo profile and the Hubble parameter from the resulting multiple image systems. We explore the major degeneracies between the Hubble parameter and several parameters of the lensing model, finding that without a way to accurately break these degeneracies accurate estimates of the Hubble parameter are not possible. Crucially, we find that triaxiality does not significantly bias estimates of the Hubble constant, and offer an analytic explanation for this behaviour in the case of isothermal profiles. Neglected triaxial halo shape cannot contribute to the low Hubble constant values derived in a number of galaxy lens systems.