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.     

Kinematic effect in gravitational lensing by clusters of galaxies

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or the hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact, either a translational motion or a coherent rotation of the mass distribution can affect the lensing properties. Here, light deflection by galaxy clusters in motion is considered. Even if gravitational lensing mass measurements of galaxy clusters are regarded as very reliable estimates, the kinematic effect should be considered. A typical peculiar motion with respect to the Hubble flow brings about a systematic error ≲0.3 per cent, independent of the mass of the cluster. On the other hand, the effect of the spin increases with the total mass. For cluster masses  ∼10¹⁵ M_⊙  , the effect of the gravitomagnetic term is ≲0.04 per cent on strong lensing estimates and ≲0.5 per cent in the weak-lensing analyses. The total kinematic effect on the mass estimate is then ≲1 per cent, which is negligible in current statistical studies. In the weak-lensing regime, the rotation imprints a typical angular modulation in the tangential shear distortion. This would allow, in principle, a detection of the gravitomagnetic field and a direct measurement of the angular velocity of the cluster but the required background source densities are well beyond current technological capabilities.     

Cluster strong lensing in the Millennium simulation: the effect of galaxies and structures along the line-of-sight

We use ray-tracing through the Millennium simulation to study how secondary matter structures along the line-of-sight and the stellar mass in galaxies affect strong cluster lensing, in particular the cross-section for giant arcs. Furthermore, we investigate the distribution of the cluster Einstein radii and the radial distribution of giant arcs. We find that additional structures along the line-of-sight increase the strong-lensing optical depth by  ∼10–25 per cent  , while strong-lensing cross-sections of individual clusters are frequently boosted by as much as  ∼50 per cent  . The enhancement is mainly due to structures that are not correlated with the lens. Cluster galaxies increase the strong-lensing optical depth by up to a factor of 2, while interloping galaxies are not significant. We conclude that these effects need to be taken into account for predictions of the giant arc abundance, but they are not large enough to fully account for the reported discrepancy between predicted and observed abundances.
Furthermore, we find that Einstein radii defined via the area enclosed by the critical curve are 10–30 per cent larger than those defined via radial surface mass density profiles. The contributions of radial and tangential arcs to the radial distribution of arcs can be clearly distinguished. The radial distribution of tangential arcs is very broad and extends out to several Einstein radii. Thus, individual arcs are not well suited for constraining Einstein radii.     

Gravitational lensing of type Ia supernovae by galaxy clusters

We propose a method to remove the mass-sheet degeneracy that arises when the mass of galaxy clusters is inferred from gravitational shear. The method utilizes high-redshift standard candles that undergo weak lensing. Natural candidates for such standard candles are type Ia supernovae (SNe Ia).
When corrected with the light-curve shape (LCS), the peak magnitude of SNe Ia provides a standard candle with an uncertainty in apparent magnitude of Δ m ≃0.1–0.2. Gravitational magnification of a background SN Ia by an intervening cluster would cause a mismatch between the observed SN Ia peak magnitude compared with that expected from its LCS and redshift. The average detection rate for SNe Ia with a significant mismatch of ≥2Δ m behind a cluster at z ≃0.05–0.15 is about 1–2 supernovae per cluster per year at J , I , R ≲25–26.
Since SNe are point-like sources for a limited period, they can experience significant microlensing by massive compact halo objects (MACHOs) in the intracluster medium. Microlensing events caused by MACHOs of ∼10⁻⁴ M⊙ are expected to have time-scales similar to that of the SN light curve. Both the magnification curve by a MACHO and the light curve of a SN Ia have characteristic shapes that allow us to separate them. Microlensing events caused by MACHOs of smaller mass can unambiguously be identified in the SN light curve if the latter is continuously monitored. The average number of identifiable microlensing events per nearby cluster ( z ≲0.05) per year is ∼0.02 ( f /0.01), where f is the fraction of the cluster mass in MACHOs of masses 10⁻⁷< M _macho/M⊙<10⁻⁴.     

A genetic algorithm for the non-parametric inversion of strong lensing systems

We present a non-parametric technique to infer the projected mass distribution of a gravitational lens system with multiple strong-lensed images. The technique involves a dynamic grid in the lens plane on which the mass distribution of the lens is approximated by a sum of basis functions, one per grid cell. We used the projected mass densities of Plummer spheres as basis functions. A genetic algorithm then determines the mass distribution of the lens by forcing images of a single source, projected back on to the source plane, to coincide as well as possible. Averaging several tens of solutions removes the random fluctuations that are introduced by the reproduction process of genomes in the genetic algorithm and highlights those features common to all solutions. Given the positions of the images and the redshifts of the sources and the lens, we show that the mass of a gravitational lens can be retrieved with an accuracy of a few percent and that, if the sources sufficiently cover the caustics, the mass distribution of the gravitational lens can also be reliably retrieved. A major advantage of the algorithm is that it makes full use of the information contained in the radial images, unlike methods that minimize the residuals of the lens equation, and is thus able to accurately reconstruct also the inner parts of the lens.