Cluster lensing has become an important tool in the search for high redshift galaxies through its ability to magnify sources. In order to determine the intrinsic properties of these galaxies, lensing mass models must be constructed to determine the m
agnification of the images. These models are traditionally two-dimensional, focusing on the mass within the cluster and either ignoring or approximating any contribution from line-of-sight galaxies. In this paper, we present the first full set of three-dimensional mass models of the six Hubble Frontier Fields and use them to test for systematic biases in magnifications due to using the traditional 2D approach. We find that omitting foreground or background galaxies causes image position offsets between 0.1-0.4, a non-negligible fraction of the typical 0.3-0.7 residuals of current state-of-the-art models. We also find that median image magnifications can shift by up to 6%, though it is dependent on the field. This can be alleviated in some cases by approximating the mass in the lensing plane, but a 5% magnification bias still exists in other cases; image position offsets are also improved, but are still present at 0.10.
We show that the asymptotic scaling of the magnification volume cross section corresponding to an elliptic umbilic caustic surface is $mu^{-2.5}$ in the two-image region and $mu^{-2}$ in the four-image region, where $mu$ is the total unsigned magnification.
Gravitational lensing has emerged as a powerful probe of the matter distribution on subgalactic scales, which itself may contain important clues about the fundamental origins and properties of dark matter. Broadly speaking, two different approaches h
ave been taken in the literature to map the small-scale structure of the Universe using strong lensing, with one focused on measuring the position and mass of a small number of discrete massive subhalos appearing close in projection to lensed images, and the other focused on detecting the collective effect of all the small-scale structure between the lensed source and the observer. In this paper, we follow the latter approach and perform a detailed study of the sensitivity of galaxy-scale gravitational lenses to the ensemble properties of small-scale structure. As in some previous studies, we adopt the language of the substructure power spectrum to characterize the statistical properties of the small-scale density field. We present a comprehensive theory that treats lenses with extended sources as well as those with time-dependent compact sources (such as quasars) in a unified framework for the first time. Our approach uses mode functions to provide both computational advantages and insights about couplings between the lens and source. The goal of this paper is to develop the theory and gain the intuition necessary to understand how the sensitivity to the substructure power spectrum depends on the source and lens properties, with the eventual aim of identifying the most promising targets for such studies.
Strong gravitational lensing provides an independent measurement of the Hubble parameter ($H_0$). One remaining systematic is a bias from the additional mass due to a galaxy group at the lens redshift or along the sightline. We quantify this bias for
more than 20 strong lenses that have well-sampled sightline mass distributions, focusing on the convergence $kappa$ and shear $gamma$. In 23% of these fields, a lens group contributes a $ge$1% convergence bias; in 57%, there is a similarly significant line-of-sight group. For the nine time delay lens systems, $H_0$ is overestimated by 11$^{+3}_{-2}$% on average when groups are ignored. In 67% of fields with total $kappa ge$ 0.01, line-of-sight groups contribute $gtrsim 2times$ more convergence than do lens groups, indicating that the lens group is not the only important mass. Lens environment affects the ratio of four (quad) to two (double) image systems; all seven quads have lens groups while only three of 10 doubles do, and the highest convergences due to lens groups are in quads. We calibrate the $gamma$-$kappa$ relation: $log(kappa_{rm{tot}}) = (1.94 pm 0.34) log(gamma_{rm{tot}}) + (1.31 pm 0.49)$ with a rms scatter of 0.34 dex. Shear, which, unlike convergence, can be measured directly from lensed images, can be a poor predictor of $kappa$; for 19% of our fields, $kappa$ is $gtrsim 2gamma$. Thus, accurate cosmology using strong gravitational lenses requires precise measurement and correction for all significant structures in each lens field.
In the standard structure formation scenario based on the cold dark matter paradigm, galactic halos are predicted to contain a large population of dark matter subhalos. While the most massive members of the subhalo population can appear as luminous s
atellites and be detected in optical surveys, establishing the existence of the low mass and mostly dark subhalos has proven to be a daunting task. Galaxy-scale strong gravitational lenses have been successfully used to study mass substructures lying close to lensed images of bright background sources. However, in typical galaxy-scale lenses, the strong lensing region only covers a small projected area of the lenss dark matter halo, implying that the vast majority of subhalos cannot be directly detected in lensing observations. In this paper, we point out that this large population of dark satellites can collectively affect gravitational lensing observables, hence possibly allowing their statistical detection. Focusing on the region of the galactic halo outside the strong lensing area, we compute from first principles the statistical properties of perturbations to the gravitational time delay and position of lensed images in the presence of a mass substructure population. We find that in the standard cosmological scenario, the statistics of these lensing observables are well approximated by Gaussian distributions. The formalism developed as part of this calculation is very general and can be applied to any halo geometry and choice of subhalo mass function. Our results significantly reduce the computational cost of including a large substructure population in lens models and enable the use of Bayesian inference techniques to detect and characterize the distributed satellite population of distant lens galaxies.
We investigate the gravitational lensing properties of lines of sight containing multiple cluster-scale halos, motivated by their ability to lens very high-redshift (z ~ 10) sources into detectability. We control for the total mass along the line of
sight, isolating the effects of distributing the mass among multiple halos and of varying the physical properties of the halos. Our results show that multiple-halo lines of sight can increase the magnified source-plane region compared to the single cluster lenses typically targeted for lensing studies, and thus are generally better fields for detecting very high-redshift sources. The configurations that result in optimal lensing cross sections benefit from interactions between the lens potentials of the halos when they overlap somewhat on the sky, creating regions of high magnification in the source plane not present when the halos are considered individually. The effect of these interactions on the lensing cross section can even be comparable to changing the total mass of the lens from 10^15 M_sun to 3x10^15 M_sun. The gain in lensing cross section increases as the mass is split into more halos, provided that the lens potentials are projected close enough to interact with each other. A nonzero projected halo angular separation, equal halo mass ratio, and high projected halo concentration are the best mass configurations, whereas projected halo ellipticity, halo triaxiality, and the relative orientations of the halos are less important. Such high mass, multiple-halo lines of sight exist in the SDSS.
We examine the wavelength dependence of flux ratios for six gravitationally lensed quasars using K and L images obtained at the Gemini North 8m telescope. We select lenses with source redshifts z_s < 2.8 so that K-band images probe rest-frame optical
emission from accretion disks, while L-band images probe rest-frame near-infrared flux emitted (in part) from the more extended surrounding torus. Since the observations correspond to different source sizes, the K and L flux ratios are sensitive to structure on different scales and may be useful for studying small-structure in the lens galaxies. Four of the six lenses show differences between K and L flux ratios. In HE 0435$-1223, SDSS 0246-0825, and HE 2149-2745 the differences may be attributable to known microlensing and/or intrinsic variability. In SDSS 0806+2006 the wavelength dependence is not easily attributed to known variations, and may indicate the presence of substructure. By contrast, in Q0142-100 and SBS 0909+523 the K and L flux ratios are consistent within the uncertainties. We discuss the utility of the current data for studying chromatic effects related to microlensing, dust extinction, and dark matter substructure.
Using new photometric and spectroscopic data in the fields of nine strong gravitational lenses that lie in galaxy groups, we analyze the effects of both the local group environment and line-of-sight galaxies on the lens potential. We use Monte Carlo
simulations to derive the shear directly from measurements of the complex lens environment, providing the first detailed independent check of the shear obtained from lens modeling. We account for possible tidal stripping of the group galaxies by varying the fraction of total mass apportioned between the group dark matter halo and individual group galaxies. The environment produces an average shear of gamma = 0.08 (ranging from 0.02 to 0.17), significant enough to affect quantities derived from lens observables. However, the direction and magnitude of the shears do not match those obtained from lens modeling in three of the six 4-image systems in our sample (B1422, RXJ1131, and WFI2033). The source of this disagreement is not clear, implying that the assumptions inherent in both the environment and lens model approaches must be reconsidered. If only the local group environment of the lens is included, the average shear is gamma = 0.05 (ranging from 0.01 to 0.14), indicating that line-of-sight contributions to the lens potential are not negligible. We isolate the effects of various theoretical and observational uncertainties on our results. Of those uncertainties, the scatter in the Faber-Jackson relation and error in the group centroid position dominate. Future surveys of lens environments should prioritize spectroscopic sampling of both the local lens environment and objects along the line of sight, particularly those bright (I < 21.5) galaxies projected within 5 of the lens.
We present results from high-resolution radio and optical observations of PMN J0134-0931, a gravitational lens with a unique radio morphology and an extremely red optical counterpart. Our data support the theory of Keeton & Winn (2003): five of the s
ix observed radio components are multiple images of a single quasar, produced by a pair of lens galaxies. Multi-frequency VLBA maps show that the sixth and faintest component has a different radio spectrum than the others, confirming that it represents a second component of the background source rather than a sixth image. The lens models predict that there should be additional faint images of this second source component, and we find evidence for one of the predicted images. The previously-observed large angular sizes of two of the five bright components are not intrinsic (which would have excluded the possibility that they are lensed images), but are instead due to scatter broadening. Both the extended radio emission observed at low frequencies, and the intrinsic image shapes observed at high frequencies, can be explained by the lens models. The pair of lens galaxies is marginally detected in HST images. The differential extinction of the quasar images suggests that the extreme red color of the quasar is at least partly due to dust in the lens galaxies.
