Realistic Lens Research Articles

THE POPULATION OF GALAXY–GALAXY STRONG LENSES IN FORTHCOMING OPTICAL IMAGING SURVEYS

Ongoing and future imaging surveys represent significant improvements in depth, area, and seeing compared to current data sets. These improvements offer the opportunity to discover up to three orders of magnitude more galaxy–galaxy strong lenses than are currently known. In this work we forecast the number of lenses that will be discoverable in forthcoming surveys and simulate their properties. We generate a population of statistically realistic strong lenses and simulate observations of this population for the Dark Energy Survey (DES), the Large Synoptic Survey Telescope (LSST), and Euclid surveys. We verify our model against the galaxy-scale lens search of the Canada–France–Hawaii Telescope Legacy Survey, predicting 250 discoverable lenses compared to 220 found by Gavazzi et al. The predicted Einstein radius distribution is also remarkably similar to that found by Sonnenfeld et al. For future surveys we find that, assuming Poisson limited lens galaxy subtraction, searches of the DES, LSST, and Euclid data sets should discover 2400, 120000, and 170000 galaxy–galaxy strong lenses, respectively. Finders using blue-minus-red () difference imaging for lens subtraction can discover 1300 and 62000 lenses in DES and LSST. The uncertainties on the model are dominated by the high-redshift source population, which typically gives fractional errors on the discoverable lens number at the level of tens of percent. We find that doubling the signal-to-noise ratio required for a lens to be detectable approximately halves the number of detectable lenses in each survey, indicating the importance of understanding the selection function and the sensitivity of future lens finders in interpreting strong lens statistics. We make our population forecasting and simulated observation codes publicly available so that the selection function of strong lens finders can easily be calibrated.

Precision cosmology with time delay lenses: high resolution imaging requirements

Lens time delays are a powerful probe of cosmology, provided that the gravitational potential of the main deflector can be modeled with sufficient precision. Recent work has shown that this can be achieved by detailed modeling of the host galaxies of lensed quasars, which appear as ``Einstein Rings'' in high resolution images. The distortion of these arcs and counter-arcs, as measured over a large number of pixels, provides tight constraints on the difference between the gravitational potential between the quasar image positions, and thus on cosmology in combination with the measured time delay. We carry out a systematic exploration of the high resolution imaging required to exploit the thousands of lensed quasars that will be discovered by current and upcoming surveys with the next decade. Specifically, we simulate realistic lens systems as imaged by the Hubble Space Telescope (HST), James Webb Space Telescope (JWST), and ground based adaptive optics images taken with Keck or the Thirty Meter Telescope (TMT). We compare the performance of these pointed observations with that of images taken by the Euclid (VIS), Wide-Field Infrared Survey Telescope (WFIRST) and Large Synoptic Survey Telescope (LSST) surveys. We use as our metric the precision with which the slope γ′ of the total mass density profile ρtot∝ r−γ′ for the main deflector can be measured. Ideally, we require that the statistical error on γ′ be less than 0.02, such that it is subdominant to other sources of random and systematic uncertainties. We find that survey data will likely have sufficient depth and resolution to meet the target only for the brighter gravitational lens systems, comparable to those discovered by the SDSS survey. For fainter systems, that will be discovered by current and future surveys, targeted follow-up will be required. However, the exposure time required with upcoming facilitites such as JWST, the Keck Next Generation Adaptive Optics System, and TMT, will only be of order a few minutes per system, thus making the follow-up of hundreds of systems a practical and efficient cosmological probe.

How well can cold dark matter substructures account for the observed radio flux-ratio anomalies

Discrepancies between the observed and model-predicted radio flux ratios are seen in a number of quadruply-lensed quasars. The most favored interpretation of these anomalies is that CDM substructures present in lensing galaxies perturb the lens potentials and alter image magnifications and thus flux ratios. So far no consensus has emerged regarding whether or not the predicted CDM substructure abundance fully accounts for the lensing flux anomaly observations. Accurate modeling relies on a realistic lens sample in terms of both the lens environment and internal structures and substructures. In this paper we construct samples of generalised and specific lens potentials, to which we add (rescaled) subhalo populations from the galaxy-scale Aquarius and the cluster-scale Phoenix simulation suites. We further investigate the lensing effects from subhalos of masses several orders of magnitude below the simulation resolution limit. The resulting flux ratio distributions are compared to the currently best available sample of radio lenses. The observed anomalies in B0128+437, B0712+472 and B1555+375 are more likely to be caused by propagation effects or oversimplified lens modeling, signs of which are already seen in the data. Among the quadruple systems that have closely located image triplets/pairs, the anomalous flux ratios of MG0414+0534 can be reproduced by adding CDM subhalos to its macroscopic lens potential, with a probability of 5%-20%; for B0712+472, B1422+231, B1555+375 and B2045+265, these probabilities are only of a few percent. We hence find that CDM substructures are unlikely to be the whole reason for radio flux anomalies. We discuss other possible effects that might also be at work.

EFFECTIVE MODELS FOR STATISTICAL STUDIES OF GALAXY-SCALE GRAVITATIONAL LENSING

We have worked out simple analytical formulae that accurately approximate the relationship between the position of the source with respect to the lens center and the amplification of the images, hence the lens cross section, for realistic lens profiles. We find that, for essentially the full range of parameters either observationally determined or yielded by numerical simulations, the combination of dark matter and star distribution can be very well described, for lens radii relevant to strong lensing, by a simple power-law whose slope is very weakly dependent on the parameters characterizing the global matter surface density profile and close to isothermal in agreement with direct estimates for individual lens galaxies. Our simple treatment allows an easy insight into the role of the different ingredients that determine the lens cross section and the distribution of gravitational amplifications. They also ease the reconstruction of the lens mass distribution from the observed images and, vice-versa, allow a fast application of ray-tracing techniques to model the effect of lensing on a variety of source structures. The maximum amplification depends primarily on the source size. Amplifications larger than ~20 are indicative of compact source sizes at high-z, in agreement with expectations if galaxies formed most of their stars during the dissipative collapse of cold gas. Our formalism has allowed us to reproduce the counts of strongly lensed galaxies found in the H-ATLAS SDP field. While our analysis is focussed on spherical lenses, we also discuss the effect of ellipticity and the case of late-type lenses (showing why they are much less common, even though late-type galaxies are more numerous). Furthermore we discuss the effect of a cluster halo surrounding the early-type lens and of a supermassive black hole at its center.

Moka: a new tool for strong lensing studies

Strong gravitational lensing is a powerful tool for probing the matter distribution in the cores of massive dark matter haloes. Recent and ongoing analyses of galaxy cluster surveys (MACS, CFHTLS, SDSS, SGAS, CLASH, LoCuSS) have adressed the question of the nature of the dark matter distribution in clusters. N-body simulations of cold dark-matter haloes consistently find that haloes should be characterized by a concentration-mass relation that decreases monotonically with halo mass, and populated by a large amount of substructures, representing the cores of accreted progenitor halos. It is important for our understanding of dark matter to test these predictions. We present MOKA, a new algorithm for simulating the gravitational lensing signal from cluster-sized haloes. It implements the most recent results from numerical simulations to create realistic cluster-scale lenses with properties independent of numerical resolution. We perform systematic studies of the strong lensing cross section as a function of halo structures. We find that the strong lensing cross sections depend most strongly on the concentration and on the inner slope of the density profile of a halo, followed in order of importance by halo triaxiality and the presence of a bright central galaxy.

Distribution of temperature in a single lens due to absorption of light and heat conduction: an adaptive solver

We develop an algorithm for the solution of the stationary heat-equation in a single lens due to absorption of light, heat-conduction and transfer of the heat to the environment while we assume rotational symmetry for the whole situation. The proceeding is based on an easy to implement finite difference scheme, which is best suited for rectangular areas. Therefore, we have to transform the heat equation and the boundary conditions from the original domain, i.e. the surface of section of the lens by the aid of tensor methods to a rectangle. So the algorithm generates a grid, which adopts automatically to the actual shape of the lens. In this sense, we characterize the method as adaptive. In the examples, we investigate the effect of a high-transmission glass on the distribution of temperature and further demonstrate the adjustment to a realistic lens shape with a strong deviation from a spherical surface in form of a kink near the edge. We compare the results with a simple model for the distribution of temperature and show the strong dependency of the results on the transmission of the materials.

Temporal distortions in magnetic lenses

Abstract We consider the temporal aberrations of femtosecond electron pulses in magnetic lens systems. We identify two mechanisms for distortions: Within the lens, rotational motion around the propagation axis results in outer parts of the pulse being delayed. After the lens, conversion from radial to longitudinal velocity causes a dynamical reshaping of the electron pulse during propagation towards the image plane. In combination, the pulses refocus back closely to the original pulse duration, but at a position far away from the image plane. Only for a magnification of two there is an approximate coincidence. Calculations of simplified trajectories provide a conceptual picture of signs and magnitudes; details are studied by numerical simulations of realistic lenses. For typical geometries in ultrafast diffraction and microscopy, distortions can amount to tens of femtoseconds and thus limit the temporal resolution even when using single-electron sources without space charge. Compensation of temporal aberrations can be achieved by combining lenses in sequence, resulting in what we call an ‘isochronic’ lens system for charged particles. We discuss the implications for ultrafast atomic-scale imaging by 4D electron microscopy and diffraction.

Gradient-index lenses for near-ideal imaging and concentration with realistic materials

Fundamentally new classes of spherical gradient-index lenses with imaging and concentration properties that approach the fundamental limits are derived. These analytic solutions admit severely constrained maximum and minimum refractive indices commensurate with existing manufacturable materials, for realistic optical and solar lenses.

Nominally stationary high-concentration solar optics by gradient-index lenses

It is shown how novel solutions for realistic gradient-index lenses create the possibility of nominally stationary solar photovoltaic concentrators capable of daylong averaged flux concentration levels of order 10(3).

Substructure lensing in galaxy clusters as a constraint on low-mass sterile neutrinos in tensor-vector-scalar theory: The straight arc of Abell 2390

Certain covariant theories of the modified Newtonian dynamics paradigm seem to require an additional hot dark matter (HDM) component - in the form of either heavy ordinary neutrinos or more recently light sterile neutrinos (SNs) with a mass around 11eV - to be relieved of problems ranging from cosmological scales down to intermediate ones relevant for galaxy clusters. Here we suggest using gravitational lensing by galaxy clusters to test such a marriage of neutrino HDM and modified gravity, adopting the framework of tensor-vector-scalar theory (TeVeS). Unlike conventional cold dark matter (CDM), such HDM is subject to strong phase-space constraints, which allows one to check cluster lens models inferred within the modified framework for consistency. Since the considered HDM particles cannot collapse into arbitrarily dense clumps and only form structures well above the galactic scale, systems which indicate the need for dark substructure are of particular interest. As a first example, we study the cluster lens Abell 2390 and its impressive straight arc with the help of numerical simulations. Based on our results, we outline a general and systematic approach to model cluster lenses in TeVeS which significantly reduces the calculation complexity. We further consider a simple bimodal lens configuration, capable of producing the straight arc, to demonstrate our approach. We find that such a model is marginally consistent with the hypothesis of 11eV SNs. Future work including more detailed and realistic lens models may further constrain the necessary SN distribution and help to conclusively assess this point. Cluster lenses could therefore provide an interesting discriminator between CDM and such modified gravity scenarios supplemented by SNs or other choices of HDM.

Realistic metamaterial lenses: Limitations imposed by discrete structure

Realistic metamaterial lenses: Limitations imposed by discrete structure

IDENTIFYING ANOMALIES IN GRAVITATIONAL LENS TIME DELAYS

We examine the ability of gravitational lens time delays to reveal complex structure in lens potentials. In a previous paper, we predicted how the time delay between the bright pair of images in a "fold" lens scales with the image separation, for smooth lens potentials. Here we show that the proportionality constant increases with the quadrupole moment of the lens potential, and depends only weakly on the position of the source along the caustic. We use Monte Carlo simulations to determine the range of time delays that can be produced by realistic smooth lens models consisting of isothermal ellipsoid galaxies with tidal shear. We can then identify outliers as "time delay anomalies." We find evidence for anomalies in close image pairs in the cusp lenses RX J1131 − 1231 and B1422+231. The anomalies in RX J1131 − 1231 provide strong evidence for substructure in the lens potential, while at this point the apparent anomalies in B1422+231 mainly indicate that the time delay measurements need to be improved. We also find evidence for time delay anomalies in larger-separation image pairs in the fold lenses, B1608+656 and WFI 2033 − 4723, and the cusp lens RX J0911+0551. We suggest that these anomalies are caused by some combination of substructure and a complex lens environment. Finally, to assist future monitoring campaigns we use our smooth models with shear to predict the time delays for all known four-image lenses.

AUTOMATED DETECTION OF GALAXY-SCALE GRAVITATIONAL LENSES IN HIGH-RESOLUTION IMAGING DATA

Lens modeling is the key to successful and meaningful automated strong galaxy-scale gravitational lens detection. We have implemented a lens-modeling "robot" that treats every bright red galaxy (BRG) in a large imaging survey as a potential gravitational lens system. Using a simple model optimized for "typical" galaxy-scale lenses, we generate four assessments of model quality that are used in an automated classification. The robot infers the lens classification parameter H that a human would have assigned; the inference is performed using a probability distribution generated from a human-classified training set, including realistic simulated lenses and known false positives drawn from the HST/EGS survey. We compute the expected purity, completeness and rejection rate, and find that these can be optimized for a particular application by changing the prior probability distribution for H, equivalent to defining the robot's "character." Adopting a realistic prior based on the known abundance of lenses, we find that a lens sample may be generated that is ~100% pure, but only ~20% complete. This shortfall is due primarily to the over-simplicity of the lens model. With a more optimistic robot, ~90% completeness can be achieved while rejecting ~90% of the candidate objects. The remaining candidates must be classified by human inspectors. We are able to classify lens candidates by eye at a rate of a few seconds per system, suggesting that a future 1000 square degree imaging survey containing 10^7 BRGs, and some 10^4 lenses, could be successfully, and reproducibly, searched in a modest amount of time. [Abridged]

Bayesian strong gravitational-lens modelling on adaptive grids: objective detection of mass substructure in Galaxies

We introduce a new adaptive and fully Bayesian grid-based method to model strong gravitational lenses with extended images. The primary goal of this method is to quantify the level of luminous and dark mass substructure in massive galaxies, through their effect on highly magnified arcs and Einstein rings. The method is adaptive on the source plane, where a Delaunay tessellation is defined according to the lens mapping of a regular grid on to the source plane. The Bayesian penalty function allows us to recover the best non-linear potential-model parameters and/or a grid-based potential correction and to objectively quantify the level of regularization for both the source and potential. In addition, we implement a Nested-Sampling technique to quantify the errors on all non-linear mass model parameters - marginalized over all source and regularization parameters - and allow an objective ranking of different potential models in terms of the marginalized evidence. In particular, we are interested in comparing very smooth lens mass models with ones that contain mass substructures. The algorithm has been tested on a range of simulated data sets, created from a model of a realistic lens system. One of the lens systems is characterized by a smooth potential with a power-law density profile, 12 include a Navarro, Frenk and White (NFW) dark matter substructure of different masses and at different positions and one contains two NFW dark substructures with the same mass but with different positions. Reconstruction of the source and lens potential for all of these systems shows the method is able, in a realistic scenario, to identify perturbations with masses similar to 10(7)M(circle dot) when located on the Einstein ring. For positions both inside and outside of the ring, masses of at least 10(9)M(circle dot) are required (i.e. roughly the Einstein ring of the perturber needs to overlap with that of the main lens). Our method provides a fully novel and objective test of mass substructure in massive galaxies.

The Role of Animal Models in Evaluating Reasonable Safety and Efficacy for Human Trials of Cell-Based Interventions for Neurologic Conditions

Progress in regenerative medicine seems likely to produce new treatments for neurologic conditions that use human cells as therapeutic agents; at least one trial for such an intervention is already under way. The development of cell-based interventions for neurologic conditions (CBI-NCs) will likely include preclinical studies using animals as models for humans with conditions of interest. This paper explores predictive validity challenges and the proper role for animal models in developing CBI-NCs. In spite of limitations, animal models are and will remain an essential tool for gathering data in advance of first-in-human clinical trials. The goal of this paper is to provide a realistic lens for viewing the role of animal models in the context of CBI-NCs and to provide recommendations for moving forward through this challenging terrain.

A new separator design for aberration corrected photoemission electron microscopes

Aberration correction of photoemission electron microscopes (PEEM) by electron mirrors requires use of a magnetic beam separator. Due to the stringent requirement on aberrations, such a device is a complex integrated magnetic system. The one that has been installed at BESSY II is essentially fixed in its optical properties hence very susceptible to problems caused by mechanical or magnetic imperfections. Here we present a separate function design that is simple to construct and fully adjustable, which allows more relaxed tolerances on alignment errors and power supply ripples. The simulation with realistic lenses shows that this design gives as good, if not better, a performance as the existing design.

Simulation of electron optical systems by differential algebraic method combined with Hermite fitting for practical lens fields

The differential algebraic (DA) method has been applied to compute the aberrations of realistic electron lenses to arbitrary order. The aberrations are computed with a single ray trace, performed o...

Simulation of electron optical systems by differential algebraic method combined with Hermite fitting for practical lens fields

The differential algebraic (DA) method has been applied to compute the aberrations of realistic electron lenses to arbitrary order. The aberrations are computed with a single ray trace, performed on a non-standard extension of real space. Previously, the power of the DA method has been demonstrated by simulating the high-order aberrations of magnetic systems using analytic field models. In order to simulate realistic electron optical systems, we have enhanced our DA software to handle practical lens geometries, by combining it with Hermite fitting of the numerically computed lens fields. Computed results are presented for an electron lens with superimposed magnetic and electrostatic fields. The DA results of third-order and fifth-order aberration coefficients are compared with those computed with conventional aberration formulae. All the aberration coefficients agree well, with maximum relative deviation less than 0.015%. The developed software therefore now enables the aberrations of any real electron lens to be calculated accurately to any aberration order.

Identifying Lenses with Small‐Scale Structure. II. Fold Lenses

When the source in a four-image gravitational lens system lies sufficiently close to a fold caustic, two of the lensed images lie very close together. If the lens potential is smooth on the scale of the separation between the two close images, the difference between their fluxes should approximately vanish, Rfold ≡ (F+ - F-)/(F+ + F-) ≈ 0. (The subscript indicates the image parity.) Violations of this fold relation in observed lenses are thought to indicate the presence of structure on scales smaller than the separation between the close images. We present a detailed study of the fold relation in realistic smooth lenses, finding it to be more subtle and rich than was previously realized. The degree to which Rfold can differ from zero for smooth lenses depends not only on the distance of the source from the caustic, but also on its location along the caustic, and then on the angular structure of the lens potential (ellipticity, multipole modes, and external shear). Since the source position is unobservable, it is impossible to say from Rfold alone whether the flux ratios in an observed lens are anomalous or not. Instead, we must consider the full distribution of Rfold values that can be obtained from smooth lens potentials that reproduce the separation d1 between the two close images and the distance d2 to the next nearest image. (By reducing the image configuration to these two numbers, we limit our model dependence and obtain a generic analysis.) We show that the generic features of this distribution can be understood, which means that the fold relation provides a robust probe of small-scale structure in lens galaxies. We then compute the full distribution using Monte Carlo simulations of realistic smooth lenses. Comparing these predictions with the data, we find that five of the 12 known lenses with fold configurations have flux ratio anomalies: B0712+472, SDSS 0924+0219, PG 1115+080, B1555+375, and B1933+503. Combining this with our previous analysis revealing anomalies in three of the four known lenses with cusp configurations, we conclude that at least half (8/16) of all four-image lenses that admit generic, local analyses exhibit flux ratio anomalies. The fold and cusp relations do not reveal the nature of the implied small-scale structure, but do provide the formal foundation for substructure studies, and also indicate which lenses deserve further study. Although our focus is on close pairs of images, we show that the fold relation can be used—with great care—to analyze all image pairs in all 22 known four-image lenses and reveal lenses with some sort of interesting structure.

Changes in the measured image separation of the gravitational lens system PKS 1830-211

We present eight epochs of 43-GHz, dual-polarization VLBA observations of the gravitational lens system PKS 1830-211, made over fourteen weeks. A bright, compact ‘core’ and a faint extended ‘jet’ are clearly seen in maps of both lensed images at all eight epochs. The relative separation of the radio centroid of the cores (as measured on the sky) changes by up to 87 μ as between subsequent epochs. A comparison with the previous 43-GHz VLBA observations made 8 months earlier shows even larger deviations in the separation of up to 201 μas. The measured changes are most likely produced by changes in the brightness distribution of the background source, enhanced by the magnification of the lens. A relative magnification matrix that is applicable on the milliarcsecond scale has been determined by relating two vectors (the ‘core–jet’ separations and the offsets of the polarized and total intensity emission) in the two lensed images. The determinant of this matrix, −1.13 ( ± 0.61), is in good agreement with the measured flux density ratio of the two images. The matrix predicts that the 10-mas-long jet, which is clearly seen in previous 15- and 8.4-GHz VLBA observations, should correspond to a 4-mas-long jet trailing to the south-east of the south-western image. The clear non-detection of this trailing jet is a strong evidence for substructure in the lens and may require more realistic lens models to be invoked, such as that of Nair & Garrett.