Lensing Systems Research Articles

Testing the anisotropy of the Universe with the distance duality relation

The distance duality relation (DDR) is valid in Riemannian spacetime. The astronomical data hint that the universe may have certain preferred direction. If the universe is described by anisotropic cosmological models based on Riemannian spacetime, then DDR still valid. If the anisotropy universe is described by other models which are not based on Riemannian spacetime, then DDR is violated. Thus, DDR could be used to test the validity of these anisotropic cosmological models. In this paper, we perform anisotropic DDR parametrization with the dipolar structures. The DDR is tested by comparing the luminosity distance from type-Ia supernovae (Union 2.1 and JLA compilations) and the angular diameter distance from strong gravitational lensing (SL) systems at the same redshift. It is shown that, the DDR is valid with the Union2.1 compilation, while is violated more than 1$\sigma$ confidence level with the JLA compilation. Additionally, we verify the statistical signification of our method with Monte Carlo simulations. Due to the large uncertainty of available data, no strong evidence is found to violate the DDR in the anisotropic models.

Lenstronomy: Multi-purpose gravitational lens modelling software package

We present lenstronomy, a multi-purpose open-source gravitational lens modelling pythonpackage. lenstronomy is able to reconstruct the lens mass and surface brightness distributions of strong lensing systems using forward modelling. lenstronomy supports a wide range of analytic lens and light models in arbitrary combination. The software is also able to reconstruct complex extended sources (Birrer et. al 2015) as well as being able to model point sources. We designed lenstronomy to be stable, flexible and numerically accurate, with a clear user interface that could be deployed across different platforms. Throughout its development, we have actively used lenstronomy to make several measurements including deriving constraints on dark matter properties in strong lenses, measuring the expansion history of the universe with time-delay cosmography, measuring cosmic shear with Einstein rings and decomposing quasar and host galaxy light. The software is distributed under the MIT license. The documentation, starter guide, example notebooks, source code and installation guidelines can be found at https://lenstronomy.readthedocs.io.

Testing the Speed of Light over Cosmological Distances: The Combination of Strongly Lensed and Unlensed Type Ia Supernovae

Abstract Probing the speed of light is an important test of general relativity, but the measurements of c using objects in the distant universe have been almost completely unexplored. In this paper, we propose an idea to use the multiple measurements of galactic-scale strong gravitational lensing systems with Type Ia supernovae acting as background sources to estimate the speed of light. This provides an original method to measure the speed of light using objects located at different redshifts that emitted their light in a distant past. Moreover, we predict that strongly lensed Type Ia supernovae observed by the Large Synoptic Survey Telescope (LSST) would produce robust constraints on Δc/c at the level of 10−3. We also discuss whether future surveys such as LSST may succeed in detecting any hypothetical variation of c predicted by theories in which fundamental constants have a dynamical nature.

Through a Smoother Lens: An expected absence of LCDM substructure detections from hydrodynamic and dark matter only simulations.

A fundamental prediction of the cold dark matter cosmology is the existence of a large number of dark subhalos around galaxies, most of which should be entirely devoid of stars. Confirming the existence of dark substructures stands among the most important empirical challenges in modern cosmology: if they are found and quantified with the mass spectrum expected, then this would close the door on a vast array of competing theories. But in order for observational programs of this kind to reach fruition, we need robust predictions. Here we explore substructure predictions for lensing using galaxy lens-like hosts at z=0.2 from the Illustris simulations both in full hydrodynamics and dark matter only. We quantify substructures more massive than ~ 109 M☉, comparable to current lensing detections derived from HST, Keck, and ALMA. The addition of full hydrodynamics reduces the overall subhalo mass function by about a factor of two. Even for the dark matter only runs, most (~85 per cent) projections through the halo of size close to an Einstein radius contain no substructures larger than 109 M☉. The fraction of empty projections through the halo rises to ~95 per cent in full physics simulations. This suggests we will likely need hundreds of strong lensing systems suitable for substructure studies, as well as predictions that include the effects of baryon physics on substructure, to properly constrain cosmological models. Fortunately, the field is poised to fulfill these requirements.

Using Strong Gravitational Lensing to Identify Fossil Group Progenitors

Abstract Fossil galaxy systems are classically thought to be the end result of galaxy group/cluster evolution, as galaxies experiencing dynamical friction sink to the center of the group potential and merge into a single, giant elliptical that dominates the rest of the members in both mass and luminosity. Most fossil systems discovered lie within z < 0.2, which leads to the question, what were these systems’ progenitors? Such progenitors are expected to have imminent or ongoing major merging near the brightest group galaxy that, when concluded, will meet the fossil criteria within the look forward time. Since strong gravitational lensing preferentially selects groups merging along the line of sight, or systems with a high mass concentration like fossil systems, we searched the CASSOWARY survey of strong-lensing events with the goal of determining whether lensing systems have any predisposition to being fossil systems or progenitors. We find that ∼13% of lensing groups are identified as traditional fossils while only ∼3% of nonlensing control groups are. We also find that ∼23% of lensing systems are traditional fossil progenitors compared to ∼17% for the control sample. Our findings show that strong-lensing systems are more likely to be fossil/pre-fossil systems than comparable nonlensing systems. Cumulative galaxy luminosity functions of the lensing and nonlensing groups also indicate a possible, fundamental difference between strong-lensing and nonlensing systems’ galaxy populations, with lensing systems housing a greater number of bright galaxies even in the outskirts of groups.

The Discrepancy between Einstein Mass and Dynamical Mass for SIS and Power-law Mass Models

Abstract We investigate the discrepancy between the two-dimensional projected lensing mass and the dynamical mass for an ensemble of 97 strong gravitational lensing systems discovered by the Sloan Lens ACS Survey, the BOSS Emission-Line Lens Survey (BELLS), and the BELLS for GALaxy-Lyα EmitteR sYstems Survey. We fit the lensing data to obtain the Einstein mass and use the velocity dispersion of the lensing galaxies provided by the Sloan Digital Sky Survey to get the projected dynamical mass within the Einstein radius by assuming the power-law mass approximation. The discrepancy is found to be obvious and quantified by Bayesian analysis. For the singular isothermal sphere mass model, we obtain that the Einstein mass is 20.7% more than the dynamical mass, and the discrepancy increases with the redshift of the lensing galaxies. For the more general power-law mass model, the discrepancy still exists within a 1σ credible region. We suspect the main reason for this discrepancy is mass contamination, including all invisible masses along the line of sight. In addition, the measurement errors and the approximation of the mass models could also contribute to the discrepancy.

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

Abstract In Hezaveh et al. we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational-lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data, as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single variational parameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that the application of approximate Bayesian neural networks to astrophysical modeling problems can be a fast alternative to Monte Carlo Markov Chains, allowing orders of magnitude improvement in speed.

Probing the distance-duality relation with high-z data

Measurements of strong gravitational lensing jointly with type Ia supernovae (SNe Ia) observations have been used to test the validity of the cosmic distance duality relation (CDDR), DL(z)/[(1+z)2DA(z)]=η=1, where DL(z) and DA(z) are the luminosity and the angular diameter distances to a given redshift z, respectively. However, several lensing systems lie in the interval 1.4 ⩽ z ⩽ 3.6 i.e., beyond the redshift range of current SNe Ia compilations (z ≈ 1.50), which prevents this kind of test to be fully explored. In this paper, we circumvent this problem by testing the CDDR considering observations of strong gravitational lensing along with SNe Ia and {a subsample from} the latest gamma-ray burst distance modulus data, whose redshift range is 0.033 ⩽ z ⩽ 9.3. We parameterize their luminosity distances with a second degree polynomial function and search for possible deviations from the CDDR validity by using four different η(z) functions: η(z)=1+η0z, η(z)=1+η0z/(1+z), η(z)=(1+z)η0 and η(z)=1+η0 ln (1+z). Unlike previous tests done at redshifts lower than 1.50, the likelihood for η0 depends strongly on the η(z) function considered, but we find no significant deviation from the CDDR validity (η0=0). However, our analyses also point to the fact that caution is needed when one fits data in higher redshifts to test the CDDR as well as a better understanding of the mass distribution of lenses also is required for more accurate results.

Fast automated analysis of strong gravitational lenses with convolutional neural networks.

Quantifying image distortions caused by strong gravitational lensing-the formation of multiple images of distant sources due to the deflection of their light by the gravity of intervening structures-and estimating the corresponding matter distribution of these structures (the 'gravitational lens') has primarily been performed using maximum likelihood modelling of observations. This procedure is typically time- and resource-consuming, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single gravitational lens can take up to a few weeks and requires expert knowledge of the physical processes and methods involved. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys. Here we report the use of deep convolutional neural networks to estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties that are faced by maximum likelihood methods. We also show that the removal of lens light can be made fast and automated using independent component analysis of multi-filter imaging data. Our networks can recover the parameters of the 'singular isothermal ellipsoid' density profile, which is commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models but about ten million times faster: 100 systems in approximately one second on a single graphics processing unit. These networks can provide a way for non-experts to obtain estimates of lensing parameters for large samples of data.

Constraints on a possible evolution of mass density power-law index in strong gravitational lensing from cosmological data

In this work, by using strong gravitational lensing (SGL) observations along with Type Ia Supernovae (Union2.1) and gamma ray burst data (GRBs), we propose a new method to study a possible redshift evolution of $\gamma(z)$, the mass density power-law index of strong gravitational lensing systems. In this analysis, we assume the validity of cosmic distance duality relation and the flat universe. In order to explore the $\gamma(z)$ behavior, three different parametrizations are considered, namely: (P1) $\gamma(z_l)=\gamma_0+\gamma_1 z_l$, (P2) $\gamma(z_l)=\gamma_0+\gamma_1 z_l/(1+z_l)$ and (P3) $\gamma(z_l)=\gamma_0+\gamma_1 \ln(1+z_l)$, where $z_l$ corresponds to lens redshift. If $\gamma_0=2$ and $\gamma_1=0$ the singular isothermal sphere model is recovered. Our method is performed on SGL sub-samples defined by different lens redshifts and velocity dispersions. For the former case, the results are in full agreement with each other, while a 1$\sigma$ tension between the sub-samples with low ($\leq 250$ km/s) and high ($>250$ km/s) velocity dispersions was obtained on the ($\gamma_0$-$\gamma_1$) plane. By considering the complete SGL sample, we obtain $\gamma_0 \approx 2$ and $ \gamma_1 \approx 0$ within 1$\sigma$ c.l. for all $\gamma(z)$ parametrizations. However, we find the following best fit values of $\gamma_1$: $-0.085$, $-0.16$ and $-0.12$ for P1, P2 and P3 parametrizations, respectively, suggesting a mild evolution for $\gamma(z)$. By repeating the analysis with Type Ia Supernovae from JLA compilation, GRBs and SGL systems this mild evolution is reinforced.

Probing the cosmic distance duality relation using time delay lenses

The construction of the cosmic distance-duality relation (CDDR) has been widely studied. However, its consistency with various new observables remains a topic of interest. We present a new way to constrain the CDDR η(z) using different dynamic and geometric properties of strong gravitational lenses (SGL) along with SNe Ia observations. We use a sample of 102 SGL with the measurement of corresponding velocity dispersion σ0 and Einstein radius θE. In addition, we also use a dataset of 12 two image lensing systems containing the measure of time delay Δ t between source images. Jointly these two datasets give us the angular diameter distance DAol of the lens. Further, for luminosity distance, we use the 740 observations from JLA compilation of SNe Ia. To study the combined behavior of these datasets we use a model independent method, Gaussian Process (GP). We also check the efficiency of GP by applying it on simulated datasets, which are generated in a phenomenological way by using realistic cosmological error bars. Finally, we conclude that the combined bounds from the SGL and SNe Ia observation do not favor any deviation of CDDR and are in concordance with the standard value (η=1) within 2σ confidence region, which further strengthens the theoretical acceptance of CDDR.

Finding strong lenses in CFHTLS using convolutional neural networks

We train and apply convolutional neural networks, a machine learning technique developed to learn from and classify image data, to Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) imaging for the identification of potential strong lensing systems. An ensemble of four convolutional neural networks was trained on images of simulated galaxy-galaxy lenses. The training sets consisted of a total of 62,406 simulated lenses and 64,673 non-lens negative examples generated with two different methodologies. The networks were able to learn the features of simulated lenses with accuracy of up to 99.8% and a purity and completeness of 94-100% on a test set of 2000 simulations. An ensemble of trained networks was applied to all of the 171 square degrees of the CFHTLS wide field image data, identifying 18,861 candidates including 63 known and 139 other potential lens candidates. A second search of 1.4 million early type galaxies selected from the survey catalog as potential deflectors, identified 2,465 candidates including 117 previously known lens candidates, 29 confirmed lenses/high-quality lens candidates, 266 novel probable or potential lenses and 2097 candidates we classify as false positives. For the catalog-based search we estimate a completeness of 21-28% with respect to detectable lenses and a purity of 15%, with a false-positive rate of 1 in 671 images tested. We predict a human astronomer reviewing candidates produced by the system would identify ~20 probable lenses and 100 possible lenses per hour in a sample selected by the robot. Convolutional neural networks are therefore a promising tool for use in the search for lenses in current and forthcoming surveys such as the Dark Energy Survey and the Large Synoptic Survey Telescope.

Multiply imaged quasars in the Gaia DR1

AbstractBecause of to its exceptional resolving power, Gaia should detect a few thousands gravitational lensed systems. These consist in multiple images of background quasars. The estimated number of lens phenomena in the sky, however, depends on the cosmological model considered. By taking into account the observational bias that will restrict the detection of lensed quasars, identification of these up to a given limiting magnitude will constrain the cosmological parameters.We have investigated the known gravitationally lensed quasars present in the Gaia DR1, and found that a significant number of components of these systems have been measured and are present in the Gaia DR1 catalogue although quasi none of them have all their components detected. We additionally examined the immediate surroundings of QSOs from the large Quasar catalogue, LQAC3, and detected several configurations compatible with gravitational lensing phenomena. A more global strategy to systematically detect the potential candidates in the various releases of the Gaia catalogue is presented.

Discovery of the Lensed Quasar System DES J0408-5354

Abstract We report the discovery and spectroscopic confirmation of the quad-like lensed quasar system DES J0408-5354 found in the Dark Energy Survey (DES) Year 1 (Y1) data. This system was discovered during a search for DES Y1 strong lensing systems using a method that identified candidates as red galaxies with multiple blue neighbors. DES J0408-5354 consists of a central red galaxy surrounded by three bright ( ) blue objects and a fourth red object. Subsequent spectroscopic observations using the Gemini South telescope confirmed that the three blue objects are indeed the lensed images of a quasar with redshift z = 2.375, and that the central red object is an early-type lensing galaxy with redshift z = 0.597. DES J0408-5354 is the first quad lensed quasar system to be found in DES and begins to demonstrate the potential of DES to discover and dramatically increase the sample size of these very rare objects.

Projection effects in the strong lensing study of subhaloes

The defining characteristic of the cold dark matter (CDM) hypothesis is the presence of a very large number of low-mass haloes, too small to have made a visible galaxy. Other hypotheses for the nature of the dark matter, such as warm dark matter (WDM), predict a much smaller number of such low-mass haloes. Strong lensing systems offer the possibility of detecting small-mass haloes through the distortions they induce in the lensed image. Here we show that the main contribution to the image distortions comes from haloes along the line of sight rather than subhaloes in the lens as has normally been assumed so far. These interlopers enhance the differences between the predictions of CDM and WDM models. We derive the total perturber mass function, including both subhaloes and interlopers, and show that measurements of approximately 20 strong lens systems with a detection limit of $M_{\rm low}=10^7 h^{-1} M_{\odot}$ would distinguish (at 3 sigma) between CDM and a WDM model consisting of 7 keV sterile neutrinos such as those required to explain the recently detected 3.5 keV X-ray emission line from the centres of galaxies and clusters.

TEST OF PARAMETRIZED POST-NEWTONIAN GRAVITY WITH GALAXY-SCALE STRONG LENSING SYSTEMS

ABSTRACT Based on a mass-selected sample of galaxy-scale strong gravitational lenses from the SLACS, BELLS, LSD, and SL2S surveys and using a well-motivated fiducial set of lens-galaxy parameters, we tested the weak-field metric on kiloparsec scales and found a constraint on the post-Newtonian parameter under the assumption of a flat ΛCDM universe with parameters taken from Planck observations. General relativity (GR) predicts exactly γ = 1. Uncertainties concerning the total mass density profile, anisotropy of the velocity dispersion, and the shape of the light profile combine to systematic uncertainties of ∼25%. By applying a cosmological model-independent method to the simulated future LSST data, we found a significant degeneracy between the PPN γ parameter and the spatial curvature of the universe. Setting a prior on the cosmic curvature parameter −0.007 < Ω k < 0.006, we obtained the constraint on the PPN parameter that . We conclude that strong lensing systems with measured stellar velocity dispersions may serve as another important probe to investigate validity of the GR, if the mass-dynamical structure of the lensing galaxies is accurately constrained in future lens surveys.

REVISITING STUDIES OF THE STATISTICAL PROPERTY OF A STRONG GRAVITATIONAL LENS SYSTEM AND MODEL-INDEPENDENT CONSTRAINT ON THE CURVATURE OF THE UNIVERSE

ABSTRACT In this paper, we use a recently compiled data set, which comprises 118 galactic-scale strong gravitational lensing (SGL) systems to constrain the statistical property of the SGL system as well as the curvature of the universe without assuming any fiducial cosmological model. Based on the singular isothermal ellipsoid (SIE) model of the SGL system, we obtain that the constrained curvature parameter is close to zero from the SGL data, which is consistent with the latest result of Planck measurement. More interestingly, we find that the parameter f in the SIE model is strongly correlated with the curvature . Neglecting this correlation in the analysis will significantly overestimate the constraining power of SGL data on the curvature. Furthermore, the obtained constraint on f is different from previous results: (68% confidence level [C.L.]), which means that the standard singular isothermal sphere (SIS) model (f = 1) is disfavored by the current SGL data at more than a C.L. We also divide all of the SGL data into two parts according to the centric stellar velocity dispersion and find that the larger the value of for the subsample, the more favored the standard SIS model is. Finally, we extend the SIE model by assuming the power-law density profiles for the total mass density, , and luminosity density, , and obtain the constraints on the power-law indices: and at a 68% C.L. When assuming the power-law index , this scenario is totally disfavored by the current SGL data, .

A neural network gravitational arc finder based on the Mediatrix filamentation method

Automated arc detection methods are needed to scan the ongoing and next-generation wide-field imaging surveys, which are expected to contain thousands of strong lensing systems. Arc finders are also required for a quantitative comparison between predictions and observations of arc abundance. Several algorithms have been proposed to this end, but machine learning methods have remained as a relatively unexplored step in the arc finding process. In this work we introduce a new arc finder based on pattern recognition, which uses a set of morphological measurements derived from the Mediatrix Filamentation Method as entries to an Artificial Neural Network (ANN). We show a full example of the application of the arc finder, first training and validating the ANN on simulated arcs and then applying the code on four Hubble Space Telescope (HST) images of strong lensing systems. The simulated arcs use simple prescriptions for the lens and the source, while mimicking HST observational conditions. We also consider a sample of objects from HST images with no arcs in the training of the ANN classification. We use the training and validation process to determine a suitable set of ANN configurations, including the combination of inputs from the Mediatrix method, so as to maximize the completeness while keeping the false positives low. In the simulations the method was able to achieve a completeness of about 90% with respect to the arcs that are input to the ANN after a preselection. However, this completeness drops to $\sim$ 70% on the HST images. The false detections are of the order of 3% of the objects detected in these images. The combination of Mediatrix measurements with an ANN is a promising tool for the pattern recognition phase of arc finding. More realistic simulations and a larger set of real systems are needed for a better training and assessment of the efficiency of the method.

Gravitational lensing by ring-like structures

We study a class of gravitational lensing systems consisting of an inclined ring/belt, with and without an added point mass at the centre. We show that a common feature of such systems are so-called "pseudo-caustics", across which the magnification of a point source changes discontinuously and yet remains finite. Such a magnification change can be associated with either a change in image multiplicity or a sudden change in the size of a lensed image. The existence of pseudo-caustics and the complex interplay between them and the formal caustics (which correspond to points of infinite magnification) can lead to interesting consequences, such as truncated or open caustics and a non-conservation of total image parity. The origin of the pseudo-caustics is found to be the non-differentiability of the solutions to the lens equation across the ring/belt boundaries, with the pseudo-caustics corresponding to ring/belt boundaries mapped into the source plane. We provide a few illustrative examples to understand the pseudo-caustic features, and in a separate paper consider a specific astronomical application of our results to study microlensing by extrasolar asteroid belts.

Campaign 9 of the K2 Mission: Observational Parameters, Scientific Drivers, and Community Involvement for a Simultaneous Space- and Ground-based Microlensing Survey

K2's Campaign 9 (K2C9) will conduct a ∼3.7 deg2 survey toward the Galactic bulge from 2016 April 22 through July 2 that will leverage the spatial separation between K2 and the Earth to facilitate measurement of the microlens parallax for microlensing events. These will include several that are planetary in nature as well as many short-timescale microlensing events, which are potentially indicative of free-floating planets (FFPs). These satellite parallax measurements will in turn allow for the direct measurement of the masses of and distances to the lensing systems. In this article we provide an overview of the K2C9 space- and ground-based microlensing survey. Specifically, we detail the demographic questions that can be addressed by this program, including the frequency of FFPs and the Galactic distribution of exoplanets, the observational parameters of K2C9, and the array of resources dedicated to concurrent observations. Finally, we outline the avenues through which the larger community can become involved, and generally encourage participation in K2C9, which constitutes an important pathfinding mission and community exercise in anticipation of WFIRST.