We report the observation and confirmation of the first group-and cluster-scale strong gravitational lensing systems found in Dark Energy Survey data. Through visual inspection of data from the Science Verification season, we identified 53 candidate systems. We then obtained spectroscopic follow-up of 21 candidates using the Gemini Multi-object Spectrograph at the Gemini South telescope and the Inamori-Magellan Areal Camera and Spectrograph at the Magellan/Baade telescope. With this follow-up, we confirmed six candidates as gravitational lenses: three of the systems are newly discovered, and the remaining three were previously known. Of the 21 observed candidates, the remaining 15 either were not detected in spectroscopic observations, were observed and did not exhibit continuum emission (or spectral features), or were ruled out as lensing systems. The confirmed sample consists of one group-scale and five galaxy-cluster-scale lenses. The lensed sources range in redshift z ∼ 0.80-3.2 and in i-band surface brightness i SB ∼ 23-25 mag arcsec −2 (2″ aperture). For each of the six systems, we estimate the Einstein radius θ E and the enclosed mass M enc , which have ranges θ E ∼ 5″-9″ and M enc ∼ 8 × 10 12 to 6 × 10 13 M e , respectively.
Context. Owing to their computational simplicity, models with elliptical potentials (pseudo-elliptical) are often used in gravitational lensing applications, in particular for mass modeling using arcs and for arc statistics. However, these models generally lead to negative mass distributions in some regions and to dumbbell-shaped surface density contours for high ellipticities. Aims. We revisit the physical limitations of the pseudo-elliptical Navarro-Frenk-White (PNFW) model, focusing on the behavior of the mass distribution close to the tangential critical curve, where tangential arcs are expected to be formed. We investigate the shape of the mass distribution on this region and the presence of negative convergence. We obtain a mapping from the PNFW to the NFW model with elliptical mass distribution (ENFW). We compare the arc cross section for both models, aiming to determine a domain of validity for the PNFW model in terms of its mass distribution and for the cross section. Methods. We defined a figure of merit to i) measure the deviation of the iso-convergence contours of the PNFW model to an elliptical shape, ii) assigned an ellipticity ε Σ to these contours, iii) defined a corresponding iso-convergence contour for the ENFW model. We computed the arc cross section using the "infinitesimal circular source approximation". Results. We extend previous work by investigating the shape of the mass distribution of the PNFW model for a broad range of the potential ellipticity parameter ε and characteristic convergence κ ϕ s . We show that the maximum value of ε to avoid dumbbellshaped mass distributions is explicitly dependent on κ ϕ s , with higher ellipticities (ε 0.5, i.e., ε Σ 0.65) allowed for small κ ϕ s . We determine a relation between the ellipticity of the mass distribution ε Σ and ε valid for any ellipticity. We also derive the relation of characteristic convergences, obtaining a complete mapping from PNFW to ENFW models, and provide fitting formulae for connecting the parameters of both models. Using this mapping, the cross sections for both models are compared, setting additional constraints on the parameter space of the PNFW model such that it reproduces the ENFW results. We also find that the negative convergence regions occur far from the arc formation region and should therefore not be a problem for studies with gravitational arcs. Conclusions. We conclude that the PNFW model is well-suited to model an elliptical mass distribution on a larger ε-κ ϕ s parameter space than previously expected. However, if we require the PNFW model to reproduce the arc cross section of the ENFW well, the ellipticity is more restricted, particularly for low κ ϕ s . The determination of a domain of validity for the PNFW model and the mapping to ENFW models could have implications for the use of PNFW models for the inverse modeling of lenses and for fast arc simulations, for example.
The strong galaxy-galaxy lensing produces highly magnified and distorted images of background galaxies in the form of arcs and Einstein rings. Statistically, these effects are quantified, for example, in the number counts of highly luminous sub-millimeter galaxies and of gravitational arcs. Two key quantities to model these statistics are the magnification and the arc cross sections. These are usually computed using either the circular infinitesimal source approximation or ray-tracing simulations for sources of finite size. In this work, we use an analytic solution for gravitational arcs to obtain these cross sections as a function of image magnification and length-to-width ratio in closed form, for finite sources. These analytical solutions provide simple interpretations to the numerical results, can be employed to test the computational codes, and can be used for fast a computation of the abundance of distant sources and arcs. In this paper, the lens is modeled by a Singular Isothermal Sphere, which is an excellent approximation to radial density profile of Early-Type galaxies, and the sources are also axisymmetric. We derive expressions for the geometrical properties of the images, such as the area and several definitions of length and width. We obtain the magnification cross section in exact form and derive a simple analytic approximation covering the arc and Einstein ring regimes. The arc cross section is obtained down to the formation of an Einstein ring and given in terms of elementary functions. Perturbative expansions of these results are worked out, showing explicitly the correction terms for finite sources.
The Perturbative Approach (PA) introduced by Alard (2007) provides analytic solutions for gravitational arcs by solving the lens equation linearized around the Einstein ring solution. This is a powerful method for lens inversion and simulations in that it can be used, in principle, for generic lens models. In this paper we aim to quantify the domain of validity of this method for three quantities derived from the linearized mapping: caustics, critical curves, and the deformation cross section (i.e. the arc cross section in the infinitesimal circular source approximation). We consider lens models with elliptical potentials, in particular the Singular Isothermal Elliptic Potential and Pseudo-Elliptical Navarro-Frenk-White models. We show that the PA is exact for this first model. For the second, we obtain constraints on the model parameter space (given by the potential ellipticity parameter ε and characteristic convergence κ s ) such that the PA is accurate for the aforementioned quantities. In this process we obtain analytic expressions for several lensing functions, which are valid for the PA in general. The determination of this domain of validity could have significant implications for the use of the PA, but it still needs to be probed with extended sources.
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