Related papers: Images for an Isothermal Ellipsoidal Gravitational…
We study the effect of the core radius of an isothermal ellipsoidal gravitational lens on the caustics and the critical curves. We derive an analytic expression of the caustics for an isothermal ellipsoidal gravitational lens via a…
It is shown that the lens equation for a binary gravitational lens being a set of two coupled real fifth-order algebraic equations (equivalent to a single complex equation of the same order) can be reduced to a single real fifth-order…
The equation in the title describes the number of bright images of a point source under lensing by an elliptic object with isothermal density. We prove that this equation has at most 6 solutions. Any number of solutions from 1 to 6 can…
We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image…
We study the problem of gravitational lensing by binary galaxies, idealized as two isothermal spheres. In a wide binary, each galaxy possesses individual tangential, nearly astroidal, caustics and roundish radial caustics. As the separation…
The Euclidean algorithm in algebra is applied to a class of gravitational lenses for which the lens equation consists of any set of coupled polynomial equations in the image position. In general, this algorithm allows us to reduce an…
The gravitational lens equation for the tilted Plummer family of models can be reduced to a one-dimensional non-linear equation. For certain values of the slope of the radial profile it can be reduced to a polynomial form. Both forms are…
It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic…
We first define what we mean by gravitational lensing equations in a general space-time. A set of exact relations are then derived that can be used as the gravitational lens equations in all physical situations. The caveat is that into…
Three point mass gravitational lens equation is a two-dimensional vector equation that can be embedded in a tenth order analytic polynomial equation of one complex variable, and we can solve the one variable equation on the source…
Many astrophysical systems can be approximated as isothermal spheres. In an isothermal sphere, the ``foreground'' objects can act as lenses on ``background'' objects in the same distribution. We study gravitational lensing by a singular…
Two exact lens equations have been recently shown to be equivalent to each other, being consistent with the gravitational deflection angle of light from a source to an observer, both of which can be within a finite distance from a lens…
Gravitational lensing galaxies are commonly modeled with elliptical density profiles, to which angular complexity is sometimes added through a multipole expansion - encoding deformations of the elliptical iso-density contours. The formalism…
Real astrophysical lenses typically lack axisymmetry, necessitating the study of gravitational-wave (GW) lensing by elliptical mass distributions to accurately assess detectability and waveform interpretation. We investigate strong lensing…
We find a simple expression for critical curves of a binary gravitational lens. On the basis of this, we present a parametric representation of such curves. The caustics can also be expressed with the same parameterization. The present…
The jets image modelling of gravitationally lensed sources have been performed. Several basic models of the lens mass distribution were considered, in particular, a singular isothermal ellipsoid, an isothermal ellipsoid with the core,…
We study analytically a gravitational lens due to a deformed star, which is modeled by using a monopole and a quadrupole moment. Positions of the images are discussed for a source on the principal axis. We present explicit expressions for…
The quadruple image configurations of gravitational lenses with vanishing ellipticity are examined. Even though such lenses asymptotically approach circularity, the configurations are stable if the position of the source relative to the…
Using the Schwarz function of an ellipse, it was recently shown that galaxies with density constant on confocal ellipses can produce at most four ``bright'' images of a single source. The more physically interesting example of an isothermal…
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…