Algebraic Properties of the Real Quintic Equation for a Binary Gravitational Lens
نویسندگان
چکیده
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 equation are revealed. We find that the number of images on each side of the separation axis is independent of the mass ratio and separation unless the source crosses the caustics. Furthermore, the discriminant of the quintic equation enables us to study changes in the number of solutions, namely in the number of images. It is shown that this discriminant can be factorized into two parts: One represents the condition that the lens equation can be reduced to a single quintic equation, while the other corresponds to the caustics.
منابع مشابه
Images for a Binary Gravitational Lens from a Single Real Algebraic Equation
It is shown that the lens equation for a binary gravitational lens being a set of two coupled real fifthorder algebraic equations (equivalent to a single complex equation of the same order) can be reduced to a single real fifth-order algebraic equation, which provides a much simpler way to study lensing by binary objects.
متن کاملEuclidean Algorithm for a Gravitational Lens in a Polynomial Equation
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 apparently coupled system to a single polynomial in one variable (say x in Cartesian coordinates) without the other component (say y), which is expressed as a func...
متن کاملEffects of a deformation of a star on the gravitational lensing
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 lens equation for this gravitational lens as a single real tenth-order algebraic equation. Furthermore, we compute an expression for the caustics as a dis...
متن کاملHow Cumbersome is a Tenth Order Polynomial?: The Case of Gravitational Triple Lens Equation
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 trajectories using recipies for Fortran or C (portable for C++ or Cjj) in Numerical Recipes, or using packages such as Mathemetica, Matlab, etc. This ready solvabilit...
متن کاملEffects of the core radius of an isothermal ellipsoidal gravitational lens on the caustics and the critical curves
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 sixth-order algebraic equation. Since the expression is too long, by using another method we obtain a parametric representation of the critical curves in order to sh...
متن کامل