DOI: https://doi.org/10.18524/1810-4215.2019.32.182511

### IMAGES DISTRIBUTION OF BINARY SYMMETRICAL GRAVITATIONAL LENS

A. T. Kotvytskiy, S. D. Bronza, V. Yu. Shablenko

#### Анотація

In this paper, we study the distribu-
tion of images from a point source in N - point gravi-
tational lenses.
It is well known that in a Schwarzschild lens (N =
1) from a point source, there are always two images.
Moreover, one of them is always inside the Einstein
ring, and the second outside it. It follows that:
a) the image plane is divided into two areas;
b) in each area there is always only one image;
c) the source plane, with the exception of the
caustic point (origin), is uniquely mapped onto each of
the two areas of the image plane.
In our study, we describe an algorithm that allows
us to determine the single-valued regions in a 2-point
gravitational lens and demonstrate it using an exam-
ple of a binary symmetric lens in which the distance
between the point masses is 1. We have shown that
in this case the full prototype of the caustic divides
the image plane into eight simply connected areas that
have the following properties:
a) if the point source is inside the caustic, then it
has five images in five (internal) areas;
b) if the point source is outside the caustic, then
it has three images in three (external) areas;
c) in each area there can be no more than one
image;
d) if the image of a point source is located in
one of the five internal areas, then the remaining four
also have images, while none of the three external areas
have images of the source;
e) if the image of the source is located in one of
the three external areas, then its images also exist in
the remaining two, while none of the five internal areas
contains a prototype of this source;
f) a caustic is a continuous, piecewise smooth,
closed Jordan curve that has a finite number of singular
points; each smooth, open part of the caustic, the ends
of which are singular points (the caustic arc) has four
inverse images, of which only one belongs to the critical
set, the caustic arcs are positively oriented (when going
around, the interior of the caustic remains to the left;
g) the boundaries of the regions consist of arcs
(closure of the image of arcs) with a hereditary orien-
tation; all eight regions are divided into the following
two classes: four regions in which the orientation of the
boundary coincides with the orientation on the caustic
and four regions in which the orientation of the bound-
ary is opposite to the orientation on the caustic.

#### Ключові слова

gravitational lensing; lens mapping; single-valued regions; image distribution

PDF (English)

#### Посилання

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