4,433 research outputs found

### Effects 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 show analytically that there exist three cases: There are
two curves for a small core radius, one for a quite large one, and no curves
appear for an extremely large one, though the latter two cases are not
realistic. The caustics are represented also by the same parameter.Comment: 4 pages; accepted for publication in A&

### Effects 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 discriminant for the polynomial. Another simple parametric
representation of the caustics is also presented in a more tractable form. A
simple expression for the critical curves is obtained to clarify a topological
feature of the critical curves; the curves are simply connected if and only if
the distortion is sufficiently large.Comment: 8 pages; accepted for publication in MNRA

### Images for an Isothermal Ellipsoidal Gravitational Lens from a Single Real Algebraic Equation

We present explicit expressions for the lens equation for a cored isothermal
ellipsoidal gravitational lens as a single real sixth-order algebraic equation
in two approaches; 2-dimensional Cartesian coordinates and 3-dimensional polar
ones. We find a condition for physical solutions which correspond to at most
five images. For a singular isothermal ellipsoid, the sixth-order equation is
reduced to fourth-order one for which analytic solutions are well-known.
Furthermore, we derive analytic criteria for determining the number of images
for the singular lens, which give us simple expressions for the caustics and
critical curves. The present formulation offers a useful way for studying
galaxy lenses frequently modeled as isothermal ellipsoids.Comment: 5 pages; accepted for publication in A&

### On the Speed of Gravity and the $v/c$ Corrections to the Shapiro Time Delay

Using a relatively simple method, I compute the v/c correction to the
gravitational time delay for light passing by a massive object moving with
speed v. It turns out that the v/c effects are too small to have been measured
in the recent experiment involving Jupiter and quasar J0842+1845 that was used
to measure the speed of gravity.Comment: 8 pages, LaTeX (or Latex, etc), one figure, which is also available
at http://www-theory.lbl.gov/~samuel/sog_figure.pdf; Revised version is the
one to appear in Phys. Rev. Lett

### Algebraic Properties of the Real Quintic Equation for a Binary Gravitational Lens

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.Comment: 7 pages (PTPTeX); accepted for publication in Prog. Theor. Phy

### Properties of Planetary Caustics in Gravitational Microlensing

Although some of the properties of the caustics in planetary microlensing
have been known, our understanding of them is mostly from scattered information
based on numerical approaches. In this paper, we conduct a comprehensive and
analytic analysis of the properties of the planetary caustics, which are one of
the two sets of caustics in planetary microlensing, those located away from the
central star. Under the perturbative approximation, we derive analytic
expressions for the location, size, and shape of the planetary caustic as a
function of the star-planet separation and the planet/star mass ratio. Based on
these expressions combined with those for the central caustic, which is the
other set of caustics located close to the central star, we compare the
similarities and differences between the planetary and central caustics. We
also present the expressions for the size ratio between the two types of
caustics and for the condition of the merging of the two types of caustics.
These analytic expressions will be useful in understanding the dependence of
the planetary lensing behavior on the planet parameters and thus in
interpreting the planetary lensing signalsComment: total 6 pages, including 6 figures, ApJ, submitte

### Simplified solution to determination of a binary orbit

We present a simplified solution to orbit determination of a binary system
from astrometric observations. An exact solution was found by Asada, Akasaka
and Kasai by assuming no observational errors. We extend the solution
considering observational data. The generalized solution is expressed in terms
of elementary functions, and therefore requires neither iterative nor numerical
methods.Comment: 15 pages; text improved, Accepted for publication in the Astronomical
Journa

### Analysis of Microlensing Light Curves Induced by Multiple-Planet Systems

To maximize the number of planet detections by increasing efficiency, current
microlensing follow-up observation experiments are focusing on
high-magnification events to search for planet-induced perturbations near the
peak of lensing light curves. It was known that by monitoring
high-magnification events, it is possible to detect multiplicity signatures of
planetary systems. However, it was believed that the interpretation of the
signals and the characterization of the detected multiple-planet systems would
be difficult due to the complexity of the magnification pattern in the central
region combined with the large number of lensing parameters required to model
multiple-planet systems. In this paper, we demonstrate that in many cases the
central planetary perturbations induced by multiple planets can be well
approximated by the superposition of the single planetary perturbations where
the individual planet-primary pairs act as independent binary lens systems
(binary superposition). The validity of the binary-superposition approximation
implies that the analysis of perturbations induced by multiple planets can be
greatly simplified because the anomalies produced by the individual planet
components can be investigated separately by using relatively much simpler
single-planetary analysis, and thus enables better characterization of these
systems.Comment: Manuscript with high-resolution figures are available at
http://astroph.chungbuk.ac.kr/~cheongho/preprint.htm

### A Parametric Representation of Critical Curves and Caustics for a Binary Gravitational Lens

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 result is helpful for efficiently constructing many templates of light
curves due to binary systems, particularly extrasolar planets, which cause
spikes in the light curves when a source crosses the caustics.Comment: 8 pages (PTPTeX); accepted for publication in Prog. Theor. Phy

- â€¦