5,371 research outputs found
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&
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
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
Enhanced Polarized Emission from the One-Parsec-Scale Hotspot of 3C 84 as a Result of the Interaction with Clumpy Ambient Medium
We present Very Long Baseline Array polarimetric observations of the
innermost jet of 3C84 (NGC1275) at 43GHz. A significant
polarized emission is detected at the hotspot of the innermost re-started jet,
which is located 1 pc south from the radio core. While the previous
report presented a hotspot at the southern end of the western limb, the hotspot
location has been moved to the southern end of the eastern limb. Faraday
rotation is detected within an entire bandwidth of the 43-GHz band. The
measured rotation measure (RM) is at most
(6.31.9)radm and might be slightly time
variable on the timescale of a month by a factor of a few. Our measured RM and
the RM previously reported by the CARMA and SMA observations cannot be
consistently explained by the spherical accretion flow with a power-law
profile. We propose that a clumpy/inhomogeneous ambient medium is responsible
for the observed rotation measure. Using equipartition magnetic field, we
derive the electron density of cm. Such an electron
density is consistent with the cloud of narrow line emission region around the
central engine. We also discuss the magnetic field configuration from black
hole scale to pc scale and the origin of low polarization.Comment: 8 pages, 8 figures, accepted for publication in Ap
Surprising Evolution of the Parsec-scale Faraday Rotation Gradients in the Jet of the BL Lac Object B1803+784
Several multi-frequency polarization studies have shown the presence of
systematic Faraday Rotation gradients across the parsec-scale jets of Active
Galactic Nuclei (AGN), taken to be due to the systematic variation of the
line-of-sight component of a helical magnetic (B) field across the jet. Other
studies have confirmed the presence and sense of these gradients in several
sources, thus providing evidence that these gradients persist over time and
over large distances from the core. However, we find surprising new evidence
for a reversal in the direction of the Faraday Rotation gradient across the jet
of B1803+784, for which multi-frequency polarization observations are available
at four epochs. At our three epochs and the epoch of Zavala & Taylor (2003), we
observe transverse Rotation Measure (RM) gradients across the jet, consistent
with the presence of a helical magnetic field wrapped around the jet. However,
we also observe a "flip" in the direction of the gradient between June 2000 and
August 2002. Although the origins of this phenomena are not entirely clear,
possibly explanations include (i) the sense of rotation of the central
supermassive black hole and accretion disc has remained the same, but the
dominant magnetic pole facing the Earth has changed from North to South; (ii) a
change in the direction of the azimuthal B field component as a result of
torsional oscillations of the jet; and (iii) a change in the relative
contributions to the observed rotation measures of the "inner" and "outer"
helical fields in a magnetic-tower model. Although we cannot entirely rule out
the possibility that the observed changes in the RM distribution are associated
instead with changes in the thermal-electron distribution in the vicinity of
the jet, we argue that this explanation is unlikely.Comment: 21 pages, 10 figures. Accepted for publication in MNRA
Choreographic solution to the general relativistic three-body problem
We revisit the three-body problem in the framework of general relativity. The
Newtonian N-body problem admits choreographic solutions, where a solution is
called choreographic if every massive particles move periodically in a single
closed orbit. One is a stable figure-eight orbit for a three-body system, which
was found first by Moore (1993) and re-discovered with its existence proof by
Chenciner and Montgomery (2000). In general relativity, however, the periastron
shift prohibits a binary system from orbiting in a single closed curve.
Therefore, it is unclear whether general relativistic effects admit a
choreographic solution such as the figure eight. We carefully examine general
relativistic corrections to initial conditions so that an orbit for a
three-body system can be closed and a figure eight. This solution is still
choreographic. This illustration suggests that the general relativistic N-body
problem also may admit a certain class of choreographic solutions.Comment: 10 pages, 4 figures, text improved, accepted for publication in PR
- …