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

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 3C$\sim$84 (NGC$\sim$1275) at 43$\sim$GHz. A significant polarized emission is detected at the hotspot of the innermost re-started jet, which is located $\sim$1 pc south from the radio core. While the previous report presented a hotspot at the southern end of the western limb, the hotspot location has been moved to the southern end of the eastern limb. Faraday rotation is detected within an entire bandwidth of the 43-GHz band. The measured rotation measure (RM) is at most (6.3$\pm$1.9)$\times10^{5}$$\sim$rad$\sim$m$^{-2}$ and might be slightly time variable on the timescale of a month by a factor of a few. Our measured RM and the RM previously reported by the CARMA and SMA observations cannot be consistently explained by the spherical accretion flow with a power-law profile. We propose that a clumpy/inhomogeneous ambient medium is responsible for the observed rotation measure. Using equipartition magnetic field, we derive the electron density of $2\times10^{4}$$\sim$cm$^{-3}$. 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

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

Concurrent 43 and 86 GHz Very Long Baseline Polarimetry of 3C273

We present sub-milliarcsecond resolution total intensity and linear polarization VLBI images of 3C273, using concurrent 43 and 86 GHz data taken with the Very Long Baseline Array in May 2002. The structure seen in the innermost jet suggest that we have fortuitously caught the jet in the act of changing direction. The polarization images confirm that the core is unpolarized (fractional polarization m < 1 %) at 86 GHz, but also show well ordered magnetic fields (m ~ 15 %) in the inner jet, at a projected distance of 2.3 pc from the core. In this strongly polarized region, the rotation measure changes across the jet by 4.2 x 10^{4} rad m^{-2} over an angular width of about 0.3 milliarcseconds. If the lack of polarization in the core is also attributed to a Faraday screen, then a rotation measure dispersion > 5.2 x 10^{4} rad m^{-2} must be present in or in front of that region. These are among the highest rotation measures reported so far in the nucleus of any active galaxy or quasar, and must occur outside (but probably close to) the radio emitting region. The transverse rotation measure gradient is in the same sense as that observed by Asada et al and by Zavala and Taylor at greater core distances. The magnitude of the transverse gradient decreases rapidly with distance down the jet, and appears to be variable.Comment: 4 pages, LaTeX, 3 postscript figures, submitted to Astrophysical Journal Letter

Gravitational wave forms for a three-body system in Lagrange's orbit: parameter determinations and a binary source test

Continuing work initiated in an earlier publication [Torigoe et al. Phys. Rev. Lett. {\bf 102}, 251101 (2009)], gravitational wave forms for a three-body system in Lagrange's orbit are considered especially in an analytic method. First, we derive an expression of the three-body wave forms at the mass quadrupole, octupole and current quadrupole orders. By using the expressions, we solve a gravitational-wave {\it inverse} problem of determining the source parameters to this particular configuration (three masses, a distance of the source to an observer, and the orbital inclination angle to the line of sight) through observations of the gravitational wave forms alone. For this purpose, the chirp mass to a three-body system in the particular configuration is expressed in terms of only the mass ratios by deleting initial angle positions. We discuss also whether and how a binary source can be distinguished from a three-body system in Lagrange's orbit or others.Comment: 21 pages, 3 figures, 1 table; text improved, typos corrected; accepted for publication in PR

M87 black hole mass and spin estimate through the position of the jet boundary shape break

We propose a new method of estimating a mass of a super massive black hole residing in the center of an active galaxy. The active galaxy M87 offers a convenient test case for the method due to the existence of a large amount of observational data on the jet and ambient environment properties in the central area of the object. We suggest that the observed transition of a jet boundary shape from a parabolic to a conical form is associated with the flow transiting from the magnetically dominated regime to the energy equipartition between plasma bulk motion and magnetic field. By coupling the unique set of observations available for the jet kinematics, environment and boundary profile with our MHD modelling under assumption on the presence of a dynamically important magnetic field in the M87 jet, we estimate the central black hole mass and spin. The method leads us to believe that the M87 super massive black hole has a mass somewhat larger than typically accepted so far.Comment: 10 pages, 1 figure, 3 tables, accepted for publication by MNRA

Fluctuations of the Lyapunov exponent in 2D disordered systems

We report a numerical investigation of the fluctuations of the Lyapunov exponent of a two dimensional non-interacting disordered system. While the ratio of the mean to the variance of the Lyapunov exponent is not constant, as it is in one dimension, its variation is consistent with the single parameter scaling hypothesis