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

Astrometric Method to Break the Photometric Degeneracy between Binary-source and Planetary Microlensing Perturbations

An extra-solar planet can be detected by microlensing because the planet can perturb the smooth lensing light curve created by the primary lens. However, it was shown by Gaudi that a subset of binary-source events can produce light curves that closely resemble those produced by a significant fraction of planet/star lens systems, causing serious contamination of a sample of suspected planetary systems detected via microlensing. In this paper, we show that if a lensing event is observed astrometrically, one can unambiguously break the photometric degeneracy between binary-source and planetary lensing perturbations. This is possible because while the planet-induced perturbation in the trajectory of the lensed source image centroid shifts points away from the opening of the unperturbed elliptical trajectory, while the perturbation induced by the binary source companion points always towards the opening. Therefore, astrometric microlensing observations by using future high-precision interferometers will be important for solid confirmation of microlensing planet detections.Comment: total 5 pages, including 1 figure and no table, ApJ, submitted, better quality pdf file is avalilable at http://astroph.chungbuk.ac.kr/~cheongho/publication.htm

Boundary conditions in the Dirac approach to graphene devices

We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the ones which are in closest agreement with available experiments. For nanotubes of arbitrary chirality satisfying these last boundary conditions, we evaluate the Casimir energy via zeta function regularization, in such a way that the limit of nanoribbons is clearly determined.Comment: 10 pages, no figure. Section on Casimir energy adde

From Group Recommendations to Group Formation

There has been significant recent interest in the area of group recommendations, where, given groups of users of a recommender system, one wants to recommend top-k items to a group that maximize the satisfaction of the group members, according to a chosen semantics of group satisfaction. Examples semantics of satisfaction of a recommended itemset to a group include the so-called least misery (LM) and aggregate voting (AV). We consider the complementary problem of how to form groups such that the users in the formed groups are most satisfied with the suggested top-k recommendations. We assume that the recommendations will be generated according to one of the two group recommendation semantics - LM or AV. Rather than assuming groups are given, or rely on ad hoc group formation dynamics, our framework allows a strategic approach for forming groups of users in order to maximize satisfaction. We show that the problem is NP-hard to solve optimally under both semantics. Furthermore, we develop two efficient algorithms for group formation under LM and show that they achieve bounded absolute error. We develop efficient heuristic algorithms for group formation under AV. We validate our results and demonstrate the scalability and effectiveness of our group formation algorithms on two large real data sets.Comment: 14 pages, 22 figure

Finding the Leptonic WWWW Decay Mode of a Heavy Higgs Boson

We reanalyze the extraction of the heavy Higgs boson signal $H\rightarrow W^+W^-\rightarrow \bar\ell\nu,\ell\bar\nu$ $(\ell=e\hbox{ or }\mu)$ from the Standard Model background at hadron supercolliders, taking into account revised estimates of the top quark background. With new acceptance criteria the detection of the signal remains viable. Requiring a forward jet-tag, a central jet-veto, and a large relative transverse momentum of the two charged leptons yields $S/\sqrt B>6$ for one year of running at the SSC or LHC.Comment: LaTex(Revtex), 9 pages, 6 figures (available upon request), MAD/PH/75

A Characteristic Planetary Feature in Double-Peaked, High-Magnification Microlensing Events

A significant fraction of microlensing planets have been discovered in high-magnification events, and a significant fraction of these events exhibit a double-peak structure at their peak. However, very wide or very close binaries can also produce double-peaked high-magnification events, with the same gross properties as those produced by planets. Traditionally, distinguishing between these two interpretations has relied upon detailed modeling, which is both time-consuming and generally does not provide insight into the observable properties that allow discrimination between these two classes of models. We study the morphologies of these two classes of double-peaked high-magnification events, and identify a simple diagnostic that can be used to immediately distinguish between perturbations caused by planetary and binary companions, without detailed modeling. This diagnostic is based on the difference in the shape of the intra-peak region of the light curves. The shape is smooth and concave for binary lensing, while it tends to be either boxy or convex for planetary lensing. In planetary lensing this intra-peak morphology is due to the small, weak cusp of the planetary central caustic located between the two stronger cusps. We apply this diagnostic to five observed double-peaked high-magnification events to infer their underlying nature. A corollary of our study is that good coverage of the intra-peak region of double-peaked high-magnification events is likely to be important for their unique interpretation.Comment: 6 pages, 3 figure