Direct Detection of Giant Close-In Planets Around the Source Stars of Caustic-Crossing Microlensing Events

We propose a direct method to detect close-in giant planets orbiting stars in the Galactic bulge. This method uses caustic-crossing binary microlensing events discovered by survey teams monitoring the bulge to measure light from a planet orbiting the source star. When the planet crosses the caustic, it is more magnified than the source star; its light is magnified by two orders of magnitude for Jupiter size planets. If the planet is a giant close to the star, it may be bright enough to make a significant deviation in the light curve of the star. Detection of this deviation requires intensive monitoring of the microlensing light curve using a 10-meter class telescope for a few hours after the caustic. This is the only method yet proposed to directly detect close-in planets around stars outside the solar neighborhood.Comment: 4 pages, 2 figures. Submitted to ApJ Letter

Microlensing of gamma ray bursts by stars and MACHOs

The microlensing interpretation of the optical afterglow of GRB 000301C seems naively surprising, since a simple estimate of the stellar microlensing rate gives less than one in four hundred for a flat Omega_Lambda=0.7 cosmology, whereas one event was seen in about thirty afterglows. Considering baryonic MACHOs making up half of the baryons in the universe, the microlensing probability per burst can be roughly 5% for a GRB at redshift z=2. We explore two effects that may enhance the probability of observing microlensed gamma-ray burst afterglows: binary lenses and double magnification bias. We find that the consideration of binary lenses can increase the rate only at the ~15% level. On the other hand, because gamma-ray bursts for which afterglow observations exist are typically selected based on fluxes at widely separated wavebands which are not necessarily well correlated (e.g. localization in X-ray, afterglow in optical/infrared), magnification bias can operate at an enhanced level compared to the usual single-bias case. We find that existing estimates of the slope of the luminosity function of gamma-ray bursts, while as yet quite uncertain, point to enhancement factors of more than three above the simple estimates of the microlensing rate. We find that the probability to observe at least one microlensing event in the sample of 27 measured afterglows can be 3-4% for stellar lenses, or as much as 25 Omega_lens for baryonic MACHOs. We note that the probability to observe at least one event over the available sample of afterglows is significant only if a large fraction of the baryons in the universe are condensed in stellar-mass objects. (ABRIDGED)Comment: 22 pages, 4 figures, 2 table

Gravitational lensing as folds in the sky

We revisit the gravitational lensing phenomenon using a new visualization technique. It consists in projecting the observers sky into the source plane, what gives rise to a folded and stretched surface. This provides a clear graphical tool to visualize some interesting well-known effects, such as the development of multiple images of a source, the structure of the caustic curves, the parity of the images and their magnification as a function of the source position.Comment: 11 pages, 8 figure

Beyond Caustic Crossings: Properties of Binary Microlensing Light Curves

Binary microlensing light curves have a variety of morphologies. Many are indistinguishable from point lens light curves. Of those that deviate from the point lens form, caustic crossing light curves have tended to dominate identified binary lens events. Other distinctive signatures of binary lenses include significant asymmetry, multiple peaks, and repeating events. We have quantified, using high resolution simulations, the theoretically expected relative numbers of each type of binary lens event, based on its measurable characteristics. We find that a microlensing survey with current levels of photometric uncertainty and sampling should find at least as many non-caustic crossing binary lens events as caustic crossing events; in future surveys with more sensitive photometry, the contribution of distinctive non-caustic crossing events will be even greater. To try to explain why caustic crossing light curves appear to be so dominant among the published binary lensing events, we investigate the influence of several physical effects, including blending, sampling rate, and various binary populations.Comment: 17 pages, 17 figures, submitted to Ap

Images for a Binary Gravitational Lens from a Single Real Algebraic Equation

It is shown that the lens equation for a binary gravitational lens being a set of two coupled real fifth-order algebraic equations (equivalent to a single complex equation of the same order) can be reduced to a single real fifth-order algebraic equation, which provides a much simpler way to study lensing by binary objects.Comment: 4 pages; accepted for publication in A&A Letter

Gravitational Lenses With More Than Four Images: I. Classification of Caustics

We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are likely to be rare because they require special lens configurations, but a full calculation of the likelihood will have to include both the existence of lenses with multiple lens galaxies and the strong magnification bias that affects sextuple and octuple lenses. At optical wavelengths these lenses would probably appear as partial or complete Einstein rings, but at radio wavelengths the individual images could probably be resolved.Comment: 30 pages, including 12 postscript figures; accepted for publication in Ap

Probing Structures of Distant Extrasolar Planets with Microlensing

Planetary companions to the source stars of a caustic-crossing binary microlensing events can be detected via the deviation from the parent light curves created when the caustic magnifies the star light reflecting off the atmosphere or surface of the planets. The magnitude of the deviation is delta_p e_p rho_p^{-1/2}, where e_p is the fraction of starlight reflected by the planet and rho_p is the angular radius of the planet in units of angular Einstein ring radius. Due to the extraordinarily high resolution achieved during the caustic crossing, the detailed shapes of these perturbations are sensitive to fine structures on and around the planets. We consider the signatures of rings, satellites, and atmospheric features on caustic-crossing microlensing light curves. We find that, for reasonable assumptions, rings produce deviations of order 10% delta_p, whereas satellites, spots, and zonal bands produce deviations of order 1% delta_p. We consider the detectability of these features using current and future telescopes, and find that, with very large apertures (>30m), ring systems may be detectable, whereas spots, satellites, and zonal bands will generally be difficult to detect. We also present a short discussion of the stability of rings around close-in planets, noting that rings are likely to be lost to Poynting-Robertson drag on a timescale of order 10^5 years, unless they are composed of large (>>1 cm) particles, or are stabilized by satellites.Comment: 34 pages, 10 figures. Revised version, minor changes, figures fixed. Accepted to ApJ, to appear in the March 20, 2003 issue (v586

A systematic fitting scheme for caustic-crossing microlensing events

We outline a method for fitting binary-lens caustic-crossing microlensing events based on the alternative model parameterisation proposed and detailed in Cassan (2008). As an illustration of our methodology, we present an analysis of OGLE-2007-BLG-472, a double-peaked Galactic microlensing event with a source crossing the whole caustic structure in less than three days. In order to identify all possible models we conduct an extensive search of the parameter space, followed by a refinement of the parameters with a Markov Chain-Monte Carlo algorithm. We find a number of low-chi2 regions in the parameter space, which lead to several distinct competitive best models. We examine the parameters for each of them, and estimate their physical properties. We find that our fitting strategy locates several minima that are difficult to find with other modelling strategies and is therefore a more appropriate method to fit this type of events.Comment: 12 pages, 11 figure

OGLE-2009-BLG-092/MOA-2009-BLG-137: A Dramatic Repeating Event With the Second Perturbation Predicted by Real-Time Analysis

We report the result of the analysis of a dramatic repeating gravitational microlensing event OGLE-2009-BLG-092/MOA-2009-BLG-137, for which the light curve is characterized by two distinct peaks with perturbations near both peaks. We find that the event is produced by the passage of the source trajectory over the central perturbation regions associated with the individual components of a wide-separation binary. The event is special in the sense that the second perturbation, occurring $\sim 100$ days after the first, was predicted by the real-time analysis conducted after the first peak, demonstrating that real-time modeling can be routinely done for binary and planetary events. With the data obtained from follow-up observations covering the second peak, we are able to uniquely determine the physical parameters of the lens system. We find that the event occurred on a bulge clump giant and it was produced by a binary lens composed of a K and M-type main-sequence stars. The estimated masses of the binary components are $M_1=0.69 \pm 0.11\ M_\odot$ and $M_2=0.36\pm 0.06\ M_\odot$, respectively, and they are separated in projection by $r_\perp=10.9\pm 1.3\ {\rm AU}$. The measured distance to the lens is $D_{\rm L}=5.6 \pm 0.7\ {\rm kpc}$. We also detect the orbital motion of the lens system.Comment: 18 pages, 5 figures, 1 tabl