Planetary microlensing at high magnification

Simulations of planetary microlensing at high magnification that were carried out on a cluster computer are presented. It was found that the perturbations owing to two-thirds of all planets occur in the time interval  −0.5 t _FWHM,0.5 t _FWHM  with respect to the peak of the microlensing light curve, where   t _FWHM  is typically ∼14 h. This implies that only this restricted portion of the light curve need be intensively monitored for planets – a very significant practical advantage. Nearly all planetary detections in high-magnification events will not involve caustic crossings. We discuss the issues involved in determining the planetary parameters in high magnification events. Earth-mass planets may be detected with 1-m class telescopes if their projected orbital radii lie within about 1.5–2.5 au. Giant planets are detectable over a much larger region. For multiplanet systems the perturbations caused by individual planets can be separated under certain conditions. The size of the source star needs to be determined independently, but the presence of spots on the source star is likely to be negligible, as is the effect of planetary motion during an event.     

Improving the prospects for detecting extrasolar planets in gravitational microlensing events in 2002

Gravitational microlensing events of high magnification have been shown to be promising targets for detecting extrasolar planets. However, only a few events of high magnification have been found using conventional survey techniques. Here we demonstrate that high-magnification events can be readily found in microlensing surveys using a strategy that combines high-frequency sampling of target fields with on-line difference imaging analysis. We present 10 microlensing events with peak magnifications greater than 40 that were detected in real-time towards the Galactic bulge during 2001 by the Microlensing Observations in Astrophysics (MOA) project. We show that Earth-mass planets can be detected in future events such as these through intensive follow-up observations around the event peaks. We report this result with urgency as a similar number of such events are expected in 2002.     

Repeating microlensing events in the OGLE data

Microlensing events are usually selected among single-peaked non-repeating light curves in order to avoid confusion with variable stars. However, a microlensing event may exhibit a second microlensing brightening episode when the source or/and the lens is a binary system. A careful analysis of these repeating events provides an independent way to study the statistics of wide binary stars and to detect extrasolar planets. Previous theoretical studies predicted that 0.5–2 per cent of events should repeat due to wide binary lenses. We present a systematic search for such events in about 4000 light curves of microlensing candidates detected by the Optical Gravitational Lensing Experiment (OGLE) towards the Galactic bulge from 1992 to 2007. The search reveals a total of 19 repeating candidates, with six clearly due to a wide binary lens. As a by-product, we find that 64 events (∼2 per cent of the total OGLE-III sample) have been misclassified as microlensing; these misclassified events are mostly nova or other types of eruptive stars. The number and importance of repeating events will increase considerably when the next-generation wide-field microlensing experiments become fully operational in the future.     

Asymptotic formulas for the magnification of a gravitational lens system near a fold caustic

An approximate formula for the magnification of a point source near a fold caustic obtained in the first linear caustic approximation is widely used in the theory of gravitational lens systems. Here, this formula is refined to include the post-linear terms that have been found both for a point source and for an extended Gaussian source in the absence of continuous matter on the line of sight. The formulas are reduced to a form containing three additional parameters; the derivation of nontrivial corrections requires including the expansion terms in the lens equation up to the fourth order. The modified formula for an extended source is used to analyze strong microlensing events in the gravitational lens system Q2237+0305 (the Einstein Cross). For such an event on the light curve of image C (1999, OGLE data), the corrections found are statistically significant.     

On the probability of microlensing in gamma-ray burst afterglows

The declining light curve of the optical afterglow of gamma-ray burst (GRB) GRB000301C showed rapid variability with one particularly bright feature at about t − t ₀=3.8 d. This event was interpreted as gravitational microlensing by Garnavich, Loeb & Stanek and subsequently used to derive constraints on the structure of the GRB optical afterglow. In this paper, we use these structural parameters to calculate the probability of such a microlensing event in a realistic scenario, where all compact objects in the universe are associated with observable galaxies. For GRB000301C at a redshift of z =2.04, the a posteriori probability for a microlensing event with an amplitude of Δ m 0.95 mag (as observed) is 0.7 per cent (2.7 per cent) for the most plausible scenario of a flat Λ-dominated Friedmann–Robertson–Walker (FRW) universe with Ω_m=0.3 and a fraction f ∗=0.2 (1.0) of dark matter in the form of compact objects. If we lower the magnification threshold to Δ m 0.10 mag, the probabilities for microlensing events of GRB afterglows increase to 17 per cent (57 per cent). We emphasize that this low probability for a microlensing signature of almost 1 mag does not exclude that the observed event in the afterglow light curve of GRB000301C was caused by microlensing, especially in light of the fact that a galaxy was found within 2 arcsec from the GRB. In that case, however, a more robust upper limit on the a posteriori probability of ≈5 per cent is found. It does show, however, that it will not be easy to create a large sample of strong GRB afterglow microlensing events for statistical studies of their physical conditions on microarcsec scales.     

Could the optical transient SCP 06F6 be due to microlensing?

In this paper, we consider the mysterious optical transient SCP 06F6 displaying a symmetric light curve with a (half-time) duration of about 100 days. The projected location of the event falls close to the center of the galaxy cluster CL 1432.5 + 332.8 lying at the redshift z = 1.112. Guided by suggestive symmetry of the light curve and its similarity in two photometric bands, which is a typical signature of microlensing events, we discuss this possibility in several scenarios. As a consistency check we use the lens mass inferred from the event duration and the size of the source. The second check comes from a plausible assumption that since the event was highly magnified there was a perfect alignment at the maximum magnification.     

Predicting the second caustic crossing in binary microlensing events

We fit binary lens models to the data covering the initial part of real microlensing events in an attempt to predict the time of the second caustic crossing. We use approximations during the initial search through the parameter space for light curves that roughly match the observed ones. Exact methods for calculating the lens magnification of an extended source are used when we refine our best initial models. Our calculations show that the reliable prediction of the second crossing can only be made very late, when the light curve has risen appreciably after the minimum between the two caustic crossings. The best observational strategy is therefore to sample as frequently as possible once the light curve starts to rise after the minimum.     

On the astrometric behaviour of binary microlensing events

Despite the suspected binarity for a significant fraction of Galactic lenses, the current photometric surveys detected binary microlensing events only for a small fraction of the total events. The detection efficiency is especially low for non-caustic crossing events, which comprise the majority of the binary lensing events, as a result of the absence of distinctive features in their light curves combined with small deviations from the standard light curve of a single point-mass event. In addition, even if they are detected, it will be difficult to determine the solution of the binary lens parameters owing to the severe degeneracy problem. In this paper, we investigate the properties of binary lensing event expected when they are astrometrically observed by using high-precision interferometers. For this, we construct vector field maps of excess centroid shifts, which represent the deviations of the binary lensing centroid shifts from those of a single lensing event as a function of source position. From the analysis of the maps, we find that the excess centroid shifts are substantial in a considerably large area around caustics. In addition, they have characteristic sizes and directions depending strongly on the source positions with respect to the caustics and the resulting trajectories of the light centroid (astrometric trajectories) have distinctive features, which can be distinguished from the deviations caused by other reasons. We classify the types of the deviations and investigate where they occur. Because of the strong dependence of the centroid shifts on the lens system geometry combined with the distinctive features in the observed astrometric trajectories, astrometric binary lensing observations will provide an important tool that can probe the properties of the Galactic binary lens population.     

Gravitational microlensing of planets: the influence of planetary phase and caustic orientation

Recent studies have demonstrated that detailed monitoring of gravitational microlensing events can reveal the presence of planets orbiting the microlensed source stars. With the potential of probing planets in the Galactic bulge and Magellanic Clouds, such detections greatly increase the volume over which planets can be found. This paper expands on the original studies by considering the effect of planetary phase on the form of the resultant microlensing light curve. It is found that crescent-like sources can undergo substantially more magnification than a uniformly illuminated disc, the model typically employed in studying such planets. In fact, such a circularly symmetric model is found to suffer a minimal degree of magnification when compared with the crescent models. The degree of magnification is also a strong function of the planet's orientation with respect to the microlensing caustic. The form of the magnification variability is strongly dependent on the planetary phase and from which direction the planet is swept by the caustic, providing further clues to the geometry of the planetary system. As the amount of light reflected from a planet also depends on its phase, the detection of extreme crescent-like planets requires the advent of 30-m class telescopes, while light curves of planets at more moderate phases can be determined with today's 10-m telescopes.     

Search for dark matter using the phenomenon of strong gravitational lensing

We provide a brief overview of the methods for estimating the dark matter content in the Universe based on the phenomenon of strong gravitational lensing—the method of macroimage flux ratio anomalies and the method based on an analysis of the probability distribution for the magnification of macroimages due to microlensing events. Both methods require the specification of a macrolens model, knowledge of the spatial structure or at least the effective size of the source, and numerical simulation of microlensing events followed by a comparison of the simulation results with observational data. Using the quadruply lensed quasar Q2237+0305 as an example, we show the effect of the spatial source structure on the shape of the magnification probability distribution in microlensing events. We also point out the need to take into account the contribution from the intrinsic quasar variability to the observed light curve and to develop a physically justified algorithm to fit the observational data. For the first time, based on all the available observations of Q2237+0305, we have constructed the magnification probability histograms for all four macroimages. We analyze the possibility of using them to estimate the content of continuously distributed (dark) matter in the galaxy Q2237+0305 at a distance from its nucleus that corresponds to the macroimage locations.     

Can Jupiters be found by monitoring Galactic bulge microlensing events from northern sites?

In 1998 the EXPORT team monitored microlensing event light curves using a charge-coupled device (CCD) camera on the IAC 0.8-m telescope on Tenerife to evaluate the prospect of using northern telescopes to find microlens anomalies that reveal planets orbiting the lens stars. The high airmass and more limited time available for observations of Galactic bulge sources make a northern site less favourable for microlensing planet searches. However, there are potentially a large number of northern 1-m class telescopes that could devote a few hours per night to monitor ongoing microlensing events. Our IAC observations indicate that accuracies sufficient to detect planets can be achieved despite the higher airmass.     

The effect of a binary source companion on the astrometric microlensing behaviour

If gravitational microlensing occurs in a binary source system, both source components are magnified, and the resulting light curve deviates from the standard one of a single source event. However, in most cases only one source component is highly magnified and the other component (the companion) can be treated as a simple blending source: this is a blending approximation. In this paper we show that, unlike the light curves, the astrometric curves, representing the trajectories of the source image centroid, of an important fraction of binary source events will not be sufficiently well-modelled by the blending effect alone. This is because the centroid shift induced by the source companion endures to considerable distances from the lens. Therefore, in determining the lens parameters from astrometric curves to be measured by future high-precision astrometric instruments, it will be important to take the full effect of the source companion into consideration.     

Another channel to detect close-in binary companions via gravitational microlensing

Gaudi & Gould showed that close companions of remote binary systems can be efficiently detected by using gravitational microlensing via the deviations in the lensing light curves induced by the existence of the lens companions. In this paper, we introduce another channel to detect faint close-in binary companions by using microlensing. This method utilizes a caustic-crossing binary lens event with a source also composed of binary stars, where the companion is a faint star. Detection of the companion is possible because the flux of the companion can be highly amplified when it crosses the lens caustic. The detection is facilitated since the companion is more amplified than the primary because it, in general, has a smaller size than the primary, and thus experiences less finite source effect. The method is an extension of the previous one suggested to detect close-in giant planets by Graff & Gaudi and Lewis & Ibata and further developed by Ashton & Lewis. From the simulations of realistic Galactic bulge events, we find that companions of K-type main-sequence or brighter stars can be efficiently detected from the current type of microlensing follow-up observations by using the proposed method. We also find that compared with the method of detecting lens companions for which the efficiency drops significantly for binaries with separations ≲0.2 of the angular Einstein ring radius, θ _E, the proposed method has an important advantage of being able to detect companions with substantially smaller separations down to ∼     .     

Planetary microlensing signals from the orbital motion of the source star around the common barycentre

With several detections, the technique of gravitational microlensing has proven useful for studying planets that orbit stars at Galactic distances, and it can even be applied to detect planets in neighbouring galaxies. So far, planet detections by microlensing have been considered to result from a change in the bending of light and the resulting magnification caused by a planet around the foreground lens star. However, in complete analogy to the annual parallax effect caused by the revolution of the Earth around the Sun, the motion of the source star around the common barycentre with an orbiting planet can also lead to observable deviations in microlensing light curves that can provide evidence for the unseen companion. We discuss this effect in some detail and study the prospects of microlensing observations for revealing planets through this alternative detection channel. Given that small distances between lens and source star are favoured, and that the effect becomes nearly independent of the source distance, planets would remain detectable even if their host star is located outside the Milky Way with a sufficiently good photometry (exceeding present-day technology) being possible. From synthetic light curves arising from a Monte Carlo simulation, we find that the chances for such detections are not overwhelming and appear practically limited to the most massive planets (at least with current observational set-ups), but they are large enough for leaving the possibility that one or the other signal has already been observed. However, it may remain undetermined whether the planet actually orbits the source star or rather the lens star, which leaves us with an ambiguity not only with respect to its location, but also to its properties.     

Analytic relations between the observed gravitational microlensing parameters with and without the effect of blending

When a microlensing light curve is contaminated by blended light from unresolved stars near the line of sight to the lensed star, the light curve shape and corresponding parametrization for the event will differ from the values expected when the event is not affected by blending. As a result, blending makes it difficult to identify the major lens population and to estimate the amount of lensing matter. In order to estimate the effect of blending on the result of lensing experiments, it is, therefore, essential to know how the observed lensing parameters change depending on the fraction of blended light. Previously, the changed lensing parameters were obtained with a statistical method that not only required a large amount of computation time but also was prone to uncertainty. In this paper, we derive analytic relations between the lensing parameters with and without the effect of blending. By using these relations, we investigate the dependence of the observed lensing parameters on the amount of blended light, the impact parameter and the threshold amplification for event detection.     

Adaptive contouring – an efficient way to calculate microlensing light curves of extended sources

The availability of a robust and efficient routine for calculating light curves of a finite source magnified due to bending of its light by the gravitational field of an intervening binary lens is essential for determining the characteristics of planets in such microlensing events, as well as for modelling stellar lens binaries and resolving the brightness profile of the source star. However, the presence of extended caustics, and the fact that the images of the source star cannot be determined analytically while their number depends on the source position (relative to the lens system), makes such a task difficult in general. Combining the advantages of several earlier approaches, an adaptive contouring algorithm is presented, which only relies on a small number of simple rules and operations on the adaptive search grid. By using the parametric representation of critical curves and caustics found by Erdl & Schneider, seed solutions to the adaptive grid are found, which ensures that no images or holes are missed.     

Chromaticity of gravitational microlensing events

In this paper, we investigate the colour changes of gravitational microlensing events caused by the two different mechanisms of differential amplification for a limb-darkened extended source and blending. From this investigation, we find that the colour changes of limb-darkened extended source events (colour curves) have dramatically different characteristics depending on whether the lens transits the source star or not. We show that for a source transit event, the lens proper motion can be determined by simply measuring the turning time of the colour curve instead of fitting the overall colour or light curves. We also find that even for a very small fraction of blended light, the colour changes induced by blending are equivalent to those induced by limb darkening, causing serious distortion in the observed colour curve. Therefore, to obtain useful information about the lens and source star from the colour curve of an event, it will be essential to correct for blending. We discuss various methods of blending correction .     

Parallax microlensing events in the OGLE II data base toward the Galactic bulge

We present a systematic search for parallax microlensing events among a total of 512 microlensing candidates in the OGLE II data base for the  1997–1999  seasons. We fit each microlensing candidate with both the standard microlensing model and a parallax model that accounts for the Earth's motion around the Sun. We then search for the parallax signature by comparing the χ ² of the standard and parallax models. For the events which show a significant improvement, we further use the 'duration' of the event and the signal-to-noise ratio as criteria to separate true parallax events from other noisy microlensing events. We have discovered one convincing new candidate, sc33_4505, and seven other marginal cases. The convincing candidate (sc33_4505) is caused by a slow-moving, and likely low-mass, object, similar to other known parallax events. We found that irregular sampling and gaps between observing seasons hamper the recovery of parallax events. We have also searched for long-duration events that do not show parallax signatures. The lack of parallax effects in a microlensing event puts a lower limit on the Einstein radius projected on to the observer plane, which in turn imposes a lower limit on the lens mass divided by the relative lens–source parallax. Most of the constraints are however quite weak.     

Real-time difference imaging analysis of MOA Galactic bulge observations during 2000

We describe observations carried out by the MOA group of the Galactic bulge during 2000 that were designed to detect efficiently gravitational microlensing of faint stars in which the magnification is high and/or of short duration. These events are particularly useful for studies of extrasolar planets and faint stars. Approximately 17 deg² were monitored at a sampling rate of up to six times per night. The images were analysed in real time using a difference imaging technique. 20 microlensing candidates were detected, of which eight were alerted to the microlensing community whilst in progress. Approximately half of the candidates had high magnifications (≳10), at least one had very high magnification (≳50), and one exhibited a clear parallax effect. The details of these events are reported here, together with details of the on-line difference imaging technique. Some nova-like events were also observed and these are described, together with one asteroid.     

Search for exotic matter from gravitational microlensing observations of stars

We consider small-scale spheroidal clusters of weakly interacting massive particles in our Galaxy as non-compact gravitational microlenses and predict the appearance of caustics in the plane of a lensed source. The crossing of these caustics by a lensed star can produce a large variety of light curves, including some observed in actual microlensing events that have been interpreted as manifestations of binary gravitational lenses. We consider also observable effects during the gravitational microlensing of stars of non-zero angular size with a given brightness distribution across their disks by such an exotic objects as natural wormholes and objects whose space-time environment is described with the NUT metric. We demonstrate that, under certain conditions, the microlensing light curves, chromatic and polarizational effects due to the properties of the lens and the star disk brightness distributions can differ considerably from those observed for a Schwarzschild gravitational lens, so that their analysis can facilitate the identification of such objects.