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.     

Study by MOA of extrasolar planets in gravitational microlensing events of high magnification

A search for extrasolar planets was carried out in three gravitational microlensing events of high magnification, MACHO  98–BLG–35  , MACHO  99–LMC–2  and OGLE  00–BUL–12  . Photometry was derived from observational images by the MOA and OGLE groups using an image subtraction technique. For MACHO  98–BLG–35  , additional photometry derived from the MPS and PLANET groups was included. Planetary modelling of the three events was carried out in a supercluster computing environment. The estimated probability for explaining the data on MACHO  98–BLG–35  without a planet is <1 per cent. The best planetary model has a planet of mass ∼(0.4–1.5)× M _Earth at a projected radius of either ∼1.5 or ∼2.3 au. We show how multiplanet models can be applied to the data. We calculate exclusion regions for the three events and find that Jupiter-mass planets can be excluded with projected radii from as wide as about 30 au to as close as around 0.5 au for MACHO  98–BLG–35  and OGLE  00–BUL–12  . For MACHO  99–LMC–2  , the exclusion region extends out to around 10 au and constitutes the first limit placed on a planetary companion to an extragalactic star. We derive a particularly high peak magnification of ∼160 for OGLE  00–BUL–12  . We discuss the detectability of planets with masses as low as Mercury in this and similar events.     

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.     

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.     

Parameter degeneracies and (un)predictability of gravitational microlensing events

Some of the difficulties in determining the underlying physical properties that are relevant for observed anomalies in microlensing light curves, such as the mass and separation of extrasolar planets orbiting the lens star, or the relative source–lens parallax, are already anchored in factors that limit the amount of information available from ordinary microlensing events and in the way these are being parametrized. Moreover, a real-time detection of deviations from an ordinary light curve while these are still in progress can only be done against a known model of the latter, and such is also required for properly prioritizing ongoing events for monitoring in order to maximize scientific returns. Despite the fact that ordinary microlensing light curves are described by an analytic function that only involves a handful of parameters, modelling these is far less trivial than one might be tempted to think. A well-known degeneracy for small impacts, and another one for the initial rise of an event, makes an interprediction of different phases impossible, while in order to determine a complete set of model parameters, the fundamental characteristics of all these phases need to be properly assessed. While it is found that the wing of the light curve provides valuable information about the time-scale that absorbs the physical properties, the peak flux of the event can be meaningfully predicted only after about a third of the total magnification has been reached. Parametrizations based on observable features not only ease modelling by bringing the covariance matrix close to diagonal form, but also allow good predictions of the measured flux without the need to determine all parameters accurately. Campaigns intending to infer planet populations from observed microlensing events need to invest some fraction of the available time into acquiring data that allow to properly determine the magnification function.     

Realisation of a fully‐deterministic microlensing observing strategy for inferring planet populations

Within less than 15 years, the count of known planets orbiting stars other than the Sun has risen from none to more than 400 with detections arising from four successfully applied techniques: Doppler‐wobbles, planetary transits, gravitational microlensing, and direct imaging. While the hunt for twin Earths is on, a statistically well‐defined sample of the population of planets in all their variety is required for probing models of planet formation and orbital evolution so that the origin of planets that harbour life, like and including ours, can be understood. Given the different characteristics of the detection techniques, a complete picture can only arise from a combination of their respective results. Microlensing observations are well‐suited to reveal statistical properties of the population of planets orbiting stars in either the Galactic disk or bulge from microlensing observations, but a mandatory requirement is the adoption of strictly‐deterministic criteria for selecting targets and identifying signals. Here, we describe a fully‐deterministic strategy realised by means of the ARTEMiS (Automated Robotic Terrestrial Exoplanet Microlensing Search) system at the Danish 1.54‐m telescope at ESO La Silla between June and August 2008 as part of the MiNDSTEp (Microlensing Network for the Detection of Small Terrestrial Exoplanets) campaign, making use of immediate feedback on suspected anomalies recognized by the SIGNALMEN anomaly detector. We demonstrate for the first time the feasibility of such an approach, and thereby the readiness for studying planet populations down to Earth mass and even below, with ground‐based observations. While the quality of the real‐time photometry is a crucial factor on the efficiency of the campaign, an impairment of the target selection by data of bad quality can be successfully avoided. With a smaller slew time, smaller dead time, and higher through‐put, modern robotic telescopes could significantly outperform the 1.54‐m Danish, whereas lucky‐imaging cameras could set new standards for high‐precision follow‐up monitoring of microlensing events (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

Extended source effects in astrometric gravitational microlensing

Extended source size effects have been detected in photometric monitoring of gravitational microlensing events. We study similar effects in the centroid motion of an extended source lensed by a point mass. We show that the centroid motion of a source with uniform surface brightness can be obtained analytically. For a source with a circularly symmetric limb-darkening profile, the centroid motion can be expressed as a one-dimensional integral, which can be evaluated numerically. We find that when the impact parameter is comparable to the source radius, the centroid motion is significantly modified by the finite source size. In particular, when the impact parameter is smaller than the source radius, the trajectories become clover-leaf like. Such astrometric motions can be detected using space interferometers such as the Space Interferometry Mission . Such measurements offer exciting possibilities for determining stellar parameters, such as stellar radius, to excellent accuracy.     

Identification of bright lenses from the astrometric observations of gravitational microlensing events

When a source star is gravitationally microlensed by a dark lens, the centroid of the source star image is displaced relative to the position of the unlensed source star, with an elliptical trajectory. Recently, routine astrometric follow-up measurements of these source star image centroid shifts by using high-precision interferometers have been proposed to measure the lens proper motion, which can resolve the lens parameter degeneracy in the photometrically determined Einstein time-scale. When an event is caused by a bright lens, on the other hand, the astrometric shift is affected by the light from the lens, but one cannot identify the existence of the bright lens from the observed trajectory because the resulting trajectory of the bright lens event is also an ellipse. As results, lensing parameters determined from the trajectory differ from those of a dark lens event, causing an incorrect identification of the lens population. In this paper, we show that although the shape and size of the astrometric centroid shift trajectory are changed because of the bright lens, the angular speed of centroid shifts around the apparent position of the unlensed source star is not affected by the lens brightness. Therefore, one can identify the existence of a bright lens and determine its brightness by comparing the lens parameters determined from the 'angular speed curve' with those determined from the trajectory of observed centroid shifts. Once the lens brightness is determined, one can correct for the lens proper motion. As the proposed method provides information about both the lens brightness (dark or bright) and the corrected values of the physical parameters of the lens, one can constrain the nature of massive compact halo objects (MACHOs) significantly better.     

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.     

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.     

Constraints on Jupiters from observations of Galactic bulge microlensing events during 2000

We present observations of eight Galactic bulge microlensing events taken with the 1.0-m Jacobus Kapteyn Telescope (JKT) on La Palma during 2000 June and July. The JKT observing schedule was optimized using a prioritizing algorithm to automatically update the target list. For most of these events we have sampled the light curves at times where no information was available from the OGLE alert team. We assume a point-source point-lens (PSPL) model and perform a maximum likelihood fit to both our data and the OGLE data to constrain the event parameters of the fit. We then refit the data assuming a binary lens and proceed to calculate the probability of detecting planets with mass ratio   q = 10⁻³  . We have seen no clear signatures of planetary deviations on any of the eight events and we quantify constraints on the presence of planetary companions to the lensing stars. For two well-observed events, 2000BUL31 and 2000BUL33, our detection probabilities peak at ∼30 and ∼20 per cent respectively for   q = 10⁻³  and   a ∼ R _E  for a  Δχ²  threshold value of 60.     

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 parametrization proposed and detailed by Cassan. 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-  χ²  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 event.     

Background-field effects in astrometric microlensing

We consider the motion of the image of a distant radiation source microlensed by one and many point masses in the presence of an external background field, which produces a shear in the lens equation. The trajectories of the image brightness centroid (BC) in a Chang-Refsdal lens are very sensitive to the magnitude of the shear and to the direction of motion of the microlenses, allowing these parameters to be unambiguously determined from the BC motion. Stochastic motions of the BC for an extended source are simulated in a problem with a large number of randomly arranged microlenses. We derive dependences of the root-mean-square variations in BC velocity on microlense density, on external shear, and on the continuous component of the mass density, which may be related to dark matter in extragalactic lenses.     

Gravitational wave detection through microlensing?

It is shown that accurate photometric observations of a relatively high-magnification microlensing event  ( A ≫ 1)  , occurring close to the line of sight of a gravitational wave (GW) source, represented by a binary star, can allow the detection of subtle gravitational effects. After reviewing the physical nature of such effects, it is discussed to what extent these phenomena can actually be caused by GWs. Expressions for the amplitude of the phenomena and the detection probability are supplied.