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)     

ARTEMiS (Automated Robotic Terrestrial Exoplanet Microlensing Search): A possible expert‐system based cooperative effort to hunt for planets of Earth mass and below

The technique of gravitational microlensing is currently unique in its ability to provide a sample of terrestrial exoplanets around both Galactic disk and bulge stars, allowing to measure their abundance and determine their distribution with respect to mass and orbital separation. Thus, valuable information for testing models of planet formation and orbital migration is gathered, constituting an important piece in the puzzle for the existence of life forms throughout the Universe. In order to achieve these goals in reasonable time, a well‐coordinated effort involving a network of either 2m or 4×1m telescopes at each site is required. It could lead to the first detection of an Earth‐mass planet outside the Solar system, and even planets less massive than Earth could be discovered. From April 2008, ARTEMiS (Automated Robotic Terrestrial Exoplanet Microlensing Search) is planned to provide a platform for a three‐step strategy of survey, follow‐up, and anomaly monitoring. As an expert system embedded in eSTAR (e‐Science Telescopes for Astronomical Research), ARTEMiS will give advice for follow‐up based on a priority algorithm that selects targets to be observed in order to maximize the expected number of planet detections, and will also alert on deviations from ordinary microlensing light curves by means of the SIGNALMEN anomaly detector. While the use of the VOEvent (Virtual Observatory Event) protocol allows a direct interaction with the telescopes that are part of the HTN (Heterogeneous Telescope Networks) consortium, additional interfaces provide means of communication with all existing microlensing campaigns that rely on human observers. The success of discovering a planet by microlensing critically depends on the availability of a telescope in a suitable location at the right time, which can mean within 10 min. To encourage follow‐up observations, microlensing campaigns are therefore releasing photometric data in real time. On ongoing planetary anomalies, world‐wide efforts are being undertaken to make sure that sufficient data are obtained, since there is no second chance. Real‐time modelling offers the opportunity of live discovery of extra‐solar planets, thereby providing “Science live to your home”. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Prospects for spectroscopic reflected-light planet searches

High-resolution spectroscopic searches for the starlight reflected from close-in extrasolar giant planets have the capability of determining the optical albedo spectra and scattering properties of these objects. When combined with radial velocity measurements they also yield the true mass of the planet. To date, only two such planets have been targeted for reflected-light signals, yielding upper limits on the optical albedos of the planets. Here we examine the prospects for future searches of this kind. We present Monte Carlo estimates of prior probability distributions for the orbital velocity amplitudes and planet/star flux ratios of six bright stars known to harbour giant planets in orbits with periods of less than 5 d. Using these estimates, we assess the viability of these targets for future reflected-light searches using 4- and 8-m class telescopes.     

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.     

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.     

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.     

Observations of time delays in gravitational lenses from intensity fluctuations: the coherence function

Measurements of the spectrum of the fluctuations of the output current of the quadratic detector of a telescope can be used to find unresolved astronomical gravitational lenses and determine time delays between their image components. These time delays can be used for astronomical studies. The spatial correlation coefficient of a source is an important parameter that quantifies the loss of contrast, caused by the extendedness of the source, in the spectral modulation of the intensity fluctuations. This work shows that the correlation coefficient must not be evaluated at the frequency of observation, but must instead be evaluated at the much lower beat frequencies of the spectrum of the fluctuations. This opens up a powerful, novel technique to find unresolved gravitational lenses and to study the lensing event and the source.     

Stochastic distributions of lens and source properties for observed galactic microlensing events

A comprehensive new approach is presented for deriving probability densities of physical properties characterizing the lens and source that constitute an observed galactic microlensing event. While previously encountered problems are overcome, constraints from event anomalies and model parameter uncertainties can be incorporated into the estimates. Probability densities for given events need to be carefully distinguished from the statistical distribution of the same parameters among the underlying population from which the actual lenses and sources are drawn. Using given model distributions of the mass spectrum, the mass density, and the velocity distribution of Galactic disc and bulge constituents, probability densities of lens mass, distance, and the effective lens–source velocities are derived, where the effect on the distribution that arises from additional observations of annual parallax or finite-source effects, or the absence of significant effects, is shown. The presented formalism can also be used to calculate probabilities for the lens to belong to one or another population and to estimate parameters that characterize anomalies. Finally, it is shown how detection efficiency maps for binary-lens companions in the physical parameters, such as companion mass and orbital semimajor axis, arise from values determined for the mass ratio and dimensionless projected separation parameter, including the deprojection of the orbital motion for elliptical orbits. Compared to the naive estimate based on 'typical values', the detection efficiency for low-mass companions is increased by mixing in higher detection efficiencies for smaller mass ratios (i.e. smaller masses of the primary).