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How can anomalies tell us about extra-solar planets?

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A special type of binary lens is a planet orbiting a star. In the direction of the center of the Galaxy, most microlenses are believed to be stars, so it is natural to imagine that some of these lenses may have planets. Such planetary systems are complicated lenses like binaries, and so would have distorted amplification patterns that would create gentle anomalies outside the caustic region and sharp increases in brightness whenever a source chanced to pass directly behind the caustic structure. Planets located at angular radii between about 0.5 and 1.5 times the Einstein ring radius of their parent star are said to be in the ``lensing zone,'' since they are the most likely to produce, with the help of the parent, sizeable caustic structure. This distance between planet and parent (lensing) star is comparable to a few Earth-Sun radii (ie, a few AU), precisely the distances at which several planets in our Solar System are separated from the Sun. In principle, then, detection and measurement of microlensing anomalies could be a method to detect and study planets outside our own Solar System. What would these planetary anomalies look like? Would they be large enough and occur often enough for astronomers to detect them?

The primary difference between a binary lens composed of two stars and one composed of a star and a planet is the angular size of the caustic structure is smaller for the planetary lensing system. This means that there is a smaller chance that the source will pass behind or near the caustic region. In addition, even if the source does pass behind the distorted region, the anomalous part of the light curve will be more short-lived for a planetary anomaly than one caused by double-star lens. The smaller the mass of the planet compared to the mass of its parent star, the less likely that the source will pass behind the anomalous amplification pattern and the shorter the duration (on average) of any anomaly in the light curve.

Fig. 10 --- Left: A very small mass planet creates very small and distorted caustic structure. Shown here is a highly magnified caustic structure caused by an Earth-mass planet orbiting a stellar lens at a distance approximately equal to its Einstein ring radius of a few Earth-Sun radii. (This figure is highly zoomed compared to the caustic pattern shown in Fig. 9 for a binary star lens.) It is quite unlikely that a source would pass directly behind this tiny caustic structure. The caustic structure of a Jupiter-mass planet would be about 20 times larger. Right: The light curves of sources passing behind planetary caustic structure due to Earth-mass planets will not experience sharp increases in brightness unless the source star is quite small. The anomalies last only a few hours for an Earth-mass planet, but about 1-3 days for a Jupiter-mass planet. Click on the figures for a zoom. (Adapted from Paczynski 1996.)

Suppose that all lenses in our Galaxy are stars like our Sun that have a Jupiter-mass planet orbiting them at the same orbital radius as our own Jupiter, namely 5 times the Earth's orbital radius (or 5 AU). Further suppose that all these lenses are located halfway between our telescopes and the center of the Galaxy. Calculations by several scientists indicate that careful monitoring of microlensing light curves should be able reveal the anomalies in about 20% of the cases. Detectable anomalies from Jupiter-mass planets would last one to three days. Smaller mass planets will be more difficult to detect and their anomalies be even shorter in duration (Fig. 10). Of course not all lenses are like our Sun, not all stars are likely to have planetary systems like our own, and not all lens are located halfway between us and the center of the Galaxy. So the actual ``detection sensitivity'' of a such a planet-searching experiment may be somewhat different than this estimate. Even so, the numbers were encouraging enough to cause one group of astronomers to attempt the task.

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