# Microlensing exoplanets

Post-publication activity

Curator: Penny D Sackett

A microlensing exoplanet is a planet orbiting a star other than our own Sun that is detectable due to the effects that the gravitational field of its planetary system has on the passing light of a distant background star. The microlensing technique is particularly well-suited to finding low-mass planets and planets around distant or very dim stars. Astronomers have published findings on several different microlensing exoplanets, with masses ranging from more than Jupiter to only a few times more massive than our own Earth.

## Microlensing

Microlensing is a form of gravitational lensing in which the light from a background source is bent by the gravitational field of a foreground lens to create distorted, multiple and/or brightened images. In microlensing, the separation of order a milli-arcsecond between multiple images is generally too small to be resolved by modern telescopes. The combined light of all images is instead observed as a single image of the source, blended with any light that may be emanating from the lens itself. The brightness of the combined image is a function of the projected separation of the source and lens on the observer's sky, and thus can change as the source, lens and observer move relative to one another. The time variability of the combined image --- namely an apparent change in source brightness as a function of time recorded as a microlensing lightcurve--- is the usual observational signature of microlensing.

Figure 1: Left: Possible source trajectories are shown in different colours with respect to a single microlens L with an Einstein radius of $$\theta_E\ .$$ Right: Lightcurves of the background source star are shown, colour-coded to match their corresponding trajectories at left.

### A single microlens

If the lens is a single, isolated, compact object and relative motions are rectilinear, the lightcurve of the background source is simple, smooth and symmetric (see Figure 1). The background star appears to brighten and then dim as the projected separation between the source and lens first decreases and then increases. For sources and microlenses are in our own Galaxy, a typical timescale for the detectable rise and fall of the apparent brightness of the source star is on the order of weeks to months. The basic shape is the same (see Fig. 1) regardless of the relative path the source takes on the sky; the amplitude of the the lightcurve is determined by the minimum angular separation between the lens and source in units of the Einstein radius, ie $$\theta_{LS}/\theta_E\ .$$

Beginning in the 1990s and proceeding to this day, millions of stars have been monitored every night in search of the few that are microlensed by an observable amount at that time. These surveys were motivated by the desire to measure the contribution of dim stars, stellar remnants, black holes, and brown dwarfs to the unseen dark matter in the Milky Way. Soon thereafter, however, they became important to the search for exoplanets orbiting faint stars and brown dwarfs, which would be difficult to detect by any means other than microlensing.

### Microlens with multiple components

If the lens is multiple, as is the case when the lens is a binary star or a star with planets, the magnification pattern experienced by a background source is no longer circularly symmetric on the sky. In this case, the shape and maximum amplitude of the lightcurve depends on relative path the background source takes through the lens magnification pattern. The resulting lightcurve can exhibit large changes in shape over rather short periods of time if the background star passes near what is known as a caustic in the lensing pattern (Mao and Paczynski 1991).

## Detecting planets with microlensing

Figure 2: Microlensing exoplanets can cause sharp deviations in the otherwise smooth lightcurve of a background star during a microlensing event, but only if the path of the background star passes near one of the caustics (shown as red zones) caused by the combined gravitational potential of the planet and its host lensing star. Two possible background star trajectories are shown at left, and the resulting lightcurves are displayed on the right. The green circle is the Einstein ring, and the position of the planet is marked with a P. The Einstein time depends on the relative proper motion $$\mu$$ of the lens with respect to the source through $$t_E = \theta_E/\mu\ ,$$ and thus is different for different microlensing events.

Because the planet has a gravitational mass that is much smaller than that of the lensing star, the percentage of the lensing pattern area influenced by the planet will be relatively small. This means that the probability that the source trajectory will cross the planet-affected area is low, and thus the chance of detecting a planet by microlensing is also low, even if the planet is present. On the other hand, the combined gravitational field of the star and planet can create strong deviations in the lensing pattern (caustics) over this small area. This means that the changes in the lightcurve of the background source can be quite dramatic if it does happen to cross the planet-affected area. This is true even for planets with masses as low as that of Earth, as long as the size of the background source star is not more than about 5 times larger that the area of anomalous lensing pattern created by the planet.

### What can be learned

The parameters that are easiest to measure from microlensing lightcurves that exhibit the presence of the planet are the mass ratio between the planet and its parent star, $$q = M_p/M_*\ ,$$ and the angular separation between the planet and star on the sky at the time of the lensing event, $$d = \theta_{*,p}/\theta_E\ ,$$ in units of the Einstein ring radius. Both denominators depend on the mass of the lensing star (not the source star), while the Einstein radius depends on the relative distance of the lensing star along the sight line of the observer. The quantity $$q$$ indicates how massive the planet is compared to its host star. If the size of $$\theta_E$$ can be measured (which is usually possible for planetary microlensing events), then $$d$$ places a lower limit on the size of the orbit. In about 1/2 of all microlensing planets discovered to date, the mass and distance of the planet have been determined by a variety of auxiliary techniques.

Advantages of the microlensing technique to detect exoplanets include:

• More sensitive than most other techniques to small-mass planets (like Earth)
• Most sensitive to planets in our Galaxy that have orbit sizes of a few astronomical units (like those of Mars or Jupiter)
• Only method capable of detecting planets in other galaxies
• The most common stars in the Galaxy will be the most likely lenses
• Capable of detecting (with some probability) multiple planets in a single lightcurve

In summary, the microlensing can be used to study the statistical abundance of exoplanets in our Galaxy with properties similar to the planets in our own Solar System.

Disadvantages of the microlensing technique to detect exoplanets include:

• Millions of stars must be monitored to find the few that are microlensing at any given time
• Planetary deviations in lightcurve are short-lived and could be missed due to inopportune timing
• Substantial probability that any planet will not be detected in lens system, even if present
• Deviations in microlensing lightcurves due to planets will not repeat (as they are due to a chance alignment)
• Planetary parameters (such as mass, orbit size, etc) depend on the properties of the host star, which are typically unknown

In sum, the microlensing technique requires intensive use of telescope time, and is unsuitable for continued detailed study of individual exoplanets.

## Known microlensing exoplanets

An up-to-date list of known microlensing exoplanets can be found in the microlensing section of the Extrasolar Planets Encyclopaedia

## References

• Mao, S. and Pacsynski, B. (1991) Gravitational microlensing by double stars and planetary systems. Astrophysical Journal, 374:L37-L40.

Internal references

• France Allard and Derek Homeier (2007) Brown dwarfs. Scholarpedia, 2(12):4475.