gravitational microlensing

Gravitational microlensing (or just microlensing) is gravitational lensing by smaller objects, e.g., by a single star within a galaxy rather than by an entire galaxy. (The term also applies to lensing by objects smaller than stars, such as planets, but the term nanolensing has also been used for that specific regime.) From microlensing observations, some information can be gleaned about both the lensing and lensed objects. Most observable instances show nothing but a magnification of the light of the lensed object, the angle of the light's redirection being an immeasurable tiny fraction of an arcsecond. They are detected by the light curve which occurs as one object passes in front of the other (a microlensing event). Among their uses have been surveys aimed at finding MACHOs that are lensing more-distant stars, and the study of distant active galactic nuclei (AGNs) as they are lensed by stars.

The observed phenomena can be described in relation to the event's Einstein radius (aka Einstein angle), which is the angular radius of an Einstein ring, the angular radius of a ring of light that would be formed if the two were exactly aligned, and which can be estimated by the length of the event. It is also related to the mass of the lensing object and the distances to both objects, and if two of these three can be determined by other means, the other can be calculated based upon the event. For example, also having parallax measurements of both stars (if both are close enough for that) allows the mass of the lensing object to be determined.

A number of factors affect exactly what is observed at a given instant during the event, including:

• the position of the observer (differing positions are termed an Einstein parallax): observations at more than one position might be due to the movement of Earth, or might be the difference between observations by a space observatory and one on Earth.
• the position of the lensed object: for example, if it were a binary companion undergoing significant orbital motion during the event (producing xallarap, a parallax-like measurement due to the displacement of the lensed object rather than the observer; the name consisting of parallax spelled backward).
• an extra-solar planet orbiting the lens, i.e., an additional small lens.
• significant size of the objects causing a divergence from the typical analyses that model them as point sources.

Such effects can be used to glean more information, yielding additional equations that can be used to break a degeneracy to yield stellar parameters.